Tidy Syntax and SpadAst.

author: dos-reis <gdr@axiomatics.org> 2008-09-22 03:05:49 +0000
committer: dos-reis <gdr@axiomatics.org> 2008-09-22 03:05:49 +0000
commit: ce18c80b41c0dc210d9bab1d0bfeadaf9845d853 (patch)
tree: cca9330df601ff7e225024f1d6e911f577699f7c /src/share/algebra/browse.daase
parent: b79e1543c220c230e3c88dbbee3837d9859f54bf (diff)
download: open-axiom-ce18c80b41c0dc210d9bab1d0bfeadaf9845d853.tar.gz
1 files changed, 87 insertions, 87 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 952959e6..17c8cc29 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2265459 . 3431030411)       
+(2266183 . 3431041358)       
 (-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 -1421 UP UPUP -2107) 
+(-40 -1421 UP UPUP -2067) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
 ((-4329 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) (-4328 |has| (-400 |#2|) (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 ((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1536 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1536 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1536 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1536 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356))))) 
@@ -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."))) 
 ((-4336 . T) (-4337 . T)) 
-((-1536 (-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|))))))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-1536 (-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|))))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
@@ -168,59 +168,59 @@ NIL
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
 ((-4336 . T) (-4337 . T)) 
 ((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) 
-(-60 -2479) 
+(-60 -2480) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|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 
-(-61 -2479) 
+(-61 -2480) 
 ((|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 
-(-62 -2479) 
+(-62 -2480) 
 ((|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 
-(-63 -2479) 
+(-63 -2480) 
 ((|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 
-(-64 -2479) 
+(-64 -2480) 
 ((|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}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-65 -2479) 
+(-65 -2480) 
 ((|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 
-(-66 -2479) 
+(-66 -2480) 
 ((|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 
-(-67 -2479) 
+(-67 -2480) 
 ((|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 
-(-68 -2479) 
+(-68 -2480) 
 ((|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 
-(-69 -2479) 
+(-69 -2480) 
 ((|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 
-(-70 -2479) 
+(-70 -2480) 
 ((|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 
-(-71 -2479) 
+(-71 -2480) 
 ((|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 
-(-72 -2479) 
+(-72 -2480) 
 ((|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 
-(-73 -2479) 
+(-73 -2480) 
 ((|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 
@@ -232,55 +232,55 @@ 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 
-(-76 -2479) 
+(-76 -2480) 
 ((|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 
-(-77 -2479) 
+(-77 -2480) 
 ((|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 
-(-78 -2479) 
+(-78 -2480) 
 ((|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 
-(-79 -2479) 
+(-79 -2480) 
 ((|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 
-(-80 -2479) 
+(-80 -2480) 
 ((|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}")) (|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 -2479) 
+(-81 -2480) 
 ((|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 
-(-82 -2479) 
+(-82 -2480) 
 ((|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 
-(-83 -2479) 
+(-83 -2480) 
 ((|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 
-(-84 -2479) 
+(-84 -2480) 
 ((|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 
-(-85 -2479) 
+(-85 -2480) 
 ((|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 
-(-86 -2479) 
+(-86 -2480) 
 ((|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 
-(-87 -2479) 
+(-87 -2480) 
 ((|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 
-(-88 -2479) 
+(-88 -2480) 
 ((|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 
@@ -464,11 +464,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) 
 (((-4338 "*") . T)) 
 NIL 
-(-134 |minix| -2724 S T$) 
+(-134 |minix| -2728 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-135 |minix| -2724 R) 
+(-135 |minix| -2728 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
@@ -806,7 +806,7 @@ NIL
 NIL 
 (-219) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-2659 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
+((-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
 (-220) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) 
@@ -852,19 +852,19 @@ 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 
-(-231 S -2724 R) 
+(-231 S -2728 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 (-356))) (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (QUOTE (-821))) (|HasAttribute| |#3| (QUOTE -4333)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (QUOTE (-703))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (QUOTE (-1066)))) 
-(-232 -2724 R) 
+(-232 -2728 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"))) 
 ((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . T) (-2623 . T)) 
 NIL 
-(-233 -2724 A B) 
+(-233 -2728 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 
-(-234 -2724 R) 
+(-234 -2728 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."))) 
 ((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . T)) 
 ((-1536 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (QUOTE (-356))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-769))) (-1536 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-170))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-170)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-361)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-703)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-821)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066))))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| (-549) (QUOTE (-823))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (|HasCategory| |#2| (QUOTE (-1018))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasAttribute| |#2| (QUOTE -4333)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) 
@@ -902,11 +902,11 @@ NIL
 NIL 
 (-243 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4333 -1536 (-1819 (|has| |#4| (-1018)) (|has| |#4| (-227))) (-1819 (|has| |#4| (-1018)) (|has| |#4| (-871 (-1142)))) (|has| |#4| (-6 -4333)) (-1819 (|has| |#4| (-1018)) (|has| |#4| (-617 (-549))))) (-4330 |has| |#4| (-1018)) (-4331 |has| |#4| (-1018)) ((-4338 "*") |has| |#4| (-170)) (-4336 . T)) 
+((-4333 -1536 (-1820 (|has| |#4| (-1018)) (|has| |#4| (-227))) (-1820 (|has| |#4| (-1018)) (|has| |#4| (-871 (-1142)))) (|has| |#4| (-6 -4333)) (-1820 (|has| |#4| (-1018)) (|has| |#4| (-617 (-549))))) (-4330 |has| |#4| (-1018)) (-4331 |has| |#4| (-1018)) ((-4338 "*") |has| |#4| (-170)) (-4336 . T)) 
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(|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#4| (QUOTE (-356))) (-1536 (|HasCategory| |#4| (QUOTE (-170))) (|HasCategory| |#4| (QUOTE (-356))) (|HasCategory| |#4| (QUOTE (-1018)))) (-1536 (|HasCategory| |#4| (QUOTE (-170))) (|HasCategory| |#4| (QUOTE (-356)))) (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (QUOTE (-769))) (-1536 (|HasCategory| |#4| (QUOTE (-769))) (|HasCategory| |#4| (QUOTE (-821)))) (|HasCategory| |#4| (QUOTE (-821))) (|HasCategory| |#4| (QUOTE (-703))) (|HasCategory| |#4| (QUOTE (-170))) (-1536 (|HasCategory| |#4| (QUOTE (-170))) (|HasCategory| |#4| (QUOTE (-1018)))) (|HasCategory| |#4| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#4| (QUOTE (-170))) (|HasCategory| |#4| (QUOTE (-227))) (|HasCategory| |#4| (QUOTE (-1018)))) (|HasCategory| |#4| (QUOTE (-227))) (|HasCategory| |#4| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-170)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-227)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-356)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-361)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-703)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-769)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-821)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-1018)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-1066))))) (-1536 (-12 (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-227))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-356))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-703))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-769))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-821))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| (-549) (QUOTE (-823))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#4| (QUOTE (-227))) (|HasCategory| |#4| (QUOTE (-1018)))) (-1536 (-12 (|HasCategory| |#4| (QUOTE (-227))) (|HasCategory| |#4| (QUOTE (-1018)))) (|HasCategory| |#4| (QUOTE (-703))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142)))))) (-1536 (|HasCategory| |#4| (QUOTE (-1018))) (-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549)))))) (-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (QUOTE (-1066)))) (-1536 (|HasAttribute| |#4| (QUOTE -4333)) (-12 (|HasCategory| |#4| (QUOTE (-227))) (|HasCategory| |#4| (QUOTE (-1018)))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#4| (QUOTE (-1018))) (|HasCategory| |#4| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#4| (QUOTE (-130))) (|HasCategory| |#4| (QUOTE (-25))) (-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-244 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
-((-4333 -1536 (-1819 (|has| |#3| (-1018)) (|has| |#3| (-227))) (-1819 (|has| |#3| (-1018)) (|has| |#3| (-871 (-1142)))) (|has| |#3| (-6 -4333)) (-1819 (|has| |#3| (-1018)) (|has| |#3| (-617 (-549))))) (-4330 |has| |#3| (-1018)) (-4331 |has| |#3| (-1018)) ((-4338 "*") |has| |#3| (-170)) (-4336 . T)) 
+((-4333 -1536 (-1820 (|has| |#3| (-1018)) (|has| |#3| (-227))) (-1820 (|has| |#3| (-1018)) (|has| |#3| (-871 (-1142)))) (|has| |#3| (-6 -4333)) (-1820 (|has| |#3| (-1018)) (|has| |#3| (-617 (-549))))) (-4330 |has| |#3| (-1018)) (-4331 |has| |#3| (-1018)) ((-4338 "*") |has| |#3| (-170)) (-4336 . T)) 
 ((-1536 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-703))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-821))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#3| (QUOTE (-356))) (-1536 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1018)))) (-1536 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (QUOTE (-769))) (-1536 (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (QUOTE (-821)))) (|HasCategory| |#3| (QUOTE (-821))) (|HasCategory| |#3| (QUOTE (-703))) (|HasCategory| |#3| (QUOTE (-170))) (-1536 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-1018)))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-170)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-227)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-356)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-361)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-703)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-769)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-821)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-1018)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-1066))))) (-1536 (-12 (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-703))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-821))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| (-549) (QUOTE (-823))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (-1536 (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (|HasCategory| |#3| (QUOTE (-703))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))))) (-1536 (|HasCategory| |#3| (QUOTE (-1018))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549)))))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#3| (QUOTE (-1066)))) (-1536 (|HasAttribute| |#3| (QUOTE -4333)) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-245 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."))) 
@@ -1056,7 +1056,7 @@ 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 
-(-282 S R |Mod| -2012 -3050 |exactQuo|) 
+(-282 S R |Mod| -3628 -3260 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
@@ -1083,7 +1083,7 @@ NIL
 (-288 |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."))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-289) 
 ((|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 
@@ -1166,7 +1166,7 @@ NIL
 NIL 
 (-309 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-4333 -1536 (-1819 (|has| |#1| (-1018)) (|has| |#1| (-617 (-549)))) (-12 (|has| |#1| (-541)) (-1536 (-1819 (|has| |#1| (-1018)) (|has| |#1| (-617 (-549)))) (|has| |#1| (-1018)) (|has| |#1| (-465)))) (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) ((-4338 "*") |has| |#1| (-541)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-541)) (-4328 |has| |#1| (-541))) 
+((-4333 -1536 (-1820 (|has| |#1| (-1018)) (|has| |#1| (-617 (-549)))) (-12 (|has| |#1| (-541)) (-1536 (-1820 (|has| |#1| (-1018)) (|has| |#1| (-617 (-549)))) (|has| |#1| (-1018)) (|has| |#1| (-465)))) (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) ((-4338 "*") |has| |#1| (-541)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-541)) (-4328 |has| |#1| (-541))) 
 ((-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1078)))) (-1536 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))))) (-1536 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1078)))) (-1536 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-549))))) 
 (-310 R -1421) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) 
@@ -1179,7 +1179,7 @@ NIL
 (-312 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."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2270) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3582) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
 (-313 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 
@@ -1418,7 +1418,7 @@ NIL
 NIL 
 (-372) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4319 . T) (-4327 . T) (-2659 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
+((-4319 . T) (-4327 . T) (-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
 (-373 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) 
@@ -1492,7 +1492,7 @@ 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 
-(-391 -2479 |returnType| -2870 |symbols|) 
+(-391 -2480 |returnType| -2871 |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 
@@ -1518,7 +1518,7 @@ NIL
 ((|HasAttribute| |#1| (QUOTE -4319)) (|HasAttribute| |#1| (QUOTE -4327))) 
 (-397) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-2659 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
+((-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
 (-398 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
@@ -1795,11 +1795,11 @@ NIL
 (-466 |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."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) 
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 (-467 |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."))) 
 ((-4337 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-468 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)}"))) 
 ((-4337 . T) (-4336 . T)) 
@@ -1815,7 +1815,7 @@ NIL
 (-471 |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."))) 
 ((-4336 . T) (-4337 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-472) 
 ((|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 
@@ -1824,7 +1824,7 @@ 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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-(-474 -2724 S) 
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 ((|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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(|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-170)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-361)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-703)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-821)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066))))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| (-549) (QUOTE (-823))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (|HasCategory| |#2| (QUOTE (-1018))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasAttribute| |#2| (QUOTE -4333)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) 
@@ -2071,7 +2071,7 @@ NIL
 (-535 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-536 R -1421) 
 ((|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 
@@ -2086,7 +2086,7 @@ NIL
 NIL 
 (-539 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-2659 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
+((-2660 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
 (-540 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
@@ -2154,7 +2154,7 @@ NIL
 NIL 
 (-556 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) 
-((-2659 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
+((-2660 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
 (-557) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
@@ -2278,12 +2278,12 @@ NIL
 NIL 
 (-587 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4333 -1536 (-1819 (|has| |#2| (-360 |#1|)) (|has| |#1| (-541))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-541)))) (-4331 . T) (-4330 . T)) 
+((-4333 -1536 (-1820 (|has| |#2| (-360 |#1|)) (|has| |#1| (-541))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-541)))) (-4331 . T) (-4330 . T)) 
 ((-1536 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) 
 (-588 |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."))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-589 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 
@@ -2371,7 +2371,7 @@ NIL
 (-610) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 ((-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-1124) (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1792) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-1124) (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-611 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2382,7 +2382,7 @@ NIL
 NIL 
 (-613 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4333 -1536 (-1819 (|has| |#2| (-360 |#1|)) (|has| |#1| (-541))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-541)))) (-4331 . T) (-4330 . T)) 
+((-4333 -1536 (-1820 (|has| |#2| (-360 |#1|)) (|has| |#1| (-541))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-541)))) (-4331 . T) (-4330 . T)) 
 ((-1536 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) 
 (-614 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))}."))) 
@@ -2464,7 +2464,7 @@ 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)))) 
-(-634 A -3916) 
+(-634 A -1675) 
 ((|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}}"))) 
 ((-4330 . T) (-4331 . T) (-4333 . T)) 
 ((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) 
@@ -2630,7 +2630,7 @@ NIL
 NIL 
 (-675) 
 ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) 
-((-2659 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
+((-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
 (-676 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
@@ -2660,7 +2660,7 @@ 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 
-(-683 S -1699 I) 
+(-683 S -1701 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 
@@ -2680,7 +2680,7 @@ 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 
-(-688 R |Mod| -2012 -3050 |exactQuo|) 
+(-688 R |Mod| -3628 -3260 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) 
 NIL 
@@ -2696,7 +2696,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
 ((-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) (-4333 . T)) 
 ((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145)))) 
-(-692 R |Mod| -2012 -3050 |exactQuo|) 
+(-692 R |Mod| -3628 -3260 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
 ((-4333 . T)) 
 NIL 
@@ -3092,7 +3092,7 @@ 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(\\spad{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(\\spad{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 
-(-791 -2724 S |f|) 
+(-791 -2728 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}."))) 
 ((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . T)) 
 ((-1536 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (QUOTE (-356))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-769))) (-1536 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-170))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1018)))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-170)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-361)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-703)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-821)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066))))) (-1536 (-12 (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-769))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| (-549) (QUOTE (-823))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (|HasCategory| |#2| (QUOTE (-1018))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasAttribute| |#2| (QUOTE -4333)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) 
@@ -3200,7 +3200,7 @@ NIL
 ((|constructor| (NIL "Ordered finite sets."))) 
 NIL 
 NIL 
-(-818 -2724 S) 
+(-818 -2728 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 
@@ -3236,11 +3236,11 @@ 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 (-356))) (|HasCategory| |#1| (QUOTE (-541)))) 
-(-827 R |sigma| -2658) 
+(-827 R |sigma| -2661) 
 ((|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."))) 
 ((-4330 . T) (-4331 . T) (-4333 . T)) 
 ((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) 
-(-828 |x| R |sigma| -2658) 
+(-828 |x| R |sigma| -2661) 
 ((|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}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) 
 ((-4330 . T) (-4331 . T) (-4333 . T)) 
 ((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-356)))) 
@@ -3372,7 +3372,7 @@ 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 
-(-861 R -1699) 
+(-861 R -1701) 
 ((|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 
@@ -3560,11 +3560,11 @@ 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 -857) (|devaluate| |#1|)))) 
-(-908 R -1421 -1699) 
+(-908 R -1421 -1701) 
 ((|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 
-(-909 -1699) 
+(-909 -1701) 
 ((|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 
@@ -3955,7 +3955,7 @@ NIL
 (-1006) 
 ((|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.}"))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-52) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -1792) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-52) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-1007) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
@@ -4051,7 +4051,7 @@ NIL
 (-1030) 
 ((|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}"))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (QUOTE (-1066))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-52) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 (-1142)) (|:| -1791 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -1792) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-52) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-1031 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 
@@ -4341,7 +4341,7 @@ NIL
 NIL 
 NIL 
 (-1103) 
-((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) 
+((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) 
 ((-2623 . T)) 
 NIL 
 (-1104) 
@@ -4395,7 +4395,7 @@ NIL
 (-1116 |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."))) 
 ((-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-1117) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
@@ -4431,7 +4431,7 @@ NIL
 (-1125 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)))))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (QUOTE (-1066))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 (-1124)) (|:| -1791 |#1|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#1|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-1126 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 1.")) (|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,{}\\spad{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 
@@ -4462,8 +4462,8 @@ NIL
 NIL 
 (-1133 |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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 (-1134 R -1421) 
 ((|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 
@@ -4487,11 +4487,11 @@ NIL
 (-1139 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2270) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3582) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
 (-1140 |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}."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2270) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3582) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
 (-1141) 
 ((|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 
@@ -4539,7 +4539,7 @@ NIL
 (-1152 |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}"))) 
 ((-4336 . T) (-4337 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3336) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3336 |#1|) (|:| -1791 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
+((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) 
 (-1153 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) 
 NIL 
@@ -4683,11 +4683,11 @@ NIL
 (-1188 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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 (-1190 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 
@@ -4767,11 +4767,11 @@ NIL
 (-1209 |Coef| ULS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) 
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 (-1210 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2270) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3582) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
 (-1211 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) 
 (((-4338 "*") |has| (-1210 |#2| |#3| |#4|) (-170)) (-4329 |has| (-1210 |#2| |#3| |#4|) (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) 
@@ -4791,7 +4791,7 @@ NIL
 (-1215 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-549)))) (|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-1164))) (|HasSignature| |#2| (LIST (QUOTE -2270) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3405) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1142))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356)))) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-1164))) (|HasSignature| |#2| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3582) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1142))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356)))) 
 (-1216 |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."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) 
@@ -4799,7 +4799,7 @@ NIL
 (-1217 |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|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|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}."))) 
 (((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2270) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3582) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) 
 (-1218 |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 
@@ -4960,4 +4960,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2265439 2265444 2265449 2265454) (-2 NIL 2265419 2265424 2265429 2265434) (-1 NIL 2265399 2265404 2265409 2265414) (0 NIL 2265379 2265384 2265389 2265394) (-1253 "ZMOD.spad" 2265188 2265201 2265317 2265374) (-1252 "ZLINDEP.spad" 2264232 2264243 2265178 2265183) (-1251 "ZDSOLVE.spad" 2254081 2254103 2264222 2264227) (-1250 "YSTREAM.spad" 2253574 2253585 2254071 2254076) (-1249 "XRPOLY.spad" 2252794 2252814 2253430 2253499) (-1248 "XPR.spad" 2250523 2250536 2252512 2252611) (-1247 "XPOLY.spad" 2250078 2250089 2250379 2250448) (-1246 "XPOLYC.spad" 2249395 2249411 2250004 2250073) (-1245 "XPBWPOLY.spad" 2247832 2247852 2249175 2249244) (-1244 "XF.spad" 2246293 2246308 2247734 2247827) (-1243 "XF.spad" 2244734 2244751 2246177 2246182) (-1242 "XFALG.spad" 2241758 2241774 2244660 2244729) (-1241 "XEXPPKG.spad" 2241009 2241035 2241748 2241753) (-1240 "XDPOLY.spad" 2240623 2240639 2240865 2240934) (-1239 "XALG.spad" 2240221 2240232 2240579 2240618) (-1238 "WUTSET.spad" 2236060 2236077 2239867 2239894) (-1237 "WP.spad" 2235074 2235118 2235918 2235985) (-1236 "WHILEAST.spad" 2234872 2234881 2235064 2235069) (-1235 "WHEREAST.spad" 2234543 2234552 2234862 2234867) (-1234 "WFFINTBS.spad" 2232106 2232128 2234533 2234538) (-1233 "WEIER.spad" 2230320 2230331 2232096 2232101) (-1232 "VSPACE.spad" 2229993 2230004 2230288 2230315) (-1231 "VSPACE.spad" 2229686 2229699 2229983 2229988) (-1230 "VOID.spad" 2229276 2229285 2229676 2229681) (-1229 "VIEW.spad" 2226898 2226907 2229266 2229271) (-1228 "VIEWDEF.spad" 2222095 2222104 2226888 2226893) (-1227 "VIEW3D.spad" 2205930 2205939 2222085 2222090) (-1226 "VIEW2D.spad" 2193667 2193676 2205920 2205925) (-1225 "VECTOR.spad" 2192342 2192353 2192593 2192620) (-1224 "VECTOR2.spad" 2190969 2190982 2192332 2192337) (-1223 "VECTCAT.spad" 2188857 2188868 2190925 2190964) (-1222 "VECTCAT.spad" 2186565 2186578 2188635 2188640) (-1221 "VARIABLE.spad" 2186345 2186360 2186555 2186560) (-1220 "UTYPE.spad" 2185979 2185988 2186325 2186340) (-1219 "UTSODETL.spad" 2185272 2185296 2185935 2185940) (-1218 "UTSODE.spad" 2183460 2183480 2185262 2185267) (-1217 "UTS.spad" 2178249 2178277 2181927 2182024) (-1216 "UTSCAT.spad" 2175700 2175716 2178147 2178244) (-1215 "UTSCAT.spad" 2172795 2172813 2175244 2175249) (-1214 "UTS2.spad" 2172388 2172423 2172785 2172790) (-1213 "URAGG.spad" 2167010 2167021 2172368 2172383) (-1212 "URAGG.spad" 2161606 2161619 2166966 2166971) (-1211 "UPXSSING.spad" 2159249 2159275 2160687 2160820) (-1210 "UPXS.spad" 2156276 2156304 2157381 2157530) (-1209 "UPXSCONS.spad" 2154033 2154053 2154408 2154557) (-1208 "UPXSCCA.spad" 2152491 2152511 2153879 2154028) (-1207 "UPXSCCA.spad" 2151091 2151113 2152481 2152486) (-1206 "UPXSCAT.spad" 2149672 2149688 2150937 2151086) (-1205 "UPXS2.spad" 2149213 2149266 2149662 2149667) (-1204 "UPSQFREE.spad" 2147625 2147639 2149203 2149208) (-1203 "UPSCAT.spad" 2145218 2145242 2147523 2147620) (-1202 "UPSCAT.spad" 2142517 2142543 2144824 2144829) (-1201 "UPOLYC.spad" 2137495 2137506 2142359 2142512) (-1200 "UPOLYC.spad" 2132365 2132378 2137231 2137236) (-1199 "UPOLYC2.spad" 2131834 2131853 2132355 2132360) (-1198 "UP.spad" 2128876 2128891 2129384 2129537) (-1197 "UPMP.spad" 2127766 2127779 2128866 2128871) (-1196 "UPDIVP.spad" 2127329 2127343 2127756 2127761) (-1195 "UPDECOMP.spad" 2125566 2125580 2127319 2127324) (-1194 "UPCDEN.spad" 2124773 2124789 2125556 2125561) (-1193 "UP2.spad" 2124135 2124156 2124763 2124768) (-1192 "UNISEG.spad" 2123488 2123499 2124054 2124059) (-1191 "UNISEG2.spad" 2122981 2122994 2123444 2123449) (-1190 "UNIFACT.spad" 2122082 2122094 2122971 2122976) (-1189 "ULS.spad" 2112636 2112664 2113729 2114158) (-1188 "ULSCONS.spad" 2106675 2106695 2107047 2107196) (-1187 "ULSCCAT.spad" 2104272 2104292 2106495 2106670) (-1186 "ULSCCAT.spad" 2102003 2102025 2104228 2104233) (-1185 "ULSCAT.spad" 2100219 2100235 2101849 2101998) (-1184 "ULS2.spad" 2099731 2099784 2100209 2100214) (-1183 "UFD.spad" 2098796 2098805 2099657 2099726) (-1182 "UFD.spad" 2097923 2097934 2098786 2098791) (-1181 "UDVO.spad" 2096770 2096779 2097913 2097918) (-1180 "UDPO.spad" 2094197 2094208 2096726 2096731) (-1179 "TYPE.spad" 2094119 2094128 2094177 2094192) (-1178 "TYPEAST.spad" 2094038 2094047 2094109 2094114) (-1177 "TWOFACT.spad" 2092688 2092703 2094028 2094033) (-1176 "TUPLE.spad" 2092074 2092085 2092587 2092592) (-1175 "TUBETOOL.spad" 2088911 2088920 2092064 2092069) (-1174 "TUBE.spad" 2087552 2087569 2088901 2088906) (-1173 "TS.spad" 2086141 2086157 2087117 2087214) (-1172 "TSETCAT.spad" 2073256 2073273 2086097 2086136) (-1171 "TSETCAT.spad" 2060369 2060388 2073212 2073217) (-1170 "TRMANIP.spad" 2054735 2054752 2060075 2060080) (-1169 "TRIMAT.spad" 2053694 2053719 2054725 2054730) (-1168 "TRIGMNIP.spad" 2052211 2052228 2053684 2053689) (-1167 "TRIGCAT.spad" 2051723 2051732 2052201 2052206) (-1166 "TRIGCAT.spad" 2051233 2051244 2051713 2051718) (-1165 "TREE.spad" 2049804 2049815 2050840 2050867) (-1164 "TRANFUN.spad" 2049635 2049644 2049794 2049799) (-1163 "TRANFUN.spad" 2049464 2049475 2049625 2049630) (-1162 "TOPSP.spad" 2049138 2049147 2049454 2049459) (-1161 "TOOLSIGN.spad" 2048801 2048812 2049128 2049133) (-1160 "TEXTFILE.spad" 2047358 2047367 2048791 2048796) (-1159 "TEX.spad" 2044375 2044384 2047348 2047353) (-1158 "TEX1.spad" 2043931 2043942 2044365 2044370) (-1157 "TEMUTL.spad" 2043486 2043495 2043921 2043926) (-1156 "TBCMPPK.spad" 2041579 2041602 2043476 2043481) (-1155 "TBAGG.spad" 2040603 2040626 2041547 2041574) (-1154 "TBAGG.spad" 2039647 2039672 2040593 2040598) (-1153 "TANEXP.spad" 2039023 2039034 2039637 2039642) (-1152 "TABLE.spad" 2037434 2037457 2037704 2037731) (-1151 "TABLEAU.spad" 2036915 2036926 2037424 2037429) (-1150 "TABLBUMP.spad" 2033698 2033709 2036905 2036910) (-1149 "SYSTEM.spad" 2032972 2032981 2033688 2033693) (-1148 "SYSSOLP.spad" 2030445 2030456 2032962 2032967) (-1147 "SYNTAX.spad" 2026637 2026646 2030435 2030440) (-1146 "SYMTAB.spad" 2024693 2024702 2026627 2026632) (-1145 "SYMS.spad" 2020678 2020687 2024683 2024688) (-1144 "SYMPOLY.spad" 2019685 2019696 2019767 2019894) (-1143 "SYMFUNC.spad" 2019160 2019171 2019675 2019680) (-1142 "SYMBOL.spad" 2016496 2016505 2019150 2019155) (-1141 "SWITCH.spad" 2013253 2013262 2016486 2016491) (-1140 "SUTS.spad" 2010152 2010180 2011720 2011817) (-1139 "SUPXS.spad" 2007166 2007194 2008284 2008433) (-1138 "SUP.spad" 2003935 2003946 2004716 2004869) (-1137 "SUPFRACF.spad" 2003040 2003058 2003925 2003930) (-1136 "SUP2.spad" 2002430 2002443 2003030 2003035) (-1135 "SUMRF.spad" 2001396 2001407 2002420 2002425) (-1134 "SUMFS.spad" 2001029 2001046 2001386 2001391) (-1133 "SULS.spad" 1991570 1991598 1992676 1993105) (-1132 "SUCHTAST.spad" 1991339 1991348 1991560 1991565) (-1131 "SUCH.spad" 1991019 1991034 1991329 1991334) (-1130 "SUBSPACE.spad" 1983026 1983041 1991009 1991014) (-1129 "SUBRESP.spad" 1982186 1982200 1982982 1982987) (-1128 "STTF.spad" 1978285 1978301 1982176 1982181) (-1127 "STTFNC.spad" 1974753 1974769 1978275 1978280) (-1126 "STTAYLOR.spad" 1967151 1967162 1974634 1974639) (-1125 "STRTBL.spad" 1965656 1965673 1965805 1965832) (-1124 "STRING.spad" 1965065 1965074 1965079 1965106) (-1123 "STRICAT.spad" 1964841 1964850 1965021 1965060) (-1122 "STREAM.spad" 1961609 1961620 1964366 1964381) (-1121 "STREAM3.spad" 1961154 1961169 1961599 1961604) (-1120 "STREAM2.spad" 1960222 1960235 1961144 1961149) (-1119 "STREAM1.spad" 1959926 1959937 1960212 1960217) (-1118 "STINPROD.spad" 1958832 1958848 1959916 1959921) (-1117 "STEP.spad" 1958033 1958042 1958822 1958827) (-1116 "STBL.spad" 1956559 1956587 1956726 1956741) (-1115 "STAGG.spad" 1955624 1955635 1956539 1956554) (-1114 "STAGG.spad" 1954697 1954710 1955614 1955619) (-1113 "STACK.spad" 1954048 1954059 1954304 1954331) (-1112 "SREGSET.spad" 1951752 1951769 1953694 1953721) (-1111 "SRDCMPK.spad" 1950297 1950317 1951742 1951747) (-1110 "SRAGG.spad" 1945382 1945391 1950253 1950292) (-1109 "SRAGG.spad" 1940499 1940510 1945372 1945377) (-1108 "SQMATRIX.spad" 1938123 1938141 1939031 1939118) (-1107 "SPLTREE.spad" 1932675 1932688 1937559 1937586) (-1106 "SPLNODE.spad" 1929263 1929276 1932665 1932670) (-1105 "SPFCAT.spad" 1928040 1928049 1929253 1929258) (-1104 "SPECOUT.spad" 1926590 1926599 1928030 1928035) (-1103 "SPADXPT.spad" 1919443 1919452 1926570 1926585) (-1102 "spad-parser.spad" 1918908 1918917 1919433 1919438) (-1101 "SPADAST.spad" 1918609 1918618 1918898 1918903) (-1100 "SPACEC.spad" 1902622 1902633 1918599 1918604) (-1099 "SPACE3.spad" 1902398 1902409 1902612 1902617) (-1098 "SORTPAK.spad" 1901943 1901956 1902354 1902359) (-1097 "SOLVETRA.spad" 1899700 1899711 1901933 1901938) (-1096 "SOLVESER.spad" 1898220 1898231 1899690 1899695) (-1095 "SOLVERAD.spad" 1894230 1894241 1898210 1898215) (-1094 "SOLVEFOR.spad" 1892650 1892668 1894220 1894225) (-1093 "SNTSCAT.spad" 1892238 1892255 1892606 1892645) (-1092 "SMTS.spad" 1890498 1890524 1891803 1891900) (-1091 "SMP.spad" 1887937 1887957 1888327 1888454) (-1090 "SMITH.spad" 1886780 1886805 1887927 1887932) (-1089 "SMATCAT.spad" 1884878 1884908 1886712 1886775) (-1088 "SMATCAT.spad" 1882920 1882952 1884756 1884761) (-1087 "SKAGG.spad" 1881869 1881880 1882876 1882915) (-1086 "SINT.spad" 1880177 1880186 1881735 1881864) (-1085 "SIMPAN.spad" 1879905 1879914 1880167 1880172) (-1084 "SIG.spad" 1879233 1879242 1879895 1879900) (-1083 "SIGNRF.spad" 1878341 1878352 1879223 1879228) (-1082 "SIGNEF.spad" 1877610 1877627 1878331 1878336) (-1081 "SIGAST.spad" 1876991 1877000 1877600 1877605) (-1080 "SHP.spad" 1874909 1874924 1876947 1876952) (-1079 "SHDP.spad" 1865894 1865921 1866403 1866534) (-1078 "SGROUP.spad" 1865502 1865511 1865884 1865889) (-1077 "SGROUP.spad" 1865108 1865119 1865492 1865497) (-1076 "SGCF.spad" 1857989 1857998 1865098 1865103) (-1075 "SFRTCAT.spad" 1856905 1856922 1857945 1857984) (-1074 "SFRGCD.spad" 1855968 1855988 1856895 1856900) (-1073 "SFQCMPK.spad" 1850605 1850625 1855958 1855963) (-1072 "SFORT.spad" 1850040 1850054 1850595 1850600) (-1071 "SEXOF.spad" 1849883 1849923 1850030 1850035) (-1070 "SEX.spad" 1849775 1849784 1849873 1849878) (-1069 "SEXCAT.spad" 1846879 1846919 1849765 1849770) (-1068 "SET.spad" 1845179 1845190 1846300 1846339) (-1067 "SETMN.spad" 1843613 1843630 1845169 1845174) (-1066 "SETCAT.spad" 1843098 1843107 1843603 1843608) (-1065 "SETCAT.spad" 1842581 1842592 1843088 1843093) (-1064 "SETAGG.spad" 1839090 1839101 1842549 1842576) (-1063 "SETAGG.spad" 1835619 1835632 1839080 1839085) (-1062 "SEQAST.spad" 1835322 1835331 1835609 1835614) (-1061 "SEGXCAT.spad" 1834434 1834447 1835302 1835317) (-1060 "SEG.spad" 1834247 1834258 1834353 1834358) (-1059 "SEGCAT.spad" 1833066 1833077 1834227 1834242) (-1058 "SEGBIND.spad" 1832138 1832149 1833021 1833026) (-1057 "SEGBIND2.spad" 1831834 1831847 1832128 1832133) (-1056 "SEGAST.spad" 1831548 1831557 1831824 1831829) (-1055 "SEG2.spad" 1830973 1830986 1831504 1831509) (-1054 "SDVAR.spad" 1830249 1830260 1830963 1830968) (-1053 "SDPOL.spad" 1827639 1827650 1827930 1828057) (-1052 "SCPKG.spad" 1825718 1825729 1827629 1827634) (-1051 "SCOPE.spad" 1824863 1824872 1825708 1825713) (-1050 "SCACHE.spad" 1823545 1823556 1824853 1824858) (-1049 "SASTCAT.spad" 1823454 1823463 1823535 1823540) (-1048 "SAOS.spad" 1823326 1823335 1823444 1823449) (-1047 "SAERFFC.spad" 1823039 1823059 1823316 1823321) (-1046 "SAE.spad" 1821214 1821230 1821825 1821960) (-1045 "SAEFACT.spad" 1820915 1820935 1821204 1821209) (-1044 "RURPK.spad" 1818556 1818572 1820905 1820910) (-1043 "RULESET.spad" 1817997 1818021 1818546 1818551) (-1042 "RULE.spad" 1816201 1816225 1817987 1817992) (-1041 "RULECOLD.spad" 1816053 1816066 1816191 1816196) (-1040 "RSTRCAST.spad" 1815770 1815779 1816043 1816048) (-1039 "RSETGCD.spad" 1812148 1812168 1815760 1815765) (-1038 "RSETCAT.spad" 1801920 1801937 1812104 1812143) (-1037 "RSETCAT.spad" 1791724 1791743 1801910 1801915) (-1036 "RSDCMPK.spad" 1790176 1790196 1791714 1791719) (-1035 "RRCC.spad" 1788560 1788590 1790166 1790171) (-1034 "RRCC.spad" 1786942 1786974 1788550 1788555) (-1033 "RPTAST.spad" 1786644 1786653 1786932 1786937) (-1032 "RPOLCAT.spad" 1766004 1766019 1786512 1786639) (-1031 "RPOLCAT.spad" 1745078 1745095 1765588 1765593) (-1030 "ROUTINE.spad" 1740941 1740950 1743725 1743752) (-1029 "ROMAN.spad" 1740173 1740182 1740807 1740936) (-1028 "ROIRC.spad" 1739253 1739285 1740163 1740168) (-1027 "RNS.spad" 1738156 1738165 1739155 1739248) (-1026 "RNS.spad" 1737145 1737156 1738146 1738151) (-1025 "RNG.spad" 1736880 1736889 1737135 1737140) (-1024 "RMODULE.spad" 1736518 1736529 1736870 1736875) (-1023 "RMCAT2.spad" 1735926 1735983 1736508 1736513) (-1022 "RMATRIX.spad" 1734605 1734624 1735093 1735132) (-1021 "RMATCAT.spad" 1730126 1730157 1734549 1734600) (-1020 "RMATCAT.spad" 1725549 1725582 1729974 1729979) (-1019 "RINTERP.spad" 1725437 1725457 1725539 1725544) (-1018 "RING.spad" 1724794 1724803 1725417 1725432) (-1017 "RING.spad" 1724159 1724170 1724784 1724789) (-1016 "RIDIST.spad" 1723543 1723552 1724149 1724154) (-1015 "RGCHAIN.spad" 1722122 1722138 1723028 1723055) (-1014 "RF.spad" 1719736 1719747 1722112 1722117) (-1013 "RFFACTOR.spad" 1719198 1719209 1719726 1719731) (-1012 "RFFACT.spad" 1718933 1718945 1719188 1719193) (-1011 "RFDIST.spad" 1717921 1717930 1718923 1718928) (-1010 "RETSOL.spad" 1717338 1717351 1717911 1717916) (-1009 "RETRACT.spad" 1716687 1716698 1717328 1717333) (-1008 "RETRACT.spad" 1716034 1716047 1716677 1716682) (-1007 "RETAST.spad" 1715846 1715855 1716024 1716029) (-1006 "RESULT.spad" 1713906 1713915 1714493 1714520) (-1005 "RESRING.spad" 1713253 1713300 1713844 1713901) (-1004 "RESLATC.spad" 1712577 1712588 1713243 1713248) (-1003 "REPSQ.spad" 1712306 1712317 1712567 1712572) (-1002 "REP.spad" 1709858 1709867 1712296 1712301) (-1001 "REPDB.spad" 1709563 1709574 1709848 1709853) (-1000 "REP2.spad" 1699135 1699146 1709405 1709410) (-999 "REP1.spad" 1693126 1693136 1699085 1699090) (-998 "REGSET.spad" 1690924 1690940 1692772 1692799) (-997 "REF.spad" 1690254 1690264 1690879 1690884) (-996 "REDORDER.spad" 1689431 1689447 1690244 1690249) (-995 "RECLOS.spad" 1688215 1688234 1688918 1689011) (-994 "REALSOLV.spad" 1687348 1687356 1688205 1688210) (-993 "REAL.spad" 1687221 1687229 1687338 1687343) (-992 "REAL0Q.spad" 1684504 1684518 1687211 1687216) (-991 "REAL0.spad" 1681333 1681347 1684494 1684499) (-990 "RDUCEAST.spad" 1681055 1681063 1681323 1681328) (-989 "RDIV.spad" 1680707 1680731 1681045 1681050) (-988 "RDIST.spad" 1680271 1680281 1680697 1680702) (-987 "RDETRS.spad" 1679068 1679085 1680261 1680266) (-986 "RDETR.spad" 1677176 1677193 1679058 1679063) (-985 "RDEEFS.spad" 1676250 1676266 1677166 1677171) (-984 "RDEEF.spad" 1675247 1675263 1676240 1676245) (-983 "RCFIELD.spad" 1672434 1672442 1675149 1675242) (-982 "RCFIELD.spad" 1669707 1669717 1672424 1672429) (-981 "RCAGG.spad" 1667610 1667620 1669687 1669702) (-980 "RCAGG.spad" 1665450 1665462 1667529 1667534) (-979 "RATRET.spad" 1664811 1664821 1665440 1665445) (-978 "RATFACT.spad" 1664504 1664515 1664801 1664806) (-977 "RANDSRC.spad" 1663824 1663832 1664494 1664499) (-976 "RADUTIL.spad" 1663579 1663587 1663814 1663819) (-975 "RADIX.spad" 1660370 1660383 1662047 1662140) (-974 "RADFF.spad" 1658784 1658820 1658902 1659058) (-973 "RADCAT.spad" 1658378 1658386 1658774 1658779) (-972 "RADCAT.spad" 1657970 1657980 1658368 1658373) (-971 "QUEUE.spad" 1657313 1657323 1657577 1657604) (-970 "QUAT.spad" 1655895 1655905 1656237 1656302) (-969 "QUATCT2.spad" 1655514 1655532 1655885 1655890) (-968 "QUATCAT.spad" 1653679 1653689 1655444 1655509) (-967 "QUATCAT.spad" 1651595 1651607 1653362 1653367) (-966 "QUAGG.spad" 1650409 1650419 1651551 1651590) (-965 "QQUTAST.spad" 1650178 1650186 1650399 1650404) (-964 "QFORM.spad" 1649641 1649655 1650168 1650173) (-963 "QFCAT.spad" 1648332 1648342 1649531 1649636) (-962 "QFCAT.spad" 1646627 1646639 1647828 1647833) (-961 "QFCAT2.spad" 1646318 1646334 1646617 1646622) (-960 "QEQUAT.spad" 1645875 1645883 1646308 1646313) (-959 "QCMPACK.spad" 1640622 1640641 1645865 1645870) (-958 "QALGSET.spad" 1636697 1636729 1640536 1640541) (-957 "QALGSET2.spad" 1634693 1634711 1636687 1636692) (-956 "PWFFINTB.spad" 1632003 1632024 1634683 1634688) (-955 "PUSHVAR.spad" 1631332 1631351 1631993 1631998) (-954 "PTRANFN.spad" 1627458 1627468 1631322 1631327) (-953 "PTPACK.spad" 1624546 1624556 1627448 1627453) (-952 "PTFUNC2.spad" 1624367 1624381 1624536 1624541) (-951 "PTCAT.spad" 1623449 1623459 1624323 1624362) (-950 "PSQFR.spad" 1622756 1622780 1623439 1623444) (-949 "PSEUDLIN.spad" 1621614 1621624 1622746 1622751) (-948 "PSETPK.spad" 1607047 1607063 1621492 1621497) (-947 "PSETCAT.spad" 1600955 1600978 1607015 1607042) (-946 "PSETCAT.spad" 1594849 1594874 1600911 1600916) (-945 "PSCURVE.spad" 1593832 1593840 1594839 1594844) (-944 "PSCAT.spad" 1592599 1592628 1593730 1593827) (-943 "PSCAT.spad" 1591456 1591487 1592589 1592594) (-942 "PRTITION.spad" 1590299 1590307 1591446 1591451) (-941 "PRTDAST.spad" 1590018 1590026 1590289 1590294) (-940 "PRS.spad" 1579580 1579597 1589974 1589979) (-939 "PRQAGG.spad" 1578999 1579009 1579536 1579575) (-938 "PROPLOG.spad" 1578402 1578410 1578989 1578994) (-937 "PROPFRML.spad" 1576320 1576331 1578392 1578397) (-936 "PROPERTY.spad" 1575814 1575822 1576310 1576315) (-935 "PRODUCT.spad" 1573494 1573506 1573780 1573835) (-934 "PR.spad" 1571880 1571892 1572585 1572712) (-933 "PRINT.spad" 1571632 1571640 1571870 1571875) (-932 "PRIMES.spad" 1569883 1569893 1571622 1571627) (-931 "PRIMELT.spad" 1567864 1567878 1569873 1569878) (-930 "PRIMCAT.spad" 1567487 1567495 1567854 1567859) (-929 "PRIMARR.spad" 1566492 1566502 1566670 1566697) (-928 "PRIMARR2.spad" 1565215 1565227 1566482 1566487) (-927 "PREASSOC.spad" 1564587 1564599 1565205 1565210) (-926 "PPCURVE.spad" 1563724 1563732 1564577 1564582) (-925 "PORTNUM.spad" 1563499 1563507 1563714 1563719) (-924 "POLYROOT.spad" 1562271 1562293 1563455 1563460) (-923 "POLY.spad" 1559568 1559578 1560085 1560212) (-922 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539631) (-335 "FFCAT.spad" 531676 531698 538488 538644) (-334 "FFCAT.spad" 524782 524806 531596 531601) (-333 "FFCAT2.spad" 524527 524567 524772 524777) (-332 "FEXPR.spad" 516236 516282 524283 524322) (-331 "FEVALAB.spad" 515942 515952 516226 516231) (-330 "FEVALAB.spad" 515433 515445 515719 515724) (-329 "FDIV.spad" 514875 514899 515423 515428) (-328 "FDIVCAT.spad" 512917 512941 514865 514870) (-327 "FDIVCAT.spad" 510957 510983 512907 512912) (-326 "FDIV2.spad" 510611 510651 510947 510952) (-325 "FCPAK1.spad" 509164 509172 510601 510606) (-324 "FCOMP.spad" 508543 508553 509154 509159) (-323 "FC.spad" 498368 498376 508533 508538) (-322 "FAXF.spad" 491303 491317 498270 498363) (-321 "FAXF.spad" 484290 484306 491259 491264) (-320 "FARRAY.spad" 482436 482446 483473 483500) (-319 "FAMR.spad" 480556 480568 482334 482431) (-318 "FAMR.spad" 478660 478674 480440 480445) (-317 "FAMONOID.spad" 478310 478320 478614 478619) (-316 "FAMONC.spad" 476532 476544 478300 478305) (-315 "FAGROUP.spad" 476138 476148 476428 476455) (-314 "FACUTIL.spad" 474334 474351 476128 476133) (-313 "FACTFUNC.spad" 473510 473520 474324 474329) (-312 "EXPUPXS.spad" 470343 470366 471642 471791) (-311 "EXPRTUBE.spad" 467571 467579 470333 470338) (-310 "EXPRODE.spad" 464443 464459 467561 467566) (-309 "EXPR.spad" 459718 459728 460432 460839) (-308 "EXPR2UPS.spad" 455810 455823 459708 459713) (-307 "EXPR2.spad" 455513 455525 455800 455805) (-306 "EXPEXPAN.spad" 452452 452477 453086 453179) (-305 "EXIT.spad" 452123 452131 452442 452447) (-304 "EXITAST.spad" 451859 451867 452113 452118) (-303 "EVALCYC.spad" 451317 451331 451849 451854) (-302 "EVALAB.spad" 450881 450891 451307 451312) (-301 "EVALAB.spad" 450443 450455 450871 450876) (-300 "EUCDOM.spad" 447985 447993 450369 450438) (-299 "EUCDOM.spad" 445589 445599 447975 447980) (-298 "ESTOOLS.spad" 437429 437437 445579 445584) (-297 "ESTOOLS2.spad" 437030 437044 437419 437424) (-296 "ESTOOLS1.spad" 436715 436726 437020 437025) (-295 "ES.spad" 429262 429270 436705 436710) (-294 "ES.spad" 421715 421725 429160 429165) (-293 "ESCONT.spad" 418488 418496 421705 421710) (-292 "ESCONT1.spad" 418237 418249 418478 418483) (-291 "ES2.spad" 417732 417748 418227 418232) (-290 "ES1.spad" 417298 417314 417722 417727) (-289 "ERROR.spad" 414619 414627 417288 417293) (-288 "EQTBL.spad" 413091 413113 413300 413327) (-287 "EQ.spad" 407965 407975 410764 410876) (-286 "EQ2.spad" 407681 407693 407955 407960) (-285 "EP.spad" 403995 404005 407671 407676) (-284 "ENV.spad" 402697 402705 403985 403990) (-283 "ENTIRER.spad" 402365 402373 402641 402692) (-282 "EMR.spad" 401566 401607 402291 402360) (-281 "ELTAGG.spad" 399806 399825 401556 401561) (-280 "ELTAGG.spad" 398010 398031 399762 399767) (-279 "ELTAB.spad" 397457 397475 398000 398005) (-278 "ELFUTS.spad" 396836 396855 397447 397452) (-277 "ELEMFUN.spad" 396525 396533 396826 396831) (-276 "ELEMFUN.spad" 396212 396222 396515 396520) (-275 "ELAGG.spad" 394143 394153 396180 396207) (-274 "ELAGG.spad" 392023 392035 394062 394067) (-273 "ELABEXPR.spad" 390954 390962 392013 392018) (-272 "EFUPXS.spad" 387730 387760 390910 390915) (-271 "EFULS.spad" 384566 384589 387686 387691) (-270 "EFSTRUC.spad" 382521 382537 384556 384561) (-269 "EF.spad" 377287 377303 382511 382516) (-268 "EAB.spad" 375563 375571 377277 377282) (-267 "E04UCFA.spad" 375099 375107 375553 375558) (-266 "E04NAFA.spad" 374676 374684 375089 375094) (-265 "E04MBFA.spad" 374256 374264 374666 374671) (-264 "E04JAFA.spad" 373792 373800 374246 374251) (-263 "E04GCFA.spad" 373328 373336 373782 373787) (-262 "E04FDFA.spad" 372864 372872 373318 373323) (-261 "E04DGFA.spad" 372400 372408 372854 372859) (-260 "E04AGNT.spad" 368242 368250 372390 372395) (-259 "DVARCAT.spad" 364927 364937 368232 368237) (-258 "DVARCAT.spad" 361610 361622 364917 364922) (-257 "DSMP.spad" 359041 359055 359346 359473) (-256 "DROPT.spad" 352986 352994 359031 359036) (-255 "DROPT1.spad" 352649 352659 352976 352981) (-254 "DROPT0.spad" 347476 347484 352639 352644) (-253 "DRAWPT.spad" 345631 345639 347466 347471) (-252 "DRAW.spad" 338231 338244 345621 345626) (-251 "DRAWHACK.spad" 337539 337549 338221 338226) (-250 "DRAWCX.spad" 334981 334989 337529 337534) (-249 "DRAWCURV.spad" 334518 334533 334971 334976) (-248 "DRAWCFUN.spad" 323690 323698 334508 334513) (-247 "DQAGG.spad" 321846 321856 323646 323685) (-246 "DPOLCAT.spad" 317187 317203 321714 321841) (-245 "DPOLCAT.spad" 312614 312632 317143 317148) (-244 "DPMO.spad" 305917 305933 306055 306356) (-243 "DPMM.spad" 299233 299251 299358 299659) (-242 "DOMAIN.spad" 298504 298512 299223 299228) (-241 "DMP.spad" 295726 295741 296298 296425) (-240 "DLP.spad" 295074 295084 295716 295721) (-239 "DLIST.spad" 293486 293496 294257 294284) (-238 "DLAGG.spad" 291887 291897 293466 293481) (-237 "DIVRING.spad" 291429 291437 291831 291882) (-236 "DIVRING.spad" 291015 291025 291419 291424) (-235 "DISPLAY.spad" 289195 289203 291005 291010) (-234 "DIRPROD.spad" 280049 280065 280689 280820) (-233 "DIRPROD2.spad" 278857 278875 280039 280044) (-232 "DIRPCAT.spad" 277787 277803 278709 278852) (-231 "DIRPCAT.spad" 276458 276476 277382 277387) (-230 "DIOSP.spad" 275283 275291 276448 276453) (-229 "DIOPS.spad" 274255 274265 275251 275278) (-228 "DIOPS.spad" 273213 273225 274211 274216) (-227 "DIFRING.spad" 272505 272513 273193 273208) (-226 "DIFRING.spad" 271805 271815 272495 272500) (-225 "DIFEXT.spad" 270964 270974 271785 271800) (-224 "DIFEXT.spad" 270040 270052 270863 270868) (-223 "DIAGG.spad" 269658 269668 270008 270035) (-222 "DIAGG.spad" 269296 269308 269648 269653) (-221 "DHMATRIX.spad" 267600 267610 268753 268780) (-220 "DFSFUN.spad" 261008 261016 267590 267595) (-219 "DFLOAT.spad" 257611 257619 260898 261003) (-218 "DFINTTLS.spad" 255820 255836 257601 257606) (-217 "DERHAM.spad" 253730 253762 255800 255815) (-216 "DEQUEUE.spad" 253048 253058 253337 253364) (-215 "DEGRED.spad" 252663 252677 253038 253043) (-214 "DEFINTRF.spad" 250188 250198 252653 252658) (-213 "DEFINTEF.spad" 248684 248700 250178 250183) (-212 "DEFAST.spad" 248052 248060 248674 248679) (-211 "DECIMAL.spad" 245934 245942 246520 246613) (-210 "DDFACT.spad" 243733 243750 245924 245929) (-209 "DBLRESP.spad" 243331 243355 243723 243728) (-208 "DBASE.spad" 241903 241913 243321 243326) (-207 "DATABUF.spad" 241391 241404 241893 241898) (-206 "D03FAFA.spad" 241219 241227 241381 241386) (-205 "D03EEFA.spad" 241039 241047 241209 241214) (-204 "D03AGNT.spad" 240119 240127 241029 241034) (-203 "D02EJFA.spad" 239581 239589 240109 240114) (-202 "D02CJFA.spad" 239059 239067 239571 239576) (-201 "D02BHFA.spad" 238549 238557 239049 239054) (-200 "D02BBFA.spad" 238039 238047 238539 238544) (-199 "D02AGNT.spad" 232843 232851 238029 238034) (-198 "D01WGTS.spad" 231162 231170 232833 232838) (-197 "D01TRNS.spad" 231139 231147 231152 231157) (-196 "D01GBFA.spad" 230661 230669 231129 231134) (-195 "D01FCFA.spad" 230183 230191 230651 230656) (-194 "D01ASFA.spad" 229651 229659 230173 230178) (-193 "D01AQFA.spad" 229097 229105 229641 229646) (-192 "D01APFA.spad" 228521 228529 229087 229092) (-191 "D01ANFA.spad" 228015 228023 228511 228516) (-190 "D01AMFA.spad" 227525 227533 228005 228010) (-189 "D01ALFA.spad" 227065 227073 227515 227520) (-188 "D01AKFA.spad" 226591 226599 227055 227060) (-187 "D01AJFA.spad" 226114 226122 226581 226586) (-186 "D01AGNT.spad" 222173 222181 226104 226109) (-185 "CYCLOTOM.spad" 221679 221687 222163 222168) (-184 "CYCLES.spad" 218511 218519 221669 221674) (-183 "CVMP.spad" 217928 217938 218501 218506) (-182 "CTRIGMNP.spad" 216418 216434 217918 217923) (-181 "CTORCALL.spad" 216006 216014 216408 216413) (-180 "CSTTOOLS.spad" 215249 215262 215996 216001) (-179 "CRFP.spad" 208953 208966 215239 215244) (-178 "CRCEAST.spad" 208673 208681 208943 208948) (-177 "CRAPACK.spad" 207716 207726 208663 208668) (-176 "CPMATCH.spad" 207216 207231 207641 207646) (-175 "CPIMA.spad" 206921 206940 207206 207211) (-174 "COORDSYS.spad" 201814 201824 206911 206916) (-173 "CONTOUR.spad" 201216 201224 201804 201809) (-172 "CONTFRAC.spad" 196828 196838 201118 201211) (-171 "CONDUIT.spad" 196586 196594 196818 196823) (-170 "COMRING.spad" 196260 196268 196524 196581) (-169 "COMPPROP.spad" 195774 195782 196250 196255) (-168 "COMPLPAT.spad" 195541 195556 195764 195769) (-167 "COMPLEX.spad" 189567 189577 189811 190072) (-166 "COMPLEX2.spad" 189280 189292 189557 189562) (-165 "COMPFACT.spad" 188882 188896 189270 189275) (-164 "COMPCAT.spad" 186938 186948 188604 188877) (-163 "COMPCAT.spad" 184700 184712 186368 186373) (-162 "COMMUPC.spad" 184446 184464 184690 184695) (-161 "COMMONOP.spad" 183979 183987 184436 184441) (-160 "COMM.spad" 183788 183796 183969 183974) (-159 "COMMAAST.spad" 183551 183559 183778 183783) (-158 "COMBOPC.spad" 182456 182464 183541 183546) (-157 "COMBINAT.spad" 181201 181211 182446 182451) (-156 "COMBF.spad" 178569 178585 181191 181196) (-155 "COLOR.spad" 177406 177414 178559 178564) (-154 "COLONAST.spad" 177072 177080 177396 177401) (-153 "CMPLXRT.spad" 176781 176798 177062 177067) (-152 "CLLCTAST.spad" 176443 176451 176771 176776) (-151 "CLIP.spad" 172535 172543 176433 176438) (-150 "CLIF.spad" 171174 171190 172491 172530) (-149 "CLAGG.spad" 167649 167659 171154 171169) (-148 "CLAGG.spad" 164005 164017 167512 167517) (-147 "CINTSLPE.spad" 163330 163343 163995 164000) (-146 "CHVAR.spad" 161408 161430 163320 163325) (-145 "CHARZ.spad" 161323 161331 161388 161403) (-144 "CHARPOL.spad" 160831 160841 161313 161318) (-143 "CHARNZ.spad" 160584 160592 160811 160826) (-142 "CHAR.spad" 158452 158460 160574 160579) (-141 "CFCAT.spad" 157768 157776 158442 158447) (-140 "CDEN.spad" 156926 156940 157758 157763) (-139 "CCLASS.spad" 155075 155083 156337 156376) (-138 "CATEGORY.spad" 154854 154862 155065 155070) (-137 "CATAST.spad" 154481 154489 154844 154849) (-136 "CASEAST.spad" 154195 154203 154471 154476) (-135 "CARTEN.spad" 149298 149322 154185 154190) (-134 "CARTEN2.spad" 148684 148711 149288 149293) (-133 "CARD.spad" 145973 145981 148658 148679) (-132 "CAPSLAST.spad" 145747 145755 145963 145968) (-131 "CACHSET.spad" 145369 145377 145737 145742) (-130 "CABMON.spad" 144922 144930 145359 145364) (-129 "BYTE.spad" 144316 144324 144912 144917) (-128 "BYTEARY.spad" 143391 143399 143485 143512) (-127 "BTREE.spad" 142460 142470 142998 143025) (-126 "BTOURN.spad" 141463 141473 142067 142094) (-125 "BTCAT.spad" 140839 140849 141419 141458) (-124 "BTCAT.spad" 140247 140259 140829 140834) (-123 "BTAGG.spad" 139357 139365 140203 140242) (-122 "BTAGG.spad" 138499 138509 139347 139352) (-121 "BSTREE.spad" 137234 137244 138106 138133) (-120 "BRILL.spad" 135429 135440 137224 137229) (-119 "BRAGG.spad" 134343 134353 135409 135424) (-118 "BRAGG.spad" 133231 133243 134299 134304) (-117 "BPADICRT.spad" 131213 131225 131468 131561) (-116 "BPADIC.spad" 130877 130889 131139 131208) (-115 "BOUNDZRO.spad" 130533 130550 130867 130872) (-114 "BOP.spad" 125997 126005 130523 130528) (-113 "BOP1.spad" 123383 123393 125953 125958) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP8.spad" 98087 98100 99034 99039) (-86 "ASP80.spad" 97409 97422 98077 98082) (-85 "ASP7.spad" 96569 96582 97399 97404) (-84 "ASP78.spad" 96020 96033 96559 96564) (-83 "ASP77.spad" 95389 95402 96010 96015) (-82 "ASP74.spad" 94481 94494 95379 95384) (-81 "ASP73.spad" 93752 93765 94471 94476) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP4.spad" 88005 88018 88700 88705) (-76 "ASP49.spad" 87004 87017 87995 88000) (-75 "ASP42.spad" 85411 85450 86994 86999) (-74 "ASP41.spad" 83990 84029 85401 85406) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP1.spad" 67191 67204 67800 67805) (-62 "ASP19.spad" 61877 61890 67181 67186) (-61 "ASP12.spad" 61291 61304 61867 61872) (-60 "ASP10.spad" 60562 60575 61281 61286) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY1.spad" 58757 58766 59105 59132) (-57 "ARRAY12.spad" 57426 57437 58747 58752) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY.spad" 45959 45966 47607 47612) (-51 "ANY1.spad" 45030 45039 45949 45954) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) 
-\ No newline at end of file
+((-3 NIL 2266163 2266168 2266173 2266178) (-2 NIL 2266143 2266148 2266153 2266158) (-1 NIL 2266123 2266128 2266133 2266138) (0 NIL 2266103 2266108 2266113 2266118) (-1253 "ZMOD.spad" 2265912 2265925 2266041 2266098) (-1252 "ZLINDEP.spad" 2264956 2264967 2265902 2265907) (-1251 "ZDSOLVE.spad" 2254805 2254827 2264946 2264951) (-1250 "YSTREAM.spad" 2254298 2254309 2254795 2254800) (-1249 "XRPOLY.spad" 2253518 2253538 2254154 2254223) (-1248 "XPR.spad" 2251247 2251260 2253236 2253335) (-1247 "XPOLY.spad" 2250802 2250813 2251103 2251172) (-1246 "XPOLYC.spad" 2250119 2250135 2250728 2250797) (-1245 "XPBWPOLY.spad" 2248556 2248576 2249899 2249968) (-1244 "XF.spad" 2247017 2247032 2248458 2248551) (-1243 "XF.spad" 2245458 2245475 2246901 2246906) (-1242 "XFALG.spad" 2242482 2242498 2245384 2245453) (-1241 "XEXPPKG.spad" 2241733 2241759 2242472 2242477) (-1240 "XDPOLY.spad" 2241347 2241363 2241589 2241658) (-1239 "XALG.spad" 2240945 2240956 2241303 2241342) (-1238 "WUTSET.spad" 2236784 2236801 2240591 2240618) (-1237 "WP.spad" 2235798 2235842 2236642 2236709) (-1236 "WHILEAST.spad" 2235596 2235605 2235788 2235793) (-1235 "WHEREAST.spad" 2235267 2235276 2235586 2235591) (-1234 "WFFINTBS.spad" 2232830 2232852 2235257 2235262) (-1233 "WEIER.spad" 2231044 2231055 2232820 2232825) (-1232 "VSPACE.spad" 2230717 2230728 2231012 2231039) (-1231 "VSPACE.spad" 2230410 2230423 2230707 2230712) (-1230 "VOID.spad" 2230000 2230009 2230400 2230405) (-1229 "VIEW.spad" 2227622 2227631 2229990 2229995) (-1228 "VIEWDEF.spad" 2222819 2222828 2227612 2227617) (-1227 "VIEW3D.spad" 2206654 2206663 2222809 2222814) (-1226 "VIEW2D.spad" 2194391 2194400 2206644 2206649) (-1225 "VECTOR.spad" 2193066 2193077 2193317 2193344) (-1224 "VECTOR2.spad" 2191693 2191706 2193056 2193061) (-1223 "VECTCAT.spad" 2189581 2189592 2191649 2191688) (-1222 "VECTCAT.spad" 2187289 2187302 2189359 2189364) (-1221 "VARIABLE.spad" 2187069 2187084 2187279 2187284) (-1220 "UTYPE.spad" 2186703 2186712 2187049 2187064) (-1219 "UTSODETL.spad" 2185996 2186020 2186659 2186664) (-1218 "UTSODE.spad" 2184184 2184204 2185986 2185991) (-1217 "UTS.spad" 2178973 2179001 2182651 2182748) (-1216 "UTSCAT.spad" 2176424 2176440 2178871 2178968) (-1215 "UTSCAT.spad" 2173519 2173537 2175968 2175973) (-1214 "UTS2.spad" 2173112 2173147 2173509 2173514) (-1213 "URAGG.spad" 2167734 2167745 2173092 2173107) (-1212 "URAGG.spad" 2162330 2162343 2167690 2167695) (-1211 "UPXSSING.spad" 2159973 2159999 2161411 2161544) (-1210 "UPXS.spad" 2157000 2157028 2158105 2158254) (-1209 "UPXSCONS.spad" 2154757 2154777 2155132 2155281) (-1208 "UPXSCCA.spad" 2153215 2153235 2154603 2154752) (-1207 "UPXSCCA.spad" 2151815 2151837 2153205 2153210) (-1206 "UPXSCAT.spad" 2150396 2150412 2151661 2151810) (-1205 "UPXS2.spad" 2149937 2149990 2150386 2150391) (-1204 "UPSQFREE.spad" 2148349 2148363 2149927 2149932) (-1203 "UPSCAT.spad" 2145942 2145966 2148247 2148344) (-1202 "UPSCAT.spad" 2143241 2143267 2145548 2145553) (-1201 "UPOLYC.spad" 2138219 2138230 2143083 2143236) (-1200 "UPOLYC.spad" 2133089 2133102 2137955 2137960) (-1199 "UPOLYC2.spad" 2132558 2132577 2133079 2133084) (-1198 "UP.spad" 2129600 2129615 2130108 2130261) (-1197 "UPMP.spad" 2128490 2128503 2129590 2129595) (-1196 "UPDIVP.spad" 2128053 2128067 2128480 2128485) (-1195 "UPDECOMP.spad" 2126290 2126304 2128043 2128048) (-1194 "UPCDEN.spad" 2125497 2125513 2126280 2126285) (-1193 "UP2.spad" 2124859 2124880 2125487 2125492) (-1192 "UNISEG.spad" 2124212 2124223 2124778 2124783) (-1191 "UNISEG2.spad" 2123705 2123718 2124168 2124173) (-1190 "UNIFACT.spad" 2122806 2122818 2123695 2123700) (-1189 "ULS.spad" 2113360 2113388 2114453 2114882) (-1188 "ULSCONS.spad" 2107399 2107419 2107771 2107920) (-1187 "ULSCCAT.spad" 2104996 2105016 2107219 2107394) (-1186 "ULSCCAT.spad" 2102727 2102749 2104952 2104957) (-1185 "ULSCAT.spad" 2100943 2100959 2102573 2102722) (-1184 "ULS2.spad" 2100455 2100508 2100933 2100938) (-1183 "UFD.spad" 2099520 2099529 2100381 2100450) (-1182 "UFD.spad" 2098647 2098658 2099510 2099515) (-1181 "UDVO.spad" 2097494 2097503 2098637 2098642) (-1180 "UDPO.spad" 2094921 2094932 2097450 2097455) (-1179 "TYPE.spad" 2094843 2094852 2094901 2094916) (-1178 "TYPEAST.spad" 2094762 2094771 2094833 2094838) (-1177 "TWOFACT.spad" 2093412 2093427 2094752 2094757) (-1176 "TUPLE.spad" 2092798 2092809 2093311 2093316) (-1175 "TUBETOOL.spad" 2089635 2089644 2092788 2092793) (-1174 "TUBE.spad" 2088276 2088293 2089625 2089630) (-1173 "TS.spad" 2086865 2086881 2087841 2087938) (-1172 "TSETCAT.spad" 2073980 2073997 2086821 2086860) (-1171 "TSETCAT.spad" 2061093 2061112 2073936 2073941) (-1170 "TRMANIP.spad" 2055459 2055476 2060799 2060804) (-1169 "TRIMAT.spad" 2054418 2054443 2055449 2055454) (-1168 "TRIGMNIP.spad" 2052935 2052952 2054408 2054413) (-1167 "TRIGCAT.spad" 2052447 2052456 2052925 2052930) (-1166 "TRIGCAT.spad" 2051957 2051968 2052437 2052442) (-1165 "TREE.spad" 2050528 2050539 2051564 2051591) (-1164 "TRANFUN.spad" 2050359 2050368 2050518 2050523) (-1163 "TRANFUN.spad" 2050188 2050199 2050349 2050354) (-1162 "TOPSP.spad" 2049862 2049871 2050178 2050183) (-1161 "TOOLSIGN.spad" 2049525 2049536 2049852 2049857) (-1160 "TEXTFILE.spad" 2048082 2048091 2049515 2049520) (-1159 "TEX.spad" 2045099 2045108 2048072 2048077) (-1158 "TEX1.spad" 2044655 2044666 2045089 2045094) (-1157 "TEMUTL.spad" 2044210 2044219 2044645 2044650) (-1156 "TBCMPPK.spad" 2042303 2042326 2044200 2044205) (-1155 "TBAGG.spad" 2041327 2041350 2042271 2042298) (-1154 "TBAGG.spad" 2040371 2040396 2041317 2041322) (-1153 "TANEXP.spad" 2039747 2039758 2040361 2040366) (-1152 "TABLE.spad" 2038158 2038181 2038428 2038455) (-1151 "TABLEAU.spad" 2037639 2037650 2038148 2038153) (-1150 "TABLBUMP.spad" 2034422 2034433 2037629 2037634) (-1149 "SYSTEM.spad" 2033696 2033705 2034412 2034417) (-1148 "SYSSOLP.spad" 2031169 2031180 2033686 2033691) (-1147 "SYNTAX.spad" 2027361 2027370 2031159 2031164) (-1146 "SYMTAB.spad" 2025417 2025426 2027351 2027356) (-1145 "SYMS.spad" 2021402 2021411 2025407 2025412) (-1144 "SYMPOLY.spad" 2020409 2020420 2020491 2020618) (-1143 "SYMFUNC.spad" 2019884 2019895 2020399 2020404) (-1142 "SYMBOL.spad" 2017220 2017229 2019874 2019879) (-1141 "SWITCH.spad" 2013977 2013986 2017210 2017215) (-1140 "SUTS.spad" 2010876 2010904 2012444 2012541) (-1139 "SUPXS.spad" 2007890 2007918 2009008 2009157) (-1138 "SUP.spad" 2004659 2004670 2005440 2005593) (-1137 "SUPFRACF.spad" 2003764 2003782 2004649 2004654) (-1136 "SUP2.spad" 2003154 2003167 2003754 2003759) (-1135 "SUMRF.spad" 2002120 2002131 2003144 2003149) (-1134 "SUMFS.spad" 2001753 2001770 2002110 2002115) (-1133 "SULS.spad" 1992294 1992322 1993400 1993829) (-1132 "SUCHTAST.spad" 1992063 1992072 1992284 1992289) (-1131 "SUCH.spad" 1991743 1991758 1992053 1992058) (-1130 "SUBSPACE.spad" 1983750 1983765 1991733 1991738) (-1129 "SUBRESP.spad" 1982910 1982924 1983706 1983711) (-1128 "STTF.spad" 1979009 1979025 1982900 1982905) (-1127 "STTFNC.spad" 1975477 1975493 1978999 1979004) (-1126 "STTAYLOR.spad" 1967875 1967886 1975358 1975363) (-1125 "STRTBL.spad" 1966380 1966397 1966529 1966556) (-1124 "STRING.spad" 1965789 1965798 1965803 1965830) (-1123 "STRICAT.spad" 1965565 1965574 1965745 1965784) (-1122 "STREAM.spad" 1962333 1962344 1965090 1965105) (-1121 "STREAM3.spad" 1961878 1961893 1962323 1962328) (-1120 "STREAM2.spad" 1960946 1960959 1961868 1961873) (-1119 "STREAM1.spad" 1960650 1960661 1960936 1960941) (-1118 "STINPROD.spad" 1959556 1959572 1960640 1960645) (-1117 "STEP.spad" 1958757 1958766 1959546 1959551) (-1116 "STBL.spad" 1957283 1957311 1957450 1957465) (-1115 "STAGG.spad" 1956348 1956359 1957263 1957278) (-1114 "STAGG.spad" 1955421 1955434 1956338 1956343) (-1113 "STACK.spad" 1954772 1954783 1955028 1955055) (-1112 "SREGSET.spad" 1952476 1952493 1954418 1954445) (-1111 "SRDCMPK.spad" 1951021 1951041 1952466 1952471) (-1110 "SRAGG.spad" 1946106 1946115 1950977 1951016) (-1109 "SRAGG.spad" 1941223 1941234 1946096 1946101) (-1108 "SQMATRIX.spad" 1938847 1938865 1939755 1939842) (-1107 "SPLTREE.spad" 1933399 1933412 1938283 1938310) (-1106 "SPLNODE.spad" 1929987 1930000 1933389 1933394) (-1105 "SPFCAT.spad" 1928764 1928773 1929977 1929982) (-1104 "SPECOUT.spad" 1927314 1927323 1928754 1928759) (-1103 "SPADXPT.spad" 1919443 1919452 1927294 1927309) (-1102 "spad-parser.spad" 1918908 1918917 1919433 1919438) (-1101 "SPADAST.spad" 1918609 1918618 1918898 1918903) (-1100 "SPACEC.spad" 1902622 1902633 1918599 1918604) (-1099 "SPACE3.spad" 1902398 1902409 1902612 1902617) (-1098 "SORTPAK.spad" 1901943 1901956 1902354 1902359) (-1097 "SOLVETRA.spad" 1899700 1899711 1901933 1901938) (-1096 "SOLVESER.spad" 1898220 1898231 1899690 1899695) (-1095 "SOLVERAD.spad" 1894230 1894241 1898210 1898215) (-1094 "SOLVEFOR.spad" 1892650 1892668 1894220 1894225) (-1093 "SNTSCAT.spad" 1892238 1892255 1892606 1892645) (-1092 "SMTS.spad" 1890498 1890524 1891803 1891900) (-1091 "SMP.spad" 1887937 1887957 1888327 1888454) (-1090 "SMITH.spad" 1886780 1886805 1887927 1887932) (-1089 "SMATCAT.spad" 1884878 1884908 1886712 1886775) (-1088 "SMATCAT.spad" 1882920 1882952 1884756 1884761) (-1087 "SKAGG.spad" 1881869 1881880 1882876 1882915) (-1086 "SINT.spad" 1880177 1880186 1881735 1881864) (-1085 "SIMPAN.spad" 1879905 1879914 1880167 1880172) (-1084 "SIG.spad" 1879233 1879242 1879895 1879900) (-1083 "SIGNRF.spad" 1878341 1878352 1879223 1879228) (-1082 "SIGNEF.spad" 1877610 1877627 1878331 1878336) (-1081 "SIGAST.spad" 1876991 1877000 1877600 1877605) (-1080 "SHP.spad" 1874909 1874924 1876947 1876952) (-1079 "SHDP.spad" 1865894 1865921 1866403 1866534) (-1078 "SGROUP.spad" 1865502 1865511 1865884 1865889) (-1077 "SGROUP.spad" 1865108 1865119 1865492 1865497) (-1076 "SGCF.spad" 1857989 1857998 1865098 1865103) (-1075 "SFRTCAT.spad" 1856905 1856922 1857945 1857984) (-1074 "SFRGCD.spad" 1855968 1855988 1856895 1856900) (-1073 "SFQCMPK.spad" 1850605 1850625 1855958 1855963) (-1072 "SFORT.spad" 1850040 1850054 1850595 1850600) (-1071 "SEXOF.spad" 1849883 1849923 1850030 1850035) (-1070 "SEX.spad" 1849775 1849784 1849873 1849878) (-1069 "SEXCAT.spad" 1846879 1846919 1849765 1849770) (-1068 "SET.spad" 1845179 1845190 1846300 1846339) (-1067 "SETMN.spad" 1843613 1843630 1845169 1845174) (-1066 "SETCAT.spad" 1843098 1843107 1843603 1843608) (-1065 "SETCAT.spad" 1842581 1842592 1843088 1843093) (-1064 "SETAGG.spad" 1839090 1839101 1842549 1842576) (-1063 "SETAGG.spad" 1835619 1835632 1839080 1839085) (-1062 "SEQAST.spad" 1835322 1835331 1835609 1835614) (-1061 "SEGXCAT.spad" 1834434 1834447 1835302 1835317) (-1060 "SEG.spad" 1834247 1834258 1834353 1834358) (-1059 "SEGCAT.spad" 1833066 1833077 1834227 1834242) (-1058 "SEGBIND.spad" 1832138 1832149 1833021 1833026) (-1057 "SEGBIND2.spad" 1831834 1831847 1832128 1832133) (-1056 "SEGAST.spad" 1831548 1831557 1831824 1831829) (-1055 "SEG2.spad" 1830973 1830986 1831504 1831509) (-1054 "SDVAR.spad" 1830249 1830260 1830963 1830968) (-1053 "SDPOL.spad" 1827639 1827650 1827930 1828057) (-1052 "SCPKG.spad" 1825718 1825729 1827629 1827634) (-1051 "SCOPE.spad" 1824863 1824872 1825708 1825713) (-1050 "SCACHE.spad" 1823545 1823556 1824853 1824858) (-1049 "SASTCAT.spad" 1823454 1823463 1823535 1823540) (-1048 "SAOS.spad" 1823326 1823335 1823444 1823449) (-1047 "SAERFFC.spad" 1823039 1823059 1823316 1823321) (-1046 "SAE.spad" 1821214 1821230 1821825 1821960) (-1045 "SAEFACT.spad" 1820915 1820935 1821204 1821209) (-1044 "RURPK.spad" 1818556 1818572 1820905 1820910) (-1043 "RULESET.spad" 1817997 1818021 1818546 1818551) (-1042 "RULE.spad" 1816201 1816225 1817987 1817992) (-1041 "RULECOLD.spad" 1816053 1816066 1816191 1816196) (-1040 "RSTRCAST.spad" 1815770 1815779 1816043 1816048) (-1039 "RSETGCD.spad" 1812148 1812168 1815760 1815765) (-1038 "RSETCAT.spad" 1801920 1801937 1812104 1812143) (-1037 "RSETCAT.spad" 1791724 1791743 1801910 1801915) (-1036 "RSDCMPK.spad" 1790176 1790196 1791714 1791719) (-1035 "RRCC.spad" 1788560 1788590 1790166 1790171) (-1034 "RRCC.spad" 1786942 1786974 1788550 1788555) (-1033 "RPTAST.spad" 1786644 1786653 1786932 1786937) (-1032 "RPOLCAT.spad" 1766004 1766019 1786512 1786639) (-1031 "RPOLCAT.spad" 1745078 1745095 1765588 1765593) (-1030 "ROUTINE.spad" 1740941 1740950 1743725 1743752) (-1029 "ROMAN.spad" 1740173 1740182 1740807 1740936) (-1028 "ROIRC.spad" 1739253 1739285 1740163 1740168) (-1027 "RNS.spad" 1738156 1738165 1739155 1739248) (-1026 "RNS.spad" 1737145 1737156 1738146 1738151) (-1025 "RNG.spad" 1736880 1736889 1737135 1737140) (-1024 "RMODULE.spad" 1736518 1736529 1736870 1736875) (-1023 "RMCAT2.spad" 1735926 1735983 1736508 1736513) (-1022 "RMATRIX.spad" 1734605 1734624 1735093 1735132) (-1021 "RMATCAT.spad" 1730126 1730157 1734549 1734600) (-1020 "RMATCAT.spad" 1725549 1725582 1729974 1729979) (-1019 "RINTERP.spad" 1725437 1725457 1725539 1725544) (-1018 "RING.spad" 1724794 1724803 1725417 1725432) (-1017 "RING.spad" 1724159 1724170 1724784 1724789) (-1016 "RIDIST.spad" 1723543 1723552 1724149 1724154) (-1015 "RGCHAIN.spad" 1722122 1722138 1723028 1723055) (-1014 "RF.spad" 1719736 1719747 1722112 1722117) (-1013 "RFFACTOR.spad" 1719198 1719209 1719726 1719731) (-1012 "RFFACT.spad" 1718933 1718945 1719188 1719193) (-1011 "RFDIST.spad" 1717921 1717930 1718923 1718928) (-1010 "RETSOL.spad" 1717338 1717351 1717911 1717916) (-1009 "RETRACT.spad" 1716687 1716698 1717328 1717333) (-1008 "RETRACT.spad" 1716034 1716047 1716677 1716682) (-1007 "RETAST.spad" 1715846 1715855 1716024 1716029) (-1006 "RESULT.spad" 1713906 1713915 1714493 1714520) (-1005 "RESRING.spad" 1713253 1713300 1713844 1713901) (-1004 "RESLATC.spad" 1712577 1712588 1713243 1713248) (-1003 "REPSQ.spad" 1712306 1712317 1712567 1712572) (-1002 "REP.spad" 1709858 1709867 1712296 1712301) (-1001 "REPDB.spad" 1709563 1709574 1709848 1709853) (-1000 "REP2.spad" 1699135 1699146 1709405 1709410) (-999 "REP1.spad" 1693126 1693136 1699085 1699090) (-998 "REGSET.spad" 1690924 1690940 1692772 1692799) (-997 "REF.spad" 1690254 1690264 1690879 1690884) (-996 "REDORDER.spad" 1689431 1689447 1690244 1690249) (-995 "RECLOS.spad" 1688215 1688234 1688918 1689011) (-994 "REALSOLV.spad" 1687348 1687356 1688205 1688210) (-993 "REAL.spad" 1687221 1687229 1687338 1687343) (-992 "REAL0Q.spad" 1684504 1684518 1687211 1687216) (-991 "REAL0.spad" 1681333 1681347 1684494 1684499) (-990 "RDUCEAST.spad" 1681055 1681063 1681323 1681328) (-989 "RDIV.spad" 1680707 1680731 1681045 1681050) (-988 "RDIST.spad" 1680271 1680281 1680697 1680702) (-987 "RDETRS.spad" 1679068 1679085 1680261 1680266) (-986 "RDETR.spad" 1677176 1677193 1679058 1679063) (-985 "RDEEFS.spad" 1676250 1676266 1677166 1677171) (-984 "RDEEF.spad" 1675247 1675263 1676240 1676245) (-983 "RCFIELD.spad" 1672434 1672442 1675149 1675242) (-982 "RCFIELD.spad" 1669707 1669717 1672424 1672429) (-981 "RCAGG.spad" 1667610 1667620 1669687 1669702) (-980 "RCAGG.spad" 1665450 1665462 1667529 1667534) (-979 "RATRET.spad" 1664811 1664821 1665440 1665445) (-978 "RATFACT.spad" 1664504 1664515 1664801 1664806) (-977 "RANDSRC.spad" 1663824 1663832 1664494 1664499) (-976 "RADUTIL.spad" 1663579 1663587 1663814 1663819) (-975 "RADIX.spad" 1660370 1660383 1662047 1662140) (-974 "RADFF.spad" 1658784 1658820 1658902 1659058) (-973 "RADCAT.spad" 1658378 1658386 1658774 1658779) (-972 "RADCAT.spad" 1657970 1657980 1658368 1658373) (-971 "QUEUE.spad" 1657313 1657323 1657577 1657604) (-970 "QUAT.spad" 1655895 1655905 1656237 1656302) (-969 "QUATCT2.spad" 1655514 1655532 1655885 1655890) (-968 "QUATCAT.spad" 1653679 1653689 1655444 1655509) (-967 "QUATCAT.spad" 1651595 1651607 1653362 1653367) (-966 "QUAGG.spad" 1650409 1650419 1651551 1651590) (-965 "QQUTAST.spad" 1650178 1650186 1650399 1650404) (-964 "QFORM.spad" 1649641 1649655 1650168 1650173) (-963 "QFCAT.spad" 1648332 1648342 1649531 1649636) (-962 "QFCAT.spad" 1646627 1646639 1647828 1647833) (-961 "QFCAT2.spad" 1646318 1646334 1646617 1646622) (-960 "QEQUAT.spad" 1645875 1645883 1646308 1646313) (-959 "QCMPACK.spad" 1640622 1640641 1645865 1645870) (-958 "QALGSET.spad" 1636697 1636729 1640536 1640541) (-957 "QALGSET2.spad" 1634693 1634711 1636687 1636692) (-956 "PWFFINTB.spad" 1632003 1632024 1634683 1634688) (-955 "PUSHVAR.spad" 1631332 1631351 1631993 1631998) (-954 "PTRANFN.spad" 1627458 1627468 1631322 1631327) (-953 "PTPACK.spad" 1624546 1624556 1627448 1627453) (-952 "PTFUNC2.spad" 1624367 1624381 1624536 1624541) (-951 "PTCAT.spad" 1623449 1623459 1624323 1624362) (-950 "PSQFR.spad" 1622756 1622780 1623439 1623444) (-949 "PSEUDLIN.spad" 1621614 1621624 1622746 1622751) (-948 "PSETPK.spad" 1607047 1607063 1621492 1621497) (-947 "PSETCAT.spad" 1600955 1600978 1607015 1607042) (-946 "PSETCAT.spad" 1594849 1594874 1600911 1600916) (-945 "PSCURVE.spad" 1593832 1593840 1594839 1594844) (-944 "PSCAT.spad" 1592599 1592628 1593730 1593827) (-943 "PSCAT.spad" 1591456 1591487 1592589 1592594) (-942 "PRTITION.spad" 1590299 1590307 1591446 1591451) (-941 "PRTDAST.spad" 1590018 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392035 394062 394067) (-273 "ELABEXPR.spad" 390954 390962 392013 392018) (-272 "EFUPXS.spad" 387730 387760 390910 390915) (-271 "EFULS.spad" 384566 384589 387686 387691) (-270 "EFSTRUC.spad" 382521 382537 384556 384561) (-269 "EF.spad" 377287 377303 382511 382516) (-268 "EAB.spad" 375563 375571 377277 377282) (-267 "E04UCFA.spad" 375099 375107 375553 375558) (-266 "E04NAFA.spad" 374676 374684 375089 375094) (-265 "E04MBFA.spad" 374256 374264 374666 374671) (-264 "E04JAFA.spad" 373792 373800 374246 374251) (-263 "E04GCFA.spad" 373328 373336 373782 373787) (-262 "E04FDFA.spad" 372864 372872 373318 373323) (-261 "E04DGFA.spad" 372400 372408 372854 372859) (-260 "E04AGNT.spad" 368242 368250 372390 372395) (-259 "DVARCAT.spad" 364927 364937 368232 368237) (-258 "DVARCAT.spad" 361610 361622 364917 364922) (-257 "DSMP.spad" 359041 359055 359346 359473) (-256 "DROPT.spad" 352986 352994 359031 359036) (-255 "DROPT1.spad" 352649 352659 352976 352981) (-254 "DROPT0.spad" 347476 347484 352639 352644) (-253 "DRAWPT.spad" 345631 345639 347466 347471) (-252 "DRAW.spad" 338231 338244 345621 345626) (-251 "DRAWHACK.spad" 337539 337549 338221 338226) (-250 "DRAWCX.spad" 334981 334989 337529 337534) (-249 "DRAWCURV.spad" 334518 334533 334971 334976) (-248 "DRAWCFUN.spad" 323690 323698 334508 334513) (-247 "DQAGG.spad" 321846 321856 323646 323685) (-246 "DPOLCAT.spad" 317187 317203 321714 321841) (-245 "DPOLCAT.spad" 312614 312632 317143 317148) (-244 "DPMO.spad" 305917 305933 306055 306356) (-243 "DPMM.spad" 299233 299251 299358 299659) (-242 "DOMAIN.spad" 298504 298512 299223 299228) (-241 "DMP.spad" 295726 295741 296298 296425) (-240 "DLP.spad" 295074 295084 295716 295721) (-239 "DLIST.spad" 293486 293496 294257 294284) (-238 "DLAGG.spad" 291887 291897 293466 293481) (-237 "DIVRING.spad" 291429 291437 291831 291882) (-236 "DIVRING.spad" 291015 291025 291419 291424) (-235 "DISPLAY.spad" 289195 289203 291005 291010) (-234 "DIRPROD.spad" 280049 280065 280689 280820) (-233 "DIRPROD2.spad" 278857 278875 280039 280044) (-232 "DIRPCAT.spad" 277787 277803 278709 278852) (-231 "DIRPCAT.spad" 276458 276476 277382 277387) (-230 "DIOSP.spad" 275283 275291 276448 276453) (-229 "DIOPS.spad" 274255 274265 275251 275278) (-228 "DIOPS.spad" 273213 273225 274211 274216) (-227 "DIFRING.spad" 272505 272513 273193 273208) (-226 "DIFRING.spad" 271805 271815 272495 272500) (-225 "DIFEXT.spad" 270964 270974 271785 271800) (-224 "DIFEXT.spad" 270040 270052 270863 270868) (-223 "DIAGG.spad" 269658 269668 270008 270035) (-222 "DIAGG.spad" 269296 269308 269648 269653) (-221 "DHMATRIX.spad" 267600 267610 268753 268780) (-220 "DFSFUN.spad" 261008 261016 267590 267595) (-219 "DFLOAT.spad" 257611 257619 260898 261003) (-218 "DFINTTLS.spad" 255820 255836 257601 257606) (-217 "DERHAM.spad" 253730 253762 255800 255815) (-216 "DEQUEUE.spad" 253048 253058 253337 253364) (-215 "DEGRED.spad" 252663 252677 253038 253043) (-214 "DEFINTRF.spad" 250188 250198 252653 252658) (-213 "DEFINTEF.spad" 248684 248700 250178 250183) (-212 "DEFAST.spad" 248052 248060 248674 248679) (-211 "DECIMAL.spad" 245934 245942 246520 246613) (-210 "DDFACT.spad" 243733 243750 245924 245929) (-209 "DBLRESP.spad" 243331 243355 243723 243728) (-208 "DBASE.spad" 241903 241913 243321 243326) (-207 "DATABUF.spad" 241391 241404 241893 241898) (-206 "D03FAFA.spad" 241219 241227 241381 241386) (-205 "D03EEFA.spad" 241039 241047 241209 241214) (-204 "D03AGNT.spad" 240119 240127 241029 241034) (-203 "D02EJFA.spad" 239581 239589 240109 240114) (-202 "D02CJFA.spad" 239059 239067 239571 239576) (-201 "D02BHFA.spad" 238549 238557 239049 239054) (-200 "D02BBFA.spad" 238039 238047 238539 238544) (-199 "D02AGNT.spad" 232843 232851 238029 238034) (-198 "D01WGTS.spad" 231162 231170 232833 232838) (-197 "D01TRNS.spad" 231139 231147 231152 231157) (-196 "D01GBFA.spad" 230661 230669 231129 231134) (-195 "D01FCFA.spad" 230183 230191 230651 230656) (-194 "D01ASFA.spad" 229651 229659 230173 230178) (-193 "D01AQFA.spad" 229097 229105 229641 229646) (-192 "D01APFA.spad" 228521 228529 229087 229092) (-191 "D01ANFA.spad" 228015 228023 228511 228516) (-190 "D01AMFA.spad" 227525 227533 228005 228010) (-189 "D01ALFA.spad" 227065 227073 227515 227520) (-188 "D01AKFA.spad" 226591 226599 227055 227060) (-187 "D01AJFA.spad" 226114 226122 226581 226586) (-186 "D01AGNT.spad" 222173 222181 226104 226109) (-185 "CYCLOTOM.spad" 221679 221687 222163 222168) (-184 "CYCLES.spad" 218511 218519 221669 221674) (-183 "CVMP.spad" 217928 217938 218501 218506) (-182 "CTRIGMNP.spad" 216418 216434 217918 217923) (-181 "CTORCALL.spad" 216006 216014 216408 216413) (-180 "CSTTOOLS.spad" 215249 215262 215996 216001) (-179 "CRFP.spad" 208953 208966 215239 215244) (-178 "CRCEAST.spad" 208673 208681 208943 208948) (-177 "CRAPACK.spad" 207716 207726 208663 208668) (-176 "CPMATCH.spad" 207216 207231 207641 207646) (-175 "CPIMA.spad" 206921 206940 207206 207211) (-174 "COORDSYS.spad" 201814 201824 206911 206916) (-173 "CONTOUR.spad" 201216 201224 201804 201809) (-172 "CONTFRAC.spad" 196828 196838 201118 201211) (-171 "CONDUIT.spad" 196586 196594 196818 196823) (-170 "COMRING.spad" 196260 196268 196524 196581) (-169 "COMPPROP.spad" 195774 195782 196250 196255) (-168 "COMPLPAT.spad" 195541 195556 195764 195769) (-167 "COMPLEX.spad" 189567 189577 189811 190072) (-166 "COMPLEX2.spad" 189280 189292 189557 189562) (-165 "COMPFACT.spad" 188882 188896 189270 189275) (-164 "COMPCAT.spad" 186938 186948 188604 188877) (-163 "COMPCAT.spad" 184700 184712 186368 186373) (-162 "COMMUPC.spad" 184446 184464 184690 184695) (-161 "COMMONOP.spad" 183979 183987 184436 184441) (-160 "COMM.spad" 183788 183796 183969 183974) (-159 "COMMAAST.spad" 183551 183559 183778 183783) (-158 "COMBOPC.spad" 182456 182464 183541 183546) (-157 "COMBINAT.spad" 181201 181211 182446 182451) (-156 "COMBF.spad" 178569 178585 181191 181196) (-155 "COLOR.spad" 177406 177414 178559 178564) (-154 "COLONAST.spad" 177072 177080 177396 177401) (-153 "CMPLXRT.spad" 176781 176798 177062 177067) (-152 "CLLCTAST.spad" 176443 176451 176771 176776) (-151 "CLIP.spad" 172535 172543 176433 176438) (-150 "CLIF.spad" 171174 171190 172491 172530) (-149 "CLAGG.spad" 167649 167659 171154 171169) (-148 "CLAGG.spad" 164005 164017 167512 167517) (-147 "CINTSLPE.spad" 163330 163343 163995 164000) (-146 "CHVAR.spad" 161408 161430 163320 163325) (-145 "CHARZ.spad" 161323 161331 161388 161403) (-144 "CHARPOL.spad" 160831 160841 161313 161318) (-143 "CHARNZ.spad" 160584 160592 160811 160826) (-142 "CHAR.spad" 158452 158460 160574 160579) (-141 "CFCAT.spad" 157768 157776 158442 158447) (-140 "CDEN.spad" 156926 156940 157758 157763) (-139 "CCLASS.spad" 155075 155083 156337 156376) (-138 "CATEGORY.spad" 154854 154862 155065 155070) (-137 "CATAST.spad" 154481 154489 154844 154849) (-136 "CASEAST.spad" 154195 154203 154471 154476) (-135 "CARTEN.spad" 149298 149322 154185 154190) (-134 "CARTEN2.spad" 148684 148711 149288 149293) (-133 "CARD.spad" 145973 145981 148658 148679) (-132 "CAPSLAST.spad" 145747 145755 145963 145968) (-131 "CACHSET.spad" 145369 145377 145737 145742) (-130 "CABMON.spad" 144922 144930 145359 145364) (-129 "BYTE.spad" 144316 144324 144912 144917) (-128 "BYTEARY.spad" 143391 143399 143485 143512) (-127 "BTREE.spad" 142460 142470 142998 143025) (-126 "BTOURN.spad" 141463 141473 142067 142094) (-125 "BTCAT.spad" 140839 140849 141419 141458) (-124 "BTCAT.spad" 140247 140259 140829 140834) (-123 "BTAGG.spad" 139357 139365 140203 140242) (-122 "BTAGG.spad" 138499 138509 139347 139352) (-121 "BSTREE.spad" 137234 137244 138106 138133) (-120 "BRILL.spad" 135429 135440 137224 137229) (-119 "BRAGG.spad" 134343 134353 135409 135424) (-118 "BRAGG.spad" 133231 133243 134299 134304) (-117 "BPADICRT.spad" 131213 131225 131468 131561) (-116 "BPADIC.spad" 130877 130889 131139 131208) (-115 "BOUNDZRO.spad" 130533 130550 130867 130872) (-114 "BOP.spad" 125997 126005 130523 130528) (-113 "BOP1.spad" 123383 123393 125953 125958) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP8.spad" 98087 98100 99034 99039) (-86 "ASP80.spad" 97409 97422 98077 98082) (-85 "ASP7.spad" 96569 96582 97399 97404) (-84 "ASP78.spad" 96020 96033 96559 96564) (-83 "ASP77.spad" 95389 95402 96010 96015) (-82 "ASP74.spad" 94481 94494 95379 95384) (-81 "ASP73.spad" 93752 93765 94471 94476) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP4.spad" 88005 88018 88700 88705) (-76 "ASP49.spad" 87004 87017 87995 88000) (-75 "ASP42.spad" 85411 85450 86994 86999) (-74 "ASP41.spad" 83990 84029 85401 85406) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP1.spad" 67191 67204 67800 67805) (-62 "ASP19.spad" 61877 61890 67181 67186) (-61 "ASP12.spad" 61291 61304 61867 61872) (-60 "ASP10.spad" 60562 60575 61281 61286) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY1.spad" 58757 58766 59105 59132) (-57 "ARRAY12.spad" 57426 57437 58747 58752) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY.spad" 45959 45966 47607 47612) (-51 "ANY1.spad" 45030 45039 45949 45954) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) 
+\ No newline at end of file
author	dos-reis <gdr@axiomatics.org>	2008-09-22 03:05:49 +0000
committer	dos-reis <gdr@axiomatics.org>	2008-09-22 03:05:49 +0000
commit	ce18c80b41c0dc210d9bab1d0bfeadaf9845d853 (patch)
tree	cca9330df601ff7e225024f1d6e911f577699f7c /src/share/algebra/browse.daase
parent	b79e1543c220c230e3c88dbbee3837d9859f54bf (diff)
download	open-axiom-ce18c80b41c0dc210d9bab1d0bfeadaf9845d853.tar.gz