diff options
Diffstat (limited to 'src/share/algebra/browse.daase')
| -rw-r--r-- | src/share/algebra/browse.daase | 140 |
1 files changed, 70 insertions, 70 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 80bc4a2e..21253206 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2267397 . 3485478046) +(2267485 . 3485510916) (-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 -1384 UP UPUP -2189) +(-40 -1384 UP UPUP -1929) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-2813 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-2813 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-2813 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) @@ -172,59 +172,59 @@ NIL ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4454 . T) (-4455 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) -(-61 -2029) +(-61 -2030) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2029) +(-62 -2030) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2029) +(-63 -2030) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2029) +(-64 -2030) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2029) +(-65 -2030) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2029) +(-66 -2030) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2029) +(-67 -2030) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2029) +(-68 -2030) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2029) +(-69 -2030) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2029) +(-70 -2030) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2029) +(-71 -2030) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2029) +(-72 -2030) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2029) +(-73 -2030) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2029) +(-74 -2030) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2029) +(-77 -2030) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2029) +(-78 -2030) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2029) +(-79 -2030) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2029) +(-80 -2030) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2029) +(-81 -2030) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2029) +(-82 -2030) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2029) +(-83 -2030) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2029) +(-84 -2030) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2029) +(-85 -2030) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2029) +(-86 -2030) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2029) +(-87 -2030) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2029) +(-88 -2030) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2029) +(-89 -2030) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -472,11 +472,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4456 "*") . T)) NIL -(-136 |minix| -4131 S T$) +(-136 |minix| -4127 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -4131 R) +(-137 |minix| -4127 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -892,22 +892,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-241 S -4131 R) +(-241 S -4127 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 (-370))) (|HasCategory| |#3| (QUOTE (-801))) (|HasCategory| |#3| (QUOTE (-856))) (|HasAttribute| |#3| (QUOTE -4451)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-734))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (QUOTE (-1111)))) -(-242 -4131 R) +(-242 -4127 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"))) ((-4448 |has| |#2| (-1060)) (-4449 |has| |#2| (-1060)) (-4451 |has| |#2| (-6 -4451)) ((-4456 "*") |has| |#2| (-174)) (-4454 . T)) NIL -(-243 -4131 A B) +(-243 -4127 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}."))) 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 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(|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (-257 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -1108,7 +1108,7 @@ 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 -(-295 S R |Mod| -3635 -1867 |exactQuo|) +(-295 S R |Mod| -3104 -1767 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -1218,8 +1218,8 @@ NIL NIL (-322 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."))) -((-4451 -2813 (-2085 (|has| |#1| (-1060)) (|has| |#1| (-647 (-572)))) (-12 (|has| |#1| (-564)) (-2813 (-2085 (|has| |#1| (-1060)) (|has| |#1| (-647 (-572)))) (|has| |#1| (-1060)) (|has| |#1| (-481)))) (|has| |#1| (-1060)) (|has| |#1| (-481))) (-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) ((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4452 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(QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-1060)))) (-12 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))))) (-2813 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-1123)))) (-2813 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))))) (-2813 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1123))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| $ (QUOTE (-1060))) (|HasCategory| $ (LIST (QUOTE -1049) (QUOTE (-572))))) (-323 R -1384) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL @@ -1231,7 +1231,7 @@ NIL (-325 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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-326 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 @@ -1466,7 +1466,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-384 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4451 . T)) +NIL NIL (-385 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1552,7 +1552,7 @@ 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 -(-406 -2029 |returnType| -1563 |symbols|) +(-406 -2030 |returnType| -1563 |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 @@ -1859,7 +1859,7 @@ NIL (-482 |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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . 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((-4455 . T)) @@ -1888,10 +1888,10 @@ 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"))) (((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . 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(|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))))) (|HasCategory| (-572) (QUOTE (-858))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1060)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188))))) (-2813 (|HasCategory| |#2| (QUOTE (-1060))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))))) (-491) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -2517,8 +2517,8 @@ NIL NIL ((-2074 (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-370)))) (-647 R) -((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4451 . T)) +((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) +NIL NIL (-648 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2592,7 +2592,7 @@ 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)))) -(-666 A -2514) +(-666 A -3027) ((|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}}"))) ((-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) @@ -2643,7 +2643,7 @@ NIL (-678 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4451 . T) (-4454 . T) (-4448 . T) (-4449 . T)) -((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-564))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-564))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-679) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2804,7 +2804,7 @@ 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 -(-719 R |Mod| -3635 -1867 |exactQuo|) +(-719 R |Mod| -3104 -1767 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-723 R |Mod| -3635 -1867 |exactQuo|) +(-723 R |Mod| -3104 -1767 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4451 . T)) NIL @@ -3220,10 +3220,10 @@ NIL ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) 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(|HasCategory| |#3| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#3| (QUOTE (-1111)))) (|HasAttribute| |#3| (QUOTE -4451)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (-1125 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4543,7 +4543,7 @@ NIL (-1153 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4451 . T) (-4443 |has| |#2| (-6 (-4456 "*"))) (-4454 . T) (-4448 . T) (-4449 . T)) -((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1154 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4647,7 +4647,7 @@ NIL (-1179 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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.")) 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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 @@ -4983,11 +4983,11 @@ NIL (-1263 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. 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T)) -((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) +((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-1264 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1265 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4456 "*") |has| (-1264 |#2| |#3| |#4|) (-174)) (-4447 |has| (-1264 |#2| |#3| |#4|) (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -5007,7 +5007,7 @@ NIL (-1269 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3921) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3034) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) (-1270 |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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -5015,7 +5015,7 @@ NIL (-1271 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1272 |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 @@ -5180,4 +5180,4 @@ NIL NIL NIL NIL -((-3 NIL 2267377 2267382 2267387 2267392) (-2 NIL 2267357 2267362 2267367 2267372) (-1 NIL 2267337 2267342 2267347 2267352) (0 NIL 2267317 2267322 2267327 2267332) (-1308 "ZMOD.spad" 2267126 2267139 2267255 2267312) (-1307 "ZLINDEP.spad" 2266192 2266203 2267116 2267121) (-1306 "ZDSOLVE.spad" 2256137 2256159 2266182 2266187) (-1305 "YSTREAM.spad" 2255632 2255643 2256127 2256132) (-1304 "YDIAGRAM.spad" 2255266 2255275 2255622 2255627) (-1303 "XRPOLY.spad" 2254486 2254506 2255122 2255191) (-1302 "XPR.spad" 2252281 2252294 2254204 2254303) (-1301 "XPOLY.spad" 2251836 2251847 2252137 2252206) (-1300 "XPOLYC.spad" 2251155 2251171 2251762 2251831) (-1299 "XPBWPOLY.spad" 2249592 2249612 2250935 2251004) (-1298 "XF.spad" 2248055 2248070 2249494 2249587) (-1297 "XF.spad" 2246498 2246515 2247939 2247944) (-1296 "XFALG.spad" 2243546 2243562 2246424 2246493) (-1295 "XEXPPKG.spad" 2242797 2242823 2243536 2243541) (-1294 "XDPOLY.spad" 2242411 2242427 2242653 2242722) (-1293 "XALG.spad" 2242071 2242082 2242367 2242406) (-1292 "WUTSET.spad" 2237910 2237927 2241717 2241744) (-1291 "WP.spad" 2237109 2237153 2237768 2237835) (-1290 "WHILEAST.spad" 2236907 2236916 2237099 2237104) (-1289 "WHEREAST.spad" 2236578 2236587 2236897 2236902) (-1288 "WFFINTBS.spad" 2234241 2234263 2236568 2236573) (-1287 "WEIER.spad" 2232463 2232474 2234231 2234236) (-1286 "VSPACE.spad" 2232136 2232147 2232431 2232458) (-1285 "VSPACE.spad" 2231829 2231842 2232126 2232131) (-1284 "VOID.spad" 2231506 2231515 2231819 2231824) (-1283 "VIEW.spad" 2229186 2229195 2231496 2231501) (-1282 "VIEWDEF.spad" 2224387 2224396 2229176 2229181) (-1281 "VIEW3D.spad" 2208348 2208357 2224377 2224382) (-1280 "VIEW2D.spad" 2196239 2196248 2208338 2208343) (-1279 "VECTOR.spad" 2194913 2194924 2195164 2195191) (-1278 "VECTOR2.spad" 2193552 2193565 2194903 2194908) (-1277 "VECTCAT.spad" 2191456 2191467 2193520 2193547) (-1276 "VECTCAT.spad" 2189167 2189180 2191233 2191238) (-1275 "VARIABLE.spad" 2188947 2188962 2189157 2189162) (-1274 "UTYPE.spad" 2188591 2188600 2188937 2188942) (-1273 "UTSODETL.spad" 2187886 2187910 2188547 2188552) (-1272 "UTSODE.spad" 2186102 2186122 2187876 2187881) (-1271 "UTS.spad" 2180906 2180934 2184569 2184666) (-1270 "UTSCAT.spad" 2178385 2178401 2180804 2180901) (-1269 "UTSCAT.spad" 2175508 2175526 2177929 2177934) (-1268 "UTS2.spad" 2175103 2175138 2175498 2175503) (-1267 "URAGG.spad" 2169776 2169787 2175093 2175098) (-1266 "URAGG.spad" 2164413 2164426 2169732 2169737) (-1265 "UPXSSING.spad" 2162058 2162084 2163494 2163627) (-1264 "UPXS.spad" 2159212 2159240 2160190 2160339) (-1263 "UPXSCONS.spad" 2156971 2156991 2157344 2157493) (-1262 "UPXSCCA.spad" 2155542 2155562 2156817 2156966) (-1261 "UPXSCCA.spad" 2154255 2154277 2155532 2155537) (-1260 "UPXSCAT.spad" 2152844 2152860 2154101 2154250) (-1259 "UPXS2.spad" 2152387 2152440 2152834 2152839) (-1258 "UPSQFREE.spad" 2150801 2150815 2152377 2152382) (-1257 "UPSCAT.spad" 2148588 2148612 2150699 2150796) (-1256 "UPSCAT.spad" 2146081 2146107 2148194 2148199) (-1255 "UPOLYC.spad" 2141121 2141132 2145923 2146076) (-1254 "UPOLYC.spad" 2136053 2136066 2140857 2140862) (-1253 "UPOLYC2.spad" 2135524 2135543 2136043 2136048) (-1252 "UP.spad" 2132723 2132738 2133110 2133263) (-1251 "UPMP.spad" 2131623 2131636 2132713 2132718) (-1250 "UPDIVP.spad" 2131188 2131202 2131613 2131618) (-1249 "UPDECOMP.spad" 2129433 2129447 2131178 2131183) (-1248 "UPCDEN.spad" 2128642 2128658 2129423 2129428) (-1247 "UP2.spad" 2128006 2128027 2128632 2128637) (-1246 "UNISEG.spad" 2127359 2127370 2127925 2127930) (-1245 "UNISEG2.spad" 2126856 2126869 2127315 2127320) (-1244 "UNIFACT.spad" 2125959 2125971 2126846 2126851) (-1243 "ULS.spad" 2116517 2116545 2117604 2118033) (-1242 "ULSCONS.spad" 2108913 2108933 2109283 2109432) (-1241 "ULSCCAT.spad" 2106650 2106670 2108759 2108908) (-1240 "ULSCCAT.spad" 2104495 2104517 2106606 2106611) (-1239 "ULSCAT.spad" 2102727 2102743 2104341 2104490) (-1238 "ULS2.spad" 2102241 2102294 2102717 2102722) (-1237 "UINT8.spad" 2102118 2102127 2102231 2102236) (-1236 "UINT64.spad" 2101994 2102003 2102108 2102113) (-1235 "UINT32.spad" 2101870 2101879 2101984 2101989) (-1234 "UINT16.spad" 2101746 2101755 2101860 2101865) (-1233 "UFD.spad" 2100811 2100820 2101672 2101741) (-1232 "UFD.spad" 2099938 2099949 2100801 2100806) (-1231 "UDVO.spad" 2098819 2098828 2099928 2099933) (-1230 "UDPO.spad" 2096312 2096323 2098775 2098780) (-1229 "TYPE.spad" 2096244 2096253 2096302 2096307) (-1228 "TYPEAST.spad" 2096163 2096172 2096234 2096239) (-1227 "TWOFACT.spad" 2094815 2094830 2096153 2096158) (-1226 "TUPLE.spad" 2094301 2094312 2094714 2094719) (-1225 "TUBETOOL.spad" 2091168 2091177 2094291 2094296) (-1224 "TUBE.spad" 2089815 2089832 2091158 2091163) (-1223 "TS.spad" 2088414 2088430 2089380 2089477) (-1222 "TSETCAT.spad" 2075541 2075558 2088382 2088409) (-1221 "TSETCAT.spad" 2062654 2062673 2075497 2075502) (-1220 "TRMANIP.spad" 2057020 2057037 2062360 2062365) (-1219 "TRIMAT.spad" 2055983 2056008 2057010 2057015) (-1218 "TRIGMNIP.spad" 2054510 2054527 2055973 2055978) (-1217 "TRIGCAT.spad" 2054022 2054031 2054500 2054505) (-1216 "TRIGCAT.spad" 2053532 2053543 2054012 2054017) (-1215 "TREE.spad" 2052107 2052118 2053139 2053166) (-1214 "TRANFUN.spad" 2051946 2051955 2052097 2052102) (-1213 "TRANFUN.spad" 2051783 2051794 2051936 2051941) (-1212 "TOPSP.spad" 2051457 2051466 2051773 2051778) (-1211 "TOOLSIGN.spad" 2051120 2051131 2051447 2051452) (-1210 "TEXTFILE.spad" 2049681 2049690 2051110 2051115) (-1209 "TEX.spad" 2046827 2046836 2049671 2049676) (-1208 "TEX1.spad" 2046383 2046394 2046817 2046822) (-1207 "TEMUTL.spad" 2045938 2045947 2046373 2046378) (-1206 "TBCMPPK.spad" 2044031 2044054 2045928 2045933) (-1205 "TBAGG.spad" 2043081 2043104 2044011 2044026) (-1204 "TBAGG.spad" 2042139 2042164 2043071 2043076) (-1203 "TANEXP.spad" 2041547 2041558 2042129 2042134) (-1202 "TALGOP.spad" 2041271 2041282 2041537 2041542) (-1201 "TABLE.spad" 2039682 2039705 2039952 2039979) (-1200 "TABLEAU.spad" 2039163 2039174 2039672 2039677) (-1199 "TABLBUMP.spad" 2035966 2035977 2039153 2039158) (-1198 "SYSTEM.spad" 2035194 2035203 2035956 2035961) (-1197 "SYSSOLP.spad" 2032677 2032688 2035184 2035189) (-1196 "SYSPTR.spad" 2032576 2032585 2032667 2032672) (-1195 "SYSNNI.spad" 2031758 2031769 2032566 2032571) (-1194 "SYSINT.spad" 2031162 2031173 2031748 2031753) (-1193 "SYNTAX.spad" 2027368 2027377 2031152 2031157) (-1192 "SYMTAB.spad" 2025436 2025445 2027358 2027363) (-1191 "SYMS.spad" 2021459 2021468 2025426 2025431) (-1190 "SYMPOLY.spad" 2020466 2020477 2020548 2020675) (-1189 "SYMFUNC.spad" 2019967 2019978 2020456 2020461) (-1188 "SYMBOL.spad" 2017470 2017479 2019957 2019962) (-1187 "SWITCH.spad" 2014241 2014250 2017460 2017465) (-1186 "SUTS.spad" 2011146 2011174 2012708 2012805) (-1185 "SUPXS.spad" 2008287 2008315 2009278 2009427) (-1184 "SUP.spad" 2005100 2005111 2005873 2006026) (-1183 "SUPFRACF.spad" 2004205 2004223 2005090 2005095) (-1182 "SUP2.spad" 2003597 2003610 2004195 2004200) (-1181 "SUMRF.spad" 2002571 2002582 2003587 2003592) (-1180 "SUMFS.spad" 2002208 2002225 2002561 2002566) (-1179 "SULS.spad" 1992753 1992781 1993853 1994282) (-1178 "SUCHTAST.spad" 1992522 1992531 1992743 1992748) (-1177 "SUCH.spad" 1992204 1992219 1992512 1992517) (-1176 "SUBSPACE.spad" 1984319 1984334 1992194 1992199) (-1175 "SUBRESP.spad" 1983489 1983503 1984275 1984280) (-1174 "STTF.spad" 1979588 1979604 1983479 1983484) (-1173 "STTFNC.spad" 1976056 1976072 1979578 1979583) (-1172 "STTAYLOR.spad" 1968691 1968702 1975937 1975942) (-1171 "STRTBL.spad" 1967196 1967213 1967345 1967372) (-1170 "STRING.spad" 1966605 1966614 1966619 1966646) (-1169 "STRICAT.spad" 1966393 1966402 1966573 1966600) (-1168 "STREAM.spad" 1963311 1963322 1965918 1965933) (-1167 "STREAM3.spad" 1962884 1962899 1963301 1963306) (-1166 "STREAM2.spad" 1962012 1962025 1962874 1962879) (-1165 "STREAM1.spad" 1961718 1961729 1962002 1962007) (-1164 "STINPROD.spad" 1960654 1960670 1961708 1961713) (-1163 "STEP.spad" 1959855 1959864 1960644 1960649) (-1162 "STEPAST.spad" 1959089 1959098 1959845 1959850) (-1161 "STBL.spad" 1957615 1957643 1957782 1957797) (-1160 "STAGG.spad" 1956690 1956701 1957605 1957610) (-1159 "STAGG.spad" 1955763 1955776 1956680 1956685) (-1158 "STACK.spad" 1955120 1955131 1955370 1955397) (-1157 "SREGSET.spad" 1952824 1952841 1954766 1954793) (-1156 "SRDCMPK.spad" 1951385 1951405 1952814 1952819) (-1155 "SRAGG.spad" 1946528 1946537 1951353 1951380) (-1154 "SRAGG.spad" 1941691 1941702 1946518 1946523) (-1153 "SQMATRIX.spad" 1939307 1939325 1940223 1940310) (-1152 "SPLTREE.spad" 1933859 1933872 1938743 1938770) (-1151 "SPLNODE.spad" 1930447 1930460 1933849 1933854) (-1150 "SPFCAT.spad" 1929256 1929265 1930437 1930442) (-1149 "SPECOUT.spad" 1927808 1927817 1929246 1929251) (-1148 "SPADXPT.spad" 1919403 1919412 1927798 1927803) (-1147 "spad-parser.spad" 1918868 1918877 1919393 1919398) (-1146 "SPADAST.spad" 1918569 1918578 1918858 1918863) (-1145 "SPACEC.spad" 1902768 1902779 1918559 1918564) (-1144 "SPACE3.spad" 1902544 1902555 1902758 1902763) (-1143 "SORTPAK.spad" 1902093 1902106 1902500 1902505) (-1142 "SOLVETRA.spad" 1899856 1899867 1902083 1902088) (-1141 "SOLVESER.spad" 1898384 1898395 1899846 1899851) (-1140 "SOLVERAD.spad" 1894410 1894421 1898374 1898379) (-1139 "SOLVEFOR.spad" 1892872 1892890 1894400 1894405) (-1138 "SNTSCAT.spad" 1892472 1892489 1892840 1892867) (-1137 "SMTS.spad" 1890744 1890770 1892037 1892134) (-1136 "SMP.spad" 1888219 1888239 1888609 1888736) (-1135 "SMITH.spad" 1887064 1887089 1888209 1888214) (-1134 "SMATCAT.spad" 1885174 1885204 1887008 1887059) (-1133 "SMATCAT.spad" 1883216 1883248 1885052 1885057) (-1132 "SKAGG.spad" 1882179 1882190 1883184 1883211) (-1131 "SINT.spad" 1881119 1881128 1882045 1882174) (-1130 "SIMPAN.spad" 1880847 1880856 1881109 1881114) (-1129 "SIG.spad" 1880177 1880186 1880837 1880842) (-1128 "SIGNRF.spad" 1879295 1879306 1880167 1880172) (-1127 "SIGNEF.spad" 1878574 1878591 1879285 1879290) (-1126 "SIGAST.spad" 1877959 1877968 1878564 1878569) (-1125 "SHP.spad" 1875887 1875902 1877915 1877920) (-1124 "SHDP.spad" 1865598 1865625 1866107 1866238) (-1123 "SGROUP.spad" 1865206 1865215 1865588 1865593) (-1122 "SGROUP.spad" 1864812 1864823 1865196 1865201) (-1121 "SGCF.spad" 1857951 1857960 1864802 1864807) (-1120 "SFRTCAT.spad" 1856881 1856898 1857919 1857946) (-1119 "SFRGCD.spad" 1855944 1855964 1856871 1856876) (-1118 "SFQCMPK.spad" 1850581 1850601 1855934 1855939) (-1117 "SFORT.spad" 1850020 1850034 1850571 1850576) (-1116 "SEXOF.spad" 1849863 1849903 1850010 1850015) (-1115 "SEX.spad" 1849755 1849764 1849853 1849858) (-1114 "SEXCAT.spad" 1847536 1847576 1849745 1849750) (-1113 "SET.spad" 1845860 1845871 1846957 1846996) (-1112 "SETMN.spad" 1844310 1844327 1845850 1845855) (-1111 "SETCAT.spad" 1843632 1843641 1844300 1844305) (-1110 "SETCAT.spad" 1842952 1842963 1843622 1843627) (-1109 "SETAGG.spad" 1839501 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1049316 1049321) (-678 "LSQM.spad" 1047340 1047354 1047734 1047785) (-677 "LSPP.spad" 1046875 1046892 1047330 1047335) (-676 "LSMP.spad" 1045725 1045753 1046865 1046870) (-675 "LSMP1.spad" 1043543 1043557 1045715 1045720) (-674 "LSAGG.spad" 1043212 1043222 1043511 1043538) (-673 "LSAGG.spad" 1042901 1042913 1043202 1043207) (-672 "LPOLY.spad" 1041855 1041874 1042757 1042826) (-671 "LPEFRAC.spad" 1041126 1041136 1041845 1041850) (-670 "LO.spad" 1040527 1040541 1041060 1041087) (-669 "LOGIC.spad" 1040129 1040137 1040517 1040522) (-668 "LOGIC.spad" 1039729 1039739 1040119 1040124) (-667 "LODOOPS.spad" 1038659 1038671 1039719 1039724) (-666 "LODO.spad" 1038043 1038059 1038339 1038378) (-665 "LODOF.spad" 1037089 1037106 1038000 1038005) (-664 "LODOCAT.spad" 1035755 1035765 1037045 1037084) (-663 "LODOCAT.spad" 1034419 1034431 1035711 1035716) (-662 "LODO2.spad" 1033692 1033704 1034099 1034138) (-661 "LODO1.spad" 1033092 1033102 1033372 1033411) (-660 "LODEEF.spad" 1031894 1031912 1033082 1033087) (-659 "LNAGG.spad" 1028041 1028051 1031884 1031889) (-658 "LNAGG.spad" 1024152 1024164 1027997 1028002) (-657 "LMOPS.spad" 1020920 1020937 1024142 1024147) (-656 "LMODULE.spad" 1020688 1020698 1020910 1020915) (-655 "LMDICT.spad" 1019975 1019985 1020239 1020266) (-654 "LLINSET.spad" 1019372 1019382 1019965 1019970) (-653 "LITERAL.spad" 1019278 1019289 1019362 1019367) (-652 "LIST.spad" 1017013 1017023 1018425 1018452) (-651 "LIST3.spad" 1016324 1016338 1017003 1017008) (-650 "LIST2.spad" 1015026 1015038 1016314 1016319) (-649 "LIST2MAP.spad" 1011929 1011941 1015016 1015021) (-648 "LINSET.spad" 1011551 1011561 1011919 1011924) (-647 "LINEXP.spad" 1010985 1010995 1011531 1011546) (-646 "LINDEP.spad" 1009794 1009806 1010897 1010902) (-645 "LIMITRF.spad" 1007722 1007732 1009784 1009789) (-644 "LIMITPS.spad" 1006625 1006638 1007712 1007717) (-643 "LIE.spad" 1004641 1004653 1005915 1006060) (-642 "LIECAT.spad" 1004117 1004127 1004567 1004636) (-641 "LIECAT.spad" 1003621 1003633 1004073 1004078) (-640 "LIB.spad" 1001834 1001842 1002280 1002295) (-639 "LGROBP.spad" 999187 999206 1001824 1001829) (-638 "LF.spad" 998142 998158 999177 999182) (-637 "LFCAT.spad" 997201 997209 998132 998137) (-636 "LEXTRIPK.spad" 992704 992719 997191 997196) (-635 "LEXP.spad" 990707 990734 992684 992699) (-634 "LETAST.spad" 990406 990414 990697 990702) (-633 "LEADCDET.spad" 988804 988821 990396 990401) (-632 "LAZM3PK.spad" 987508 987530 988794 988799) (-631 "LAUPOL.spad" 986201 986214 987101 987170) (-630 "LAPLACE.spad" 985784 985800 986191 986196) (-629 "LA.spad" 985224 985238 985706 985745) (-628 "LALG.spad" 985000 985010 985204 985219) (-627 "LALG.spad" 984784 984796 984990 984995) (-626 "KVTFROM.spad" 984519 984529 984774 984779) (-625 "KTVLOGIC.spad" 984031 984039 984509 984514) (-624 "KRCFROM.spad" 983769 983779 984021 984026) (-623 "KOVACIC.spad" 982492 982509 983759 983764) (-622 "KONVERT.spad" 982214 982224 982482 982487) (-621 "KOERCE.spad" 981951 981961 982204 982209) (-620 "KERNEL.spad" 980606 980616 981735 981740) (-619 "KERNEL2.spad" 980309 980321 980596 980601) (-618 "KDAGG.spad" 979418 979440 980289 980304) (-617 "KDAGG.spad" 978535 978559 979408 979413) (-616 "KAFILE.spad" 977498 977514 977733 977760) (-615 "JORDAN.spad" 975327 975339 976788 976933) (-614 "JOINAST.spad" 975021 975029 975317 975322) (-613 "JAVACODE.spad" 974887 974895 975011 975016) (-612 "IXAGG.spad" 973020 973044 974877 974882) (-611 "IXAGG.spad" 971008 971034 972867 972872) (-610 "IVECTOR.spad" 969778 969793 969933 969960) (-609 "ITUPLE.spad" 968939 968949 969768 969773) (-608 "ITRIGMNP.spad" 967778 967797 968929 968934) (-607 "ITFUN3.spad" 967284 967298 967768 967773) (-606 "ITFUN2.spad" 967028 967040 967274 967279) (-605 "ITFORM.spad" 966383 966391 967018 967023) (-604 "ITAYLOR.spad" 964377 964392 966247 966344) (-603 "ISUPS.spad" 956814 956829 963351 963448) (-602 "ISUMP.spad" 956315 956331 956804 956809) (-601 "ISTRING.spad" 955403 955416 955484 955511) (-600 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(-559 "INTAF.spad" 887663 887679 888153 888158) (-558 "INTABL.spad" 886181 886212 886344 886371) (-557 "INT8.spad" 886061 886069 886171 886176) (-556 "INT64.spad" 885940 885948 886051 886056) (-555 "INT32.spad" 885819 885827 885930 885935) (-554 "INT16.spad" 885698 885706 885809 885814) (-553 "INS.spad" 883201 883209 885600 885693) (-552 "INS.spad" 880790 880800 883191 883196) (-551 "INPSIGN.spad" 880238 880251 880780 880785) (-550 "INPRODPF.spad" 879334 879353 880228 880233) (-549 "INPRODFF.spad" 878422 878446 879324 879329) (-548 "INNMFACT.spad" 877397 877414 878412 878417) (-547 "INMODGCD.spad" 876885 876915 877387 877392) (-546 "INFSP.spad" 875182 875204 876875 876880) (-545 "INFPROD0.spad" 874262 874281 875172 875177) (-544 "INFORM.spad" 871461 871469 874252 874257) (-543 "INFORM1.spad" 871086 871096 871451 871456) (-542 "INFINITY.spad" 870638 870646 871076 871081) (-541 "INETCLTS.spad" 870615 870623 870628 870633) (-540 "INEP.spad" 869153 869175 870605 870610) (-539 "INDE.spad" 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170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2267465 2267470 2267475 2267480) (-2 NIL 2267445 2267450 2267455 2267460) (-1 NIL 2267425 2267430 2267435 2267440) (0 NIL 2267405 2267410 2267415 2267420) (-1308 "ZMOD.spad" 2267214 2267227 2267343 2267400) (-1307 "ZLINDEP.spad" 2266280 2266291 2267204 2267209) (-1306 "ZDSOLVE.spad" 2256225 2256247 2266270 2266275) (-1305 "YSTREAM.spad" 2255720 2255731 2256215 2256220) (-1304 "YDIAGRAM.spad" 2255354 2255363 2255710 2255715) (-1303 "XRPOLY.spad" 2254574 2254594 2255210 2255279) (-1302 "XPR.spad" 2252369 2252382 2254292 2254391) (-1301 "XPOLY.spad" 2251924 2251935 2252225 2252294) (-1300 "XPOLYC.spad" 2251243 2251259 2251850 2251919) (-1299 "XPBWPOLY.spad" 2249680 2249700 2251023 2251092) (-1298 "XF.spad" 2248143 2248158 2249582 2249675) (-1297 "XF.spad" 2246586 2246603 2248027 2248032) (-1296 "XFALG.spad" 2243634 2243650 2246512 2246581) (-1295 "XEXPPKG.spad" 2242885 2242911 2243624 2243629) (-1294 "XDPOLY.spad" 2242499 2242515 2242741 2242810) (-1293 "XALG.spad" 2242159 2242170 2242455 2242494) (-1292 "WUTSET.spad" 2237998 2238015 2241805 2241832) (-1291 "WP.spad" 2237197 2237241 2237856 2237923) (-1290 "WHILEAST.spad" 2236995 2237004 2237187 2237192) (-1289 "WHEREAST.spad" 2236666 2236675 2236985 2236990) (-1288 "WFFINTBS.spad" 2234329 2234351 2236656 2236661) (-1287 "WEIER.spad" 2232551 2232562 2234319 2234324) (-1286 "VSPACE.spad" 2232224 2232235 2232519 2232546) (-1285 "VSPACE.spad" 2231917 2231930 2232214 2232219) (-1284 "VOID.spad" 2231594 2231603 2231907 2231912) (-1283 "VIEW.spad" 2229274 2229283 2231584 2231589) (-1282 "VIEWDEF.spad" 2224475 2224484 2229264 2229269) (-1281 "VIEW3D.spad" 2208436 2208445 2224465 2224470) (-1280 "VIEW2D.spad" 2196327 2196336 2208426 2208431) (-1279 "VECTOR.spad" 2195001 2195012 2195252 2195279) (-1278 "VECTOR2.spad" 2193640 2193653 2194991 2194996) (-1277 "VECTCAT.spad" 2191544 2191555 2193608 2193635) (-1276 "VECTCAT.spad" 2189255 2189268 2191321 2191326) (-1275 "VARIABLE.spad" 2189035 2189050 2189245 2189250) (-1274 "UTYPE.spad" 2188679 2188688 2189025 2189030) (-1273 "UTSODETL.spad" 2187974 2187998 2188635 2188640) (-1272 "UTSODE.spad" 2186190 2186210 2187964 2187969) (-1271 "UTS.spad" 2180994 2181022 2184657 2184754) (-1270 "UTSCAT.spad" 2178473 2178489 2180892 2180989) (-1269 "UTSCAT.spad" 2175596 2175614 2178017 2178022) (-1268 "UTS2.spad" 2175191 2175226 2175586 2175591) (-1267 "URAGG.spad" 2169864 2169875 2175181 2175186) (-1266 "URAGG.spad" 2164501 2164514 2169820 2169825) (-1265 "UPXSSING.spad" 2162146 2162172 2163582 2163715) (-1264 "UPXS.spad" 2159300 2159328 2160278 2160427) (-1263 "UPXSCONS.spad" 2157059 2157079 2157432 2157581) (-1262 "UPXSCCA.spad" 2155630 2155650 2156905 2157054) (-1261 "UPXSCCA.spad" 2154343 2154365 2155620 2155625) (-1260 "UPXSCAT.spad" 2152932 2152948 2154189 2154338) (-1259 "UPXS2.spad" 2152475 2152528 2152922 2152927) (-1258 "UPSQFREE.spad" 2150889 2150903 2152465 2152470) (-1257 "UPSCAT.spad" 2148676 2148700 2150787 2150884) (-1256 "UPSCAT.spad" 2146169 2146195 2148282 2148287) (-1255 "UPOLYC.spad" 2141209 2141220 2146011 2146164) (-1254 "UPOLYC.spad" 2136141 2136154 2140945 2140950) (-1253 "UPOLYC2.spad" 2135612 2135631 2136131 2136136) (-1252 "UP.spad" 2132811 2132826 2133198 2133351) (-1251 "UPMP.spad" 2131711 2131724 2132801 2132806) (-1250 "UPDIVP.spad" 2131276 2131290 2131701 2131706) (-1249 "UPDECOMP.spad" 2129521 2129535 2131266 2131271) (-1248 "UPCDEN.spad" 2128730 2128746 2129511 2129516) (-1247 "UP2.spad" 2128094 2128115 2128720 2128725) (-1246 "UNISEG.spad" 2127447 2127458 2128013 2128018) (-1245 "UNISEG2.spad" 2126944 2126957 2127403 2127408) (-1244 "UNIFACT.spad" 2126047 2126059 2126934 2126939) (-1243 "ULS.spad" 2116605 2116633 2117692 2118121) (-1242 "ULSCONS.spad" 2109001 2109021 2109371 2109520) (-1241 "ULSCCAT.spad" 2106738 2106758 2108847 2108996) (-1240 "ULSCCAT.spad" 2104583 2104605 2106694 2106699) (-1239 "ULSCAT.spad" 2102815 2102831 2104429 2104578) (-1238 "ULS2.spad" 2102329 2102382 2102805 2102810) (-1237 "UINT8.spad" 2102206 2102215 2102319 2102324) (-1236 "UINT64.spad" 2102082 2102091 2102196 2102201) (-1235 "UINT32.spad" 2101958 2101967 2102072 2102077) (-1234 "UINT16.spad" 2101834 2101843 2101948 2101953) (-1233 "UFD.spad" 2100899 2100908 2101760 2101829) (-1232 "UFD.spad" 2100026 2100037 2100889 2100894) (-1231 "UDVO.spad" 2098907 2098916 2100016 2100021) (-1230 "UDPO.spad" 2096400 2096411 2098863 2098868) (-1229 "TYPE.spad" 2096332 2096341 2096390 2096395) (-1228 "TYPEAST.spad" 2096251 2096260 2096322 2096327) (-1227 "TWOFACT.spad" 2094903 2094918 2096241 2096246) (-1226 "TUPLE.spad" 2094389 2094400 2094802 2094807) (-1225 "TUBETOOL.spad" 2091256 2091265 2094379 2094384) (-1224 "TUBE.spad" 2089903 2089920 2091246 2091251) (-1223 "TS.spad" 2088502 2088518 2089468 2089565) (-1222 "TSETCAT.spad" 2075629 2075646 2088470 2088497) (-1221 "TSETCAT.spad" 2062742 2062761 2075585 2075590) (-1220 "TRMANIP.spad" 2057108 2057125 2062448 2062453) (-1219 "TRIMAT.spad" 2056071 2056096 2057098 2057103) (-1218 "TRIGMNIP.spad" 2054598 2054615 2056061 2056066) (-1217 "TRIGCAT.spad" 2054110 2054119 2054588 2054593) (-1216 "TRIGCAT.spad" 2053620 2053631 2054100 2054105) (-1215 "TREE.spad" 2052195 2052206 2053227 2053254) (-1214 "TRANFUN.spad" 2052034 2052043 2052185 2052190) (-1213 "TRANFUN.spad" 2051871 2051882 2052024 2052029) (-1212 "TOPSP.spad" 2051545 2051554 2051861 2051866) (-1211 "TOOLSIGN.spad" 2051208 2051219 2051535 2051540) (-1210 "TEXTFILE.spad" 2049769 2049778 2051198 2051203) (-1209 "TEX.spad" 2046915 2046924 2049759 2049764) (-1208 "TEX1.spad" 2046471 2046482 2046905 2046910) (-1207 "TEMUTL.spad" 2046026 2046035 2046461 2046466) (-1206 "TBCMPPK.spad" 2044119 2044142 2046016 2046021) (-1205 "TBAGG.spad" 2043169 2043192 2044099 2044114) (-1204 "TBAGG.spad" 2042227 2042252 2043159 2043164) (-1203 "TANEXP.spad" 2041635 2041646 2042217 2042222) (-1202 "TALGOP.spad" 2041359 2041370 2041625 2041630) (-1201 "TABLE.spad" 2039770 2039793 2040040 2040067) (-1200 "TABLEAU.spad" 2039251 2039262 2039760 2039765) (-1199 "TABLBUMP.spad" 2036054 2036065 2039241 2039246) (-1198 "SYSTEM.spad" 2035282 2035291 2036044 2036049) (-1197 "SYSSOLP.spad" 2032765 2032776 2035272 2035277) (-1196 "SYSPTR.spad" 2032664 2032673 2032755 2032760) (-1195 "SYSNNI.spad" 2031846 2031857 2032654 2032659) (-1194 "SYSINT.spad" 2031250 2031261 2031836 2031841) (-1193 "SYNTAX.spad" 2027456 2027465 2031240 2031245) (-1192 "SYMTAB.spad" 2025524 2025533 2027446 2027451) (-1191 "SYMS.spad" 2021547 2021556 2025514 2025519) (-1190 "SYMPOLY.spad" 2020554 2020565 2020636 2020763) (-1189 "SYMFUNC.spad" 2020055 2020066 2020544 2020549) (-1188 "SYMBOL.spad" 2017558 2017567 2020045 2020050) (-1187 "SWITCH.spad" 2014329 2014338 2017548 2017553) (-1186 "SUTS.spad" 2011234 2011262 2012796 2012893) (-1185 "SUPXS.spad" 2008375 2008403 2009366 2009515) (-1184 "SUP.spad" 2005188 2005199 2005961 2006114) (-1183 "SUPFRACF.spad" 2004293 2004311 2005178 2005183) (-1182 "SUP2.spad" 2003685 2003698 2004283 2004288) (-1181 "SUMRF.spad" 2002659 2002670 2003675 2003680) (-1180 "SUMFS.spad" 2002296 2002313 2002649 2002654) (-1179 "SULS.spad" 1992841 1992869 1993941 1994370) (-1178 "SUCHTAST.spad" 1992610 1992619 1992831 1992836) (-1177 "SUCH.spad" 1992292 1992307 1992600 1992605) (-1176 "SUBSPACE.spad" 1984407 1984422 1992282 1992287) (-1175 "SUBRESP.spad" 1983577 1983591 1984363 1984368) (-1174 "STTF.spad" 1979676 1979692 1983567 1983572) (-1173 "STTFNC.spad" 1976144 1976160 1979666 1979671) (-1172 "STTAYLOR.spad" 1968779 1968790 1976025 1976030) (-1171 "STRTBL.spad" 1967284 1967301 1967433 1967460) (-1170 "STRING.spad" 1966693 1966702 1966707 1966734) (-1169 "STRICAT.spad" 1966481 1966490 1966661 1966688) (-1168 "STREAM.spad" 1963399 1963410 1966006 1966021) (-1167 "STREAM3.spad" 1962972 1962987 1963389 1963394) (-1166 "STREAM2.spad" 1962100 1962113 1962962 1962967) (-1165 "STREAM1.spad" 1961806 1961817 1962090 1962095) (-1164 "STINPROD.spad" 1960742 1960758 1961796 1961801) (-1163 "STEP.spad" 1959943 1959952 1960732 1960737) (-1162 "STEPAST.spad" 1959177 1959186 1959933 1959938) (-1161 "STBL.spad" 1957703 1957731 1957870 1957885) (-1160 "STAGG.spad" 1956778 1956789 1957693 1957698) (-1159 "STAGG.spad" 1955851 1955864 1956768 1956773) (-1158 "STACK.spad" 1955208 1955219 1955458 1955485) (-1157 "SREGSET.spad" 1952912 1952929 1954854 1954881) (-1156 "SRDCMPK.spad" 1951473 1951493 1952902 1952907) (-1155 "SRAGG.spad" 1946616 1946625 1951441 1951468) (-1154 "SRAGG.spad" 1941779 1941790 1946606 1946611) (-1153 "SQMATRIX.spad" 1939451 1939469 1940367 1940454) (-1152 "SPLTREE.spad" 1934003 1934016 1938887 1938914) (-1151 "SPLNODE.spad" 1930591 1930604 1933993 1933998) (-1150 "SPFCAT.spad" 1929400 1929409 1930581 1930586) (-1149 "SPECOUT.spad" 1927952 1927961 1929390 1929395) (-1148 "SPADXPT.spad" 1919547 1919556 1927942 1927947) (-1147 "spad-parser.spad" 1919012 1919021 1919537 1919542) (-1146 "SPADAST.spad" 1918713 1918722 1919002 1919007) (-1145 "SPACEC.spad" 1902912 1902923 1918703 1918708) (-1144 "SPACE3.spad" 1902688 1902699 1902902 1902907) (-1143 "SORTPAK.spad" 1902237 1902250 1902644 1902649) (-1142 "SOLVETRA.spad" 1900000 1900011 1902227 1902232) (-1141 "SOLVESER.spad" 1898528 1898539 1899990 1899995) (-1140 "SOLVERAD.spad" 1894554 1894565 1898518 1898523) (-1139 "SOLVEFOR.spad" 1893016 1893034 1894544 1894549) (-1138 "SNTSCAT.spad" 1892616 1892633 1892984 1893011) (-1137 "SMTS.spad" 1890888 1890914 1892181 1892278) (-1136 "SMP.spad" 1888363 1888383 1888753 1888880) (-1135 "SMITH.spad" 1887208 1887233 1888353 1888358) (-1134 "SMATCAT.spad" 1885318 1885348 1887152 1887203) (-1133 "SMATCAT.spad" 1883360 1883392 1885196 1885201) (-1132 "SKAGG.spad" 1882323 1882334 1883328 1883355) (-1131 "SINT.spad" 1881263 1881272 1882189 1882318) (-1130 "SIMPAN.spad" 1880991 1881000 1881253 1881258) (-1129 "SIG.spad" 1880321 1880330 1880981 1880986) (-1128 "SIGNRF.spad" 1879439 1879450 1880311 1880316) (-1127 "SIGNEF.spad" 1878718 1878735 1879429 1879434) (-1126 "SIGAST.spad" 1878103 1878112 1878708 1878713) (-1125 "SHP.spad" 1876031 1876046 1878059 1878064) (-1124 "SHDP.spad" 1865665 1865692 1866174 1866305) (-1123 "SGROUP.spad" 1865273 1865282 1865655 1865660) (-1122 "SGROUP.spad" 1864879 1864890 1865263 1865268) (-1121 "SGCF.spad" 1858018 1858027 1864869 1864874) (-1120 "SFRTCAT.spad" 1856948 1856965 1857986 1858013) (-1119 "SFRGCD.spad" 1856011 1856031 1856938 1856943) (-1118 "SFQCMPK.spad" 1850648 1850668 1856001 1856006) (-1117 "SFORT.spad" 1850087 1850101 1850638 1850643) (-1116 "SEXOF.spad" 1849930 1849970 1850077 1850082) (-1115 "SEX.spad" 1849822 1849831 1849920 1849925) (-1114 "SEXCAT.spad" 1847603 1847643 1849812 1849817) (-1113 "SET.spad" 1845927 1845938 1847024 1847063) (-1112 "SETMN.spad" 1844377 1844394 1845917 1845922) (-1111 "SETCAT.spad" 1843699 1843708 1844367 1844372) (-1110 "SETCAT.spad" 1843019 1843030 1843689 1843694) (-1109 "SETAGG.spad" 1839568 1839579 1842999 1843014) (-1108 "SETAGG.spad" 1836125 1836138 1839558 1839563) (-1107 "SEQAST.spad" 1835828 1835837 1836115 1836120) (-1106 "SEGXCAT.spad" 1834984 1834997 1835818 1835823) (-1105 "SEG.spad" 1834797 1834808 1834903 1834908) (-1104 "SEGCAT.spad" 1833722 1833733 1834787 1834792) (-1103 "SEGBIND.spad" 1833480 1833491 1833669 1833674) (-1102 "SEGBIND2.spad" 1833178 1833191 1833470 1833475) (-1101 "SEGAST.spad" 1832892 1832901 1833168 1833173) (-1100 "SEG2.spad" 1832327 1832340 1832848 1832853) (-1099 "SDVAR.spad" 1831603 1831614 1832317 1832322) (-1098 "SDPOL.spad" 1829029 1829040 1829320 1829447) (-1097 "SCPKG.spad" 1827118 1827129 1829019 1829024) (-1096 "SCOPE.spad" 1826271 1826280 1827108 1827113) (-1095 "SCACHE.spad" 1824967 1824978 1826261 1826266) (-1094 "SASTCAT.spad" 1824876 1824885 1824957 1824962) (-1093 "SAOS.spad" 1824748 1824757 1824866 1824871) (-1092 "SAERFFC.spad" 1824461 1824481 1824738 1824743) (-1091 "SAE.spad" 1822636 1822652 1823247 1823382) (-1090 "SAEFACT.spad" 1822337 1822357 1822626 1822631) (-1089 "RURPK.spad" 1819996 1820012 1822327 1822332) (-1088 "RULESET.spad" 1819449 1819473 1819986 1819991) (-1087 "RULE.spad" 1817689 1817713 1819439 1819444) (-1086 "RULECOLD.spad" 1817541 1817554 1817679 1817684) (-1085 "RTVALUE.spad" 1817276 1817285 1817531 1817536) (-1084 "RSTRCAST.spad" 1816993 1817002 1817266 1817271) (-1083 "RSETGCD.spad" 1813371 1813391 1816983 1816988) (-1082 "RSETCAT.spad" 1803307 1803324 1813339 1813366) (-1081 "RSETCAT.spad" 1793263 1793282 1803297 1803302) (-1080 "RSDCMPK.spad" 1791715 1791735 1793253 1793258) (-1079 "RRCC.spad" 1790099 1790129 1791705 1791710) (-1078 "RRCC.spad" 1788481 1788513 1790089 1790094) (-1077 "RPTAST.spad" 1788183 1788192 1788471 1788476) (-1076 "RPOLCAT.spad" 1767543 1767558 1788051 1788178) (-1075 "RPOLCAT.spad" 1746616 1746633 1767126 1767131) (-1074 "ROUTINE.spad" 1742499 1742508 1745263 1745290) (-1073 "ROMAN.spad" 1741827 1741836 1742365 1742494) (-1072 "ROIRC.spad" 1740907 1740939 1741817 1741822) (-1071 "RNS.spad" 1739810 1739819 1740809 1740902) (-1070 "RNS.spad" 1738799 1738810 1739800 1739805) (-1069 "RNG.spad" 1738534 1738543 1738789 1738794) (-1068 "RNGBIND.spad" 1737694 1737708 1738489 1738494) (-1067 "RMODULE.spad" 1737459 1737470 1737684 1737689) (-1066 "RMCAT2.spad" 1736879 1736936 1737449 1737454) (-1065 "RMATRIX.spad" 1735703 1735722 1736046 1736085) (-1064 "RMATCAT.spad" 1731282 1731313 1735659 1735698) (-1063 "RMATCAT.spad" 1726751 1726784 1731130 1731135) (-1062 "RLINSET.spad" 1726145 1726156 1726741 1726746) (-1061 "RINTERP.spad" 1726033 1726053 1726135 1726140) (-1060 "RING.spad" 1725503 1725512 1726013 1726028) (-1059 "RING.spad" 1724981 1724992 1725493 1725498) (-1058 "RIDIST.spad" 1724373 1724382 1724971 1724976) (-1057 "RGCHAIN.spad" 1722956 1722972 1723858 1723885) (-1056 "RGBCSPC.spad" 1722737 1722749 1722946 1722951) (-1055 "RGBCMDL.spad" 1722267 1722279 1722727 1722732) (-1054 "RF.spad" 1719909 1719920 1722257 1722262) (-1053 "RFFACTOR.spad" 1719371 1719382 1719899 1719904) (-1052 "RFFACT.spad" 1719106 1719118 1719361 1719366) (-1051 "RFDIST.spad" 1718102 1718111 1719096 1719101) (-1050 "RETSOL.spad" 1717521 1717534 1718092 1718097) (-1049 "RETRACT.spad" 1716949 1716960 1717511 1717516) (-1048 "RETRACT.spad" 1716375 1716388 1716939 1716944) (-1047 "RETAST.spad" 1716187 1716196 1716365 1716370) (-1046 "RESULT.spad" 1714247 1714256 1714834 1714861) (-1045 "RESRING.spad" 1713594 1713641 1714185 1714242) (-1044 "RESLATC.spad" 1712918 1712929 1713584 1713589) (-1043 "REPSQ.spad" 1712649 1712660 1712908 1712913) (-1042 "REP.spad" 1710203 1710212 1712639 1712644) (-1041 "REPDB.spad" 1709910 1709921 1710193 1710198) (-1040 "REP2.spad" 1699568 1699579 1709752 1709757) (-1039 "REP1.spad" 1693764 1693775 1699518 1699523) (-1038 "REGSET.spad" 1691561 1691578 1693410 1693437) (-1037 "REF.spad" 1690896 1690907 1691516 1691521) (-1036 "REDORDER.spad" 1690102 1690119 1690886 1690891) (-1035 "RECLOS.spad" 1688885 1688905 1689589 1689682) (-1034 "REALSOLV.spad" 1688025 1688034 1688875 1688880) (-1033 "REAL.spad" 1687897 1687906 1688015 1688020) (-1032 "REAL0Q.spad" 1685195 1685210 1687887 1687892) (-1031 "REAL0.spad" 1682039 1682054 1685185 1685190) (-1030 "RDUCEAST.spad" 1681760 1681769 1682029 1682034) (-1029 "RDIV.spad" 1681415 1681440 1681750 1681755) (-1028 "RDIST.spad" 1680982 1680993 1681405 1681410) (-1027 "RDETRS.spad" 1679846 1679864 1680972 1680977) (-1026 "RDETR.spad" 1677985 1678003 1679836 1679841) (-1025 "RDEEFS.spad" 1677084 1677101 1677975 1677980) (-1024 "RDEEF.spad" 1676094 1676111 1677074 1677079) (-1023 "RCFIELD.spad" 1673280 1673289 1675996 1676089) (-1022 "RCFIELD.spad" 1670552 1670563 1673270 1673275) (-1021 "RCAGG.spad" 1668480 1668491 1670542 1670547) (-1020 "RCAGG.spad" 1666335 1666348 1668399 1668404) (-1019 "RATRET.spad" 1665695 1665706 1666325 1666330) (-1018 "RATFACT.spad" 1665387 1665399 1665685 1665690) (-1017 "RANDSRC.spad" 1664706 1664715 1665377 1665382) (-1016 "RADUTIL.spad" 1664462 1664471 1664696 1664701) (-1015 "RADIX.spad" 1661383 1661397 1662929 1663022) (-1014 "RADFF.spad" 1659796 1659833 1659915 1660071) (-1013 "RADCAT.spad" 1659391 1659400 1659786 1659791) (-1012 "RADCAT.spad" 1658984 1658995 1659381 1659386) (-1011 "QUEUE.spad" 1658332 1658343 1658591 1658618) (-1010 "QUAT.spad" 1656790 1656801 1657133 1657198) (-1009 "QUATCT2.spad" 1656410 1656429 1656780 1656785) (-1008 "QUATCAT.spad" 1654580 1654591 1656340 1656405) (-1007 "QUATCAT.spad" 1652501 1652514 1654263 1654268) (-1006 "QUAGG.spad" 1651328 1651339 1652469 1652496) (-1005 "QQUTAST.spad" 1651096 1651105 1651318 1651323) (-1004 "QFORM.spad" 1650714 1650729 1651086 1651091) (-1003 "QFCAT.spad" 1649416 1649427 1650616 1650709) (-1002 "QFCAT.spad" 1647709 1647722 1648911 1648916) (-1001 "QFCAT2.spad" 1647401 1647418 1647699 1647704) (-1000 "QEQUAT.spad" 1646959 1646968 1647391 1647396) (-999 "QCMPACK.spad" 1641706 1641725 1646949 1646954) (-998 "QALGSET.spad" 1637785 1637817 1641620 1641625) (-997 "QALGSET2.spad" 1635781 1635799 1637775 1637780) (-996 "PWFFINTB.spad" 1633197 1633218 1635771 1635776) (-995 "PUSHVAR.spad" 1632536 1632555 1633187 1633192) (-994 "PTRANFN.spad" 1628664 1628674 1632526 1632531) (-993 "PTPACK.spad" 1625752 1625762 1628654 1628659) (-992 "PTFUNC2.spad" 1625575 1625589 1625742 1625747) (-991 "PTCAT.spad" 1624830 1624840 1625543 1625570) (-990 "PSQFR.spad" 1624137 1624161 1624820 1624825) (-989 "PSEUDLIN.spad" 1623023 1623033 1624127 1624132) (-988 "PSETPK.spad" 1608456 1608472 1622901 1622906) (-987 "PSETCAT.spad" 1602376 1602399 1608436 1608451) (-986 "PSETCAT.spad" 1596270 1596295 1602332 1602337) (-985 "PSCURVE.spad" 1595253 1595261 1596260 1596265) (-984 "PSCAT.spad" 1594036 1594065 1595151 1595248) (-983 "PSCAT.spad" 1592909 1592940 1594026 1594031) (-982 "PRTITION.spad" 1591607 1591615 1592899 1592904) (-981 "PRTDAST.spad" 1591326 1591334 1591597 1591602) (-980 "PRS.spad" 1580888 1580905 1591282 1591287) (-979 "PRQAGG.spad" 1580323 1580333 1580856 1580883) (-978 "PROPLOG.spad" 1579895 1579903 1580313 1580318) (-977 "PROPFUN2.spad" 1579518 1579531 1579885 1579890) (-976 "PROPFUN1.spad" 1578916 1578927 1579508 1579513) (-975 "PROPFRML.spad" 1577484 1577495 1578906 1578911) (-974 "PROPERTY.spad" 1576972 1576980 1577474 1577479) (-973 "PRODUCT.spad" 1574654 1574666 1574938 1574993) (-972 "PR.spad" 1573046 1573058 1573745 1573872) (-971 "PRINT.spad" 1572798 1572806 1573036 1573041) (-970 "PRIMES.spad" 1571051 1571061 1572788 1572793) (-969 "PRIMELT.spad" 1569132 1569146 1571041 1571046) (-968 "PRIMCAT.spad" 1568759 1568767 1569122 1569127) (-967 "PRIMARR.spad" 1567764 1567774 1567942 1567969) (-966 "PRIMARR2.spad" 1566531 1566543 1567754 1567759) (-965 "PREASSOC.spad" 1565913 1565925 1566521 1566526) (-964 "PPCURVE.spad" 1565050 1565058 1565903 1565908) (-963 "PORTNUM.spad" 1564825 1564833 1565040 1565045) (-962 "POLYROOT.spad" 1563674 1563696 1564781 1564786) (-961 "POLY.spad" 1561009 1561019 1561524 1561651) (-960 "POLYLIFT.spad" 1560274 1560297 1560999 1561004) (-959 "POLYCATQ.spad" 1558392 1558414 1560264 1560269) (-958 "POLYCAT.spad" 1551862 1551883 1558260 1558387) (-957 "POLYCAT.spad" 1544670 1544693 1551070 1551075) (-956 "POLY2UP.spad" 1544122 1544136 1544660 1544665) (-955 "POLY2.spad" 1543719 1543731 1544112 1544117) (-954 "POLUTIL.spad" 1542660 1542689 1543675 1543680) (-953 "POLTOPOL.spad" 1541408 1541423 1542650 1542655) (-952 "POINT.spad" 1540246 1540256 1540333 1540360) (-951 "PNTHEORY.spad" 1536948 1536956 1540236 1540241) (-950 "PMTOOLS.spad" 1535723 1535737 1536938 1536943) (-949 "PMSYM.spad" 1535272 1535282 1535713 1535718) (-948 "PMQFCAT.spad" 1534863 1534877 1535262 1535267) (-947 "PMPRED.spad" 1534342 1534356 1534853 1534858) (-946 "PMPREDFS.spad" 1533796 1533818 1534332 1534337) (-945 "PMPLCAT.spad" 1532876 1532894 1533728 1533733) (-944 "PMLSAGG.spad" 1532461 1532475 1532866 1532871) (-943 "PMKERNEL.spad" 1532040 1532052 1532451 1532456) (-942 "PMINS.spad" 1531620 1531630 1532030 1532035) (-941 "PMFS.spad" 1531197 1531215 1531610 1531615) (-940 "PMDOWN.spad" 1530487 1530501 1531187 1531192) (-939 "PMASS.spad" 1529497 1529505 1530477 1530482) (-938 "PMASSFS.spad" 1528464 1528480 1529487 1529492) (-937 "PLOTTOOL.spad" 1528244 1528252 1528454 1528459) (-936 "PLOT.spad" 1523167 1523175 1528234 1528239) (-935 "PLOT3D.spad" 1519631 1519639 1523157 1523162) (-934 "PLOT1.spad" 1518788 1518798 1519621 1519626) (-933 "PLEQN.spad" 1506078 1506105 1518778 1518783) (-932 "PINTERP.spad" 1505700 1505719 1506068 1506073) (-931 "PINTERPA.spad" 1505484 1505500 1505690 1505695) (-930 "PI.spad" 1505093 1505101 1505458 1505479) (-929 "PID.spad" 1504063 1504071 1505019 1505088) (-928 "PICOERCE.spad" 1503720 1503730 1504053 1504058) (-927 "PGROEB.spad" 1502321 1502335 1503710 1503715) (-926 "PGE.spad" 1493938 1493946 1502311 1502316) (-925 "PGCD.spad" 1492828 1492845 1493928 1493933) (-924 "PFRPAC.spad" 1491977 1491987 1492818 1492823) (-923 "PFR.spad" 1488640 1488650 1491879 1491972) (-922 "PFOTOOLS.spad" 1487898 1487914 1488630 1488635) (-921 "PFOQ.spad" 1487268 1487286 1487888 1487893) (-920 "PFO.spad" 1486687 1486714 1487258 1487263) (-919 "PF.spad" 1486261 1486273 1486492 1486585) (-918 "PFECAT.spad" 1483943 1483951 1486187 1486256) (-917 "PFECAT.spad" 1481653 1481663 1483899 1483904) (-916 "PFBRU.spad" 1479541 1479553 1481643 1481648) (-915 "PFBR.spad" 1477101 1477124 1479531 1479536) (-914 "PERM.spad" 1472908 1472918 1476931 1476946) (-913 "PERMGRP.spad" 1467678 1467688 1472898 1472903) (-912 "PERMCAT.spad" 1466339 1466349 1467658 1467673) (-911 "PERMAN.spad" 1464871 1464885 1466329 1466334) (-910 "PENDTREE.spad" 1464212 1464222 1464500 1464505) (-909 "PDRING.spad" 1462763 1462773 1464192 1464207) (-908 "PDRING.spad" 1461322 1461334 1462753 1462758) (-907 "PDEPROB.spad" 1460337 1460345 1461312 1461317) (-906 "PDEPACK.spad" 1454377 1454385 1460327 1460332) (-905 "PDECOMP.spad" 1453847 1453864 1454367 1454372) (-904 "PDECAT.spad" 1452203 1452211 1453837 1453842) (-903 "PCOMP.spad" 1452056 1452069 1452193 1452198) (-902 "PBWLB.spad" 1450644 1450661 1452046 1452051) (-901 "PATTERN.spad" 1445183 1445193 1450634 1450639) (-900 "PATTERN2.spad" 1444921 1444933 1445173 1445178) (-899 "PATTERN1.spad" 1443257 1443273 1444911 1444916) (-898 "PATRES.spad" 1440832 1440844 1443247 1443252) (-897 "PATRES2.spad" 1440504 1440518 1440822 1440827) (-896 "PATMATCH.spad" 1438701 1438732 1440212 1440217) (-895 "PATMAB.spad" 1438130 1438140 1438691 1438696) (-894 "PATLRES.spad" 1437216 1437230 1438120 1438125) (-893 "PATAB.spad" 1436980 1436990 1437206 1437211) (-892 "PARTPERM.spad" 1434988 1434996 1436970 1436975) (-891 "PARSURF.spad" 1434422 1434450 1434978 1434983) (-890 "PARSU2.spad" 1434219 1434235 1434412 1434417) (-889 "script-parser.spad" 1433739 1433747 1434209 1434214) (-888 "PARSCURV.spad" 1433173 1433201 1433729 1433734) (-887 "PARSC2.spad" 1432964 1432980 1433163 1433168) (-886 "PARPCURV.spad" 1432426 1432454 1432954 1432959) (-885 "PARPC2.spad" 1432217 1432233 1432416 1432421) (-884 "PARAMAST.spad" 1431345 1431353 1432207 1432212) (-883 "PAN2EXPR.spad" 1430757 1430765 1431335 1431340) (-882 "PALETTE.spad" 1429727 1429735 1430747 1430752) (-881 "PAIR.spad" 1428714 1428727 1429315 1429320) (-880 "PADICRC.spad" 1426048 1426066 1427219 1427312) (-879 "PADICRAT.spad" 1424063 1424075 1424284 1424377) (-878 "PADIC.spad" 1423758 1423770 1423989 1424058) (-877 "PADICCT.spad" 1422307 1422319 1423684 1423753) (-876 "PADEPAC.spad" 1420996 1421015 1422297 1422302) (-875 "PADE.spad" 1419748 1419764 1420986 1420991) (-874 "OWP.spad" 1418988 1419018 1419606 1419673) (-873 "OVERSET.spad" 1418561 1418569 1418978 1418983) (-872 "OVAR.spad" 1418342 1418365 1418551 1418556) (-871 "OUT.spad" 1417428 1417436 1418332 1418337) (-870 "OUTFORM.spad" 1406820 1406828 1417418 1417423) (-869 "OUTBFILE.spad" 1406238 1406246 1406810 1406815) (-868 "OUTBCON.spad" 1405244 1405252 1406228 1406233) (-867 "OUTBCON.spad" 1404248 1404258 1405234 1405239) (-866 "OSI.spad" 1403723 1403731 1404238 1404243) (-865 "OSGROUP.spad" 1403641 1403649 1403713 1403718) (-864 "ORTHPOL.spad" 1402126 1402136 1403558 1403563) (-863 "OREUP.spad" 1401579 1401607 1401806 1401845) (-862 "ORESUP.spad" 1400880 1400904 1401259 1401298) (-861 "OREPCTO.spad" 1398737 1398749 1400800 1400805) (-860 "OREPCAT.spad" 1392884 1392894 1398693 1398732) (-859 "OREPCAT.spad" 1386921 1386933 1392732 1392737) (-858 "ORDSET.spad" 1386093 1386101 1386911 1386916) (-857 "ORDSET.spad" 1385263 1385273 1386083 1386088) (-856 "ORDRING.spad" 1384653 1384661 1385243 1385258) (-855 "ORDRING.spad" 1384051 1384061 1384643 1384648) (-854 "ORDMON.spad" 1383906 1383914 1384041 1384046) (-853 "ORDFUNS.spad" 1383038 1383054 1383896 1383901) (-852 "ORDFIN.spad" 1382858 1382866 1383028 1383033) (-851 "ORDCOMP.spad" 1381323 1381333 1382405 1382434) (-850 "ORDCOMP2.spad" 1380616 1380628 1381313 1381318) (-849 "OPTPROB.spad" 1379254 1379262 1380606 1380611) (-848 "OPTPACK.spad" 1371663 1371671 1379244 1379249) (-847 "OPTCAT.spad" 1369342 1369350 1371653 1371658) (-846 "OPSIG.spad" 1368996 1369004 1369332 1369337) (-845 "OPQUERY.spad" 1368545 1368553 1368986 1368991) (-844 "OP.spad" 1368287 1368297 1368367 1368434) (-843 "OPERCAT.spad" 1367753 1367763 1368277 1368282) (-842 "OPERCAT.spad" 1367217 1367229 1367743 1367748) (-841 "ONECOMP.spad" 1365962 1365972 1366764 1366793) (-840 "ONECOMP2.spad" 1365386 1365398 1365952 1365957) (-839 "OMSERVER.spad" 1364392 1364400 1365376 1365381) (-838 "OMSAGG.spad" 1364180 1364190 1364348 1364387) (-837 "OMPKG.spad" 1362796 1362804 1364170 1364175) (-836 "OM.spad" 1361769 1361777 1362786 1362791) (-835 "OMLO.spad" 1361194 1361206 1361655 1361694) (-834 "OMEXPR.spad" 1361028 1361038 1361184 1361189) (-833 "OMERR.spad" 1360573 1360581 1361018 1361023) (-832 "OMERRK.spad" 1359607 1359615 1360563 1360568) (-831 "OMENC.spad" 1358951 1358959 1359597 1359602) (-830 "OMDEV.spad" 1353260 1353268 1358941 1358946) (-829 "OMCONN.spad" 1352669 1352677 1353250 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271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
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