diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 390 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 207 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1315 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 7786 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25542 |
5 files changed, 17619 insertions, 17621 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index a041b7cb..bc062c68 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2268134 . 3480761524) +(2268323 . 3480886511) (-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 @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1707) +(-32 R -1708) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) @@ -88,11 +88,11 @@ 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 -1707 UP UPUP -1552) +(-40 -1708 UP UPUP -1932) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) -(-41 R -1707) +(-41 R -1708) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -436) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4449 . T) (-4450 . T)) -((-2892 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|))))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|))))))) +((-2892 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1707) +(-54 |Base| R -1708) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -172,59 +172,59 @@ NIL ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-61 -3599) +(-61 -3600) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3599) +(-62 -3600) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -3599) +(-63 -3600) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3599) +(-64 -3600) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3599) +(-65 -3600) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3599) +(-66 -3600) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -3599) +(-67 -3600) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3599) +(-68 -3600) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3599) +(-69 -3600) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -3599) +(-70 -3600) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -3599) +(-71 -3600) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -3599) +(-72 -3600) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -3599) +(-73 -3600) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -3599) +(-74 -3600) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -3599) +(-77 -3600) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -3599) +(-78 -3600) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3599) +(-79 -3600) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3599) +(-80 -3600) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3599) +(-81 -3600) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -3599) +(-82 -3600) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3599) +(-83 -3600) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3599) +(-84 -3600) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3599) +(-85 -3600) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3599) +(-86 -3600) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3599) +(-87 -3600) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3599) +(-88 -3600) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -3599) +(-89 -3600) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1707 UP) +(-116 -1708 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4446 . T)) NIL -(-149 -1707 UP UPUP) +(-149 -1708 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -1707) +(-159 R -1708) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1707) +(-190 R -1708) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -697,7 +697,7 @@ NIL NIL NIL (-192) -((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|))) "\\spad{SFunction(li)} is the \\spad{S}-function of the partition \\spad{li} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) +((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{SFunction(li)} is the \\spad{S}-function of the partition \\spad{li} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) NIL NIL (-193) @@ -796,11 +796,11 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1707 UP UPUP R) +(-217 -1708 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -1707 FP) +(-218 -1708 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL @@ -812,7 +812,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1707) +(-221 R -1708) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -832,7 +832,7 @@ NIL ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4446 . T)) NIL -(-226 R -1707) +(-226 R -1708) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) 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(QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-255 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) @@ -1044,11 +1044,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-279 R -1707) +(-279 R -1708) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-280 R -1707) +(-280 R -1708) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1100,7 +1100,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-293 S R |Mod| -1332 -2800 |exactQuo|) +(-293 S R |Mod| -3449 -2024 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL @@ -1127,16 +1127,16 @@ NIL (-299 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-300) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-301 -1707 S) +(-301 -1708 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-302 E -1707) +(-302 E -1708) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1184,7 +1184,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-314 -1707) +(-314 -1708) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1210,9 +1210,9 @@ NIL NIL (-320 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4446 -2892 (-1807 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2892 (-1807 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) +((-4446 -2892 (-1809 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2892 (-1809 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) ((-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| 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(QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2892 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2892 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) -(-321 R -1707) +(-321 R -1708) ((|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 NIL @@ -1223,7 +1223,7 @@ NIL (-323 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-324 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1256,11 +1256,11 @@ NIL ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4450 . T) (-4449 . T)) ((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) -(-332 S -1707) +(-332 S -1708) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-373)))) -(-333 -1707) +(-333 -1708) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL @@ -1284,15 +1284,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-339 S -1707 UP UPUP R) +(-339 S -1708 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-340 -1707 UP UPUP R) +(-340 -1708 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-341 -1707 UP UPUP R) +(-341 -1708 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1312,11 +1312,11 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-346 S -1707 UP UPUP) +(-346 S -1708 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-368)))) -(-347 -1707 UP UPUP) +(-347 -1708 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL @@ -1348,7 +1348,7 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-355 R UP -1707) +(-355 R UP -1708) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1372,7 +1372,7 @@ NIL ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -1707 GF) +(-361 -1708 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1380,7 +1380,7 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-363 -1707 FP FPP) +(-363 -1708 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL @@ -1520,7 +1520,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-398 -1707 UP UPUP R) +(-398 -1708 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-404 -3599 |returnType| -3928 |symbols|) +(-404 -3600 |returnType| -3928 |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 -(-405 -1707 UP) +(-405 -1708 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -1707 UP A) +(-419 R -1708 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) ((-4446 . T)) NIL -(-420 R -1707 UP A |ibasis|) +(-420 R -1708 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1047) (|devaluate| |#2|)))) @@ -1656,7 +1656,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4449 . T) (-4439 . T) (-4450 . T)) NIL -(-432 R -1707) +(-432 R -1708) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4436 -12 (|has| |#1| (-6 -4436)) (|has| |#2| (-6 -4436))) (-4443 . T) (-4444 . T) (-4446 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4436)) (|HasAttribute| |#2| (QUOTE -4436)))) -(-434 R -1707) +(-434 R -1708) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1676,15 +1676,15 @@ NIL ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) ((-4446 -2892 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) NIL -(-437 R -1707) +(-437 R -1708) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-438 R -1707) +(-438 R -1708) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-439 R -1707) +(-439 R -1708) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1692,7 +1692,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-441 R -1707 UP) +(-441 R -1708 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-48))))) @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-449 R UP -1707) +(-449 R UP -1708) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-477 |lv| -1707 R) +(-477 |lv| -1708 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1851,11 +1851,11 @@ NIL (-480 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-481 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) (-482 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4450 . T) (-4449 . T)) @@ -1871,7 +1871,7 @@ NIL (-485 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-486) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1892,7 +1892,7 @@ NIL ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-491 -1707 UP UPUP R) +(-491 -1708 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1928,7 +1928,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-500 -1707 UP |AlExt| |AlPol|) +(-500 -1708 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1948,7 +1948,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-505 R UP -1707) +(-505 R UP -1708) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-510 -1707 |Expon| |VarSet| |DPoly|) +(-510 -1708 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-1186))))) @@ -2080,7 +2080,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-538 K -1707 |Par|) +(-538 K -1708 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2104,7 +2104,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-544 K -1707 |Par|) +(-544 K -1708 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2155,12 +2155,12 @@ NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -1707) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -1708) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-558 R0 -1707 UP UPUP R) +(-558 R0 -1708 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2180,7 +2180,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-563 R -1707) +(-563 R -1708) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2192,7 +2192,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-566 R -1707 L) +(-566 R -1708 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -662) (|devaluate| |#2|)))) @@ -2200,11 +2200,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-568 -1707 UP UPUP R) +(-568 -1708 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-569 -1707 UP) +(-569 -1708 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2216,15 +2216,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-572 R -1707 L) +(-572 R -1708 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -662) (|devaluate| |#2|)))) -(-573 R -1707) +(-573 R -1708) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1148)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-574 -1707 UP) +(-574 -1708 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2232,7 +2232,7 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-576 -1707) +(-576 -1708) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL @@ -2244,15 +2244,15 @@ NIL ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-579 R -1707) +(-579 R -1708) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-288))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-288)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-580 -1707 UP) +(-580 -1708 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-581 R -1707) +(-581 R -1708) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2284,11 +2284,11 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-589 R -1707) +(-589 R -1708) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-590 E -1707) +(-590 E -1708) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL @@ -2296,7 +2296,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-592 -1707) +(-592 -1708) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186))))) @@ -2313,7 +2313,7 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (-148)))) (-596) -((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young\\spad{'s} natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) +((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young\\spad{'s} natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) NIL NIL (-597 R E V P TS) @@ -2352,7 +2352,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-606 R -1707 FG) +(-606 R -1708 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2382,12 +2382,12 @@ NIL NIL (-613 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4446 -2892 (-1807 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) +((-4446 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) ((-2892 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-614 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-615 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2412,7 +2412,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -1707 UP) +(-621 -1708 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2440,7 +2440,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) -(-628 R -1707) +(-628 R -1708) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL @@ -2472,18 +2472,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-636 R -1707) +(-636 R -1708) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-637 |lv| -1707) +(-637 |lv| -1708) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-638) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109)))) (-639 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2494,7 +2494,7 @@ NIL NIL (-641 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4446 -2892 (-1807 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) +((-4446 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) ((-2892 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-642 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) @@ -2507,7 +2507,7 @@ NIL (-644 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1796 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-1795 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) (-645 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4446 . T)) @@ -2560,7 +2560,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-658 R -1707 L) +(-658 R -1708 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL @@ -2580,11 +2580,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category 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}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-663 -1707 UP) +(-663 -1708 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-664 A -2212) +(-664 A -2832) ((|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}}"))) ((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) @@ -2620,11 +2620,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4450 . T) (-4449 . T)) NIL -(-673 -1707) +(-673 -1708) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-674 -1707 |Row| |Col| M) +(-674 -1708 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2720,7 +2720,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-698 S -1707 FLAF FLAS) +(-698 S -1708 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-704 OV E -1707 PG) +(-704 OV E -1708 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL @@ -2796,7 +2796,7 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-717 R |Mod| -1332 -2800 |exactQuo|) +(-717 R |Mod| -3449 -2024 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL @@ -2812,7 +2812,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -1332 -2800 |exactQuo|) +(-721 R |Mod| -3449 -2024 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4446 . T)) NIL @@ -2824,7 +2824,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4444 . T) (-4443 . T)) NIL -(-724 -1707) +(-724 -1708) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) ((-4446 . T)) NIL @@ -2860,7 +2860,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-733 -1707 UP) +(-733 -1708 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -3012,11 +3012,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-771 -1707) +(-771 -1708) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-772 P -1707) +(-772 P -1708) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3024,7 +3024,7 @@ NIL NIL NIL NIL -(-774 UP -1707) +(-774 UP -1708) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3040,7 +3040,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4451 "*") . T)) NIL -(-778 R -1707) +(-778 R -1708) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3060,7 +3060,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-783 -1707 |ExtF| |SUEx| |ExtP| |n|) +(-783 -1708 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3075,7 +3075,7 @@ NIL (-786 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE 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(QUOTE (-1186)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (QUOTE (-551)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-787 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3156,11 +3156,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-807 R -1707 L) +(-807 R -1708 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-808 R -1707) +(-808 R -1708) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3168,7 +3168,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-810 R -1707) +(-810 R -1708) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3176,11 +3176,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-812 -1707 UP UPUP R) +(-812 -1708 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-813 -1707 UP L LQ) +(-813 -1708 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3188,27 +3188,27 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-815 -1707 UP L LQ) +(-815 -1708 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-816 -1707 UP) +(-816 -1708 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-817 -1707 L UP A LO) +(-817 -1708 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-818 -1707 UP) +(-818 -1708 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-819 -1707 LO) +(-819 -1708 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-820 -1707 LODO) +(-820 -1708 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL @@ -3489,7 +3489,7 @@ NIL NIL NIL (-890) -((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,l,n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) +((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|PositiveInteger|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{partitions(p,l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|PositiveInteger|))) (|NonNegativeInteger|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|PositiveInteger|))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{partitions(p,l,n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) NIL NIL (-891 R) @@ -3507,7 +3507,7 @@ NIL (-894 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-1796 (|HasCategory| |#2| (QUOTE (-1058)))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-1795 (|HasCategory| |#2| (QUOTE (-1058)))) (-1795 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1795 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-895 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3540,7 +3540,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-903 UP -1707) +(-903 UP -1708) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3600,7 +3600,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) -(-918 R0 -1707 UP UPUP R) +(-918 R0 -1708 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-925 -1707) +(-925 -1708) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3644,11 +3644,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4451 "*") . T)) NIL -(-929 -1707 P) +(-929 -1708 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -1707) +(-930 |xx| -1708) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL @@ -3672,7 +3672,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-936 R -1707) +(-936 R -1708) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3684,7 +3684,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-939 S R -1707) +(-939 S R -1708) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3704,7 +3704,7 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -893) (|devaluate| |#1|)))) -(-944 R -1707 -2942) +(-944 R -1708 -2942) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3756,7 +3756,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-957 E V R P -1707) +(-957 E V R P -1708) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -1707) +(-960 E V R P -1708) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-458)))) @@ -3796,7 +3796,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-967 -1707) +(-967 -1708) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3849,7 +3849,7 @@ NIL NIL NIL (-980) -((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|Integer|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) +((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL (-981 S |Coef| |Expon| |Var|) @@ -3904,7 +3904,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-994 K R UP -1707) +(-994 K R UP -1708) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -3976,7 +3976,7 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1012 -1707 UP UPUP |radicnd| |n|) +(-1012 -1708 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) @@ -4016,19 +4016,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) NIL -(-1022 R -1707) +(-1022 R -1708) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1023 R -1707) +(-1023 R -1708) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1024 -1707 UP) +(-1024 -1708 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1025 -1707 UP) +(-1025 -1708 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4064,7 +4064,7 @@ NIL ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) ((-2892 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) -(-1034 -1707 L) +(-1034 -1708 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4100,14 +4100,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1043 -1707 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -1708 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1044) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4164,7 +4164,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4446 . T)) NIL -(-1059 |xx| -1707) +(-1059 |xx| -1708) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4219,7 +4219,7 @@ NIL (-1072) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1073 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4268,11 +4268,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1085 |Base| R -1707) +(-1085 |Base| R -1708) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1086 |Base| R -1707) +(-1086 |Base| R -1708) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL @@ -4405,7 +4405,7 @@ NIL ((-4450 . T) (-4449 . T)) NIL (-1119) -((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) +((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL (-1120 S) @@ -4428,7 +4428,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1125 R -1707) +(-1125 R -1708) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4476,7 +4476,7 @@ NIL ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4450 . T) (-4449 . T)) NIL -(-1137 UP -1707) +(-1137 UP -1708) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4567,7 +4567,7 @@ NIL (-1159 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) (-1160) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4607,7 +4607,7 @@ NIL (-1169 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1170 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4638,9 +4638,9 @@ NIL NIL (-1177 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4727,7 +4727,7 @@ NIL (-1199 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1200 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -1707) +(-1216 R -1708) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4800,7 +4800,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1218 R -1707) +(-1218 R -1708) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -893) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -893) (|devaluate| |#1|))))) @@ -4828,7 +4828,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1225 -1707) +(-1225 -1708) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4891,11 +4891,11 @@ NIL (-1240 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . 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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 @@ -4975,11 +4975,11 @@ NIL (-1261 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-1262 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1263 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4451 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4442 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) @@ -4999,7 +4999,7 @@ NIL (-1267 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4201) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2898) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-1268 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) @@ -5007,12 +5007,12 @@ NIL (-1269 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1270 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1271 -1707 UP L UTS) +(-1271 -1708 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-562)))) @@ -5072,7 +5072,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1286 K R UP -1707) +(-1286 K R UP -1708) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5108,11 +5108,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-1295 S -1707) +(-1295 S -1708) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -1707) +(-1296 -1708) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL @@ -5168,4 +5168,4 @@ NIL NIL NIL NIL -((-3 NIL 2268114 2268119 2268124 2268129) (-2 NIL 2268094 2268099 2268104 2268109) (-1 NIL 2268074 2268079 2268084 2268089) (0 NIL 2268054 2268059 2268064 2268069) (-1305 "ZMOD.spad" 2267863 2267876 2267992 2268049) (-1304 "ZLINDEP.spad" 2266929 2266940 2267853 2267858) (-1303 "ZDSOLVE.spad" 2256874 2256896 2266919 2266924) (-1302 "YSTREAM.spad" 2256369 2256380 2256864 2256869) (-1301 "XRPOLY.spad" 2255589 2255609 2256225 2256294) (-1300 "XPR.spad" 2253384 2253397 2255307 2255406) (-1299 "XPOLY.spad" 2252939 2252950 2253240 2253309) (-1298 "XPOLYC.spad" 2252258 2252274 2252865 2252934) (-1297 "XPBWPOLY.spad" 2250695 2250715 2252038 2252107) (-1296 "XF.spad" 2249158 2249173 2250597 2250690) (-1295 "XF.spad" 2247601 2247618 2249042 2249047) (-1294 "XFALG.spad" 2244649 2244665 2247527 2247596) (-1293 "XEXPPKG.spad" 2243900 2243926 2244639 2244644) (-1292 "XDPOLY.spad" 2243514 2243530 2243756 2243825) (-1291 "XALG.spad" 2243174 2243185 2243470 2243509) (-1290 "WUTSET.spad" 2239013 2239030 2242820 2242847) (-1289 "WP.spad" 2238212 2238256 2238871 2238938) (-1288 "WHILEAST.spad" 2238010 2238019 2238202 2238207) (-1287 "WHEREAST.spad" 2237681 2237690 2238000 2238005) (-1286 "WFFINTBS.spad" 2235344 2235366 2237671 2237676) (-1285 "WEIER.spad" 2233566 2233577 2235334 2235339) (-1284 "VSPACE.spad" 2233239 2233250 2233534 2233561) (-1283 "VSPACE.spad" 2232932 2232945 2233229 2233234) (-1282 "VOID.spad" 2232609 2232618 2232922 2232927) (-1281 "VIEW.spad" 2230289 2230298 2232599 2232604) (-1280 "VIEWDEF.spad" 2225490 2225499 2230279 2230284) (-1279 "VIEW3D.spad" 2209451 2209460 2225480 2225485) (-1278 "VIEW2D.spad" 2197342 2197351 2209441 2209446) (-1277 "VECTOR.spad" 2196016 2196027 2196267 2196294) (-1276 "VECTOR2.spad" 2194655 2194668 2196006 2196011) (-1275 "VECTCAT.spad" 2192559 2192570 2194623 2194650) (-1274 "VECTCAT.spad" 2190270 2190283 2192336 2192341) (-1273 "VARIABLE.spad" 2190050 2190065 2190260 2190265) (-1272 "UTYPE.spad" 2189694 2189703 2190040 2190045) (-1271 "UTSODETL.spad" 2188989 2189013 2189650 2189655) (-1270 "UTSODE.spad" 2187205 2187225 2188979 2188984) (-1269 "UTS.spad" 2182009 2182037 2185672 2185769) (-1268 "UTSCAT.spad" 2179488 2179504 2181907 2182004) (-1267 "UTSCAT.spad" 2176611 2176629 2179032 2179037) (-1266 "UTS2.spad" 2176206 2176241 2176601 2176606) (-1265 "URAGG.spad" 2170879 2170890 2176196 2176201) (-1264 "URAGG.spad" 2165516 2165529 2170835 2170840) (-1263 "UPXSSING.spad" 2163161 2163187 2164597 2164730) (-1262 "UPXS.spad" 2160315 2160343 2161293 2161442) (-1261 "UPXSCONS.spad" 2158074 2158094 2158447 2158596) (-1260 "UPXSCCA.spad" 2156645 2156665 2157920 2158069) (-1259 "UPXSCCA.spad" 2155358 2155380 2156635 2156640) (-1258 "UPXSCAT.spad" 2153947 2153963 2155204 2155353) (-1257 "UPXS2.spad" 2153490 2153543 2153937 2153942) (-1256 "UPSQFREE.spad" 2151904 2151918 2153480 2153485) (-1255 "UPSCAT.spad" 2149515 2149539 2151802 2151899) (-1254 "UPSCAT.spad" 2146832 2146858 2149121 2149126) (-1253 "UPOLYC.spad" 2141872 2141883 2146674 2146827) (-1252 "UPOLYC.spad" 2136804 2136817 2141608 2141613) (-1251 "UPOLYC2.spad" 2136275 2136294 2136794 2136799) (-1250 "UP.spad" 2133474 2133489 2133861 2134014) (-1249 "UPMP.spad" 2132374 2132387 2133464 2133469) (-1248 "UPDIVP.spad" 2131939 2131953 2132364 2132369) (-1247 "UPDECOMP.spad" 2130184 2130198 2131929 2131934) (-1246 "UPCDEN.spad" 2129393 2129409 2130174 2130179) (-1245 "UP2.spad" 2128757 2128778 2129383 2129388) (-1244 "UNISEG.spad" 2128110 2128121 2128676 2128681) (-1243 "UNISEG2.spad" 2127607 2127620 2128066 2128071) (-1242 "UNIFACT.spad" 2126710 2126722 2127597 2127602) (-1241 "ULS.spad" 2117268 2117296 2118355 2118784) (-1240 "ULSCONS.spad" 2109664 2109684 2110034 2110183) (-1239 "ULSCCAT.spad" 2107401 2107421 2109510 2109659) (-1238 "ULSCCAT.spad" 2105246 2105268 2107357 2107362) (-1237 "ULSCAT.spad" 2103478 2103494 2105092 2105241) (-1236 "ULS2.spad" 2102992 2103045 2103468 2103473) (-1235 "UINT8.spad" 2102869 2102878 2102982 2102987) (-1234 "UINT64.spad" 2102745 2102754 2102859 2102864) (-1233 "UINT32.spad" 2102621 2102630 2102735 2102740) (-1232 "UINT16.spad" 2102497 2102506 2102611 2102616) (-1231 "UFD.spad" 2101562 2101571 2102423 2102492) (-1230 "UFD.spad" 2100689 2100700 2101552 2101557) (-1229 "UDVO.spad" 2099570 2099579 2100679 2100684) (-1228 "UDPO.spad" 2097063 2097074 2099526 2099531) (-1227 "TYPE.spad" 2096995 2097004 2097053 2097058) (-1226 "TYPEAST.spad" 2096914 2096923 2096985 2096990) (-1225 "TWOFACT.spad" 2095566 2095581 2096904 2096909) (-1224 "TUPLE.spad" 2095052 2095063 2095465 2095470) (-1223 "TUBETOOL.spad" 2091919 2091928 2095042 2095047) (-1222 "TUBE.spad" 2090566 2090583 2091909 2091914) (-1221 "TS.spad" 2089165 2089181 2090131 2090228) (-1220 "TSETCAT.spad" 2076292 2076309 2089133 2089160) (-1219 "TSETCAT.spad" 2063405 2063424 2076248 2076253) (-1218 "TRMANIP.spad" 2057771 2057788 2063111 2063116) (-1217 "TRIMAT.spad" 2056734 2056759 2057761 2057766) (-1216 "TRIGMNIP.spad" 2055261 2055278 2056724 2056729) (-1215 "TRIGCAT.spad" 2054773 2054782 2055251 2055256) (-1214 "TRIGCAT.spad" 2054283 2054294 2054763 2054768) (-1213 "TREE.spad" 2052858 2052869 2053890 2053917) (-1212 "TRANFUN.spad" 2052697 2052706 2052848 2052853) (-1211 "TRANFUN.spad" 2052534 2052545 2052687 2052692) (-1210 "TOPSP.spad" 2052208 2052217 2052524 2052529) (-1209 "TOOLSIGN.spad" 2051871 2051882 2052198 2052203) (-1208 "TEXTFILE.spad" 2050432 2050441 2051861 2051866) (-1207 "TEX.spad" 2047578 2047587 2050422 2050427) (-1206 "TEX1.spad" 2047134 2047145 2047568 2047573) (-1205 "TEMUTL.spad" 2046689 2046698 2047124 2047129) (-1204 "TBCMPPK.spad" 2044782 2044805 2046679 2046684) (-1203 "TBAGG.spad" 2043832 2043855 2044762 2044777) (-1202 "TBAGG.spad" 2042890 2042915 2043822 2043827) (-1201 "TANEXP.spad" 2042298 2042309 2042880 2042885) (-1200 "TALGOP.spad" 2042022 2042033 2042288 2042293) (-1199 "TABLE.spad" 2040433 2040456 2040703 2040730) (-1198 "TABLEAU.spad" 2039914 2039925 2040423 2040428) (-1197 "TABLBUMP.spad" 2036717 2036728 2039904 2039909) (-1196 "SYSTEM.spad" 2035945 2035954 2036707 2036712) (-1195 "SYSSOLP.spad" 2033428 2033439 2035935 2035940) (-1194 "SYSPTR.spad" 2033327 2033336 2033418 2033423) (-1193 "SYSNNI.spad" 2032509 2032520 2033317 2033322) (-1192 "SYSINT.spad" 2031913 2031924 2032499 2032504) (-1191 "SYNTAX.spad" 2028119 2028128 2031903 2031908) (-1190 "SYMTAB.spad" 2026187 2026196 2028109 2028114) (-1189 "SYMS.spad" 2022210 2022219 2026177 2026182) (-1188 "SYMPOLY.spad" 2021217 2021228 2021299 2021426) (-1187 "SYMFUNC.spad" 2020718 2020729 2021207 2021212) (-1186 "SYMBOL.spad" 2018221 2018230 2020708 2020713) (-1185 "SWITCH.spad" 2014992 2015001 2018211 2018216) (-1184 "SUTS.spad" 2011897 2011925 2013459 2013556) (-1183 "SUPXS.spad" 2009038 2009066 2010029 2010178) (-1182 "SUP.spad" 2005851 2005862 2006624 2006777) (-1181 "SUPFRACF.spad" 2004956 2004974 2005841 2005846) (-1180 "SUP2.spad" 2004348 2004361 2004946 2004951) (-1179 "SUMRF.spad" 2003322 2003333 2004338 2004343) (-1178 "SUMFS.spad" 2002959 2002976 2003312 2003317) (-1177 "SULS.spad" 1993504 1993532 1994604 1995033) (-1176 "SUCHTAST.spad" 1993273 1993282 1993494 1993499) (-1175 "SUCH.spad" 1992955 1992970 1993263 1993268) (-1174 "SUBSPACE.spad" 1985070 1985085 1992945 1992950) (-1173 "SUBRESP.spad" 1984240 1984254 1985026 1985031) (-1172 "STTF.spad" 1980339 1980355 1984230 1984235) (-1171 "STTFNC.spad" 1976807 1976823 1980329 1980334) (-1170 "STTAYLOR.spad" 1969442 1969453 1976688 1976693) (-1169 "STRTBL.spad" 1967947 1967964 1968096 1968123) (-1168 "STRING.spad" 1967356 1967365 1967370 1967397) (-1167 "STRICAT.spad" 1967144 1967153 1967324 1967351) (-1166 "STREAM.spad" 1964062 1964073 1966669 1966684) (-1165 "STREAM3.spad" 1963635 1963650 1964052 1964057) (-1164 "STREAM2.spad" 1962763 1962776 1963625 1963630) (-1163 "STREAM1.spad" 1962469 1962480 1962753 1962758) (-1162 "STINPROD.spad" 1961405 1961421 1962459 1962464) (-1161 "STEP.spad" 1960606 1960615 1961395 1961400) (-1160 "STEPAST.spad" 1959840 1959849 1960596 1960601) (-1159 "STBL.spad" 1958366 1958394 1958533 1958548) (-1158 "STAGG.spad" 1957441 1957452 1958356 1958361) (-1157 "STAGG.spad" 1956514 1956527 1957431 1957436) (-1156 "STACK.spad" 1955871 1955882 1956121 1956148) (-1155 "SREGSET.spad" 1953575 1953592 1955517 1955544) (-1154 "SRDCMPK.spad" 1952136 1952156 1953565 1953570) (-1153 "SRAGG.spad" 1947279 1947288 1952104 1952131) (-1152 "SRAGG.spad" 1942442 1942453 1947269 1947274) (-1151 "SQMATRIX.spad" 1940058 1940076 1940974 1941061) (-1150 "SPLTREE.spad" 1934610 1934623 1939494 1939521) (-1149 "SPLNODE.spad" 1931198 1931211 1934600 1934605) (-1148 "SPFCAT.spad" 1930007 1930016 1931188 1931193) (-1147 "SPECOUT.spad" 1928559 1928568 1929997 1930002) (-1146 "SPADXPT.spad" 1920154 1920163 1928549 1928554) (-1145 "spad-parser.spad" 1919619 1919628 1920144 1920149) (-1144 "SPADAST.spad" 1919320 1919329 1919609 1919614) (-1143 "SPACEC.spad" 1903519 1903530 1919310 1919315) (-1142 "SPACE3.spad" 1903295 1903306 1903509 1903514) (-1141 "SORTPAK.spad" 1902844 1902857 1903251 1903256) (-1140 "SOLVETRA.spad" 1900607 1900618 1902834 1902839) (-1139 "SOLVESER.spad" 1899135 1899146 1900597 1900602) (-1138 "SOLVERAD.spad" 1895161 1895172 1899125 1899130) (-1137 "SOLVEFOR.spad" 1893623 1893641 1895151 1895156) (-1136 "SNTSCAT.spad" 1893223 1893240 1893591 1893618) (-1135 "SMTS.spad" 1891495 1891521 1892788 1892885) (-1134 "SMP.spad" 1888970 1888990 1889360 1889487) (-1133 "SMITH.spad" 1887815 1887840 1888960 1888965) (-1132 "SMATCAT.spad" 1885925 1885955 1887759 1887810) (-1131 "SMATCAT.spad" 1883967 1883999 1885803 1885808) (-1130 "SKAGG.spad" 1882930 1882941 1883935 1883962) (-1129 "SINT.spad" 1881870 1881879 1882796 1882925) (-1128 "SIMPAN.spad" 1881598 1881607 1881860 1881865) (-1127 "SIG.spad" 1880928 1880937 1881588 1881593) (-1126 "SIGNRF.spad" 1880046 1880057 1880918 1880923) (-1125 "SIGNEF.spad" 1879325 1879342 1880036 1880041) (-1124 "SIGAST.spad" 1878710 1878719 1879315 1879320) (-1123 "SHP.spad" 1876638 1876653 1878666 1878671) (-1122 "SHDP.spad" 1866349 1866376 1866858 1866989) (-1121 "SGROUP.spad" 1865957 1865966 1866339 1866344) (-1120 "SGROUP.spad" 1865563 1865574 1865947 1865952) (-1119 "SGCF.spad" 1858726 1858735 1865553 1865558) (-1118 "SFRTCAT.spad" 1857656 1857673 1858694 1858721) (-1117 "SFRGCD.spad" 1856719 1856739 1857646 1857651) (-1116 "SFQCMPK.spad" 1851356 1851376 1856709 1856714) (-1115 "SFORT.spad" 1850795 1850809 1851346 1851351) (-1114 "SEXOF.spad" 1850638 1850678 1850785 1850790) (-1113 "SEX.spad" 1850530 1850539 1850628 1850633) (-1112 "SEXCAT.spad" 1848131 1848171 1850520 1850525) (-1111 "SET.spad" 1846455 1846466 1847552 1847591) (-1110 "SETMN.spad" 1844905 1844922 1846445 1846450) (-1109 "SETCAT.spad" 1844227 1844236 1844895 1844900) (-1108 "SETCAT.spad" 1843547 1843558 1844217 1844222) (-1107 "SETAGG.spad" 1840096 1840107 1843527 1843542) (-1106 "SETAGG.spad" 1836653 1836666 1840086 1840091) (-1105 "SEQAST.spad" 1836356 1836365 1836643 1836648) (-1104 "SEGXCAT.spad" 1835512 1835525 1836346 1836351) (-1103 "SEG.spad" 1835325 1835336 1835431 1835436) (-1102 "SEGCAT.spad" 1834250 1834261 1835315 1835320) (-1101 "SEGBIND.spad" 1834008 1834019 1834197 1834202) (-1100 "SEGBIND2.spad" 1833706 1833719 1833998 1834003) (-1099 "SEGAST.spad" 1833420 1833429 1833696 1833701) (-1098 "SEG2.spad" 1832855 1832868 1833376 1833381) (-1097 "SDVAR.spad" 1832131 1832142 1832845 1832850) (-1096 "SDPOL.spad" 1829557 1829568 1829848 1829975) (-1095 "SCPKG.spad" 1827646 1827657 1829547 1829552) (-1094 "SCOPE.spad" 1826799 1826808 1827636 1827641) (-1093 "SCACHE.spad" 1825495 1825506 1826789 1826794) (-1092 "SASTCAT.spad" 1825404 1825413 1825485 1825490) (-1091 "SAOS.spad" 1825276 1825285 1825394 1825399) (-1090 "SAERFFC.spad" 1824989 1825009 1825266 1825271) (-1089 "SAE.spad" 1823164 1823180 1823775 1823910) (-1088 "SAEFACT.spad" 1822865 1822885 1823154 1823159) (-1087 "RURPK.spad" 1820524 1820540 1822855 1822860) (-1086 "RULESET.spad" 1819977 1820001 1820514 1820519) (-1085 "RULE.spad" 1818217 1818241 1819967 1819972) (-1084 "RULECOLD.spad" 1818069 1818082 1818207 1818212) (-1083 "RTVALUE.spad" 1817804 1817813 1818059 1818064) (-1082 "RSTRCAST.spad" 1817521 1817530 1817794 1817799) (-1081 "RSETGCD.spad" 1813899 1813919 1817511 1817516) (-1080 "RSETCAT.spad" 1803835 1803852 1813867 1813894) (-1079 "RSETCAT.spad" 1793791 1793810 1803825 1803830) (-1078 "RSDCMPK.spad" 1792243 1792263 1793781 1793786) (-1077 "RRCC.spad" 1790627 1790657 1792233 1792238) (-1076 "RRCC.spad" 1789009 1789041 1790617 1790622) (-1075 "RPTAST.spad" 1788711 1788720 1788999 1789004) (-1074 "RPOLCAT.spad" 1768071 1768086 1788579 1788706) (-1073 "RPOLCAT.spad" 1747144 1747161 1767654 1767659) (-1072 "ROUTINE.spad" 1743027 1743036 1745791 1745818) (-1071 "ROMAN.spad" 1742355 1742364 1742893 1743022) (-1070 "ROIRC.spad" 1741435 1741467 1742345 1742350) (-1069 "RNS.spad" 1740338 1740347 1741337 1741430) (-1068 "RNS.spad" 1739327 1739338 1740328 1740333) (-1067 "RNG.spad" 1739062 1739071 1739317 1739322) (-1066 "RNGBIND.spad" 1738222 1738236 1739017 1739022) (-1065 "RMODULE.spad" 1737987 1737998 1738212 1738217) (-1064 "RMCAT2.spad" 1737407 1737464 1737977 1737982) (-1063 "RMATRIX.spad" 1736231 1736250 1736574 1736613) (-1062 "RMATCAT.spad" 1731810 1731841 1736187 1736226) (-1061 "RMATCAT.spad" 1727279 1727312 1731658 1731663) (-1060 "RLINSET.spad" 1726673 1726684 1727269 1727274) (-1059 "RINTERP.spad" 1726561 1726581 1726663 1726668) (-1058 "RING.spad" 1726031 1726040 1726541 1726556) (-1057 "RING.spad" 1725509 1725520 1726021 1726026) (-1056 "RIDIST.spad" 1724901 1724910 1725499 1725504) (-1055 "RGCHAIN.spad" 1723484 1723500 1724386 1724413) (-1054 "RGBCSPC.spad" 1723265 1723277 1723474 1723479) (-1053 "RGBCMDL.spad" 1722795 1722807 1723255 1723260) (-1052 "RF.spad" 1720437 1720448 1722785 1722790) (-1051 "RFFACTOR.spad" 1719899 1719910 1720427 1720432) (-1050 "RFFACT.spad" 1719634 1719646 1719889 1719894) (-1049 "RFDIST.spad" 1718630 1718639 1719624 1719629) (-1048 "RETSOL.spad" 1718049 1718062 1718620 1718625) (-1047 "RETRACT.spad" 1717477 1717488 1718039 1718044) (-1046 "RETRACT.spad" 1716903 1716916 1717467 1717472) (-1045 "RETAST.spad" 1716715 1716724 1716893 1716898) (-1044 "RESULT.spad" 1714775 1714784 1715362 1715389) (-1043 "RESRING.spad" 1714122 1714169 1714713 1714770) (-1042 "RESLATC.spad" 1713446 1713457 1714112 1714117) (-1041 "REPSQ.spad" 1713177 1713188 1713436 1713441) (-1040 "REP.spad" 1710731 1710740 1713167 1713172) (-1039 "REPDB.spad" 1710438 1710449 1710721 1710726) (-1038 "REP2.spad" 1700096 1700107 1710280 1710285) (-1037 "REP1.spad" 1694292 1694303 1700046 1700051) (-1036 "REGSET.spad" 1692089 1692106 1693938 1693965) (-1035 "REF.spad" 1691424 1691435 1692044 1692049) (-1034 "REDORDER.spad" 1690630 1690647 1691414 1691419) (-1033 "RECLOS.spad" 1689413 1689433 1690117 1690210) (-1032 "REALSOLV.spad" 1688553 1688562 1689403 1689408) (-1031 "REAL.spad" 1688425 1688434 1688543 1688548) (-1030 "REAL0Q.spad" 1685723 1685738 1688415 1688420) (-1029 "REAL0.spad" 1682567 1682582 1685713 1685718) (-1028 "RDUCEAST.spad" 1682288 1682297 1682557 1682562) (-1027 "RDIV.spad" 1681943 1681968 1682278 1682283) (-1026 "RDIST.spad" 1681510 1681521 1681933 1681938) (-1025 "RDETRS.spad" 1680374 1680392 1681500 1681505) (-1024 "RDETR.spad" 1678513 1678531 1680364 1680369) (-1023 "RDEEFS.spad" 1677612 1677629 1678503 1678508) (-1022 "RDEEF.spad" 1676622 1676639 1677602 1677607) (-1021 "RCFIELD.spad" 1673808 1673817 1676524 1676617) (-1020 "RCFIELD.spad" 1671080 1671091 1673798 1673803) (-1019 "RCAGG.spad" 1669008 1669019 1671070 1671075) (-1018 "RCAGG.spad" 1666863 1666876 1668927 1668932) (-1017 "RATRET.spad" 1666223 1666234 1666853 1666858) (-1016 "RATFACT.spad" 1665915 1665927 1666213 1666218) (-1015 "RANDSRC.spad" 1665234 1665243 1665905 1665910) (-1014 "RADUTIL.spad" 1664990 1664999 1665224 1665229) (-1013 "RADIX.spad" 1661911 1661925 1663457 1663550) (-1012 "RADFF.spad" 1660324 1660361 1660443 1660599) (-1011 "RADCAT.spad" 1659919 1659928 1660314 1660319) (-1010 "RADCAT.spad" 1659512 1659523 1659909 1659914) (-1009 "QUEUE.spad" 1658860 1658871 1659119 1659146) (-1008 "QUAT.spad" 1657441 1657452 1657784 1657849) (-1007 "QUATCT2.spad" 1657061 1657080 1657431 1657436) (-1006 "QUATCAT.spad" 1655231 1655242 1656991 1657056) (-1005 "QUATCAT.spad" 1653152 1653165 1654914 1654919) (-1004 "QUAGG.spad" 1651979 1651990 1653120 1653147) (-1003 "QQUTAST.spad" 1651747 1651756 1651969 1651974) (-1002 "QFORM.spad" 1651211 1651226 1651737 1651742) (-1001 "QFCAT.spad" 1649913 1649924 1651113 1651206) (-1000 "QFCAT.spad" 1648206 1648219 1649408 1649413) (-999 "QFCAT2.spad" 1647899 1647915 1648196 1648201) (-998 "QEQUAT.spad" 1647458 1647466 1647889 1647894) (-997 "QCMPACK.spad" 1642205 1642224 1647448 1647453) (-996 "QALGSET.spad" 1638284 1638316 1642119 1642124) (-995 "QALGSET2.spad" 1636280 1636298 1638274 1638279) (-994 "PWFFINTB.spad" 1633696 1633717 1636270 1636275) (-993 "PUSHVAR.spad" 1633035 1633054 1633686 1633691) (-992 "PTRANFN.spad" 1629163 1629173 1633025 1633030) (-991 "PTPACK.spad" 1626251 1626261 1629153 1629158) (-990 "PTFUNC2.spad" 1626074 1626088 1626241 1626246) (-989 "PTCAT.spad" 1625329 1625339 1626042 1626069) (-988 "PSQFR.spad" 1624636 1624660 1625319 1625324) (-987 "PSEUDLIN.spad" 1623522 1623532 1624626 1624631) (-986 "PSETPK.spad" 1608955 1608971 1623400 1623405) (-985 "PSETCAT.spad" 1602875 1602898 1608935 1608950) (-984 "PSETCAT.spad" 1596769 1596794 1602831 1602836) (-983 "PSCURVE.spad" 1595752 1595760 1596759 1596764) (-982 "PSCAT.spad" 1594535 1594564 1595650 1595747) (-981 "PSCAT.spad" 1593408 1593439 1594525 1594530) (-980 "PRTITION.spad" 1592517 1592525 1593398 1593403) (-979 "PRTDAST.spad" 1592236 1592244 1592507 1592512) (-978 "PRS.spad" 1581798 1581815 1592192 1592197) (-977 "PRQAGG.spad" 1581233 1581243 1581766 1581793) (-976 "PROPLOG.spad" 1580805 1580813 1581223 1581228) (-975 "PROPFUN2.spad" 1580428 1580441 1580795 1580800) (-974 "PROPFUN1.spad" 1579826 1579837 1580418 1580423) (-973 "PROPFRML.spad" 1578394 1578405 1579816 1579821) (-972 "PROPERTY.spad" 1577882 1577890 1578384 1578389) (-971 "PRODUCT.spad" 1575564 1575576 1575848 1575903) (-970 "PR.spad" 1573956 1573968 1574655 1574782) (-969 "PRINT.spad" 1573708 1573716 1573946 1573951) (-968 "PRIMES.spad" 1571961 1571971 1573698 1573703) (-967 "PRIMELT.spad" 1570042 1570056 1571951 1571956) (-966 "PRIMCAT.spad" 1569669 1569677 1570032 1570037) (-965 "PRIMARR.spad" 1568674 1568684 1568852 1568879) (-964 "PRIMARR2.spad" 1567441 1567453 1568664 1568669) (-963 "PREASSOC.spad" 1566823 1566835 1567431 1567436) (-962 "PPCURVE.spad" 1565960 1565968 1566813 1566818) (-961 "PORTNUM.spad" 1565735 1565743 1565950 1565955) (-960 "POLYROOT.spad" 1564584 1564606 1565691 1565696) (-959 "POLY.spad" 1561919 1561929 1562434 1562561) (-958 "POLYLIFT.spad" 1561184 1561207 1561909 1561914) (-957 "POLYCATQ.spad" 1559302 1559324 1561174 1561179) (-956 "POLYCAT.spad" 1552772 1552793 1559170 1559297) (-955 "POLYCAT.spad" 1545580 1545603 1551980 1551985) (-954 "POLY2UP.spad" 1545032 1545046 1545570 1545575) (-953 "POLY2.spad" 1544629 1544641 1545022 1545027) (-952 "POLUTIL.spad" 1543570 1543599 1544585 1544590) (-951 "POLTOPOL.spad" 1542318 1542333 1543560 1543565) (-950 "POINT.spad" 1541156 1541166 1541243 1541270) (-949 "PNTHEORY.spad" 1537858 1537866 1541146 1541151) (-948 "PMTOOLS.spad" 1536633 1536647 1537848 1537853) (-947 "PMSYM.spad" 1536182 1536192 1536623 1536628) (-946 "PMQFCAT.spad" 1535773 1535787 1536172 1536177) (-945 "PMPRED.spad" 1535252 1535266 1535763 1535768) (-944 "PMPREDFS.spad" 1534706 1534728 1535242 1535247) (-943 "PMPLCAT.spad" 1533786 1533804 1534638 1534643) (-942 "PMLSAGG.spad" 1533371 1533385 1533776 1533781) (-941 "PMKERNEL.spad" 1532950 1532962 1533361 1533366) (-940 "PMINS.spad" 1532530 1532540 1532940 1532945) (-939 "PMFS.spad" 1532107 1532125 1532520 1532525) (-938 "PMDOWN.spad" 1531397 1531411 1532097 1532102) (-937 "PMASS.spad" 1530407 1530415 1531387 1531392) (-936 "PMASSFS.spad" 1529374 1529390 1530397 1530402) (-935 "PLOTTOOL.spad" 1529154 1529162 1529364 1529369) (-934 "PLOT.spad" 1524077 1524085 1529144 1529149) (-933 "PLOT3D.spad" 1520541 1520549 1524067 1524072) (-932 "PLOT1.spad" 1519698 1519708 1520531 1520536) (-931 "PLEQN.spad" 1506988 1507015 1519688 1519693) (-930 "PINTERP.spad" 1506610 1506629 1506978 1506983) (-929 "PINTERPA.spad" 1506394 1506410 1506600 1506605) (-928 "PI.spad" 1506003 1506011 1506368 1506389) (-927 "PID.spad" 1504973 1504981 1505929 1505998) (-926 "PICOERCE.spad" 1504630 1504640 1504963 1504968) (-925 "PGROEB.spad" 1503231 1503245 1504620 1504625) (-924 "PGE.spad" 1494848 1494856 1503221 1503226) (-923 "PGCD.spad" 1493738 1493755 1494838 1494843) (-922 "PFRPAC.spad" 1492887 1492897 1493728 1493733) (-921 "PFR.spad" 1489550 1489560 1492789 1492882) (-920 "PFOTOOLS.spad" 1488808 1488824 1489540 1489545) (-919 "PFOQ.spad" 1488178 1488196 1488798 1488803) (-918 "PFO.spad" 1487597 1487624 1488168 1488173) (-917 "PF.spad" 1487171 1487183 1487402 1487495) (-916 "PFECAT.spad" 1484853 1484861 1487097 1487166) (-915 "PFECAT.spad" 1482563 1482573 1484809 1484814) (-914 "PFBRU.spad" 1480451 1480463 1482553 1482558) (-913 "PFBR.spad" 1478011 1478034 1480441 1480446) (-912 "PERM.spad" 1473696 1473706 1477841 1477856) (-911 "PERMGRP.spad" 1468458 1468468 1473686 1473691) (-910 "PERMCAT.spad" 1467016 1467026 1468438 1468453) (-909 "PERMAN.spad" 1465548 1465562 1467006 1467011) (-908 "PENDTREE.spad" 1464889 1464899 1465177 1465182) (-907 "PDRING.spad" 1463440 1463450 1464869 1464884) (-906 "PDRING.spad" 1461999 1462011 1463430 1463435) (-905 "PDEPROB.spad" 1461014 1461022 1461989 1461994) (-904 "PDEPACK.spad" 1455054 1455062 1461004 1461009) (-903 "PDECOMP.spad" 1454524 1454541 1455044 1455049) (-902 "PDECAT.spad" 1452880 1452888 1454514 1454519) (-901 "PCOMP.spad" 1452733 1452746 1452870 1452875) (-900 "PBWLB.spad" 1451321 1451338 1452723 1452728) (-899 "PATTERN.spad" 1445860 1445870 1451311 1451316) (-898 "PATTERN2.spad" 1445598 1445610 1445850 1445855) (-897 "PATTERN1.spad" 1443934 1443950 1445588 1445593) (-896 "PATRES.spad" 1441509 1441521 1443924 1443929) (-895 "PATRES2.spad" 1441181 1441195 1441499 1441504) (-894 "PATMATCH.spad" 1439378 1439409 1440889 1440894) (-893 "PATMAB.spad" 1438807 1438817 1439368 1439373) (-892 "PATLRES.spad" 1437893 1437907 1438797 1438802) (-891 "PATAB.spad" 1437657 1437667 1437883 1437888) (-890 "PARTPERM.spad" 1435057 1435065 1437647 1437652) (-889 "PARSURF.spad" 1434491 1434519 1435047 1435052) (-888 "PARSU2.spad" 1434288 1434304 1434481 1434486) (-887 "script-parser.spad" 1433808 1433816 1434278 1434283) (-886 "PARSCURV.spad" 1433242 1433270 1433798 1433803) (-885 "PARSC2.spad" 1433033 1433049 1433232 1433237) (-884 "PARPCURV.spad" 1432495 1432523 1433023 1433028) (-883 "PARPC2.spad" 1432286 1432302 1432485 1432490) (-882 "PARAMAST.spad" 1431414 1431422 1432276 1432281) (-881 "PAN2EXPR.spad" 1430826 1430834 1431404 1431409) (-880 "PALETTE.spad" 1429796 1429804 1430816 1430821) (-879 "PAIR.spad" 1428783 1428796 1429384 1429389) (-878 "PADICRC.spad" 1426117 1426135 1427288 1427381) (-877 "PADICRAT.spad" 1424132 1424144 1424353 1424446) (-876 "PADIC.spad" 1423827 1423839 1424058 1424127) (-875 "PADICCT.spad" 1422376 1422388 1423753 1423822) (-874 "PADEPAC.spad" 1421065 1421084 1422366 1422371) (-873 "PADE.spad" 1419817 1419833 1421055 1421060) (-872 "OWP.spad" 1419057 1419087 1419675 1419742) (-871 "OVERSET.spad" 1418630 1418638 1419047 1419052) (-870 "OVAR.spad" 1418411 1418434 1418620 1418625) (-869 "OUT.spad" 1417497 1417505 1418401 1418406) (-868 "OUTFORM.spad" 1406889 1406897 1417487 1417492) (-867 "OUTBFILE.spad" 1406307 1406315 1406879 1406884) (-866 "OUTBCON.spad" 1405313 1405321 1406297 1406302) (-865 "OUTBCON.spad" 1404317 1404327 1405303 1405308) (-864 "OSI.spad" 1403792 1403800 1404307 1404312) (-863 "OSGROUP.spad" 1403710 1403718 1403782 1403787) (-862 "ORTHPOL.spad" 1402195 1402205 1403627 1403632) (-861 "OREUP.spad" 1401648 1401676 1401875 1401914) (-860 "ORESUP.spad" 1400949 1400973 1401328 1401367) (-859 "OREPCTO.spad" 1398806 1398818 1400869 1400874) (-858 "OREPCAT.spad" 1392953 1392963 1398762 1398801) (-857 "OREPCAT.spad" 1386990 1387002 1392801 1392806) (-856 "ORDSET.spad" 1386162 1386170 1386980 1386985) (-855 "ORDSET.spad" 1385332 1385342 1386152 1386157) (-854 "ORDRING.spad" 1384722 1384730 1385312 1385327) (-853 "ORDRING.spad" 1384120 1384130 1384712 1384717) (-852 "ORDMON.spad" 1383975 1383983 1384110 1384115) (-851 "ORDFUNS.spad" 1383107 1383123 1383965 1383970) (-850 "ORDFIN.spad" 1382927 1382935 1383097 1383102) (-849 "ORDCOMP.spad" 1381392 1381402 1382474 1382503) (-848 "ORDCOMP2.spad" 1380685 1380697 1381382 1381387) (-847 "OPTPROB.spad" 1379323 1379331 1380675 1380680) (-846 "OPTPACK.spad" 1371732 1371740 1379313 1379318) (-845 "OPTCAT.spad" 1369411 1369419 1371722 1371727) (-844 "OPSIG.spad" 1369065 1369073 1369401 1369406) (-843 "OPQUERY.spad" 1368614 1368622 1369055 1369060) (-842 "OP.spad" 1368356 1368366 1368436 1368503) (-841 "OPERCAT.spad" 1367822 1367832 1368346 1368351) (-840 "OPERCAT.spad" 1367286 1367298 1367812 1367817) (-839 "ONECOMP.spad" 1366031 1366041 1366833 1366862) (-838 "ONECOMP2.spad" 1365455 1365467 1366021 1366026) (-837 "OMSERVER.spad" 1364461 1364469 1365445 1365450) (-836 "OMSAGG.spad" 1364249 1364259 1364417 1364456) (-835 "OMPKG.spad" 1362865 1362873 1364239 1364244) (-834 "OM.spad" 1361838 1361846 1362855 1362860) (-833 "OMLO.spad" 1361263 1361275 1361724 1361763) (-832 "OMEXPR.spad" 1361097 1361107 1361253 1361258) (-831 "OMERR.spad" 1360642 1360650 1361087 1361092) (-830 "OMERRK.spad" 1359676 1359684 1360632 1360637) (-829 "OMENC.spad" 1359020 1359028 1359666 1359671) (-828 "OMDEV.spad" 1353329 1353337 1359010 1359015) (-827 "OMCONN.spad" 1352738 1352746 1353319 1353324) (-826 "OINTDOM.spad" 1352501 1352509 1352664 1352733) (-825 "OFMONOID.spad" 1350624 1350634 1352457 1352462) (-824 "ODVAR.spad" 1349885 1349895 1350614 1350619) (-823 "ODR.spad" 1349529 1349555 1349697 1349846) (-822 "ODPOL.spad" 1346911 1346921 1347251 1347378) (-821 "ODP.spad" 1336758 1336778 1337131 1337262) (-820 "ODETOOLS.spad" 1335407 1335426 1336748 1336753) (-819 "ODESYS.spad" 1333101 1333118 1335397 1335402) (-818 "ODERTRIC.spad" 1329110 1329127 1333058 1333063) (-817 "ODERED.spad" 1328509 1328533 1329100 1329105) (-816 "ODERAT.spad" 1326124 1326141 1328499 1328504) (-815 "ODEPRRIC.spad" 1323161 1323183 1326114 1326119) (-814 "ODEPROB.spad" 1322418 1322426 1323151 1323156) (-813 "ODEPRIM.spad" 1319752 1319774 1322408 1322413) (-812 "ODEPAL.spad" 1319138 1319162 1319742 1319747) (-811 "ODEPACK.spad" 1305804 1305812 1319128 1319133) (-810 "ODEINT.spad" 1305239 1305255 1305794 1305799) (-809 "ODEIFTBL.spad" 1302634 1302642 1305229 1305234) (-808 "ODEEF.spad" 1298125 1298141 1302624 1302629) (-807 "ODECONST.spad" 1297662 1297680 1298115 1298120) (-806 "ODECAT.spad" 1296260 1296268 1297652 1297657) (-805 "OCT.spad" 1294396 1294406 1295110 1295149) (-804 "OCTCT2.spad" 1294042 1294063 1294386 1294391) (-803 "OC.spad" 1291838 1291848 1293998 1294037) (-802 "OC.spad" 1289359 1289371 1291521 1291526) (-801 "OCAMON.spad" 1289207 1289215 1289349 1289354) (-800 "OASGP.spad" 1289022 1289030 1289197 1289202) (-799 "OAMONS.spad" 1288544 1288552 1289012 1289017) (-798 "OAMON.spad" 1288405 1288413 1288534 1288539) (-797 "OAGROUP.spad" 1288267 1288275 1288395 1288400) (-796 "NUMTUBE.spad" 1287858 1287874 1288257 1288262) (-795 "NUMQUAD.spad" 1275834 1275842 1287848 1287853) (-794 "NUMODE.spad" 1267188 1267196 1275824 1275829) (-793 "NUMINT.spad" 1264754 1264762 1267178 1267183) (-792 "NUMFMT.spad" 1263594 1263602 1264744 1264749) (-791 "NUMERIC.spad" 1255708 1255718 1263399 1263404) (-790 "NTSCAT.spad" 1254216 1254232 1255676 1255703) (-789 "NTPOLFN.spad" 1253767 1253777 1254133 1254138) (-788 "NSUP.spad" 1246813 1246823 1251353 1251506) (-787 "NSUP2.spad" 1246205 1246217 1246803 1246808) (-786 "NSMP.spad" 1242435 1242454 1242743 1242870) (-785 "NREP.spad" 1240813 1240827 1242425 1242430) (-784 "NPCOEF.spad" 1240059 1240079 1240803 1240808) (-783 "NORMRETR.spad" 1239657 1239696 1240049 1240054) (-782 "NORMPK.spad" 1237559 1237578 1239647 1239652) (-781 "NORMMA.spad" 1237247 1237273 1237549 1237554) (-780 "NONE.spad" 1236988 1236996 1237237 1237242) (-779 "NONE1.spad" 1236664 1236674 1236978 1236983) (-778 "NODE1.spad" 1236151 1236167 1236654 1236659) (-777 "NNI.spad" 1235046 1235054 1236125 1236146) (-776 "NLINSOL.spad" 1233672 1233682 1235036 1235041) (-775 "NIPROB.spad" 1232213 1232221 1233662 1233667) (-774 "NFINTBAS.spad" 1229773 1229790 1232203 1232208) (-773 "NETCLT.spad" 1229747 1229758 1229763 1229768) (-772 "NCODIV.spad" 1227963 1227979 1229737 1229742) (-771 "NCNTFRAC.spad" 1227605 1227619 1227953 1227958) (-770 "NCEP.spad" 1225771 1225785 1227595 1227600) (-769 "NASRING.spad" 1225367 1225375 1225761 1225766) (-768 "NASRING.spad" 1224961 1224971 1225357 1225362) (-767 "NARNG.spad" 1224313 1224321 1224951 1224956) (-766 "NARNG.spad" 1223663 1223673 1224303 1224308) (-765 "NAGSP.spad" 1222740 1222748 1223653 1223658) (-764 "NAGS.spad" 1212401 1212409 1222730 1222735) (-763 "NAGF07.spad" 1210832 1210840 1212391 1212396) (-762 "NAGF04.spad" 1205234 1205242 1210822 1210827) (-761 "NAGF02.spad" 1199303 1199311 1205224 1205229) (-760 "NAGF01.spad" 1195064 1195072 1199293 1199298) (-759 "NAGE04.spad" 1188764 1188772 1195054 1195059) (-758 "NAGE02.spad" 1179424 1179432 1188754 1188759) (-757 "NAGE01.spad" 1175426 1175434 1179414 1179419) (-756 "NAGD03.spad" 1173430 1173438 1175416 1175421) (-755 "NAGD02.spad" 1166177 1166185 1173420 1173425) (-754 "NAGD01.spad" 1160470 1160478 1166167 1166172) (-753 "NAGC06.spad" 1156345 1156353 1160460 1160465) (-752 "NAGC05.spad" 1154846 1154854 1156335 1156340) (-751 "NAGC02.spad" 1154113 1154121 1154836 1154841) (-750 "NAALG.spad" 1153654 1153664 1154081 1154108) (-749 "NAALG.spad" 1153215 1153227 1153644 1153649) (-748 "MULTSQFR.spad" 1150173 1150190 1153205 1153210) (-747 "MULTFACT.spad" 1149556 1149573 1150163 1150168) (-746 "MTSCAT.spad" 1147650 1147671 1149454 1149551) (-745 "MTHING.spad" 1147309 1147319 1147640 1147645) (-744 "MSYSCMD.spad" 1146743 1146751 1147299 1147304) (-743 "MSET.spad" 1144701 1144711 1146449 1146488) (-742 "MSETAGG.spad" 1144546 1144556 1144669 1144696) (-741 "MRING.spad" 1141523 1141535 1144254 1144321) (-740 "MRF2.spad" 1141093 1141107 1141513 1141518) (-739 "MRATFAC.spad" 1140639 1140656 1141083 1141088) (-738 "MPRFF.spad" 1138679 1138698 1140629 1140634) (-737 "MPOLY.spad" 1136150 1136165 1136509 1136636) (-736 "MPCPF.spad" 1135414 1135433 1136140 1136145) (-735 "MPC3.spad" 1135231 1135271 1135404 1135409) (-734 "MPC2.spad" 1134877 1134910 1135221 1135226) (-733 "MONOTOOL.spad" 1133228 1133245 1134867 1134872) (-732 "MONOID.spad" 1132547 1132555 1133218 1133223) (-731 "MONOID.spad" 1131864 1131874 1132537 1132542) (-730 "MONOGEN.spad" 1130612 1130625 1131724 1131859) (-729 "MONOGEN.spad" 1129382 1129397 1130496 1130501) (-728 "MONADWU.spad" 1127412 1127420 1129372 1129377) (-727 "MONADWU.spad" 1125440 1125450 1127402 1127407) (-726 "MONAD.spad" 1124600 1124608 1125430 1125435) (-725 "MONAD.spad" 1123758 1123768 1124590 1124595) (-724 "MOEBIUS.spad" 1122494 1122508 1123738 1123753) (-723 "MODULE.spad" 1122364 1122374 1122462 1122489) (-722 "MODULE.spad" 1122254 1122266 1122354 1122359) (-721 "MODRING.spad" 1121589 1121628 1122234 1122249) (-720 "MODOP.spad" 1120254 1120266 1121411 1121478) (-719 "MODMONOM.spad" 1119985 1120003 1120244 1120249) (-718 "MODMON.spad" 1116780 1116796 1117499 1117652) (-717 "MODFIELD.spad" 1116142 1116181 1116682 1116775) (-716 "MMLFORM.spad" 1115002 1115010 1116132 1116137) (-715 "MMAP.spad" 1114744 1114778 1114992 1114997) (-714 "MLO.spad" 1113203 1113213 1114700 1114739) (-713 "MLIFT.spad" 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637906 637975) (-392 "FMONOID.spad" 637443 637453 637734 637739) (-391 "FMONCAT.spad" 634596 634606 637433 637438) (-390 "FM.spad" 634291 634303 634530 634557) (-389 "FMFUN.spad" 631321 631329 634281 634286) (-388 "FMC.spad" 630373 630381 631311 631316) (-387 "FMCAT.spad" 628041 628059 630341 630368) (-386 "FM1.spad" 627398 627410 627975 628002) (-385 "FLOATRP.spad" 625133 625147 627388 627393) (-384 "FLOAT.spad" 618447 618455 624999 625128) (-383 "FLOATCP.spad" 615878 615892 618437 618442) (-382 "FLINEXP.spad" 615590 615600 615858 615873) (-381 "FLINEXP.spad" 615256 615268 615526 615531) (-380 "FLASORT.spad" 614582 614594 615246 615251) (-379 "FLALG.spad" 612228 612247 614508 614577) (-378 "FLAGG.spad" 609270 609280 612208 612223) (-377 "FLAGG.spad" 606213 606225 609153 609158) (-376 "FLAGG2.spad" 604938 604954 606203 606208) (-375 "FINRALG.spad" 602999 603012 604894 604933) (-374 "FINRALG.spad" 600986 601001 602883 602888) (-373 "FINITE.spad" 600138 600146 600976 600981) (-372 "FINAALG.spad" 589259 589269 600080 600133) (-371 "FINAALG.spad" 578392 578404 589215 589220) (-370 "FILE.spad" 577975 577985 578382 578387) (-369 "FILECAT.spad" 576501 576518 577965 577970) (-368 "FIELD.spad" 575907 575915 576403 576496) (-367 "FIELD.spad" 575399 575409 575897 575902) (-366 "FGROUP.spad" 574046 574056 575379 575394) (-365 "FGLMICPK.spad" 572833 572848 574036 574041) (-364 "FFX.spad" 572208 572223 572549 572642) (-363 "FFSLPE.spad" 571711 571732 572198 572203) (-362 "FFPOLY.spad" 562973 562984 571701 571706) (-361 "FFPOLY2.spad" 562033 562050 562963 562968) (-360 "FFP.spad" 561430 561450 561749 561842) (-359 "FF.spad" 560878 560894 561111 561204) (-358 "FFNBX.spad" 559390 559410 560594 560687) (-357 "FFNBP.spad" 557903 557920 559106 559199) (-356 "FFNB.spad" 556368 556389 557584 557677) (-355 "FFINTBAS.spad" 553882 553901 556358 556363) (-354 "FFIELDC.spad" 551459 551467 553784 553877) (-353 "FFIELDC.spad" 549122 549132 551449 551454) (-352 "FFHOM.spad" 547870 547887 549112 549117) (-351 "FFF.spad" 545305 545316 547860 547865) (-350 "FFCGX.spad" 544152 544172 545021 545114) (-349 "FFCGP.spad" 543041 543061 543868 543961) (-348 "FFCG.spad" 541833 541854 542722 542815) (-347 "FFCAT.spad" 535006 535028 541672 541828) (-346 "FFCAT.spad" 528258 528282 534926 534931) (-345 "FFCAT2.spad" 528005 528045 528248 528253) (-344 "FEXPR.spad" 519722 519768 527761 527800) (-343 "FEVALAB.spad" 519430 519440 519712 519717) (-342 "FEVALAB.spad" 518923 518935 519207 519212) (-341 "FDIV.spad" 518365 518389 518913 518918) (-340 "FDIVCAT.spad" 516429 516453 518355 518360) (-339 "FDIVCAT.spad" 514491 514517 516419 516424) (-338 "FDIV2.spad" 514147 514187 514481 514486) (-337 "FCTRDATA.spad" 513155 513163 514137 514142) (-336 "FCPAK1.spad" 511722 511730 513145 513150) (-335 "FCOMP.spad" 511101 511111 511712 511717) (-334 "FC.spad" 501108 501116 511091 511096) (-333 "FAXF.spad" 494079 494093 501010 501103) (-332 "FAXF.spad" 487102 487118 494035 494040) (-331 "FARRAY.spad" 485252 485262 486285 486312) (-330 "FAMR.spad" 483388 483400 485150 485247) (-329 "FAMR.spad" 481508 481522 483272 483277) (-328 "FAMONOID.spad" 481176 481186 481462 481467) (-327 "FAMONC.spad" 479472 479484 481166 481171) (-326 "FAGROUP.spad" 479096 479106 479368 479395) (-325 "FACUTIL.spad" 477300 477317 479086 479091) (-324 "FACTFUNC.spad" 476494 476504 477290 477295) (-323 "EXPUPXS.spad" 473327 473350 474626 474775) (-322 "EXPRTUBE.spad" 470615 470623 473317 473322) (-321 "EXPRODE.spad" 467775 467791 470605 470610) (-320 "EXPR.spad" 463050 463060 463764 464171) (-319 "EXPR2UPS.spad" 459172 459185 463040 463045) (-318 "EXPR2.spad" 458877 458889 459162 459167) (-317 "EXPEXPAN.spad" 455817 455842 456449 456542) (-316 "EXIT.spad" 455488 455496 455807 455812) (-315 "EXITAST.spad" 455224 455232 455478 455483) (-314 "EVALCYC.spad" 454684 454698 455214 455219) (-313 "EVALAB.spad" 454256 454266 454674 454679) (-312 "EVALAB.spad" 453826 453838 454246 454251) (-311 "EUCDOM.spad" 451400 451408 453752 453821) (-310 "EUCDOM.spad" 449036 449046 451390 451395) (-309 "ESTOOLS.spad" 440882 440890 449026 449031) (-308 "ESTOOLS2.spad" 440485 440499 440872 440877) (-307 "ESTOOLS1.spad" 440170 440181 440475 440480) (-306 "ES.spad" 432985 432993 440160 440165) (-305 "ES.spad" 425706 425716 432883 432888) (-304 "ESCONT.spad" 422499 422507 425696 425701) (-303 "ESCONT1.spad" 422248 422260 422489 422494) (-302 "ES2.spad" 421753 421769 422238 422243) (-301 "ES1.spad" 421323 421339 421743 421748) (-300 "ERROR.spad" 418650 418658 421313 421318) (-299 "EQTBL.spad" 417122 417144 417331 417358) (-298 "EQ.spad" 411927 411937 414714 414826) (-297 "EQ2.spad" 411645 411657 411917 411922) (-296 "EP.spad" 407971 407981 411635 411640) (-295 "ENV.spad" 406649 406657 407961 407966) (-294 "ENTIRER.spad" 406317 406325 406593 406644) (-293 "EMR.spad" 405524 405565 406243 406312) (-292 "ELTAGG.spad" 403778 403797 405514 405519) (-291 "ELTAGG.spad" 401996 402017 403734 403739) (-290 "ELTAB.spad" 401445 401463 401986 401991) (-289 "ELFUTS.spad" 400832 400851 401435 401440) (-288 "ELEMFUN.spad" 400521 400529 400822 400827) (-287 "ELEMFUN.spad" 400208 400218 400511 400516) (-286 "ELAGG.spad" 398179 398189 400188 400203) (-285 "ELAGG.spad" 396087 396099 398098 398103) (-284 "ELABOR.spad" 395433 395441 396077 396082) (-283 "ELABEXPR.spad" 394365 394373 395423 395428) (-282 "EFUPXS.spad" 391141 391171 394321 394326) (-281 "EFULS.spad" 387977 388000 391097 391102) (-280 "EFSTRUC.spad" 385992 386008 387967 387972) (-279 "EF.spad" 380768 380784 385982 385987) (-278 "EAB.spad" 379044 379052 380758 380763) (-277 "E04UCFA.spad" 378580 378588 379034 379039) (-276 "E04NAFA.spad" 378157 378165 378570 378575) (-275 "E04MBFA.spad" 377737 377745 378147 378152) (-274 "E04JAFA.spad" 377273 377281 377727 377732) (-273 "E04GCFA.spad" 376809 376817 377263 377268) (-272 "E04FDFA.spad" 376345 376353 376799 376804) (-271 "E04DGFA.spad" 375881 375889 376335 376340) (-270 "E04AGNT.spad" 371731 371739 375871 375876) (-269 "DVARCAT.spad" 368420 368430 371721 371726) (-268 "DVARCAT.spad" 365107 365119 368410 368415) (-267 "DSMP.spad" 362574 362588 362879 363006) (-266 "DROPT.spad" 356533 356541 362564 362569) (-265 "DROPT1.spad" 356198 356208 356523 356528) (-264 "DROPT0.spad" 351055 351063 356188 356193) (-263 "DRAWPT.spad" 349228 349236 351045 351050) (-262 "DRAW.spad" 342104 342117 349218 349223) (-261 "DRAWHACK.spad" 341412 341422 342094 342099) (-260 "DRAWCX.spad" 338882 338890 341402 341407) (-259 "DRAWCURV.spad" 338429 338444 338872 338877) (-258 "DRAWCFUN.spad" 327961 327969 338419 338424) (-257 "DQAGG.spad" 326139 326149 327929 327956) (-256 "DPOLCAT.spad" 321488 321504 326007 326134) (-255 "DPOLCAT.spad" 316923 316941 321444 321449) (-254 "DPMO.spad" 309149 309165 309287 309588) (-253 "DPMM.spad" 301388 301406 301513 301814) (-252 "DOMTMPLT.spad" 301048 301056 301378 301383) (-251 "DOMCTOR.spad" 300803 300811 301038 301043) (-250 "DOMAIN.spad" 299890 299898 300793 300798) (-249 "DMP.spad" 297150 297165 297720 297847) (-248 "DLP.spad" 296502 296512 297140 297145) (-247 "DLIST.spad" 295081 295091 295685 295712) (-246 "DLAGG.spad" 293498 293508 295071 295076) (-245 "DIVRING.spad" 293040 293048 293442 293493) (-244 "DIVRING.spad" 292626 292636 293030 293035) (-243 "DISPLAY.spad" 290816 290824 292616 292621) (-242 "DIRPROD.spad" 280396 280412 281036 281167) (-241 "DIRPROD2.spad" 279214 279232 280386 280391) (-240 "DIRPCAT.spad" 278158 278174 279078 279209) (-239 "DIRPCAT.spad" 276831 276849 277753 277758) (-238 "DIOSP.spad" 275656 275664 276821 276826) (-237 "DIOPS.spad" 274652 274662 275636 275651) (-236 "DIOPS.spad" 273622 273634 274608 274613) (-235 "DIFRING.spad" 272918 272926 273602 273617) (-234 "DIFRING.spad" 272222 272232 272908 272913) (-233 "DIFEXT.spad" 271393 271403 272202 272217) (-232 "DIFEXT.spad" 270481 270493 271292 271297) (-231 "DIAGG.spad" 270111 270121 270461 270476) (-230 "DIAGG.spad" 269749 269761 270101 270106) (-229 "DHMATRIX.spad" 268061 268071 269206 269233) (-228 "DFSFUN.spad" 261701 261709 268051 268056) (-227 "DFLOAT.spad" 258432 258440 261591 261696) (-226 "DFINTTLS.spad" 256663 256679 258422 258427) (-225 "DERHAM.spad" 254577 254609 256643 256658) (-224 "DEQUEUE.spad" 253901 253911 254184 254211) (-223 "DEGRED.spad" 253518 253532 253891 253896) (-222 "DEFINTRF.spad" 251055 251065 253508 253513) (-221 "DEFINTEF.spad" 249565 249581 251045 251050) (-220 "DEFAST.spad" 248933 248941 249555 249560) (-219 "DECIMAL.spad" 247039 247047 247400 247493) (-218 "DDFACT.spad" 244852 244869 247029 247034) (-217 "DBLRESP.spad" 244452 244476 244842 244847) (-216 "DBASE.spad" 243116 243126 244442 244447) (-215 "DATAARY.spad" 242578 242591 243106 243111) (-214 "D03FAFA.spad" 242406 242414 242568 242573) (-213 "D03EEFA.spad" 242226 242234 242396 242401) (-212 "D03AGNT.spad" 241312 241320 242216 242221) (-211 "D02EJFA.spad" 240774 240782 241302 241307) (-210 "D02CJFA.spad" 240252 240260 240764 240769) (-209 "D02BHFA.spad" 239742 239750 240242 240247) (-208 "D02BBFA.spad" 239232 239240 239732 239737) (-207 "D02AGNT.spad" 234046 234054 239222 239227) (-206 "D01WGTS.spad" 232365 232373 234036 234041) (-205 "D01TRNS.spad" 232342 232350 232355 232360) (-204 "D01GBFA.spad" 231864 231872 232332 232337) (-203 "D01FCFA.spad" 231386 231394 231854 231859) (-202 "D01ASFA.spad" 230854 230862 231376 231381) (-201 "D01AQFA.spad" 230300 230308 230844 230849) (-200 "D01APFA.spad" 229724 229732 230290 230295) (-199 "D01ANFA.spad" 229218 229226 229714 229719) (-198 "D01AMFA.spad" 228728 228736 229208 229213) (-197 "D01ALFA.spad" 228268 228276 228718 228723) (-196 "D01AKFA.spad" 227794 227802 228258 228263) (-195 "D01AJFA.spad" 227317 227325 227784 227789) (-194 "D01AGNT.spad" 223384 223392 227307 227312) (-193 "CYCLOTOM.spad" 222890 222898 223374 223379) (-192 "CYCLES.spad" 219669 219677 222880 222885) (-191 "CVMP.spad" 219086 219096 219659 219664) (-190 "CTRIGMNP.spad" 217586 217602 219076 219081) (-189 "CTOR.spad" 217277 217285 217576 217581) (-188 "CTORKIND.spad" 216880 216888 217267 217272) (-187 "CTORCAT.spad" 216129 216137 216870 216875) (-186 "CTORCAT.spad" 215376 215386 216119 216124) (-185 "CTORCALL.spad" 214965 214975 215366 215371) (-184 "CSTTOOLS.spad" 214210 214223 214955 214960) (-183 "CRFP.spad" 207934 207947 214200 214205) (-182 "CRCEAST.spad" 207654 207662 207924 207929) (-181 "CRAPACK.spad" 206705 206715 207644 207649) (-180 "CPMATCH.spad" 206209 206224 206630 206635) (-179 "CPIMA.spad" 205914 205933 206199 206204) (-178 "COORDSYS.spad" 200923 200933 205904 205909) (-177 "CONTOUR.spad" 200334 200342 200913 200918) (-176 "CONTFRAC.spad" 196084 196094 200236 200329) (-175 "CONDUIT.spad" 195842 195850 196074 196079) (-174 "COMRING.spad" 195516 195524 195780 195837) (-173 "COMPPROP.spad" 195034 195042 195506 195511) (-172 "COMPLPAT.spad" 194801 194816 195024 195029) (-171 "COMPLEX.spad" 188938 188948 189182 189443) (-170 "COMPLEX2.spad" 188653 188665 188928 188933) (-169 "COMPILER.spad" 188202 188210 188643 188648) (-168 "COMPFACT.spad" 187804 187818 188192 188197) (-167 "COMPCAT.spad" 185876 185886 187538 187799) (-166 "COMPCAT.spad" 183676 183688 185340 185345) (-165 "COMMUPC.spad" 183424 183442 183666 183671) (-164 "COMMONOP.spad" 182957 182965 183414 183419) (-163 "COMM.spad" 182768 182776 182947 182952) (-162 "COMMAAST.spad" 182531 182539 182758 182763) (-161 "COMBOPC.spad" 181446 181454 182521 182526) (-160 "COMBINAT.spad" 180213 180223 181436 181441) (-159 "COMBF.spad" 177595 177611 180203 180208) (-158 "COLOR.spad" 176432 176440 177585 177590) (-157 "COLONAST.spad" 176098 176106 176422 176427) (-156 "CMPLXRT.spad" 175809 175826 176088 176093) (-155 "CLLCTAST.spad" 175471 175479 175799 175804) (-154 "CLIP.spad" 171579 171587 175461 175466) (-153 "CLIF.spad" 170234 170250 171535 171574) (-152 "CLAGG.spad" 166739 166749 170224 170229) (-151 "CLAGG.spad" 163115 163127 166602 166607) (-150 "CINTSLPE.spad" 162446 162459 163105 163110) (-149 "CHVAR.spad" 160584 160606 162436 162441) (-148 "CHARZ.spad" 160499 160507 160564 160579) (-147 "CHARPOL.spad" 160009 160019 160489 160494) (-146 "CHARNZ.spad" 159762 159770 159989 160004) (-145 "CHAR.spad" 157636 157644 159752 159757) (-144 "CFCAT.spad" 156964 156972 157626 157631) (-143 "CDEN.spad" 156160 156174 156954 156959) (-142 "CCLASS.spad" 154309 154317 155571 155610) (-141 "CATEGORY.spad" 153351 153359 154299 154304) (-140 "CATCTOR.spad" 153242 153250 153341 153346) (-139 "CATAST.spad" 152860 152868 153232 153237) (-138 "CASEAST.spad" 152574 152582 152850 152855) (-137 "CARTEN.spad" 147861 147885 152564 152569) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2268303 2268308 2268313 2268318) (-2 NIL 2268283 2268288 2268293 2268298) (-1 NIL 2268263 2268268 2268273 2268278) (0 NIL 2268243 2268248 2268253 2268258) (-1305 "ZMOD.spad" 2268052 2268065 2268181 2268238) (-1304 "ZLINDEP.spad" 2267118 2267129 2268042 2268047) (-1303 "ZDSOLVE.spad" 2257063 2257085 2267108 2267113) (-1302 "YSTREAM.spad" 2256558 2256569 2257053 2257058) (-1301 "XRPOLY.spad" 2255778 2255798 2256414 2256483) (-1300 "XPR.spad" 2253573 2253586 2255496 2255595) (-1299 "XPOLY.spad" 2253128 2253139 2253429 2253498) (-1298 "XPOLYC.spad" 2252447 2252463 2253054 2253123) (-1297 "XPBWPOLY.spad" 2250884 2250904 2252227 2252296) (-1296 "XF.spad" 2249347 2249362 2250786 2250879) (-1295 "XF.spad" 2247790 2247807 2249231 2249236) (-1294 "XFALG.spad" 2244838 2244854 2247716 2247785) (-1293 "XEXPPKG.spad" 2244089 2244115 2244828 2244833) (-1292 "XDPOLY.spad" 2243703 2243719 2243945 2244014) (-1291 "XALG.spad" 2243363 2243374 2243659 2243698) (-1290 "WUTSET.spad" 2239202 2239219 2243009 2243036) (-1289 "WP.spad" 2238401 2238445 2239060 2239127) (-1288 "WHILEAST.spad" 2238199 2238208 2238391 2238396) (-1287 "WHEREAST.spad" 2237870 2237879 2238189 2238194) (-1286 "WFFINTBS.spad" 2235533 2235555 2237860 2237865) (-1285 "WEIER.spad" 2233755 2233766 2235523 2235528) (-1284 "VSPACE.spad" 2233428 2233439 2233723 2233750) (-1283 "VSPACE.spad" 2233121 2233134 2233418 2233423) (-1282 "VOID.spad" 2232798 2232807 2233111 2233116) (-1281 "VIEW.spad" 2230478 2230487 2232788 2232793) (-1280 "VIEWDEF.spad" 2225679 2225688 2230468 2230473) (-1279 "VIEW3D.spad" 2209640 2209649 2225669 2225674) (-1278 "VIEW2D.spad" 2197531 2197540 2209630 2209635) (-1277 "VECTOR.spad" 2196205 2196216 2196456 2196483) (-1276 "VECTOR2.spad" 2194844 2194857 2196195 2196200) (-1275 "VECTCAT.spad" 2192748 2192759 2194812 2194839) (-1274 "VECTCAT.spad" 2190459 2190472 2192525 2192530) (-1273 "VARIABLE.spad" 2190239 2190254 2190449 2190454) (-1272 "UTYPE.spad" 2189883 2189892 2190229 2190234) (-1271 "UTSODETL.spad" 2189178 2189202 2189839 2189844) (-1270 "UTSODE.spad" 2187394 2187414 2189168 2189173) (-1269 "UTS.spad" 2182198 2182226 2185861 2185958) (-1268 "UTSCAT.spad" 2179677 2179693 2182096 2182193) (-1267 "UTSCAT.spad" 2176800 2176818 2179221 2179226) (-1266 "UTS2.spad" 2176395 2176430 2176790 2176795) (-1265 "URAGG.spad" 2171068 2171079 2176385 2176390) (-1264 "URAGG.spad" 2165705 2165718 2171024 2171029) (-1263 "UPXSSING.spad" 2163350 2163376 2164786 2164919) (-1262 "UPXS.spad" 2160504 2160532 2161482 2161631) (-1261 "UPXSCONS.spad" 2158263 2158283 2158636 2158785) (-1260 "UPXSCCA.spad" 2156834 2156854 2158109 2158258) (-1259 "UPXSCCA.spad" 2155547 2155569 2156824 2156829) (-1258 "UPXSCAT.spad" 2154136 2154152 2155393 2155542) (-1257 "UPXS2.spad" 2153679 2153732 2154126 2154131) (-1256 "UPSQFREE.spad" 2152093 2152107 2153669 2153674) (-1255 "UPSCAT.spad" 2149704 2149728 2151991 2152088) (-1254 "UPSCAT.spad" 2147021 2147047 2149310 2149315) (-1253 "UPOLYC.spad" 2142061 2142072 2146863 2147016) (-1252 "UPOLYC.spad" 2136993 2137006 2141797 2141802) (-1251 "UPOLYC2.spad" 2136464 2136483 2136983 2136988) (-1250 "UP.spad" 2133663 2133678 2134050 2134203) (-1249 "UPMP.spad" 2132563 2132576 2133653 2133658) (-1248 "UPDIVP.spad" 2132128 2132142 2132553 2132558) (-1247 "UPDECOMP.spad" 2130373 2130387 2132118 2132123) (-1246 "UPCDEN.spad" 2129582 2129598 2130363 2130368) (-1245 "UP2.spad" 2128946 2128967 2129572 2129577) (-1244 "UNISEG.spad" 2128299 2128310 2128865 2128870) (-1243 "UNISEG2.spad" 2127796 2127809 2128255 2128260) (-1242 "UNIFACT.spad" 2126899 2126911 2127786 2127791) (-1241 "ULS.spad" 2117457 2117485 2118544 2118973) (-1240 "ULSCONS.spad" 2109853 2109873 2110223 2110372) (-1239 "ULSCCAT.spad" 2107590 2107610 2109699 2109848) (-1238 "ULSCCAT.spad" 2105435 2105457 2107546 2107551) (-1237 "ULSCAT.spad" 2103667 2103683 2105281 2105430) (-1236 "ULS2.spad" 2103181 2103234 2103657 2103662) (-1235 "UINT8.spad" 2103058 2103067 2103171 2103176) (-1234 "UINT64.spad" 2102934 2102943 2103048 2103053) (-1233 "UINT32.spad" 2102810 2102819 2102924 2102929) (-1232 "UINT16.spad" 2102686 2102695 2102800 2102805) (-1231 "UFD.spad" 2101751 2101760 2102612 2102681) (-1230 "UFD.spad" 2100878 2100889 2101741 2101746) (-1229 "UDVO.spad" 2099759 2099768 2100868 2100873) (-1228 "UDPO.spad" 2097252 2097263 2099715 2099720) (-1227 "TYPE.spad" 2097184 2097193 2097242 2097247) (-1226 "TYPEAST.spad" 2097103 2097112 2097174 2097179) (-1225 "TWOFACT.spad" 2095755 2095770 2097093 2097098) (-1224 "TUPLE.spad" 2095241 2095252 2095654 2095659) (-1223 "TUBETOOL.spad" 2092108 2092117 2095231 2095236) (-1222 "TUBE.spad" 2090755 2090772 2092098 2092103) (-1221 "TS.spad" 2089354 2089370 2090320 2090417) (-1220 "TSETCAT.spad" 2076481 2076498 2089322 2089349) (-1219 "TSETCAT.spad" 2063594 2063613 2076437 2076442) (-1218 "TRMANIP.spad" 2057960 2057977 2063300 2063305) (-1217 "TRIMAT.spad" 2056923 2056948 2057950 2057955) (-1216 "TRIGMNIP.spad" 2055450 2055467 2056913 2056918) (-1215 "TRIGCAT.spad" 2054962 2054971 2055440 2055445) (-1214 "TRIGCAT.spad" 2054472 2054483 2054952 2054957) (-1213 "TREE.spad" 2053047 2053058 2054079 2054106) (-1212 "TRANFUN.spad" 2052886 2052895 2053037 2053042) (-1211 "TRANFUN.spad" 2052723 2052734 2052876 2052881) (-1210 "TOPSP.spad" 2052397 2052406 2052713 2052718) (-1209 "TOOLSIGN.spad" 2052060 2052071 2052387 2052392) (-1208 "TEXTFILE.spad" 2050621 2050630 2052050 2052055) (-1207 "TEX.spad" 2047767 2047776 2050611 2050616) (-1206 "TEX1.spad" 2047323 2047334 2047757 2047762) (-1205 "TEMUTL.spad" 2046878 2046887 2047313 2047318) (-1204 "TBCMPPK.spad" 2044971 2044994 2046868 2046873) (-1203 "TBAGG.spad" 2044021 2044044 2044951 2044966) (-1202 "TBAGG.spad" 2043079 2043104 2044011 2044016) (-1201 "TANEXP.spad" 2042487 2042498 2043069 2043074) (-1200 "TALGOP.spad" 2042211 2042222 2042477 2042482) (-1199 "TABLE.spad" 2040622 2040645 2040892 2040919) (-1198 "TABLEAU.spad" 2040103 2040114 2040612 2040617) (-1197 "TABLBUMP.spad" 2036906 2036917 2040093 2040098) (-1196 "SYSTEM.spad" 2036134 2036143 2036896 2036901) (-1195 "SYSSOLP.spad" 2033617 2033628 2036124 2036129) (-1194 "SYSPTR.spad" 2033516 2033525 2033607 2033612) (-1193 "SYSNNI.spad" 2032698 2032709 2033506 2033511) (-1192 "SYSINT.spad" 2032102 2032113 2032688 2032693) (-1191 "SYNTAX.spad" 2028308 2028317 2032092 2032097) (-1190 "SYMTAB.spad" 2026376 2026385 2028298 2028303) (-1189 "SYMS.spad" 2022399 2022408 2026366 2026371) (-1188 "SYMPOLY.spad" 2021406 2021417 2021488 2021615) (-1187 "SYMFUNC.spad" 2020907 2020918 2021396 2021401) (-1186 "SYMBOL.spad" 2018410 2018419 2020897 2020902) (-1185 "SWITCH.spad" 2015181 2015190 2018400 2018405) (-1184 "SUTS.spad" 2012086 2012114 2013648 2013745) (-1183 "SUPXS.spad" 2009227 2009255 2010218 2010367) (-1182 "SUP.spad" 2006040 2006051 2006813 2006966) (-1181 "SUPFRACF.spad" 2005145 2005163 2006030 2006035) (-1180 "SUP2.spad" 2004537 2004550 2005135 2005140) (-1179 "SUMRF.spad" 2003511 2003522 2004527 2004532) (-1178 "SUMFS.spad" 2003148 2003165 2003501 2003506) (-1177 "SULS.spad" 1993693 1993721 1994793 1995222) (-1176 "SUCHTAST.spad" 1993462 1993471 1993683 1993688) (-1175 "SUCH.spad" 1993144 1993159 1993452 1993457) (-1174 "SUBSPACE.spad" 1985259 1985274 1993134 1993139) (-1173 "SUBRESP.spad" 1984429 1984443 1985215 1985220) (-1172 "STTF.spad" 1980528 1980544 1984419 1984424) (-1171 "STTFNC.spad" 1976996 1977012 1980518 1980523) (-1170 "STTAYLOR.spad" 1969631 1969642 1976877 1976882) (-1169 "STRTBL.spad" 1968136 1968153 1968285 1968312) (-1168 "STRING.spad" 1967545 1967554 1967559 1967586) (-1167 "STRICAT.spad" 1967333 1967342 1967513 1967540) (-1166 "STREAM.spad" 1964251 1964262 1966858 1966873) (-1165 "STREAM3.spad" 1963824 1963839 1964241 1964246) (-1164 "STREAM2.spad" 1962952 1962965 1963814 1963819) (-1163 "STREAM1.spad" 1962658 1962669 1962942 1962947) (-1162 "STINPROD.spad" 1961594 1961610 1962648 1962653) (-1161 "STEP.spad" 1960795 1960804 1961584 1961589) (-1160 "STEPAST.spad" 1960029 1960038 1960785 1960790) (-1159 "STBL.spad" 1958555 1958583 1958722 1958737) (-1158 "STAGG.spad" 1957630 1957641 1958545 1958550) (-1157 "STAGG.spad" 1956703 1956716 1957620 1957625) (-1156 "STACK.spad" 1956060 1956071 1956310 1956337) (-1155 "SREGSET.spad" 1953764 1953781 1955706 1955733) (-1154 "SRDCMPK.spad" 1952325 1952345 1953754 1953759) (-1153 "SRAGG.spad" 1947468 1947477 1952293 1952320) (-1152 "SRAGG.spad" 1942631 1942642 1947458 1947463) (-1151 "SQMATRIX.spad" 1940247 1940265 1941163 1941250) (-1150 "SPLTREE.spad" 1934799 1934812 1939683 1939710) (-1149 "SPLNODE.spad" 1931387 1931400 1934789 1934794) (-1148 "SPFCAT.spad" 1930196 1930205 1931377 1931382) (-1147 "SPECOUT.spad" 1928748 1928757 1930186 1930191) (-1146 "SPADXPT.spad" 1920343 1920352 1928738 1928743) (-1145 "spad-parser.spad" 1919808 1919817 1920333 1920338) (-1144 "SPADAST.spad" 1919509 1919518 1919798 1919803) (-1143 "SPACEC.spad" 1903708 1903719 1919499 1919504) (-1142 "SPACE3.spad" 1903484 1903495 1903698 1903703) (-1141 "SORTPAK.spad" 1903033 1903046 1903440 1903445) (-1140 "SOLVETRA.spad" 1900796 1900807 1903023 1903028) (-1139 "SOLVESER.spad" 1899324 1899335 1900786 1900791) (-1138 "SOLVERAD.spad" 1895350 1895361 1899314 1899319) (-1137 "SOLVEFOR.spad" 1893812 1893830 1895340 1895345) (-1136 "SNTSCAT.spad" 1893412 1893429 1893780 1893807) (-1135 "SMTS.spad" 1891684 1891710 1892977 1893074) (-1134 "SMP.spad" 1889159 1889179 1889549 1889676) (-1133 "SMITH.spad" 1888004 1888029 1889149 1889154) (-1132 "SMATCAT.spad" 1886114 1886144 1887948 1887999) (-1131 "SMATCAT.spad" 1884156 1884188 1885992 1885997) (-1130 "SKAGG.spad" 1883119 1883130 1884124 1884151) (-1129 "SINT.spad" 1882059 1882068 1882985 1883114) (-1128 "SIMPAN.spad" 1881787 1881796 1882049 1882054) (-1127 "SIG.spad" 1881117 1881126 1881777 1881782) (-1126 "SIGNRF.spad" 1880235 1880246 1881107 1881112) (-1125 "SIGNEF.spad" 1879514 1879531 1880225 1880230) (-1124 "SIGAST.spad" 1878899 1878908 1879504 1879509) (-1123 "SHP.spad" 1876827 1876842 1878855 1878860) (-1122 "SHDP.spad" 1866538 1866565 1867047 1867178) (-1121 "SGROUP.spad" 1866146 1866155 1866528 1866533) (-1120 "SGROUP.spad" 1865752 1865763 1866136 1866141) (-1119 "SGCF.spad" 1858891 1858900 1865742 1865747) (-1118 "SFRTCAT.spad" 1857821 1857838 1858859 1858886) (-1117 "SFRGCD.spad" 1856884 1856904 1857811 1857816) (-1116 "SFQCMPK.spad" 1851521 1851541 1856874 1856879) (-1115 "SFORT.spad" 1850960 1850974 1851511 1851516) (-1114 "SEXOF.spad" 1850803 1850843 1850950 1850955) (-1113 "SEX.spad" 1850695 1850704 1850793 1850798) (-1112 "SEXCAT.spad" 1848296 1848336 1850685 1850690) (-1111 "SET.spad" 1846620 1846631 1847717 1847756) (-1110 "SETMN.spad" 1845070 1845087 1846610 1846615) (-1109 "SETCAT.spad" 1844392 1844401 1845060 1845065) (-1108 "SETCAT.spad" 1843712 1843723 1844382 1844387) (-1107 "SETAGG.spad" 1840261 1840272 1843692 1843707) (-1106 "SETAGG.spad" 1836818 1836831 1840251 1840256) (-1105 "SEQAST.spad" 1836521 1836530 1836808 1836813) (-1104 "SEGXCAT.spad" 1835677 1835690 1836511 1836516) (-1103 "SEG.spad" 1835490 1835501 1835596 1835601) (-1102 "SEGCAT.spad" 1834415 1834426 1835480 1835485) (-1101 "SEGBIND.spad" 1834173 1834184 1834362 1834367) (-1100 "SEGBIND2.spad" 1833871 1833884 1834163 1834168) (-1099 "SEGAST.spad" 1833585 1833594 1833861 1833866) (-1098 "SEG2.spad" 1833020 1833033 1833541 1833546) (-1097 "SDVAR.spad" 1832296 1832307 1833010 1833015) (-1096 "SDPOL.spad" 1829722 1829733 1830013 1830140) (-1095 "SCPKG.spad" 1827811 1827822 1829712 1829717) (-1094 "SCOPE.spad" 1826964 1826973 1827801 1827806) (-1093 "SCACHE.spad" 1825660 1825671 1826954 1826959) (-1092 "SASTCAT.spad" 1825569 1825578 1825650 1825655) (-1091 "SAOS.spad" 1825441 1825450 1825559 1825564) (-1090 "SAERFFC.spad" 1825154 1825174 1825431 1825436) (-1089 "SAE.spad" 1823329 1823345 1823940 1824075) (-1088 "SAEFACT.spad" 1823030 1823050 1823319 1823324) (-1087 "RURPK.spad" 1820689 1820705 1823020 1823025) (-1086 "RULESET.spad" 1820142 1820166 1820679 1820684) (-1085 "RULE.spad" 1818382 1818406 1820132 1820137) (-1084 "RULECOLD.spad" 1818234 1818247 1818372 1818377) (-1083 "RTVALUE.spad" 1817969 1817978 1818224 1818229) (-1082 "RSTRCAST.spad" 1817686 1817695 1817959 1817964) (-1081 "RSETGCD.spad" 1814064 1814084 1817676 1817681) (-1080 "RSETCAT.spad" 1804000 1804017 1814032 1814059) (-1079 "RSETCAT.spad" 1793956 1793975 1803990 1803995) (-1078 "RSDCMPK.spad" 1792408 1792428 1793946 1793951) (-1077 "RRCC.spad" 1790792 1790822 1792398 1792403) (-1076 "RRCC.spad" 1789174 1789206 1790782 1790787) (-1075 "RPTAST.spad" 1788876 1788885 1789164 1789169) (-1074 "RPOLCAT.spad" 1768236 1768251 1788744 1788871) (-1073 "RPOLCAT.spad" 1747309 1747326 1767819 1767824) (-1072 "ROUTINE.spad" 1743192 1743201 1745956 1745983) (-1071 "ROMAN.spad" 1742520 1742529 1743058 1743187) (-1070 "ROIRC.spad" 1741600 1741632 1742510 1742515) (-1069 "RNS.spad" 1740503 1740512 1741502 1741595) (-1068 "RNS.spad" 1739492 1739503 1740493 1740498) (-1067 "RNG.spad" 1739227 1739236 1739482 1739487) (-1066 "RNGBIND.spad" 1738387 1738401 1739182 1739187) (-1065 "RMODULE.spad" 1738152 1738163 1738377 1738382) (-1064 "RMCAT2.spad" 1737572 1737629 1738142 1738147) (-1063 "RMATRIX.spad" 1736396 1736415 1736739 1736778) (-1062 "RMATCAT.spad" 1731975 1732006 1736352 1736391) (-1061 "RMATCAT.spad" 1727444 1727477 1731823 1731828) (-1060 "RLINSET.spad" 1726838 1726849 1727434 1727439) (-1059 "RINTERP.spad" 1726726 1726746 1726828 1726833) (-1058 "RING.spad" 1726196 1726205 1726706 1726721) (-1057 "RING.spad" 1725674 1725685 1726186 1726191) (-1056 "RIDIST.spad" 1725066 1725075 1725664 1725669) (-1055 "RGCHAIN.spad" 1723649 1723665 1724551 1724578) (-1054 "RGBCSPC.spad" 1723430 1723442 1723639 1723644) (-1053 "RGBCMDL.spad" 1722960 1722972 1723420 1723425) (-1052 "RF.spad" 1720602 1720613 1722950 1722955) (-1051 "RFFACTOR.spad" 1720064 1720075 1720592 1720597) (-1050 "RFFACT.spad" 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index c1c235c9..c980c8be 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,6 +1,6 @@ -(188596 . 3480761531) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(188571 . 3480886518) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) ((((-570)) . T) (($) -2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) @@ -56,7 +56,7 @@ (((#0=(-876 |#1|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) ((((-1168)) . T) (((-965 (-130))) . T) (((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#4| (-373)) (|has| |#3| (-373)) (((|#1|) . T)) @@ -74,7 +74,7 @@ ((((-570)) . T) (((-413 (-570))) -2892 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) (-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) -((((-2 (|:| -2266 |#1|) (|:| -1696 |#2|))) . T)) +((((-2 (|:| -2268 |#1|) (|:| -3357 |#2|))) . T)) ((($) . T)) ((((-570)) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1186)) . T)) ((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) @@ -131,7 +131,7 @@ (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . T)) (-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-570)) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) @@ -270,8 +270,8 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (|has| |#1| (-562)) ((((-570)) -2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (-12 (|has| |#4| (-1047 (-570))) (|has| |#4| (-1109))) (|has| |#4| (-1058))) ((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-1109))) (((-413 (-570))) -12 (|has| |#4| (-1047 (-413 (-570)))) (|has| |#4| (-1109)))) ((((-570)) -2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (-12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (|has| |#3| (-1058))) ((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) @@ -300,11 +300,11 @@ ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2266 |#1|) (|:| -1696 |#2|))) . T) (((-868)) . T)) +((((-2 (|:| -2268 |#1|) (|:| -3357 |#2|))) . T) (((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) (((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) (((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) -((((-2 (|:| -2266 |#1|) (|:| -1696 |#2|))) . T)) +((((-2 (|:| -2268 |#1|) (|:| -3357 |#2|))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) @@ -312,7 +312,7 @@ (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-413 $) (-413 $)) |has| |#2| (-562)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-916)) ((((-1168) (-52)) . T)) @@ -351,7 +351,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -369,10 +369,10 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1058))) ((((-868)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (((|#1|) . T)) -((((-1277 (-344 (-3810) (-3810 (QUOTE X)) (-705)))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))))) +((((-1277 (-344 (-3811) (-3811 (QUOTE X)) (-705)))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))))) ((((-868)) . T)) ((((-570) |#1|) . T)) ((((-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#2| (-620 (-542)))) (((-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#2| (-620 (-899 (-384))))) (((-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#2| (-620 (-899 (-570)))))) @@ -491,12 +491,12 @@ ((((-145)) . T)) (((|#3|) |has| |#3| (-1109)) (((-570)) -12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) ((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-542)) |has| |#1| (-620 (-542)))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) (|has| |#1| (-368)) ((((-1191)) . T)) (((|#1|) . T)) @@ -507,13 +507,13 @@ (|has| |#1| (-854)) (-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-542)) |has| |#1| (-620 (-542)))) (((|#1| |#2|) . T)) ((((-1186)) -12 (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))))) ((((-1168) |#1|) . T)) (((|#1| |#2| |#3| (-537 |#3|)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-373)) (|has| |#1| (-373)) (|has| |#1| (-373)) @@ -710,8 +710,7 @@ (((|#2|) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-650 (-570))) . T)) -((((-650 (-570))) . T) (((-868)) . T)) +((((-650 (-928))) . T) (((-868)) . T)) ((((-413 (-570))) . T) (((-868)) . T)) ((((-542)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (|has| |#1| (-235)) @@ -729,7 +728,7 @@ ((((-1149 |#1| |#2|)) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (((|#2|) . T) (((-570)) |has| |#2| (-1047 (-570))) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (((|#1|) . T)) (((|#1| |#2|) . T)) @@ -738,7 +737,7 @@ (((|#2|) . T)) (((|#3|) . T)) (-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (((|#2|) . T)) ((((-868)) -2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (((-570)) . T) (($) . T)) @@ -838,9 +837,9 @@ (-2892 (|has| |#1| (-458)) (|has| |#1| (-916))) ((((-570) |#2|) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((($) -2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) ((((-570) |#1|) . T)) @@ -855,11 +854,11 @@ (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-394) (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) (-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) @@ -1095,7 +1094,7 @@ (|has| |#2| (-174)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-235)) (|has| |#2| (-1058))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) (-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) ((((-868)) . T)) @@ -1126,10 +1125,10 @@ (((|#1| (-413 (-570))) . T)) (((|#3|) . T) (((-618 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-570)) -2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) @@ -1138,8 +1137,8 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1155,7 +1154,7 @@ (|has| (-1103 |#1|) (-1109)) (((|#2| |#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) (((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)))) -((((-570) (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) (((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((((-570)) . T)) ((((-1191)) . T)) @@ -1200,7 +1199,7 @@ (-2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) (|has| |#2| (-1161)) -(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2339 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2340 #0#))) . T)) (((|#1| |#2|) . T)) (-2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) (((|#1| (-570) (-1091)) . T)) @@ -1229,7 +1228,7 @@ (((|#4|) . T) (((-868)) . T)) (((|#3|) . T) ((|#2|) . T) (($) -2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) (((-570)) . T) ((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) (((|#2|) . T) (($) -2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) (((-570)) . T) ((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (|has| |#1| (-562)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) @@ -1289,7 +1288,7 @@ (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1320,7 +1319,7 @@ ((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (-2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((($) . T)) -(((#0=(-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))))) +(((#0=(-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))))) ((($) . T)) ((($) . T)) (((|#2|) |has| |#2| (-1109))) @@ -1336,10 +1335,10 @@ ((((-570)) |has| #0=(-413 |#2|) (-645 (-570))) ((#0#) . T)) ((($) . T) (((-570)) . T)) ((((-570) (-145)) . T)) -((((-570) (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) ((((-917 |#1|)) . T)) (|has| |#1| (-368)) @@ -1368,7 +1367,7 @@ ((((-868)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-570) (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) @@ -1385,7 +1384,7 @@ ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-876 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-512)) . T)) (|has| |#2| (-854)) ((((-512)) . T)) @@ -1420,7 +1419,7 @@ (((|#1|) . T)) ((((-1186)) |has| (-413 |#2|) (-907 (-1186)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) ((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) ((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T) (($) -2892 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) @@ -1437,7 +1436,7 @@ (((|#2|) . T) (((-570)) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((|#2|) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-1168) (-1186) (-570) (-227) (-868)) . T)) @@ -1528,7 +1527,7 @@ ((((-1008 |#1|)) . T) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1537,7 +1536,7 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) ((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -1551,7 +1550,7 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1109)) (|has| |#2| (-368)) @@ -1596,7 +1595,7 @@ (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#2|) . T)) ((((-570) (-145)) . T)) -(((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) +(((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) ((($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| |#1| (-856)) (((|#2| (-777) (-1091)) . T)) @@ -1649,7 +1648,7 @@ ((((-394) (-1168)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) -2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2106 (-1168)) (|:| -2339 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2106 (-1168)) (|:| -2340 #0#))) . T)) (((|#1|) . T)) ((((-868)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) @@ -1700,12 +1699,12 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-1186) (-52)) . T)) ((($ $) . T)) (((|#1| (-570)) . T)) @@ -1755,11 +1754,11 @@ (-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . T)) (|has| |#1| (-854)) -(((#0=(-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))))) +(((#0=(-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-1109)) ((((-868)) . T) (((-1191)) . T)) @@ -1820,7 +1819,7 @@ (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))))) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))))) (-2892 (|has| |#2| (-458)) (|has| |#2| (-916))) (-2892 (|has| |#1| (-458)) (|has| |#1| (-916))) (((|#1|) . T) (($) . T)) @@ -1845,7 +1844,7 @@ ((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-678 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1923,7 +1922,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((($ $) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((($ $) . T)) ((((-570) (-112)) . T)) ((($) . T)) @@ -1953,7 +1952,7 @@ (((|#1| (-777)) . T)) (((|#1|) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-1109)) ((((-1168) |#1|) . T)) ((($) . T)) @@ -2001,7 +2000,7 @@ ((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) (((|#1|) . T) (($) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) ((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) @@ -2025,7 +2024,7 @@ (|has| |#1| (-854)) (((|#1| (-570) (-1091)) . T)) (-2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1| (-413 (-570)) (-1091)) . T)) (((|#1| (-777) (-1091)) . T)) (|has| |#1| (-856)) @@ -2044,11 +2043,11 @@ (|has| |#1| (-1109)) ((((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((|#2|) |has| |#1| (-368))) (-2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) -((((-695 (-344 (-3810) (-3810 (QUOTE X) (QUOTE HESS)) (-705)))) . T)) +((((-695 (-344 (-3811) (-3811 (QUOTE X) (QUOTE HESS)) (-705)))) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) ((((-868)) . T)) (|has| |#3| (-854)) ((((-868)) . T)) @@ -2064,11 +2063,11 @@ ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) (|has| |#1| (-856)) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T) (((-570)) . T)) (((|#2|) . T)) ((((-570)) . T) ((|#3|) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) |has| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))))) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) |has| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))))) (-2892 (|has| |#1| (-458)) (|has| |#1| (-916))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) ((((-868)) . T)) @@ -2127,7 +2126,7 @@ ((((-650 |#1|)) . T)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-1058))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (|has| |#1| (-368)) (((|#1|) |has| |#1| (-174))) (((|#1| |#1|) . T)) @@ -2179,7 +2178,7 @@ (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -2193,7 +2192,7 @@ (((|#2|) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) ((((-384)) . T)) ((((-705)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) @@ -2210,7 +2209,7 @@ (|has| |#1| (-368)) ((((-1186)) |has| |#2| (-907 (-1186)))) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-479)) (|has| |#1| (-373)) @@ -2238,12 +2237,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-856)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)))) ((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)))) ((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2|) . T)) (((|#3|) . T)) ((((-117 |#1|)) . T)) @@ -2263,7 +2262,7 @@ ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#1| (-1031))) (((-227)) . #0#)) (((|#1|) |has| |#1| (-368))) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((($ $) . T) (((-618 $) $) . T)) (-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) ((($) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T)) @@ -2336,7 +2335,7 @@ ((((-959 |#1|)) . T) (((-868)) . T)) (((|#3|) . T)) (((|#1| |#1|) . T) (($ $) -2892 (|has| |#1| (-294)) (|has| |#1| (-368))) ((#0=(-413 (-570)) #0#) |has| |#1| (-368))) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) ((((-959 |#1|)) . T)) ((($) . T)) ((((-570) |#1|) . T)) @@ -2383,7 +2382,7 @@ ((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570)) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))))) +((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))))) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-854)) (|has| |#1| (-38 (-413 (-570)))) @@ -2426,10 +2425,10 @@ ((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-542)) |has| |#4| (-620 (-542)))) ((((-868)) . T) (((-650 |#4|)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-854)) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))))) (|has| |#1| (-1109)) (|has| |#1| (-368)) (((|#1|) . T)) @@ -2474,7 +2473,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) (((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)))) @@ -2513,7 +2512,7 @@ (|has| |#1| (-562)) (((|#2|) . T)) ((((-570)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) (-2892 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) @@ -2652,16 +2651,16 @@ (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) @@ -2683,7 +2682,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2696,7 +2695,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2758,8 +2757,8 @@ (-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) (-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) (-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2339 #0#))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2340 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) @@ -2845,7 +2844,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2873,7 +2872,7 @@ ((((-413 (-570))) . T)) (-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))))) +(((#0=(-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) @@ -2911,7 +2910,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2957,9 +2956,9 @@ (((|#2|) . T)) (((|#2|) . T)) (-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3092,7 +3091,7 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -3154,7 +3153,7 @@ ((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3285,7 +3284,7 @@ (((|#1|) . T)) ((((-868)) . T)) (|has| |#2| (-916)) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-868)) . T)) @@ -3481,7 +3480,7 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) |has| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))))) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) |has| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))))) (-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-570) |#1|) . T)) ((((-570) |#1|) . T)) @@ -3693,7 +3692,7 @@ (-2892 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) ((((-570)) . T)) ((((-570)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) @@ -3800,11 +3799,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#2| (-1031))) (((-227)) . #0#)) ((((-298 |#3|)) . T)) @@ -3859,7 +3858,7 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3896,7 +3895,7 @@ (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3930,10 +3929,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) (((#0=(-117 |#1|)) |has| #0# (-313 #0#))) ((($ $) . T)) (-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((($ $) . T) ((#0=(-870 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-235)) ((|#2| |#1|) |has| |#1| (-235)) ((|#3| |#1|) . T) ((|#3| $) . 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T) ((-651 . -93) T) ((-326 . -1065) 182033) ((-254 . -797) 182012) ((-254 . -800) 181963) ((-31 . -496) 181944) ((-254 . -799) 181923) ((-253 . -797) 181902) ((-253 . -800) 181853) ((-253 . -799) 181832) ((-31 . -619) 181798) ((-50 . -1067) T) ((-254 . -732) 181708) ((-253 . -732) 181618) ((-1221 . -1109) T) ((-676 . -23) T) ((-587 . -1067) T) ((-524 . -1067) T) ((-384 . -1065) 181583) ((-326 . -111) 181558) ((-73 . -388) T) ((-73 . -401) T) ((-1033 . -38) 181495) ((-700 . -406) 181477) ((-99 . -102) T) ((-717 . -1109) T) ((-1305 . -1060) 181464) ((-1012 . -146) 181436) ((-1012 . -148) 181408) ((-876 . -652) 181380) ((-384 . -111) 181336) ((-323 . -1231) 181315) ((-480 . -1011) 181281) ((-359 . -38) 181246) ((-40 . -375) 181218) ((-879 . -619) 181090) ((-128 . -126) 181074) ((-122 . -126) 181058) ((-842 . -1065) 181028) ((-839 . -21) 180980) ((-833 . -1065) 180964) ((-839 . -25) 180916) ((-323 . -562) 180867) ((-523 . -622) 180848) ((-570 . -834) T) ((-242 . -1227) T) ((-1043 . -622) 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-1109) T) ((-601 . -47) 177084) ((-227 . -654) 177049) ((-587 . -1109) T) ((-524 . -1109) T) ((-493 . -826) T) ((-493 . -927) T) ((-364 . -1231) T) ((-358 . -1231) T) ((-350 . -1231) T) ((-323 . -1121) T) ((-320 . -1060) 176959) ((-317 . -1060) 176888) ((-108 . -1231) T) ((-632 . -622) 176869) ((-364 . -562) T) ((-219 . -927) T) ((-219 . -826) T) ((-320 . -646) 176779) ((-317 . -646) 176708) ((-358 . -562) T) ((-350 . -562) T) ((-489 . -622) 176689) ((-108 . -562) T) ((-664 . -723) 176659) ((-1177 . -1031) NIL) ((-220 . -622) 176640) ((-323 . -23) T) ((-67 . -1227) T) ((-1009 . -619) 176572) ((-700 . -233) 176554) ((-720 . -111) 176519) ((-650 . -34) T) ((-247 . -495) 176503) ((-1111 . -1107) 176487) ((-173 . -1109) T) ((-1305 . -1161) T) ((-1301 . -21) T) ((-1301 . -25) T) ((-1299 . -132) T) ((-1297 . -132) T) ((-959 . -916) 176466) ((-1290 . -102) T) ((-1273 . -619) 176432) ((-1262 . -1047) 176367) ((-521 . -622) 176351) ((-1241 . -1227) 176330) ((-1241 . -893) NIL) ((-1241 . -891) 176282) ((-487 . -916) 176261) ((-1241 . -1047) 176227) ((-1221 . -520) 176194) ((-1096 . -723) 176043) ((-1071 . -654) 176030) ((-959 . -654) 175955) ((-603 . -496) 175936) ((-591 . -496) 175917) ((-788 . -723) 175746) ((-603 . -619) 175712) ((-591 . -619) 175678) ((-542 . -619) 175660) ((-542 . -620) 175641) ((-786 . -723) 175490) ((-1086 . -102) T) ((-386 . -25) T) ((-629 . -652) 175462) ((-386 . -21) T) ((-487 . -654) 175387) ((-467 . -723) 175358) ((-460 . -723) 175207) ((-996 . -102) T) ((-1199 . -620) NIL) ((-1199 . -619) 175189) ((-1151 . -1132) 175134) ((-743 . -102) T) ((-118 . -652) 175064) ((-611 . -622) 175046) ((-1055 . -1220) 174975) ((-908 . -313) 174913) ((-537 . -25) T) ((-882 . -93) T) ((-720 . -622) 174867) ((-687 . -93) T) ((-651 . -496) 174848) ((-142 . -102) T) ((-44 . -132) T) ((-682 . -93) T) ((-670 . -619) 174830) ((-348 . -1067) T) ((-293 . -1121) T) ((-651 . -619) 174783) ((-484 . -93) T) ((-360 . -619) 174765) ((-357 . -619) 174747) ((-349 . -619) 174729) 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164033) ((-591 . -622) 164014) ((-542 . -624) 163917) ((-348 . -174) T) ((-88 . -619) 163899) ((-153 . -21) T) ((-153 . -25) T) ((-917 . -111) 163855) ((-40 . -723) 163800) ((-876 . -1109) T) ((-670 . -622) 163777) ((-651 . -622) 163758) ((-360 . -622) 163695) ((-357 . -622) 163632) ((-553 . -1109) T) ((-349 . -622) 163569) ((-331 . -620) 163530) ((-331 . -619) 163442) ((-267 . -622) 163195) ((-249 . -622) 162980) ((-1240 . -798) 162933) ((-1240 . -801) 162886) ((-254 . -382) 162855) ((-253 . -382) 162824) ((-660 . -38) 162794) ((-614 . -34) T) ((-488 . -1121) 162704) ((-481 . -34) T) ((-1122 . -132) 162574) ((-971 . -25) 162385) ((-917 . -622) 162335) ((-880 . -619) 162317) ((-971 . -21) 162272) ((-821 . -21) 162182) ((-821 . -25) 162033) ((-1233 . -373) T) ((-629 . -1067) T) ((-1188 . -562) 162012) ((-1182 . -47) 161989) ((-360 . -1058) T) ((-357 . -1058) T) ((-488 . -23) 161859) ((-349 . -1058) T) ((-267 . -1058) T) ((-249 . -1058) T) ((-1134 . -47) 161831) ((-118 . -1067) T) 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T) ((-570 . -1109) T) ((-501 . -1109) T) ((-247 . -292) 160931) ((-317 . -233) 160892) ((-1182 . -893) NIL) ((-55 . -1109) T) ((-1134 . -893) 160751) ((-130 . -856) T) ((-1182 . -1047) 160631) ((-1134 . -1047) 160514) ((-185 . -619) 160496) ((-860 . -1047) 160392) ((-788 . -290) 160319) ((-823 . -1121) T) ((-1043 . -732) T) ((-608 . -657) 160303) ((-1055 . -985) 160232) ((-1008 . -102) T) ((-823 . -23) T) ((-718 . -1161) 160210) ((-700 . -1067) T) ((-608 . -378) 160194) ((-356 . -458) T) ((-348 . -294) T) ((-1278 . -1109) T) ((-250 . -1109) T) ((-405 . -102) T) ((-293 . -21) T) ((-293 . -25) T) ((-366 . -732) T) ((-716 . -1109) T) ((-705 . -1109) T) ((-366 . -479) T) ((-1221 . -619) 160176) ((-1182 . -382) 160160) ((-1134 . -382) 160144) ((-1033 . -417) 160106) ((-142 . -231) 160088) ((-384 . -800) T) ((-384 . -797) T) ((-876 . -174) T) ((-384 . -732) T) ((-717 . -619) 160070) ((-718 . -38) 159899) ((-1277 . -1275) 159883) ((-356 . -408) T) ((-1277 . -1109) 159833) ((-1200 . -1109) T) 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. -1231) T) ((-1008 . -313) 158978) ((-882 . -622) 158959) ((-720 . -654) 158919) ((-219 . -1231) T) ((-687 . -622) 158900) ((-227 . -1047) 158860) ((-40 . -294) T) ((-682 . -622) 158841) ((-493 . -562) T) ((-484 . -622) 158822) ((-320 . -652) 158506) ((-317 . -652) 158420) ((-364 . -25) T) ((-364 . -21) T) ((-358 . -25) T) ((-219 . -562) T) ((-358 . -21) T) ((-350 . -25) T) ((-350 . -21) T) ((-247 . -622) 158397) ((-139 . -622) 158378) ((-138 . -622) 158359) ((-134 . -622) 158340) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1067) T) ((-586 . -174) T) ((-570 . -174) T) ((-501 . -174) T) ((-664 . -619) 158322) ((-743 . -742) 158306) ((-341 . -619) 158288) ((-68 . -388) T) ((-68 . -401) T) ((-1111 . -107) 158272) ((-1071 . -893) 158254) ((-959 . -893) 158179) ((-659 . -1121) T) ((-629 . -723) 158166) ((-487 . -893) NIL) ((-1155 . -102) T) ((-1103 . -624) 158150) ((-1071 . -1047) 158132) ((-97 . -619) 158114) ((-483 . -148) T) ((-959 . -1047) 157994) ((-118 . -723) 157939) ((-659 . -23) T) 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152751) ((-112 . -620) 152733) ((-724 . -479) T) ((-717 . -622) 152683) ((-1300 . -1060) 152667) ((-488 . -21) 152577) ((-128 . -495) 152561) ((-122 . -495) 152545) ((-488 . -25) 152396) ((-1300 . -646) 152366) ((-629 . -294) T) ((-592 . -1065) 152341) ((-443 . -1109) T) ((-1071 . -311) T) ((-118 . -294) T) ((-1113 . -102) T) ((-1012 . -102) T) ((-592 . -111) 152309) ((-1151 . -313) 152247) ((-1221 . -1058) T) ((-1071 . -1031) T) ((-66 . -1227) T) ((-1063 . -25) T) ((-1063 . -21) T) ((-717 . -1058) T) ((-390 . -21) T) ((-390 . -25) T) ((-700 . -520) NIL) ((-1033 . -174) T) ((-717 . -245) T) ((-1071 . -551) T) ((-718 . -652) 152157) ((-512 . -102) T) ((-508 . -102) T) ((-359 . -174) T) ((-348 . -619) 152139) ((-413 . -1060) 152091) ((-400 . -619) 152073) ((-1129 . -854) T) ((-480 . -732) T) ((-899 . -1047) 152041) ((-413 . -646) 151993) ((-108 . -856) T) ((-664 . -1065) 151977) ((-493 . -132) T) ((-1263 . -1067) T) ((-219 . -132) T) ((-1166 . -102) 151955) ((-99 . -1109) T) ((-247 . 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147292) ((-908 . -1109) 147270) ((-50 . -1058) T) ((-1289 . -21) T) ((-1289 . -25) T) ((-1184 . -562) 147249) ((-1183 . -1231) 147228) ((-1183 . -562) 147179) ((-587 . -1058) T) ((-524 . -1058) T) ((-1177 . -1231) 147158) ((-366 . -1047) 147142) ((-326 . -1047) 147126) ((-1033 . -294) T) ((-384 . -893) 147108) ((-1177 . -562) 147059) ((-1012 . -38) 147004) ((-1008 . -652) 146927) ((-805 . -1121) T) ((-917 . -732) T) ((-587 . -245) T) ((-587 . -235) T) ((-524 . -235) T) ((-524 . -245) T) ((-1135 . -562) 146906) ((-359 . -294) T) ((-653 . -701) 146890) ((-384 . -1047) 146850) ((-298 . -1060) 146771) ((-1129 . -1067) T) ((-103 . -126) 146755) ((-298 . -646) 146697) ((-805 . -23) T) ((-1299 . -1294) 146673) ((-1277 . -290) 146650) ((-413 . -313) 146615) ((-1297 . -1294) 146594) ((-1263 . -1109) T) ((-876 . -619) 146576) ((-842 . -1047) 146545) ((-205 . -793) T) ((-204 . -793) T) ((-203 . -793) T) ((-202 . -793) T) ((-201 . -793) T) ((-200 . -793) T) ((-199 . -793) T) ((-198 . -793) T) 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. -152) 144183) ((-348 . -235) T) ((-348 . -245) T) ((-40 . -1065) 144128) ((-878 . -891) 144112) ((-878 . -893) 144037) ((-718 . -1067) T) ((-700 . -1011) NIL) ((-1261 . -47) 144007) ((-1240 . -47) 143984) ((-1150 . -1019) 143955) ((-3 . |UnionCategory|) T) ((-1129 . -723) 143942) ((-1114 . -619) 143924) ((-1089 . -148) 143903) ((-1089 . -146) 143854) ((-973 . -622) 143838) ((-227 . -927) T) ((-40 . -111) 143767) ((-878 . -1047) 143631) ((-1013 . -368) T) ((-1012 . -233) 143608) ((-707 . -1060) 143595) ((-921 . -368) T) ((-707 . -646) 143582) ((-323 . -1215) 143548) ((-384 . -311) T) ((-323 . -1212) 143514) ((-320 . -174) 143493) ((-317 . -174) T) ((-587 . -1296) 143480) ((-524 . -1296) 143457) ((-364 . -148) 143436) ((-117 . -1060) 143423) ((-364 . -146) 143374) ((-358 . -148) 143353) ((-358 . -146) 143304) ((-350 . -148) 143283) ((-614 . -1203) 143259) ((-117 . -646) 143246) ((-350 . -146) 143197) ((-323 . -35) 143163) ((-481 . -1203) 143142) ((0 . |EnumerationCategory|) T) ((-323 . 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139764) ((-48 . -620) 139709) ((-242 . -132) 139579) ((-1300 . -652) 139538) ((-1250 . -927) 139517) ((-822 . -1231) 139496) ((-394 . -496) 139477) ((-1044 . -520) 139321) ((-394 . -619) 139287) ((-822 . -562) 139218) ((-592 . -654) 139193) ((-267 . -47) 139165) ((-249 . -47) 139122) ((-537 . -515) 139099) ((-586 . -622) 139071) ((-570 . -622) 139043) ((-501 . -622) 138976) ((-1083 . -1227) T) ((-1009 . -1227) T) ((-1269 . -23) T) ((-705 . -1065) 138941) ((-1269 . -1121) T) ((-1262 . -1121) T) ((-1262 . -23) T) ((-1241 . -1121) T) ((-1241 . -23) T) ((-1012 . -375) 138913) ((-112 . -373) T) ((-480 . -907) 138819) ((-1221 . -732) T) ((-911 . -619) 138801) ((-55 . -622) 138783) ((-91 . -107) 138767) ((-1129 . -294) T) ((-912 . -856) 138718) ((-707 . -1161) T) ((-705 . -111) 138674) ((-849 . -652) 138591) ((-602 . -1121) T) ((-601 . -1121) T) ((-718 . -723) 138420) ((-717 . -732) T) ((-1013 . -132) T) ((-980 . -132) T) ((-493 . -856) T) ((-921 . -132) T) ((-805 . -25) T) ((-805 . -21) T) 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NIL) ((-118 . -1065) 137482) ((-460 . -654) 137407) ((-670 . -1047) 137384) ((-629 . -111) 137369) ((-396 . -1060) 137353) ((-360 . -1047) 137337) ((-357 . -1047) 137321) ((-349 . -1047) 137305) ((-267 . -1047) 137149) ((-249 . -1047) 137025) ((-118 . -111) 136954) ((-59 . -1227) T) ((-396 . -646) 136938) ((-627 . -1060) 136922) ((-525 . -1227) T) ((-522 . -1227) T) ((-503 . -1227) T) ((-502 . -1227) T) ((-443 . -619) 136904) ((-440 . -619) 136886) ((-627 . -646) 136870) ((-3 . -102) T) ((-1036 . -1220) 136839) ((-839 . -102) T) ((-695 . -57) 136797) ((-705 . -1058) T) ((-641 . -652) 136766) ((-613 . -652) 136735) ((-50 . -654) 136709) ((-293 . -458) T) ((-482 . -1220) 136678) ((0 . -102) T) ((-587 . -654) 136643) ((-524 . -654) 136588) ((-49 . -102) T) ((-917 . -1047) 136575) ((-705 . -245) T) ((-1089 . -415) 136554) ((-737 . -645) 136502) ((-1008 . -1109) T) ((-718 . -174) 136393) ((-629 . -622) 136288) ((-493 . -1001) 136270) ((-267 . -382) 136254) ((-249 . -382) 136238) ((-405 . -1109) T) ((-1035 . -102) 136216) ((-344 . -38) 136200) ((-219 . -1001) 136182) ((-118 . -622) 136112) ((-176 . -38) 136044) ((-1261 . -311) 136023) ((-1240 . -311) 136002) ((-664 . -732) T) ((-99 . -619) 135984) ((-483 . -1060) 135949) ((-1177 . -645) 135901) ((-483 . -646) 135866) ((-491 . -25) T) ((-491 . -21) T) ((-1240 . -1031) 135818) ((-1066 . -1227) T) ((-629 . -1058) T) ((-384 . -410) T) ((-396 . -102) T) ((-1114 . -624) 135733) ((-267 . -907) 135679) ((-249 . -907) 135656) ((-118 . -1058) T) ((-822 . -1121) T) ((-1096 . -732) T) ((-629 . -235) 135635) ((-627 . -102) T) ((-788 . -732) T) ((-786 . -732) T) ((-419 . -1121) T) ((-118 . -245) T) ((-40 . -373) NIL) ((-118 . -235) NIL) ((-1232 . -856) T) ((-460 . -732) T) ((-822 . -23) T) ((-737 . -25) T) ((-737 . -21) T) ((-1086 . -290) 135614) ((-78 . -402) T) ((-78 . -401) T) ((-539 . -773) 135596) ((-700 . -1065) 135546) ((-1269 . -132) T) ((-1262 . -132) T) ((-1241 . -132) T) ((-1184 . -25) T) ((-1151 . -417) 135530) ((-641 . 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. -619) 131954) ((-805 . -856) 131933) ((-1169 . -152) 131880) ((-1008 . -520) 131792) ((-359 . -235) T) ((-359 . -245) T) ((-394 . -622) 131773) ((-1013 . -25) T) ((-142 . -619) 131755) ((-142 . -620) 131714) ((-917 . -311) T) ((-1013 . -21) T) ((-980 . -25) T) ((-921 . -21) T) ((-921 . -25) T) ((-433 . -21) T) ((-433 . -25) T) ((-849 . -417) 131698) ((-48 . -1058) T) ((-1299 . -1291) 131682) ((-1297 . -1291) 131666) ((-1044 . -610) 131641) ((-320 . -620) 131502) ((-320 . -619) 131484) ((-317 . -620) NIL) ((-317 . -619) 131466) ((-48 . -245) T) ((-48 . -235) T) ((-660 . -290) 131427) ((-556 . -237) 131377) ((-140 . -619) 131344) ((-137 . -619) 131326) ((-115 . -619) 131308) ((-483 . -38) 131273) ((-1301 . -1298) 131252) ((-1292 . -132) T) ((-1300 . -1067) T) ((-1091 . -102) T) ((-88 . -1227) T) ((-506 . -313) NIL) ((-1009 . -107) 131236) ((-896 . -1109) T) ((-892 . -1109) T) ((-1277 . -657) 131220) ((-1277 . -378) 131204) ((-331 . -1227) T) ((-599 . -856) T) ((-1151 . -1109) T) 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. -23) T) ((-1160 . -1092) T) ((-1134 . -23) T) ((-860 . -23) T) ((-487 . -562) 130187) ((-1151 . -723) 130119) ((-676 . -1060) 130103) ((-1155 . -520) 130036) ((-676 . -646) 130020) ((-1044 . -620) NIL) ((-1044 . -619) 130002) ((-96 . -1092) T) ((-872 . -723) 129972) ((-1221 . -47) 129941) ((-254 . -132) T) ((-253 . -132) T) ((-1113 . -1109) T) ((-1012 . -1109) T) ((-62 . -619) 129923) ((-1177 . -856) NIL) ((-1033 . -798) T) ((-1033 . -801) T) ((-1305 . -1065) 129910) ((-1305 . -111) 129895) ((-1269 . -25) T) ((-1269 . -21) T) ((-876 . -654) 129882) ((-1262 . -21) T) ((-1262 . -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 129866) ((-878 . -826) 129845) ((-878 . -927) T) ((-718 . -290) 129772) ((-602 . -21) T) ((-344 . -652) 129731) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 129648) ((-40 . -732) T) ((-224 . -520) 129581) ((-601 . -25) T) ((-482 . -152) 129565) ((-469 . -152) 129549) ((-928 . -800) T) ((-928 . -732) T) ((-777 . -799) T) ((-777 . -800) T) ((-512 . -1109) T) ((-508 . -1109) T) ((-777 . -732) T) ((-227 . -368) T) ((-1299 . -1060) 129533) ((-1297 . -1060) 129517) ((-1299 . -646) 129487) ((-1166 . -1109) 129465) ((-877 . -1231) T) ((-1297 . -646) 129435) ((-660 . -619) 129417) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 129401) ((-1305 . -622) 129383) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 129367) ((-358 . -1284) 129351) ((-44 . -646) 129335) ((-350 . -1284) 129319) ((-554 . -102) T) ((-526 . -856) 129298) ((-1055 . -1109) T) ((-823 . -458) 129277) ((-153 . -1060) 129261) ((-1055 . -1080) 129190) ((-1036 . -985) 129159) ((-825 . -1121) T) ((-1012 . -723) 129104) ((-153 . -646) 129088) ((-392 . -1121) T) ((-482 . -985) 129057) ((-469 . -985) 129026) ((-110 . -152) 129008) ((-73 . -619) 128990) ((-900 . -619) 128972) ((-1089 . -730) 128951) ((-1305 . -1058) T) ((-822 . -645) 128899) ((-298 . -1067) 128841) ((-171 . -1231) 128746) ((-227 . -1121) T) ((-328 . -23) T) ((-1177 . -1001) 128698) ((-849 . -1109) T) 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. -1121) T) ((-118 . -916) NIL) ((-1299 . -1298) 125888) ((-1297 . -1298) 125867) ((-788 . -893) NIL) ((-786 . -893) 125726) ((-1292 . -25) T) ((-1292 . -21) T) ((-1224 . -102) 125704) ((-1115 . -401) T) ((-629 . -654) 125691) ((-460 . -893) NIL) ((-681 . -102) 125669) ((-1096 . -1047) 125496) ((-877 . -23) T) ((-788 . -1047) 125355) ((-786 . -1047) 125212) ((-118 . -654) 125157) ((-460 . -1047) 125033) ((-320 . -622) 124597) ((-317 . -622) 124480) ((-396 . -652) 124449) ((-655 . -1047) 124433) ((-633 . -102) T) ((-224 . -495) 124417) ((-1277 . -34) T) ((-627 . -652) 124376) ((-293 . -1060) 124363) ((-137 . -622) 124347) ((-293 . -646) 124334) ((-641 . -723) 124318) ((-613 . -723) 124302) ((-676 . -38) 124262) ((-323 . -102) T) ((-85 . -619) 124244) ((-50 . -1047) 124228) ((-1129 . -1065) 124215) ((-1096 . -382) 124199) ((-788 . -382) 124183) ((-705 . -732) T) ((-705 . -800) T) ((-705 . -797) T) ((-587 . -1047) 124170) ((-524 . -1047) 124147) ((-60 . -57) 124109) ((-328 . -132) T) 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NIL) ((-118 . -732) T) ((-700 . -916) NIL) ((-1055 . -520) 122854) ((-487 . -132) T) ((-577 . -23) T) ((-681 . -313) 122792) ((-641 . -767) T) ((-613 . -767) T) ((-1241 . -856) NIL) ((-1089 . -1060) 122702) ((-1012 . -294) T) ((-700 . -654) 122652) ((-254 . -21) T) ((-356 . -1109) T) ((-254 . -25) T) ((-253 . -21) T) ((-253 . -25) T) ((-153 . -38) 122636) ((-2 . -102) T) ((-917 . -927) T) ((-1089 . -646) 122504) ((-488 . -1284) 122474) ((-1129 . -1058) T) ((-717 . -311) T) ((-364 . -1060) 122426) ((-358 . -1060) 122378) ((-350 . -1060) 122330) ((-364 . -646) 122282) ((-225 . -1047) 122259) ((-358 . -646) 122211) ((-108 . -1060) 122161) ((-350 . -646) 122113) ((-298 . -723) 122055) ((-707 . -1067) T) ((-493 . -458) T) ((-413 . -520) 121967) ((-108 . -646) 121917) ((-219 . -458) T) ((-1129 . -235) T) ((-299 . -152) 121867) ((-1008 . -620) 121828) ((-1008 . -619) 121810) ((-998 . -619) 121792) ((-117 . -1067) T) ((-660 . -1065) 121776) ((-227 . -499) T) ((-405 . -619) 121758) ((-405 . -620) 121735) ((-1063 . -1284) 121705) ((-660 . -111) 121684) ((-1151 . -495) 121668) ((-1301 . -652) 121627) ((-386 . -652) 121596) ((-821 . -38) 121566) ((-63 . -447) T) ((-63 . -401) T) ((-1169 . -102) T) ((-877 . -132) T) ((-490 . -102) 121544) ((-1305 . -373) T) ((-1089 . -102) T) ((-1070 . -102) T) ((-356 . -723) 121489) ((-737 . -148) 121468) ((-737 . -146) 121447) ((-660 . -622) 121365) ((-1033 . -654) 121302) ((-529 . -1109) 121280) ((-364 . -102) T) ((-358 . -102) T) ((-350 . -102) T) ((-108 . -102) T) ((-510 . -1109) T) ((-359 . -654) 121225) ((-1182 . -645) 121173) ((-1134 . -645) 121121) ((-390 . -515) 121100) ((-839 . -854) 121079) ((-384 . -1231) T) ((-700 . -732) T) ((-1241 . -1001) 121031) ((-344 . -1067) T) ((-112 . -1227) T) ((-176 . -1067) T) ((-103 . -619) 120963) ((-1184 . -146) 120942) ((-1184 . -148) 120921) ((-384 . -562) T) ((-1183 . -148) 120900) ((-1183 . -146) 120879) ((-1177 . -146) 120786) ((-413 . -294) T) ((-1177 . -148) 120693) ((-1135 . -148) 120672) 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. -235) T) ((-707 . -723) 117233) ((-344 . -1109) T) ((-176 . -1109) T) ((-335 . -856) T) ((-424 . -458) 117183) ((-384 . -23) T) ((-364 . -38) 117148) ((-358 . -38) 117113) ((-350 . -38) 117078) ((-80 . -447) T) ((-80 . -401) T) ((-227 . -25) T) ((-227 . -21) T) ((-842 . -1121) T) ((-108 . -38) 117028) ((-833 . -1121) T) ((-780 . -1109) T) ((-117 . -723) 117015) ((-678 . -1047) 116999) ((-618 . -102) T) ((-842 . -23) T) ((-833 . -23) T) ((-1166 . -290) 116976) ((-1122 . -313) 116914) ((-488 . -1060) 116811) ((-1111 . -237) 116795) ((-64 . -402) T) ((-64 . -401) T) ((-1160 . -102) T) ((-110 . -102) T) ((-488 . -646) 116737) ((-40 . -382) 116714) ((-96 . -102) T) ((-659 . -858) 116698) ((-1144 . -1092) T) ((-1071 . -21) T) ((-1071 . -25) T) ((-1063 . -1060) 116682) ((-821 . -233) 116651) ((-959 . -25) T) ((-959 . -21) T) ((-1063 . -646) 116593) ((-627 . -1067) T) ((-1129 . -373) T) ((-1036 . -313) 116531) ((-676 . -652) 116490) ((-487 . -25) T) ((-487 . -21) T) ((-390 . -1060) 116474) 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. -1047) 111511) ((-650 . -856) 111490) ((-1289 . -102) T) ((-299 . -102) T) ((-718 . -373) 111469) ((-118 . -1047) 111446) ((-396 . -723) 111430) ((-627 . -723) 111414) ((-45 . -313) 111218) ((-822 . -146) 111197) ((-822 . -148) 111176) ((-293 . -652) 111148) ((-1300 . -387) 111127) ((-825 . -856) T) ((-1279 . -1109) T) ((-1169 . -231) 111074) ((-392 . -856) 111053) ((-1269 . -1215) 111019) ((-1269 . -1212) 110985) ((-1262 . -1212) 110951) ((-521 . -132) T) ((-1262 . -1215) 110917) ((-1241 . -1212) 110883) ((-1241 . -1215) 110849) ((-1269 . -35) 110815) ((-1269 . -95) 110781) ((-641 . -619) 110750) ((-613 . -619) 110719) ((-227 . -856) T) ((-1262 . -95) 110685) ((-1262 . -35) 110651) ((-1261 . -1121) T) ((-1129 . -654) 110638) ((-1241 . -95) 110604) ((-1240 . -1121) T) ((-599 . -152) 110586) ((-1089 . -354) 110565) ((-176 . -294) T) ((-118 . -382) 110542) ((-118 . -343) 110519) ((-1241 . -35) 110485) ((-876 . -311) T) ((-317 . -800) NIL) ((-317 . -797) NIL) ((-320 . -732) 110334) 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. -622) 108117) ((-877 . -856) NIL) ((-570 . -1031) T) ((-501 . -1031) T) ((-1142 . -619) 108099) ((-1122 . -240) 108078) ((-216 . -102) T) ((-1159 . -102) T) ((-71 . -619) 108060) ((-1151 . -1058) T) ((-1188 . -38) 107957) ((-864 . -619) 107939) ((-570 . -551) T) ((-676 . -1067) T) ((-737 . -956) 107892) ((-1151 . -235) 107871) ((-1091 . -1109) T) ((-1043 . -25) T) ((-1043 . -21) T) ((-1012 . -1065) 107816) ((-912 . -102) T) ((-872 . -1058) T) ((-700 . -907) NIL) ((-360 . -333) 107800) ((-360 . -368) T) ((-357 . -333) 107784) ((-357 . -368) T) ((-349 . -333) 107768) ((-349 . -368) T) ((-493 . -102) T) ((-1289 . -38) 107738) ((-552 . -856) T) ((-529 . -693) 107688) ((-219 . -102) T) ((-1033 . -1047) 107568) ((-1012 . -111) 107497) ((-1184 . -982) 107466) ((-526 . -152) 107450) ((-1089 . -375) 107429) ((-356 . -619) 107411) ((-326 . -21) T) ((-359 . -1047) 107388) ((-326 . -25) T) ((-1183 . -982) 107350) ((-1177 . -982) 107319) ((-76 . -619) 107301) ((-1135 . -982) 107268) ((-705 . 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. -1260) 97813) ((-1262 . -1255) 97783) ((-1262 . -1258) 97767) ((-1241 . -1239) 97728) ((-1241 . -1255) 97705) ((-627 . -619) 97687) ((-1241 . -1237) 97671) ((-705 . -927) T) ((-1184 . -288) 97637) ((-1183 . -288) 97603) ((-1177 . -288) 97569) ((-1089 . -1109) T) ((-1070 . -1109) T) ((-48 . -306) T) ((-320 . -907) 97535) ((-317 . -907) NIL) ((-1070 . -1077) 97514) ((-1129 . -893) 97496) ((-805 . -38) 97480) ((-267 . -645) 97428) ((-249 . -645) 97376) ((-707 . -1065) 97363) ((-601 . -1255) 97340) ((-1135 . -288) 97306) ((-323 . -174) 97237) ((-364 . -1109) T) ((-358 . -1109) T) ((-350 . -1109) T) ((-506 . -19) 97219) ((-1129 . -1047) 97201) ((-1111 . -152) 97185) ((-108 . -1109) T) ((-117 . -1065) 97172) ((-717 . -368) T) ((-506 . -610) 97147) ((-707 . -111) 97132) ((-442 . -102) T) ((-882 . -1272) T) ((-252 . -102) T) ((-45 . -1158) 97082) ((-117 . -111) 97067) ((-641 . -726) T) ((-613 . -726) T) ((-1279 . -619) 97049) ((-1235 . -619) 97031) ((-1233 . -856) T) ((-821 . -520) 96964) 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. -313) 92245) ((-1096 . -1121) T) ((-1300 . -654) 92219) ((-788 . -1121) T) ((-786 . -1121) T) ((-460 . -1121) T) ((-1071 . -458) T) ((-1160 . -1109) T) ((-959 . -458) 92170) ((-1124 . -1092) T) ((-110 . -1109) T) ((-1096 . -23) T) ((-823 . -1067) T) ((-788 . -23) T) ((-786 . -23) T) ((-487 . -458) 92121) ((-1169 . -520) 91904) ((-386 . -387) 91883) ((-1188 . -417) 91867) ((-467 . -23) T) ((-460 . -23) T) ((-96 . -1109) T) ((-490 . -520) 91800) ((-1269 . -1060) 91683) ((-1269 . -646) 91580) ((-1262 . -646) 91421) ((-1262 . -1060) 91256) ((-293 . -294) T) ((-1241 . -1060) 91046) ((-1091 . -619) 91028) ((-1091 . -620) 91009) ((-413 . -916) 90988) ((-1241 . -646) 90784) ((-50 . -1121) T) ((-1221 . -132) T) ((-1033 . -927) T) ((-1012 . -732) T) ((-849 . -654) 90757) ((-718 . -893) NIL) ((-602 . -1060) 90717) ((-587 . -1121) T) ((-524 . -1121) T) ((-601 . -1060) 90600) ((-1177 . -406) 90552) ((-1013 . -313) NIL) ((-821 . -495) 90536) ((-602 . -646) 90509) ((-359 . -927) T) ((-601 . -646) 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. -800) 88190) ((-849 . -797) 88169) ((-849 . -732) 88148) ((-364 . -294) T) ((-358 . -294) T) ((-350 . -294) T) ((-171 . -458) 88079) ((-433 . -38) 88063) ((-108 . -294) T) ((-225 . -23) T) ((-413 . -800) 88042) ((-413 . -797) 88021) ((-413 . -732) T) ((-506 . -292) 87996) ((-483 . -1065) 87961) ((-664 . -132) T) ((-627 . -622) 87930) ((-1122 . -520) 87863) ((-341 . -132) T) ((-171 . -408) 87842) ((-488 . -723) 87784) ((-821 . -290) 87761) ((-483 . -111) 87717) ((-659 . -1067) T) ((-822 . -1060) 87560) ((-1288 . -1092) T) ((-1250 . -458) 87491) ((-822 . -646) 87340) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87282) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87215) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-45 . -1109) T) ((-390 . -723) 87185) ((-823 . -1109) T) ((-482 . -520) 87118) ((-469 . -520) 87051) ((-459 . -372) 87021) ((-45 . -616) 87000) ((-320 . -306) T) ((-483 . -622) 86950) ((-1241 . 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82697) ((-356 . -732) T) ((-867 . -619) 82679) ((-1183 . -652) 82561) ((-1177 . -652) 82398) ((-1135 . -652) 82308) ((-1241 . -406) 82260) ((-1122 . -495) 82244) ((-60 . -313) 82182) ((-335 . -102) T) ((-1221 . -21) T) ((-1221 . -25) T) ((-40 . -1121) T) ((-717 . -21) T) ((-633 . -619) 82164) ((-521 . -327) 82143) ((-717 . -25) T) ((-445 . -102) T) ((-108 . -290) NIL) ((-928 . -1121) T) ((-40 . -23) T) ((-777 . -1121) T) ((-570 . -1231) T) ((-501 . -1231) T) ((-323 . -619) 82125) ((-1013 . -233) 82107) ((-171 . -167) 82091) ((-586 . -562) T) ((-570 . -562) T) ((-501 . -562) T) ((-777 . -23) T) ((-1261 . -148) 82070) ((-1169 . -610) 82046) ((-1261 . -146) 82025) ((-1036 . -495) 82009) ((-1240 . -146) 81934) ((-1240 . -148) 81859) ((-1292 . -1298) 81838) ((-482 . -495) 81822) ((-469 . -495) 81806) ((-529 . -34) T) ((-659 . -723) 81776) ((-112 . -976) T) ((-668 . -856) 81755) ((-1188 . -174) 81706) ((-370 . -102) T) ((-242 . -240) 81685) ((-254 . -102) T) ((-253 . -102) T) ((-1250 . -956) 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. -458) T) ((-1033 . -148) T) ((-950 . -290) 31595) ((-317 . -856) NIL) ((-1261 . -652) 31477) ((-880 . -102) T) ((-1240 . -652) 31332) ((-718 . -25) T) ((-413 . -562) T) ((-718 . -21) T) ((-531 . -622) 31313) ((-359 . -148) 31295) ((-359 . -146) T) ((-1156 . -1109) 31273) ((-459 . -726) T) ((-75 . -619) 31255) ((-115 . -856) T) ((-247 . -286) 31239) ((-242 . -1065) 31136) ((-81 . -619) 31118) ((-741 . -373) 31071) ((-1186 . -834) T) ((-743 . -237) 31055) ((-1169 . -1227) T) ((-142 . -237) 31037) ((-242 . -111) 30927) ((-1250 . -723) 30756) ((-48 . -148) T) ((-877 . -174) T) ((-861 . -723) 30726) ((-490 . -1227) T) ((-959 . -520) 30673) ((-659 . -732) T) ((-577 . -723) 30660) ((-1043 . -1067) T) ((-487 . -520) 30603) ((-950 . -19) 30587) ((-950 . -610) 30564) ((-822 . -620) NIL) ((-822 . -619) 30546) ((-1221 . -1060) 30429) ((-1013 . -1065) 30379) ((-419 . -619) 30361) ((-254 . -290) 30338) ((-253 . -290) 30315) ((-493 . -916) NIL) ((-320 . -29) 30285) ((-108 . -1227) T) ((-1012 . 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. -21) T) ((-1089 . -25) T) ((-493 . -1231) T) ((-1008 . -313) 158953) ((-882 . -622) 158934) ((-720 . -654) 158894) ((-219 . -1231) T) ((-687 . -622) 158875) ((-227 . -1047) 158835) ((-40 . -294) T) ((-682 . -622) 158816) ((-493 . -562) T) ((-484 . -622) 158797) ((-320 . -652) 158481) ((-317 . -652) 158395) ((-364 . -25) T) ((-364 . -21) T) ((-358 . -25) T) ((-219 . -562) T) ((-358 . -21) T) ((-350 . -25) T) ((-350 . -21) T) ((-247 . -622) 158372) ((-139 . -622) 158353) ((-138 . -622) 158334) ((-134 . -622) 158315) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1067) T) ((-586 . -174) T) ((-570 . -174) T) ((-501 . -174) T) ((-664 . -619) 158297) ((-743 . -742) 158281) ((-341 . -619) 158263) ((-68 . -388) T) ((-68 . -401) T) ((-1111 . -107) 158247) ((-1071 . -893) 158229) ((-959 . -893) 158154) ((-659 . -1121) T) ((-629 . -723) 158141) ((-487 . -893) NIL) ((-1155 . -102) T) ((-1103 . -624) 158125) ((-1071 . -1047) 158107) ((-97 . -619) 158089) ((-483 . -148) T) ((-959 . -1047) 157969) 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. -562) T) ((-822 . -25) T) ((-822 . -21) T) ((-1151 . -520) 127607) ((-598 . -1092) T) ((-592 . -1047) 127591) ((-1263 . -622) 127465) ((-487 . -23) T) ((-356 . -1067) T) ((-1221 . -907) 127446) ((-676 . -313) 127384) ((-1122 . -1284) 127354) ((-705 . -654) 127319) ((-1012 . -174) T) ((-970 . -146) 127298) ((-641 . -1109) T) ((-613 . -1109) T) ((-970 . -148) 127277) ((-1013 . -856) T) ((-741 . -148) 127256) ((-741 . -146) 127235) ((-980 . -856) T) ((-839 . -652) 127152) ((-480 . -927) 127131) ((-323 . -1060) 126966) ((-320 . -1065) 126876) ((-317 . -1065) 126805) ((-1008 . -290) 126763) ((-413 . -723) 126715) ((-323 . -646) 126556) ((-707 . -854) T) ((-1263 . -1058) T) ((-320 . -111) 126452) ((-317 . -111) 126365) ((-971 . -102) T) ((-821 . -102) 126155) ((-718 . -620) NIL) ((-718 . -619) 126137) ((-664 . -1047) 126033) ((-1263 . -330) 125977) ((-1044 . -292) 125952) ((-586 . -732) T) ((-570 . -800) T) ((-171 . -368) 125903) ((-570 . -797) T) ((-570 . -732) T) ((-501 . -732) T) 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. -148) 120668) ((-1135 . -148) 120647) ((-1135 . -146) 120626) ((-323 . -38) 120467) ((-171 . -132) T) ((-317 . -801) NIL) ((-317 . -798) NIL) ((-660 . -1058) T) ((-48 . -654) 120432) ((-1122 . -1060) 120329) ((-900 . -622) 120306) ((-1122 . -646) 120248) ((-1176 . -102) T) ((-1003 . -102) T) ((-1002 . -21) T) ((-128 . -1019) 120232) ((-122 . -1019) 120216) ((-1002 . -25) T) ((-908 . -120) 120200) ((-1168 . -102) T) ((-1250 . -132) T) ((-1182 . -25) T) ((-1182 . -21) T) ((-861 . -132) T) ((-1134 . -25) T) ((-1134 . -21) T) ((-860 . -25) T) ((-860 . -21) T) ((-788 . -311) 120179) ((-653 . -102) 120157) ((-638 . -102) T) ((-1169 . -313) 119952) ((-577 . -132) T) ((-627 . -854) 119931) ((-1166 . -495) 119915) ((-1159 . -152) 119865) ((-1155 . -619) 119827) ((-1155 . -620) 119788) ((-1033 . -797) T) ((-1033 . -800) T) ((-1033 . -732) T) ((-718 . -1065) 119611) ((-490 . -313) 119549) ((-459 . -423) 119519) ((-356 . -174) T) ((-293 . -38) 119506) ((-277 . -102) T) ((-276 . -102) T) ((-275 . 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. -891) 111603) ((-118 . -893) NIL) ((-629 . -1047) 111486) ((-650 . -856) 111465) ((-1289 . -102) T) ((-299 . -102) T) ((-718 . -373) 111444) ((-118 . -1047) 111421) ((-396 . -723) 111405) ((-627 . -723) 111389) ((-45 . -313) 111193) ((-822 . -146) 111172) ((-822 . -148) 111151) ((-293 . -652) 111123) ((-1300 . -387) 111102) ((-825 . -856) T) ((-1279 . -1109) T) ((-1169 . -231) 111049) ((-392 . -856) 111028) ((-1269 . -1215) 110994) ((-1269 . -1212) 110960) ((-1262 . -1212) 110926) ((-521 . -132) T) ((-1262 . -1215) 110892) ((-1241 . -1212) 110858) ((-1241 . -1215) 110824) ((-1269 . -35) 110790) ((-1269 . -95) 110756) ((-641 . -619) 110725) ((-613 . -619) 110694) ((-227 . -856) T) ((-1262 . -95) 110660) ((-1262 . -35) 110626) ((-1261 . -1121) T) ((-1129 . -654) 110613) ((-1241 . -95) 110579) ((-1240 . -1121) T) ((-599 . -152) 110561) ((-1089 . -354) 110540) ((-176 . -294) T) ((-118 . -382) 110517) ((-118 . -343) 110494) ((-1241 . -35) 110460) ((-876 . -311) T) ((-317 . -800) NIL) 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. -652) 88234) ((-921 . -38) 88186) ((-849 . -800) 88165) ((-849 . -797) 88144) ((-849 . -732) 88123) ((-364 . -294) T) ((-358 . -294) T) ((-350 . -294) T) ((-171 . -458) 88054) ((-433 . -38) 88038) ((-108 . -294) T) ((-225 . -23) T) ((-413 . -800) 88017) ((-413 . -797) 87996) ((-413 . -732) T) ((-506 . -292) 87971) ((-483 . -1065) 87936) ((-664 . -132) T) ((-627 . -622) 87905) ((-1122 . -520) 87838) ((-341 . -132) T) ((-171 . -408) 87817) ((-488 . -723) 87759) ((-821 . -290) 87736) ((-483 . -111) 87692) ((-659 . -1067) T) ((-822 . -1060) 87535) ((-1288 . -1092) T) ((-1250 . -458) 87466) ((-822 . -646) 87315) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87257) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87190) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-45 . -1109) T) ((-390 . -723) 87160) ((-823 . -1109) T) ((-482 . -520) 87093) ((-469 . -520) 87026) ((-459 . -372) 86996) ((-45 . -616) 86975) ((-320 . -306) T) ((-483 . -622) 86925) ((-1241 . -313) 86810) ((-676 . -619) 86772) ((-59 . -856) 86751) ((-1013 . -406) 86733) ((-554 . -619) 86715) ((-805 . -652) 86674) ((-821 . -610) 86651) ((-522 . -856) 86630) ((-502 . -856) 86609) ((-40 . -1231) T) ((-1008 . -1047) 86505) ((-50 . -132) T) ((-587 . -132) T) ((-524 . -132) T) ((-298 . -654) 86365) ((-348 . -333) 86342) ((-348 . -368) T) ((-326 . -327) 86319) ((-323 . -290) 86304) ((-40 . -562) T) ((-384 . -1212) T) ((-384 . -1215) T) ((-1044 . -1203) 86279) ((-1199 . -237) 86229) ((-1177 . -233) 86181) ((-334 . -1109) T) ((-384 . -95) T) ((-384 . -35) T) ((-1044 . -107) 86127) ((-483 . -1058) T) ((-1301 . -1065) 86111) ((-485 . -237) 86061) ((-1169 . -495) 85995) ((-1292 . -1060) 85979) ((-386 . -1065) 85963) ((-1292 . -646) 85933) ((-483 . -245) T) ((-822 . -102) T) ((-720 . -148) 85912) ((-720 . -146) 85891) ((-490 . -495) 85875) ((-491 . -340) 85844) ((-1301 . -111) 85823) ((-518 . -1109) T) ((-488 . -174) 85802) ((-1008 . -382) 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. -245) 69918) ((-219 . -294) T) ((-130 . -373) T) ((-1261 . -458) 69897) ((-1240 . -458) 69876) ((-359 . -333) 69853) ((-359 . -368) T) ((-1149 . -619) 69835) ((-45 . -1265) 69785) ((-877 . -102) T) ((-650 . -286) 69769) ((-705 . -1069) T) ((-1288 . -102) T) ((-1287 . -102) T) ((-483 . -654) 69734) ((-474 . -1109) T) ((-45 . -610) 69659) ((-1168 . -292) 69634) ((-293 . -622) 69606) ((-40 . -645) 69545) ((-1250 . -1060) 69368) ((-861 . -1060) 69352) ((-48 . -368) T) ((-1115 . -619) 69334) ((-1250 . -646) 69163) ((-861 . -646) 69133) ((-638 . -292) 69108) ((-822 . -652) 69018) ((-577 . -1060) 69005) ((-488 . -619) 68736) ((-242 . -417) 68705) ((-959 . -313) 68692) ((-577 . -646) 68679) ((-65 . -1227) T) ((-1072 . -520) 68523) ((-677 . -1109) T) ((-629 . -132) T) ((-487 . -313) 68510) ((-612 . -1109) T) ((-552 . -102) T) ((-118 . -132) T) ((-293 . -1058) T) ((-182 . -1109) T) ((-162 . -1109) T) ((-157 . -1109) T) ((-155 . -1109) T) ((-459 . -767) T) ((-31 . -1092) T) ((-970 . -174) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 2495bdd3..ed019478 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3480761522) +(30 . 3480886509) (4452 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,664 +484,661 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |gcdcofactprim| |trivialIdeal?| |antiCommutator| - |tanSum| |pi| |divide| |csch2sinh| |mapExponents| |f02aaf| F2FG - |indicialEquations| |ode2| |divisors| |content| |cExp| |infinity| - |cAsinh| |more?| |infix| |strongGenerators| |allRootsOf| |simpsono| - |reduction| |meshPar2Var| 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|complete| - |irreducibleRepresentation| |curry| |d01anf| |d03edf| |setlast!| - |deleteRoutine!| |listLoops| |nothing| |SturmHabichtMultiple| - |showRegion| |irForm| |stFunc2| |reify| |option| |iicsch| - |domainTemplate| |extractPoint| |qualifier| |sizePascalTriangle| - |constantCoefficientRicDE| |showSummary| |cAsec| |diagonal| - |increasePrecision| |palgRDE| |shellSort| |disjunction| |localUnquote| - |commonDenominator| |pr2dmp| |algebraicSort| |empty| |viewDefaults| - |univcase| |stFuncN| |inR?| |permutationRepresentation| |bumptab| - |bigEndian| |recur| |stiffnessAndStabilityOfODEIF| |setVariableOrder| - |showAttributes| |semiResultantEuclidean2| |atanIfCan| |dualSignature| - |rightTraceMatrix| |linearMatrix| |unknown| |writeByte!| |mkcomm| - |basisOfLeftNucloid| |iipow| |separant| |iprint| |digit| |macroExpand| - |mainForm| |RemainderList| |critMonD1| |rightTrim| - |selectMultiDimensionalRoutines| |arbitrary| |nthFractionalTerm| - |iicosh| |primes| |totalGroebner| |setMaxPoints3D| |operators| - |att2Result| |OMserve| |euclideanSize| |leftTrim| |constantOpIfCan| - |increase| |systemSizeIF| |polyRicDE| |upperCase!| |iicos| |crest| - |exprHasAlgebraicWeight| |exponent| |packageCall| - |showTheRoutinesTable| |eulerPhi| |polynomialZeros| |insertionSort!| - |e01daf| |possiblyInfinite?| |btwFact| |tab1| |say| F |splitNodeOf!| - |viewport2D| |dfRange| |maxint| |leftUnits| |subscript| |critBonD| - |raisePolynomial| |enterInCache| |modularGcd| |makeViewport2D| - |parabolicCylindrical| |perfectSquare?| |cyclotomicDecomposition| - |f01rdf| |OMgetString| |makeMulti| |fixedPointExquo| - |genericLeftTrace| |prefixRagits| |createIrreduciblePoly| |eof?| - |ranges| |graphs| |rangePascalTriangle| |OMconnectTCP| |setImagSteps| - |lazy?| |ideal| |quasiComponent| |f02ajf| |parametersOf| |twoFactor| - |remove| |function| |multivariate| |fortranCarriageReturn| - |OMgetEndAttr| |nullary?| |recolor| |binomThmExpt| |sqfree| |fortran| - |quotedOperators| |hex| |evaluate| |variables| |toseInvertible?| - |slash| |result| |someBasis| |sechIfCan| |integralCoordinates| - |qinterval| |polar| |split| |doubleResultant| |lazyGintegrate| |open| - |nthr| |printHeader| |last| |showTheFTable| |eval| |reset| - |applyRules| |inconsistent?| |squareTop| |d01apf| |setAdaptive| - |assoc| |bat1| |elliptic| |OMgetAtp| |character?| |null| |top!| - |expextendedint| |tanQ| |elseBranch| |exponents| |numberOfCycles| - |smith| |functionIsContinuousAtEndPoints| |outputFixed| |setFieldInfo| - |pattern| |c06gbf| |not| |e01bef| |wronskianMatrix| |write| - |blankSeparate| |red| |ip4Address| |explogs2trigs| |calcRanges| - |e02agf| |factorPolynomial| |and| |crushedSet| |currentScope| - |rischNormalize| |Lazard2| |save| |noLinearFactor?| |leadingExponent| - |changeVar| |rotate!| |sylvesterMatrix| |OMParseError?| |operations| - |pascalTriangle| |taylor| |or| |returnTypeOf| |terms| - |screenResolution3D| |mainVariables| |ellipticCylindrical| - |OMconnOutDevice| |reduceBasisAtInfinity| |symmetricPower| - |splitDenominator| |factorOfDegree| |diag| |lepol| |probablyZeroDim?| - |realZeros| |xor| |laurent| |se2rfi| |cAcosh| |polyred| |secIfCan| - |nextsubResultant2| |reducedContinuedFraction| |nullSpace| |divisor| - |bounds| |leftRecip| |message| |symbolTableOf| |case| |puiseux| - |acotIfCan| |isPlus| |integral| |headAst| |purelyAlgebraic?| - |reducedForm| |convergents| |linSolve| |f01brf| |Zero| |sign| - |getStream| |asinhIfCan| |unravel| |number?| |changeMeasure| - |denomLODE| |hi| |isMult| |cothIfCan| |s14aaf| |inv| |One| - |getExplanations| |intersect| |showTheSymbolTable| |splitSquarefree| - |redmat| |sPol| |hspace| |moebiusMu| |conditionsForIdempotents| - |wholeRagits| |extractBottom!| |yCoordinates| |printTypes| |ground?| - |ptFunc| |fortranInteger| |odd?| |nthExpon| |pToDmp| |outlineRender| - |setErrorBound| |tan2trig| |outputMeasure| |ground| - |useSingleFactorBound?| |startTableInvSet!| |lcm| |dequeue!| - |orthonormalBasis| |s17acf| |selectfirst| |nthCoef| - |completeEchelonBasis| |solve1| |exists?| |aQuartic| |complex?| - |normal?| |rightDivide| |leadingMonomial| |cscIfCan| |fixedPoints| - |errorKind| |getCurve| |palglimint0| |subMatrix| |prologue| - |brillhartTrials| |lexTriangular| |append| |stFunc1| - |leadingCoefficient| |asechIfCan| |reducedSystem| |firstNumer| - |inverseIntegralMatrix| |randnum| |check| |solveLinear| - |maximumExponent| |s21baf| |setMinPoints3D| |primitiveMonomials| - |pade| |elt| |viewWriteDefault| |gcd| |output| |computeBasis| - |rightRemainder| |findCycle| |midpoints| |birth| |makeYoungTableau| - |f07adf| |setOrder| |ratDenom| |denominators| |rightTrace| |addMatch| - |false| |reductum| |semiDegreeSubResultantEuclidean| |ref| |droot| - |subscriptedVariables| |closedCurve| |normalElement| |factorFraction| - |cAcsc| |cyclicCopy| |normalDeriv| |inverseLaplace| |gcdprim| - |backOldPos| |f2st| |decrease| |sqfrFactor| |principal?| - |getPickedPoints| |lyndonIfCan| |semiIndiceSubResultantEuclidean| - |OMputBind| |createRandomElement| |element?| |cLog| |edf2fi| - |nilFactor| |permutations| |read!| |degree| |getMatch| - |pseudoRemainder| |solid?| |multisect| |bubbleSort!| |infLex?| - |ridHack1| |singularitiesOf| |definingInequation| |Ci| |d01fcf| - |rootSimp| |exprHasWeightCosWXorSinWX| |argument| |collect| |e04fdf| - |unitCanonical| |hasHi| |mapDown!| |resultantEuclidean| |ramified?| - |subNodeOf?| |elaborateFile| |c05nbf| |OMsend| |numberOfComposites| - |adaptive?| |copyInto!| |cCsch| |readUInt16!| |badValues| |categories| - |univariatePolynomial| |ode1| |generalizedContinuumHypothesisAssumed?| - |legendreP| |removeRedundantFactors| |graphStates| |eigenvalues| - |d01bbf| |PDESolve| |directSum| |cosh2sech| |makeVariable| - |lfextendedint| |rroot| |outputAsScript| |wreath| |leadingBasisTerm| - |d03faf| |e01bgf| |bivariatePolynomials| |iroot| |alphabetic?| - |lookupFunction| |ramifiedAtInfinity?| |imagI| |difference| |besselK| - |topFortranOutputStack| |selectIntegrationRoutines| |iiacosh| - |clearFortranOutputStack| |block| |stoseSquareFreePart| - |mapUnivariate| |screenResolution| |numericalIntegration| - |getOperator| |sin2csc| |d01asf| |radicalEigenvectors| |getProperties| - |rubiksGroup| |weakBiRank| |curryLeft| |setRow!| |distdfact| - |indiceSubResultant| |mvar| |plusInfinity| |zeroMatrix| |lflimitedint| - |leftLcm| |countRealRoots| |mapmult| |rangeIsFinite| |quotientByP| - |monic?| |inverseColeman| |c02aff| |subPolSet?| |minusInfinity| - |splitLinear| |e02bdf| |leftCharacteristicPolynomial| |nodes| - |iiacoth| |lex| |bottom!| |normalize| |principalIdeal| |nullity| - |rightNorm| |stirling2| |encodingDirectory| |linears| |csc2sin| - |unary?| |rename| |divideIfCan!| |trailingCoefficient| |singular?| - |presuper| |bat| |trace2PowMod| |algint| |s13aaf| |orbit| |key| - |sort!| |cyclotomic| |edf2ef| |minPol| |generic| |interpolate| - |stripCommentsAndBlanks| |subSet| |sinhIfCan| |high| |children| - |polyPart| |OMmakeConn| |unitNormal| |var1StepsDefault| |safeCeiling| - |infRittWu?| |simplify| |filename| |coordinates| |truncate| - |tubePointsDefault| |inRadical?| |setScreenResolution| |coord| - |extractClosed| |s17dhf| |removeZero| |type| |is?| |acscIfCan| - |ef2edf| |isConnected?| |minIndex| |divideIfCan| |variable?| - |coefChoose| |shiftRoots| |diophantineSystem| |aspFilename| - |wordsForStrongGenerators| |cycleLength| |parse| |createThreeSpace| - |sayLength| |hdmpToP| |d01ajf| |leaf?| |minPoly| |sdf2lst| - |scanOneDimSubspaces| |next| |e01bhf| |rightZero| |kmax| |var1Steps| - |iiacos| |in?| |removeCosSq| |safeFloor| |pushdterm| |cycleElt| - |clearDenominator| |setPosition| |inHallBasis?| |integralAtInfinity?| - |rationalPoint?| |ldf2vmf| |pointData| |s15aef| |OMputString| - |var2Steps| |e02ddf| |rightMult| |compose| |integralMatrixAtInfinity| - |trunc| |iiGamma| |groebgen| |explicitlyFinite?| |checkPrecision| - |scalarMatrix| |deleteProperty!| |copy!| |internalLastSubResultant| - |aLinear| |f07fef| |readLine!| |realRoots| |drawToScale| - |selectPDERoutines| |supDimElseRittWu?| EQ |nand| |qqq| |nthFactor| - |pushuconst| |harmonic| |reseed| |completeHensel| - |rewriteIdealWithQuasiMonicGenerators| |f02agf| |nextPrime| |iifact| - |leviCivitaSymbol| |diff| |B1solve| |lhs| |associates?| |octon| - |resultantReduit| |child?| |basisOfNucleus| |typeLists| |HenselLift| - |complexRoots| |complexElementary| |radicalEigenvector| |rhs| - |OMbindTCP| |getGoodPrime| |interval| |twist| |delay| |movedPoints| - |hermite| |dequeue| |generalPosition| |fprindINFO| |e01sff| |double?| - |startTableGcd!| |charClass| |ran| |powern| |push!| |buildSyntax| - |unrankImproperPartitions0| |reduceByQuasiMonic| |karatsubaDivide| - |pointSizeDefault| |basisOfCentroid| |e01baf| |associatorDependence| - |LyndonWordsList1| |iisin| |nextPartition| |sumOfDivisors| |rule| - |invmod| |selectODEIVPRoutines| |decomposeFunc| - |combineFeatureCompatibility| |stopMusserTrials| |nonLinearPart| - |isOpen?| |distFact| |revert| |merge!| |index| |prepareDecompose| - |antisymmetric?| |extractIndex| |cSech| |moreAlgebraic?| - |groebnerFactorize| |interReduce| |toScale| |coHeight| |frobenius| - |asimpson| |nextNormalPrimitivePoly| |squareFreePart| |innerSolve1| - |badNum| |constDsolve| |recip| |hexDigit| |viewDeltaXDefault| - |padicFraction| |Is| |center| |schema| |generalInfiniteProduct| - |fortranLinkerArgs| |abelianGroup| |squareFreeFactors| - |multiplyExponents| |zeroSquareMatrix| |getDatabase| |bfKeys| - |prinpolINFO| |components| |ScanFloatIgnoreSpaces| |pair| - |colorFunction| |removeCoshSq| |genericPosition| |mesh?| - |mightHaveRoots| |value| |nextItem| |multMonom| |makeSUP| - |representationType| |connectTo| |sequences| |setMinPoints| |mapUp!| - |radicalSolve| |intPatternMatch| |ratpart| |critT| |bezoutResultant| - |laguerreL| |companionBlocks| |kroneckerDelta| |complexZeros| - |OMreadFile| |compound?| |testModulus| |pointPlot| |testDim| |maxrow| - |OMgetAttr| |SturmHabichtCoefficients| |critM| |patternMatchTimes| - |rationalPoints| |scan| |divisorCascade| |topPredicate| |entry| - |pole?| |d02bbf| |resultantnaif| |setTex!| |bandedJacobian| - |intChoose| |leftTraceMatrix| |tRange| |zeroDim?| |minordet| |df2mf| - |integralBasisAtInfinity| |expenseOfEvaluation| |totalfract| - |complexLimit| |s17dlf| |safetyMargin| |contains?| |equality| LODO2FUN - |leftDiscriminant| |zeroSetSplit| |numberOfOperations| |enumerate| - |identitySquareMatrix| |trapezoidal| |eigenvector| |OMgetEndObject| - |matrixDimensions| |unvectorise| |explicitlyEmpty?| |choosemon| - |biRank| |splitConstant| |numericalOptimization| - |squareFreePolynomial| |bag| |atom?| |squareMatrix| |reverse| - |primitivePart!| |virtualDegree| |dual| |s17dgf| - |nextLatticePermutation| |wrregime| |hue| |SFunction| |polygon| - |makeFR| |f02akf| |selectNonFiniteRoutines| |call| |phiCoord| - |indicialEquationAtInfinity| |ode| |iiatan| |digamma| - |intermediateResultsIF| |hasPredicate?| |antiAssociative?| |conjugate| - |extract!| |leaves| |tree| |minPoints| |complexExpand| - |antisymmetricTensors| |dflist| |tanh2coth| |refine| |contours| - |schwerpunkt| |definingPolynomial| |setLabelValue| |move| |cAcsch| - |setfirst!| |mainKernel| |OMputAtp| |readInt32!| |times!| |zerosOf| - |plot| |mainCharacterization| |OMgetApp| |flagFactor| |makeEq| |iicsc| - |cSec| |listexp| |lazyPquo| |acosIfCan| |create| |multiset| |prem| - |connect| |generalLambert| |init| |createPrimitivePoly| |integerIfCan| - |push| |pointColorDefault| |linearPart| |iomode| |leftZero| |sub| - |recoverAfterFail| |drawCurves| |GospersMethod| |s17ajf| - |rowEchelonLocal| |e04dgf| |round| |rightLcm| |basisOfMiddleNucleus| - |nthFlag| |has?| |fortranLiteral| |belong?| |aQuadratic| |elaboration| - |startTable!| |coth2trigh| |perspective| |repeatUntilLoop| |generator| - |transcendenceDegree| |c05pbf| |OMputEndAttr| |close!| |color| - |leftFactor| RF2UTS |prime| |parametric?| |updatD| |completeEval| - |putColorInfo| |OMputEndObject| |mapUnivariateIfCan| |create3Space| - |branchPoint?| |cfirst| |iiasech| |position!| |patternMatch| |pop!| - |normalizeAtInfinity| |stoseInvertibleSet| |explimitedint| - |normDeriv2| |reducedQPowers| |closed| |matrixConcat3D| |search| - |lexico| |prepareSubResAlgo| |inspect| |find| |primextintfrac| - |rarrow| |stack| |nextSubsetGray| |OMgetEndBVar| |triangSolve| |rem| - |isPower| |curveColor| |adjoint| |rk4qc| |argscript| - |basisOfLeftAnnihilator| |rewriteIdealWithHeadRemainder| - |primeFrobenius| |f02aff| |floor| |quo| - |unprotectedRemoveRedundantFactors| |rotate| - |selectOptimizationRoutines| |deepExpand| |stoseLastSubResultant| - |createPrimitiveElement| |lazyIrreducibleFactors| |condition| - |removeRoughlyRedundantFactorsInPol| |rur| |factorials| |checkRur| - |s17adf| |minrank| |c06frf| |c06fuf| |oddintegers| |writeLine!| - |imagi| |div| |quasiMonicPolynomials| |Hausdorff| |numFunEvals3D| - |firstSubsetGray| |modularGcdPrimitive| |readUInt8!| |quote| |isList| - |setleaves!| |exprToXXP| |exquo| |f02aef| |dim| |makeCos| |comparison| - |incrementKthElement| |dmp2rfi| |linear?| |primitivePart| ~= |besselJ| - |cyclicEqual?| |pol| |psolve| |trueEqual| |FormatArabic| |updatF| - |OMputEndAtp| |d02kef| |makeCrit| |chiSquare| |#| |bernoulli| |matrix| - |oneDimensionalArray| |dec| |e02dcf| |viewDeltaYDefault| |credPol| ~ - |paren| |pdct| |getMultiplicationTable| |discreteLog| - |mergeDifference| |e04ycf| |concat| |rightUnits| |gderiv| - |deepestTail| |halfExtendedResultant2| UTS2UP |f02axf| |elaborate| - |myDegree| |alternatingGroup| |triangulate| |dark| |cyclicParents| - |leftRankPolynomial| |addPointLast| |outputFloating| |printInfo| - |fortranDoubleComplex| |identification| |s18dcf| |insertRoot!| - |clearCache| |isOr| |leadingTerm| |level| |axesColorDefault| - |ScanRoman| |lfextlimint| |modifyPoint| |uniform| |mpsode| |negative?| - |e02def| |showClipRegion| |imaginary| |leftRemainder| |index?| - |s19adf| |cartesian| |polCase| |complementaryBasis| |lprop| - |repeating?| |substring?| |setOfMinN| |inputOutputBinaryFile| |rowEch| - |axes| |char| |singularAtInfinity?| |symmetricRemainder| |solveid| - |failed| |nonSingularModel| |singRicDE| |basisOfCenter| - |rightExactQuotient| |acoshIfCan| |quasiAlgebraicSet| |s17aff| - |setPredicates| |semiResultantReduitEuclidean| |suffix?| - |expintfldpoly| |resetVariableOrder| |jacobi| |LiePolyIfCan| |digits| - |generic?| |zoom| |putProperty| |queue| |countRealRootsMultiple| - |redPol| |meshPar1Var| |OMunhandledSymbol| |rdregime| |simplifyExp| - |compile| |hyperelliptic| |lllp| |startStats!| |prefix?| |status| - |eisensteinIrreducible?| |corrPoly| |swapRows!| |quoByVar| |df2st| - |stronglyReduced?| |lifting| |rightDiscriminant| |internalIntegrate| - |irVar| |computeCycleEntry| |unitNormalize| |powers| |leftFactorIfCan| - |cycleRagits| |setprevious!| |iisqrt3| |fibonacci| |second| - |fortranDouble| |f01mcf| |bitCoef| |yCoord| |erf| |viewPhiDefault| - |float| |style| |sequence| |univariatePolynomialsGcds| |linGenPos| - |third| |elem?| |functionIsFracPolynomial?| |gcdPolynomial| - |addBadValue| |fortranTypeOf| |d02gaf| |useSingleFactorBound| - |restorePrecision| |bumprow| |fractRadix| |lyndon| |rationalFunction| - |lfinfieldint| |nsqfree| |void| |f01qdf| |readUInt32!| - |roughUnitIdeal?| |ODESolve| |associatedEquations| |monomials| - |degreePartition| |dilog| |f01rcf| |s18def| |perfectSqrt| |jacobian| - |taylorRep| |infix?| |radix| |numerators| |numberOfFractionalTerms| - |writable?| |makeSeries| |sin| |polyRDE| |mask| |viewpoint| - |OMsupportsSymbol?| |semiSubResultantGcdEuclidean1| |cylindrical| - |basisOfCommutingElements| |palgint0| |cos| |inverse| |binomial| - |branchIfCan| |expandTrigProducts| |setPrologue!| |sinh2csch| - |clipPointsDefault| |coerceP| |isTimes| |slex| |cyclicEntries| |expr| - |tan| |stopTableInvSet!| |decreasePrecision| |charpol| - |getSyntaxFormsFromFile| |supRittWu?| |exprToGenUPS| |roughSubIdeal?| - |hasSolution?| |overset?| |cot| |remainder| |low| - |isAbsolutelyIrreducible?| |routines| |leadingCoefficientRicDE| - |rootKerSimp| |getOperands| |derivationCoordinates| |commaSeparate| - |physicalLength| |sec| GE |toroidal| |preprocess| |double| - |symmetricDifference| |leadingIdeal| |option?| |unit| - |rectangularMatrix| |selectsecond| |LazardQuotient2| |csc| |log| GT - |pointLists| |callForm?| |minimalPolynomial| |goodPoint| - |partialQuotients| |createPrimitiveNormalPoly| |palgextint| |palgLODE| - |variable| |merge| |asin| LE |s18aff| |OMgetObject| |writeUInt8!| - |algebraicOf| |createNormalPoly| |elColumn2!| |firstDenom| |iterators| - BY |setMaxPoints| |redpps| |acos| LT |innerint| |sturmSequence| - |LowTriBddDenomInv| |largest| |musserTrials| |rootOf| |minimumDegree| - |OMlistSymbols| |scripted?| |atan| |e02daf| |cAcos| - |lazyPremWithDefault| |useNagFunctions| |Aleph| |tanIfCan| - |pmComplexintegrate| |patternVariable| |repSq| |acot| - |lazyResidueClass| |monomialIntegrate| |printInfo!| |c06gqf| - |positiveRemainder| |stoseInvertible?| |supersub| |rdHack1| - |symmetricSquare| |asec| |closedCurve?| |clipWithRanges| |tan2cot| - |rootPoly| |whileLoop| |associator| |c06fpf| |symbol?| |baseRDE| - |acsc| |createMultiplicationTable| |nthRootIfCan| |declare!| - |karatsubaOnce| |rationalIfCan| |separate| |listBranches| |list?| - |triangularSystems| |invertibleElseSplit?| |sinh| - |leftRegularRepresentation| |cap| |solveLinearlyOverQ| - |collectQuasiMonic| |iibinom| |parabolic| |interactiveEnv| - |returnType!| |d02ejf| |cosh| |lowerPolynomial| |f04mbf| - |showIntensityFunctions| NOT |genericLeftMinimalPolynomial| |anfactor| - |internalAugment| |showAll?| |tube| |OMread| |tanh| |alphabetic| - |OMputFloat| |lists| |bringDown| OR |s17def| |critpOrder| |besselY| - |fTable| |internalZeroSetSplit| |trapezoidalo| |coth| - |constantOperator| |getBadValues| AND |quasiRegular?| |compBound| - |stiffnessAndStabilityFactor| |setsubMatrix!| |less?| |signAround| - |removeSquaresIfCan| |bindings| |initiallyReduced?| |lifting1| |keys| - |reindex| |rootPower| |clikeUniv| |hermiteH| |depth| |iidprod| - |linearPolynomials| |bitTruth| |c06gsf| |permanent| |dimension| - |lighting| |hdmpToDmp| |makingStats?| |compdegd| |rightFactorIfCan| - |LyndonBasis| |normFactors| |debug| |point?| |segment| |complexSolve| - |conjug| |changeThreshhold| |complexForm| |f01maf| |meatAxe| - |degreeSubResultant| D |doubleRank| |cot2tan| |shuffle| - |separateDegrees| |finiteBasis| |addPoint| |postfix| - |stoseInvertibleSetreg| |host| |genericLeftDiscriminant| |colorDef| - |arity| |jordanAdmissible?| |f02adf| |dimensionsOf| |OMputBVar| - |zero?| |hypergeometric0F1| |fill!| |rightScalarTimes!| |pair?| - |cAtanh| |functionIsOscillatory| |addPoint2| |e02gaf| |headReduced?| - |removeRoughlyRedundantFactorsInContents| - |tryFunctionalDecomposition?| |semiResultantEuclideannaif| |diagonals| - |power| |rootSplit| |imagk| |e02zaf| |normalise| |shade| |frst| - |divergence| |sts2stst| |permutationGroup| |dn| |generalizedInverse| - |listYoungTableaus| |expandPower| |setFormula!| |monicDivide| |orbits| - * |controlPanel| |insertBottom!| |indices| |quadraticForm| - |countable?| |defineProperty| |iicot| |newLine| - |indiceSubResultantEuclidean| |chvar| |complexNumericIfCan| - |basisOfRightNucleus| |members| |primextendedint| |changeWeightLevel| - |properties| |setAttributeButtonStep| |optimize| |setProperties| |tab| - |collectUnder| |certainlySubVariety?| |numberOfHues| |represents| - |factorsOfCyclicGroupSize| |makeFloatFunction| |translate| - |measure2Result| |lastSubResultantEuclidean| |typeList| = - |subresultantSequence| |iilog| |fortranComplex| |mapMatrixIfCan| - |vark| |f04mcf| |exponentialOrder| |print| |toseInvertibleSet| - |resize| |ldf2lst| |internalSubQuasiComponent?| |e01bff| |mix| - |showArrayValues| |maxRowIndex| |copies| |resolve| |cycles| - |taylorIfCan| |initializeGroupForWordProblem| < |nextColeman| - |prevPrime| |evenInfiniteProduct| |tableForDiscreteLogarithm| - |rightRecip| |imagj| |Gamma| |getVariableOrder| |cCoth| > - |lazyVariations| |factorByRecursion| |mesh| |leftRank| |setStatus| - |extendedIntegrate| |bsolve| |makeViewport3D| <= |middle| - |currentSubProgram| |socf2socdf| |constantRight| |OMUnknownCD?| - |viewport3D| |OMopenFile| |minimize| |fintegrate| |rootsOf| >= - |initials| |weight| |removeRedundantFactorsInPols| |iflist2Result| - |evenlambert| |initiallyReduce| |byteBuffer| |airyAi| |operation| - |subHeight| |pdf2df| |curve| |ScanArabic| |elements| - |variationOfParameters| |f02fjf| |traverse| |completeHermite| - |selectAndPolynomials| |extractProperty| |qPot| |monomRDEsys| - |interpret| |binaryTree| |mathieu24| |firstUncouplingMatrix| - |OMencodingSGML| + |ddFact| |distance| |concat!| |before?| |true| - |trigs2explogs| |iiperm| |updateStatus!| |changeName| - |cn| - |morphism| |neglist| |besselI| |maxPoints| |composites| |rotatey| - |d02bhf| |sech2cosh| |mantissa| / |iidsum| |c06ecf| |s13acf| |leftOne| - |head| |jacobiIdentity?| |upperCase?| |leftPower| |integerBound| - |ocf2ocdf| |s19abf| |increment| |tubeRadiusDefault| |category| 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|mappingMode| |iiatanh| |FormatRoman| |module| |beauzamyBound| - |rootBound| |directory| |script| |UnVectorise| |tableau| |opeval| - |sinhcosh| |s18adf| |elRow2!| |totalDegree| |discriminant| |expIfCan| - |approxSqrt| |ScanFloatIgnoreSpacesIfCan| |rootNormalize| |kovacic| - |rational?| |OMputObject| |pureLex| |subresultantVector| - |retractIfCan| |ignore?| |chineseRemainder| |mappingAst| |flatten| - |PollardSmallFactor| |internal?| |exp| |tryFunctionalDecomposition| - |OMsupportsCD?| |OMputAttr| |selectPolynomials| |printCode| |objects| - |tex| |linearlyDependent?| |unaryFunction| |left| |singleFactorBound| - |numer| |monicModulo| |eigenMatrix| |minColIndex| |identity| - |conjugates| |appendPoint| |base| |ParCondList| |selectOrPolynomials| - |/\\| |right| |nor| |outputList| |denom| |euclideanNormalForm| - |palgintegrate| |approxNthRoot| |evaluateInverse| - |multiplyCoefficients| |\\/| |regime| |partition| |cyclePartition| - |invertible?| |cPower| |hessian| |lazyPseudoDivide| |subCase?| - |rename!| |epilogue| |nil| |infinite| |arbitraryExponent| + |Record| |Union| |sncndn| |head| |seriesToOutputForm| |ceiling| + |e02aef| |pi| |solveLinear| |OMsend| |tanh2trigh| |fmecg| |OMputFloat| + |integralLastSubResultant| |elaborate| |constantIfCan| |infinity| + |OMgetAttr| |comparison| |removeCoshSq| |doubleDisc| + |subResultantGcdEuclidean| |numerator| |internalDecompose| + |atrapezoidal| |region| |highCommonTerms| |rectangularMatrix| |cond| + |sechIfCan| |fracPart| |newReduc| |deepestTail| |argumentListOf| + |copy!| |tanSum| |minGbasis| |contract| |subResultantsChain| + |generate| |bumptab1| |applyRules| |log10| |accuracyIF| |sinIfCan| + |kovacic| |complexNumericIfCan| |length| |map| |sturmVariationsOf| + |countRealRoots| |imports| |OMgetString| |integerIfCan| + |getVariableOrder| |bitand| |iisech| |kernel| |complexSolve| |cycle| + |pointPlot| |scripts| |ramifiedAtInfinity?| |scripted?| |isQuotient| + |graeffe| |incrementBy| |PDESolve| |clikeUniv| |getBadValues| + |outerProduct| |bitior| |isEquiv| |draw| |backOldPos| |perfectSqrt| + |decomposeFunc| |insert!| |hspace| |OMputBind| |belong?| |secIfCan| + |qualifier| |zCoord| |expand| |createGenericMatrix| |pleskenSplit| + |rombergo| |f02ajf| |f04maf| |OMgetType| |resultantEuclidean| + |currentEnv| |refine| |OMgetInteger| |sub| |filterWhile| |basicSet| + |crest| |tubeRadius| |pdf2df| |build| |ratDsolve| |inputBinaryFile| + |complexElementary| |arbitrary| |exactQuotient| |SturmHabicht| + |triangular?| |filterUntil| |symbol| |getCode| |quadraticNorm| + |s19acf| |realEigenvectors| |mainVariables| |radix| |convert| |tanAn| + |maxdeg| |previous| |s14aaf| |setPrologue!| |select| + |mainCoefficients| |viewWriteAvailable| |expression| |slex| + |makeObject| |yCoordinates| |musserTrials| |OMcloseConn| |errorKind| + |addMatchRestricted| |moduloP| |pToDmp| |height| |OMencodingBinary| + |maxPoints3D| |truncate| |sqfree| |integer| |realSolve| |curve?| + |coef| |pquo| |setValue!| |point?| |sts2stst| 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|midpoints| |tail| |integralBasisAtInfinity| + |virtualDegree| |imagK| |makeYoungTableau| |readByte!| |startTable!| + |constructor| |rules| |LiePoly| |front| |addmod| |solveRetract| + |collect| |topFortranOutputStack| |numberOfChildren| |setClosed| + |mainExpression| |dmpToHdmp| |evenInfiniteProduct| |perfectNthPower?| + |nothing| |mainPrimitivePart| |ramified?| |cLog| |cschIfCan| |option| + |interactiveEnv| |f04atf| |ode| |getPickedPoints| |ridHack1| + |prepareSubResAlgo| |showSummary| |mergeFactors| |explicitlyEmpty?| + |cAcosh| |cubic| |e02dcf| |multiEuclidean| |lllp| |axes| + |bezoutDiscriminant| |pair?| |s18dcf| |graphCurves| |divisors| + |splitSquarefree| |iicos| |rightFactorCandidate| |squareFree| |trigs| + |changeWeightLevel| |e02baf| |getExplanations| |showAttributes| + |bitCoef| |factorSquareFreePolynomial| |bits| |optional?| + |setprevious!| |genus| |unknown| |OMbindTCP| + |rightRegularRepresentation| |imagk| |f2st| |symmetricPower| |iroot| + |macroExpand| |rootSimp| |headAst| |zeroMatrix| |rightTrim| |s15adf| + |intcompBasis| |radicalEigenvector| |sumSquares| + |genericRightMinimalPolynomial| |d01anf| |lowerBound| + |prolateSpheroidal| |rightDiscriminant| |bernoulli| + |semiResultantEuclidean2| |leftTrim| |increment| |nlde| |extendIfCan| + |f02awf| |light| |simpson| |normal01| |iitan| |listOfMonoms| |iibinom| + |halfExtendedResultant2| |antisymmetricTensors| |leftFactorIfCan| + |relativeApprox| |nextPrimitivePoly| |enumerate| |solid| |sample| + |say| |moduleSum| F |cyclicEqual?| |createIrreduciblePoly| + |denomRicDE| |multiplyCoefficients| |checkRur| |setelt!| |functorData| + |d01amf| |explogs2trigs| |aromberg| |algSplitSimple| |symmetricGroup| + |factorsOfDegree| |cAsin| |linGenPos| |mvar| |f01bsf| + |reduceBasisAtInfinity| |newSubProgram| |selectOptimizationRoutines| + |tab| |cycles| |mainMonomials| |maxColIndex| |wholePart| + |basisOfRightAnnihilator| |symmetric?| |charClass| |rootRadius| + |leftRegularRepresentation| |function| |push!| 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|selectIntegrationRoutines| + |operations| |se2rfi| |forLoop| |hue| |cAcot| |lagrange| |or| + |resetBadValues| |taylor| |halfExtendedSubResultantGcd2| |scaleRoots| + |rdHack1| |deleteProperty!| |leftAlternative?| |bivariateSLPEBR| + |rotatex| |e02daf| |log2| |arity| |internalSubQuasiComponent?| |xor| + |laurent| |cycleEntry| |packageCall| |OMputSymbol| |outputGeneral| + |inverseColeman| |stirling1| |weighted| |message| |usingTable?| + |content| |wronskianMatrix| |subPolSet?| |case| |puiseux| |initTable!| + |toroidal| |f04mbf| |quickSort| |groebner| |btwFact| |f01rcf| + |cylindrical| |Zero| |updateStatus!| |pointSizeDefault| + |complexIntegrate| |asinhIfCan| |iiacot| |interval| |entry?| + |cycleRagits| |hi| |OMputEndError| |solveInField| + |showFortranOutputStack| |d02gaf| |One| |roughBase?| |inv| |medialSet| + |whitePoint| |SturmHabichtMultiple| |nand| |getStream| |OMread| + |lookup| |squareTop| |ground?| |transform| |reducedDiscriminant| + |f01qcf| |monicCompleteDecompose| |groebner?| |expandLog| |makeCos| + |mathieu11| |isExpt| |s17dlf| |legendreP| |ground| |lcm| |parseString| + |limitPlus| |expextendedint| |movedPoints| |rootBound| |argument| + |halfExtendedResultant1| |lieAdmissible?| |closedCurve| |lexico| + |printTypes| |positiveSolve| |beauzamyBound| |perfectSquare?| + |shuffle| |leadingMonomial| |clearDenominator| |matrixGcd| + |mapExponents| |singleFactorBound| |integers| + |numberOfIrreduciblePoly| |dual| |basisOfCommutingElements| |append| + |hessian| |tan2cot| |leadingCoefficient| |symbol?| |binaryTournament| + |leadingIndex| |drawComplexVectorField| |modulus| |rename!| |iiasinh| + |iflist2Result| |fortranReal| |pointLists| |primitiveMonomials| + |stopTableInvSet!| |completeSmith| |elt| |gcd| |output| |meshFun2Var| + |hdmpToP| |euclideanNormalForm| |gensym| |unrankImproperPartitions1| + |acotIfCan| |lieAlgebra?| |getOperands| |cSec| + |solveLinearPolynomialEquationByFractions| |false| |fintegrate| + |reductum| |univariatePolynomials| |c05pbf| |rk4a| + |functionIsContinuousAtEndPoints| |internalSubPolSet?| |algebraicOf| + |lowerPolynomial| |removeZeroes| |computeCycleEntry| |squareMatrix| + |numFunEvals| |var2StepsDefault| |logGamma| + |primPartElseUnitCanonical| |lowerCase| |basis| |radicalEigenvalues| + |makeCrit| |internalLastSubResultant| |iidsum| + |factorSquareFreeByRecursion| |genericPosition| |rootOf| + |sortConstraints| |points| |closed?| |over| + |removeRoughlyRedundantFactorsInContents| |binaryTree| |aCubic| + |conditionsForIdempotents| |latex| |readUInt16!| |cyclicSubmodule| + |completeEval| |integralAtInfinity?| |rangePascalTriangle| |shellSort| + |linearDependenceOverZ| |reflect| |generic| |derivationCoordinates| + |mindegTerm| |moebiusMu| |cyclicParents| |degreePartition| |hcrf| + |fractionFreeGauss!| |binarySearchTree| |cCsch| |parabolic| |isOp| + |integer?| |upperCase!| |df2ef| |setFormula!| |genericLeftNorm| + |internalIntegrate0| |writeUInt8!| |lprop| |empty?| + |leftMinimalPolynomial| |categories| |conjugate| |putColorInfo| + |subResultantGcd| |hasPredicate?| |merge| |iiatan| |presub| + |companionBlocks| |sylvesterMatrix| |associates?| |seriesSolve| + |atoms| |pointColorPalette| |flexibleArray| |unitNormal| + |headReduced?| |rightMinimalPolynomial| |countable?| |cAsinh| + |numberOfVariables| |divideIfCan| |cAsech| |inconsistent?| + |leadingIdeal| |selectOrPolynomials| |adaptive| |cPower| |c02agf| + |s17dhf| |pastel| |torsion?| |SturmHabichtCoefficients| + |recoverAfterFail| |createThreeSpace| |rightRecip| |makeViewport2D| + |HermiteIntegrate| |exponents| |startTableGcd!| + |fortranCarriageReturn| |e02ahf| |simplifyLog| |putGraph| + |primeFrobenius| |characteristicSerie| |tablePow| |prod| + |plusInfinity| |rational| |commutativeEquality| |lazyEvaluate| + |OMencodingUnknown| |Lazard2| |jokerMode| |semiResultantEuclideannaif| + |changeBase| |quotedOperators| |symmetricSquare| |ODESolve| + |minusInfinity| |read!| |lexGroebner| |bag| |s15aef| |rotate!| + |stripCommentsAndBlanks| |bothWays| + |removeRoughlyRedundantFactorsInPols| |cartesian| |solve1| |multiset| + |linkToFortran| |getMatch| |lfunc| |primlimintfrac| |extractClosed| + |closeComponent| |Ei| |superHeight| |rootNormalize| |laguerre| + |monicModulo| |setImagSteps| |thenBranch| |blankSeparate| |composite| + |key| |iisinh| |host| |realEigenvalues| |odd?| |escape| + |cyclotomicFactorization| |iicsch| |cot2trig| |optpair| + |createLowComplexityTable| |reopen!| |readInt8!| |factorset| |mulmod| + |componentUpperBound| |s13aaf| |nullSpace| |largest| |bfEntry| + |specialTrigs| |filename| |removeZero| |OMclose| |degree| |mapGen| + |An| |vertConcat| |leftExactQuotient| |type| |duplicates| + |determinant| |rowEchelonLocal| |OMconnInDevice| |brillhartTrials| + |reducedContinuedFraction| |euclideanSize| |scanOneDimSubspaces| + |ricDsolve| |extendedSubResultantGcd| |traverse| |fill!| |equiv| + |radicalSolve| |parse| |leftZero| |endOfFile?| |cCot| |twoFactor| + |ptFunc| |solveLinearPolynomialEquationByRecursion| |froot| |next| + |hermite| |upperCase| |printStats!| |setchildren!| |getMeasure| + |relerror| |interReduce| |SturmHabichtSequence| |subscript| |merge!| + |sin?| |e02ajf| |commonDenominator| |d02kef| |diagonalMatrix| + |powerSum| |e02zaf| |fullDisplay| |delay| |dictionary| |multinomial| + |shrinkable| |f02aaf| |iCompose| |setMinPoints| |setleft!| + |elementary| |coefficients| |checkPrecision| |fixPredicate| |jacobian| + |crushedSet| |trailingCoefficient| |part?| |singularitiesOf| |sec2cos| + |elaborateFile| |nthr| |queue| |elRow2!| EQ + |standardBasisOfCyclicSubmodule| |irreducibleFactor| |lfextendedint| + |nextPrime| |inRadical?| |e04gcf| |nullity| |returnTypeOf| + |deepExpand| |isTimes| |sumOfSquares| |rangeIsFinite| |integral| |lhs| + |revert| |ScanFloatIgnoreSpaces| |tanh2coth| |insertBottom!| + |cyclicCopy| |row| |nextColeman| |pushdterm| |d02gbf| |e01bff| + |factorPolynomial| |rhs| |simplifyPower| |lambert| |chebyshevU| + |isAnd| |padicFraction| |internalAugment| |lex| |OMputApp| + |OMmakeConn| |prinpolINFO| |f02adf| |rootKerSimp| |safeFloor| + |cyclotomicDecomposition| |firstSubsetGray| |commaSeparate| + |fibonacci| |csubst| |domainTemplate| |absolutelyIrreducible?| + |mainSquareFreePart| |laurentRep| |quasiMonic?| |coefficient| |f02agf| + |rarrow| |doubleResultant| |wordsForStrongGenerators| |deref| |rule| + |Gamma| |plot| |pointData| |OMencodingSGML| |qroot| |hermiteH| + |withPredicates| |s18adf| |cycleLength| |setsubMatrix!| |innerSolve1| + |partition| |index| |oddlambert| |quote| |typeList| |bandedHessian| + |stoseInvertibleSet| |ipow| |makeViewport3D| |invertIfCan| |vectorise| + |iiexp| |numberOfComponents| |increasePrecision| |mainValue| |bit?| + |e02dff| |getProperties| |HenselLift| |useNagFunctions| + |identification| |center| |discreteLog| |modularFactor| |systemSizeIF| + |mainMonomial| |pureLex| |externalList| GF2FG |hitherPlane| + |viewThetaDefault| |denominators| |makeSin| |pair| |noKaratsuba| + |e01daf| |e02akf| |sayLength| |monomialIntPoly| |startStats!| + |wholeRadix| |value| |generalizedEigenvectors| |f01maf| |sqfrFactor| + |normInvertible?| |constDsolve| |showScalarValues| |generic?| + |setVariableOrder| |sizePascalTriangle| UP2UTS |hasTopPredicate?| + |cTan| |optAttributes| |karatsuba| |pushucoef| |qqq| |divergence| + |digamma| |numberOfDivisors| |epilogue| |cCosh| |coord| |littleEndian| + |cot2tan| |iicsc| |computePowers| |before?| |setStatus!| |ldf2lst| + |quatern| |leftTrace| |entry| |predicates| |drawComplex| |pushdown| + |binary| |e01sbf| |OMputEndApp| |shiftLeft| |divideIfCan!| + |modularGcdPrimitive| |primintfldpoly| |extractIndex| + |irreducibleFactors| |splitNodeOf!| |OMputObject| + |solveLinearPolynomialEquation| |tube| |resetVariableOrder| + |degreeSubResultantEuclidean| |monomial?| |showIntensityFunctions| + |setColumn!| |multiplyExponents| |setlast!| |leftDivide| |subHeight| + |representationType| |OMsupportsCD?| |e01bhf| |quasiAlgebraicSet| + |readBytes!| |digit| |derivative| |groebSolve| |leftDiscriminant| + |stosePrepareSubResAlgo| |cycleElt| |reverse| |monicRightDivide| + |pole?| |empty| |nary?| |lyndon| |minIndex| |divide| |string?| + |argscript| |ScanArabic| |errorInfo| |makeFR| |symbolTableOf| |write!| + |call| |s13acf| |expPot| |const| |constantToUnaryFunction| |hclf| + |biRank| |raisePolynomial| |trueEqual| |augment| |dfRange| |leaves| + |d01fcf| |tree| |d01apf| |resultantReduit| |genericRightDiscriminant| + |stopTable!| |OMUnknownSymbol?| |cyclicGroup| |stirling2| |htrigs| + |semiResultantEuclidean1| |mat| |unparse| |maxrank| + |initializeGroupForWordProblem| |untab| |trapezoidal| |shufflein| + |orbits| |sturmSequence| |lexTriangular| |leastPower| |npcoef| + |selectsecond| |sizeMultiplication| |chiSquare| |postfix| |extend| + |factorsOfCyclicGroupSize| |associative?| |OMputBVar| |rootProduct| + |OMgetEndBVar| |returnType!| |init| |node?| |stoseInvertibleSetsqfreg| + |OMopenFile| |isAtom| |numberOfNormalPoly| |clearTheIFTable| + |alternating| |f02aef| |attributeData| |evaluate| |romberg| + |rewriteIdealWithRemainder| |computeInt| |imagI| |mapExpon| |dark| + |definingInequation| |newTypeLists| |realRoots| |testDim| |showAll?| + |addPoint2| |inf| |s21bdf| |polyred| |bubbleSort!| |f04jgf| + |generator| |roughSubIdeal?| |lintgcd| |sincos| |pade| |phiCoord| + |iitanh| |setAdaptive| |leftRank| |irreducibleRepresentation| + |rightUnit| |prime| |normalize| |po| |integral?| |paren| |lazy?| + |permutationGroup| |measure2Result| |deepestInitial| + |numericalOptimization| |goodnessOfFit| |laplace| |taylorRep| + |shallowExpand| |irVar| |leadingTerm| |genericLeftTraceForm| + |probablyZeroDim?| |contains?| |search| |clipParametric| |ldf2vmf| + |overset?| |e02agf| |finite?| |stack| |palgLODE| |lifting1| + |semiSubResultantGcdEuclidean1| |rem| |lowerCase!| |mesh| + |transcendenceDegree| |showTheIFTable| |parent| + |functionIsOscillatory| |power!| |getIdentifier| |listRepresentation| + |csc2sin| |nthExpon| |quo| |monomRDEsys| |initiallyReduce| |range| + |partialFraction| |zerosOf| |dequeue!| |condition| |factorSFBRlcUnit| + |divideExponents| |returns| |unrankImproperPartitions0| |extractTop!| + |laguerreL| |c05nbf| |extractProperty| |credPol| |showClipRegion| + |var2Steps| |iiGamma| |div| |edf2ef| |permutations| + |inverseIntegralMatrixAtInfinity| |primitive?| |duplicates?| |null?| + |unitNormalize| |prindINFO| |exquo| |scale| + |ScanFloatIgnoreSpacesIfCan| |dim| |patternMatchTimes| |gcdcofact| + |polyRDE| |eyeDistance| |characteristicSet| |c06fpf| |twist| ~= + |getSyntaxFormsFromFile| |iisin| |algebraic?| |createNormalPoly| + |createRandomElement| |fractionPart| |zoom| |toseSquareFreePart| + |e04naf| |degreeSubResultant| |#| |removeRedundantFactorsInPols| + |matrix| |patternVariable| |quotient| |dec| |minimumDegree| |f07adf| + |validExponential| |rightZero| ~ |seed| |getProperty| |addPoint| + |shiftRoots| |concat| |combineFeatureCompatibility| |maxPoints| + |extensionDegree| |stopMusserTrials| |saturate| |doubleRank| + |lSpaceBasis| |leftMult| |nthRootIfCan| |neglist| |removeSinSq| + |iFTable| |readable?| |cTanh| |printInfo| |taylorIfCan| + |jacobiIdentity?| |newLine| |freeOf?| |plenaryPower| |clearCache| + |leaf?| |aLinear| |level| |dot| |nthFactor| |numberOfCycles| |mdeg| + |outputFixed| |d01akf| |leftUnits| |ratpart| |rotate| |isOpen?| + |nextItem| |pushup| |triangSolve| |abs| |cfirst| |makeSketch| + |graphState| |interpolate| |substring?| |mainContent| |elaboration| + |ParCondList| |monicDivide| |char| |makeSeries| |f04mcf| + |expintfldpoly| |failed| |basisOfRightNucleus| |critT| |stopTableGcd!| + |tableForDiscreteLogarithm| |bsolve| |defineProperty| |eq?| |check| + |inverseLaplace| |suffix?| |position!| |nextNormalPrimitivePoly| + |baseRDEsys| |superscript| |meshPar2Var| |primitiveElement| |pack!| + |s14baf| |viewPhiDefault| |d02ejf| |f02axf| |partialQuotients| + |d01gaf| |recolor| |genericRightNorm| |compile| |cup| + |exprHasAlgebraicWeight| |asecIfCan| |prefix?| |status| |subCase?| + |zeroDimensional?| |gcdcofactprim| |roman| |f02xef| |integralBasis| + |categoryMode| |homogeneous?| |Is| |pseudoQuotient| |ffactor| + |diagonals| |noncommutativeJordanAlgebra?| |logIfCan| + |variationOfParameters| |balancedBinaryTree| |cAcoth| |aQuartic| + |second| |block| |dominantTerm| |fortranLiteralLine| |erf| |e01bef| + |redpps| |float| |messagePrint| |permutationRepresentation| + |modifyPoint| |pr2dmp| |third| |reverseLex| |quotientByP| + |triangularSystems| |positiveRemainder| |iteratedInitials| + |basisOfRightNucloid| |rightPower| |rootDirectory| |integralMatrix| + |OMconnOutDevice| |complementaryBasis| |outputForm| |OMgetEndAttr| + |UpTriBddDenomInv| |void| |LyndonWordsList| |semicolonSeparate| + |clipSurface| |d01alf| |critpOrder| |axesColorDefault| |complexExpand| + |horizConcat| |dilog| |f01mcf| |eigenvector| |c06frf| |roughBasicSet| + |infix?| |overbar| |exportedOperators| |intersect| + |rewriteSetByReducingWithParticularGenerators| |readIfCan!| |sin| + |viewpoint| |mask| |monicDecomposeIfCan| |digits| |distance| + |wordInGenerators| |cos| |scalarMatrix| |normalForm| |toseInvertible?| + |compactFraction| |KrullNumber| |c06gsf| |iisec| |diagonal| + |att2Result| |f04qaf| |tan| |members| |expr| |real?| + |definingPolynomial| |internal?| |numberOfComposites| |changeName| + |subTriSet?| |intensity| |basisOfCentroid| |low| |doubleFloatFormat| + |geometric| |e01bgf| |cot| |factor1| |expenseOfEvaluationIF| + |quadratic| |writeBytes!| |partialDenominators| |B1solve| |sdf2lst| + |sec| |leftLcm| UTS2UP GE |isMult| |prinshINFO| |regime| |double| + |graphStates| |nor| |invmod| |red| |RemainderList| |oddintegers| |csc| + |log| GT |laplacian| |rationalPoint?| |innerSolve| + |primPartElseUnitCanonical!| |bytes| |constantRight| |unitVector| + |variable| |parametric?| |max| |asin| LE |ScanRoman| + |makeFloatFunction| |rationalIfCan| |setErrorBound| |solid?| + |anfactor| |heap| |cyclotomic| |iterators| BY |powers| |acos| LT + |deleteRoutine!| |computeCycleLength| |regularRepresentation| + |purelyAlgebraic?| |exprHasWeightCosWXorSinWX| |enterPointData| + |squareFreePrim| |f01ref| |f02bjf| |atan| |antiCommutative?| + |flagFactor| |dmp2rfi| |qfactor| |setright!| |OMwrite| |diff| + |adaptive3D?| |leftGcd| |acot| |f02akf| |principalAncestors| + |rightQuotient| |s18acf| |byteBuffer| |antisymmetric?| |patternMatch| + |symFunc| |reverse!| |asec| |ratPoly| |rotatez| |rCoord| |primeFactor| + |getConstant| |pdf2ef| |eigenvalues| |complete| |f04axf| |acsc| + |operators| |expint| |binomial| |declare!| |has?| + |createNormalPrimitivePoly| |reduced?| |perfectNthRoot| |OMgetFloat| + |hasHi| |sinh| |indicialEquation| |iiperm| |setfirst!| + |bandedJacobian| |normalizeAtInfinity| |shade| |cAcsc| |birth| |recip| + |cosh| |minColIndex| |minset| |changeThreshhold| NOT |normalElement| + |nthCoef| |primintegrate| |e01sff| |unexpand| |printHeader| |tanh| + |f2df| |df2mf| |lists| |irCtor| OR |shallowCopy| |printCode| + |mathieu12| |OMputEndAtp| |subresultantVector| |integrate| |coth| + |nextNormalPoly| |prinb| |groebgen| AND |decreasePrecision| + |complexEigenvalues| |copyInto!| |OMgetEndApp| |linears| |OMgetAtp| + |df2fi| |keys| |indiceSubResultantEuclidean| |resize| |d01gbf| + |elliptic| |karatsubaOnce| |primitivePart!| |depth| + |currentCategoryFrame| |repeating?| |Ci| + |unprotectedRemoveRedundantFactors| |nthRoot| |lazyPrem| + |lastSubResultantElseSplit| |solveid| |nextLatticePermutation| + |cotIfCan| |more?| |factorOfDegree| |replaceKthElement| |debug| + |contractSolve| |segment| |lighting| |topPredicate| |kroneckerDelta| + |generalizedInverse| |alphanumeric?| |sequences| |fortranComplex| D + |factorByRecursion| |lazyPseudoDivide| |gcdprim| |nthFlag| + |finiteBasis| |generateIrredPoly| |OMputEndBVar| + |algebraicCoefficients?| |dimension| |dflist| |euler| |nullary?| + |colorFunction| |ideal| |firstDenom| |exptMod| |norm| + |removeSuperfluousCases| |getlo| |hyperelliptic| |s14abf| + |rightExtendedGcd| |branchPoint?| |c06ecf| |nsqfree| + |mainCharacterization| |Hausdorff| |e04dgf| |infRittWu?| |cSin| + |getMultiplicationTable| |safeCeiling| |debug3D| |elements| |quartic| + |denominator| |mapCoef| |signatureAst| |iiacsc| + |halfExtendedSubResultantGcd1| |rightUnits| |irDef| |edf2efi| + |stronglyReduced?| |innerint| |setvalue!| |noValueMode| * + |linearAssociatedLog| |iiatanh| |option?| |list?| |localAbs| |d03eef| + |minPol| |identitySquareMatrix| |alternatingGroup| |OMputInteger| + |upperCase?| |d01aqf| |s17ahf| |bombieriNorm| |s17adf| |properties| + |numberOfOperations| |optimize| |s21baf| |setScreenResolution| + |s20adf| |vedf2vef| |bitLength| |LazardQuotient2| |identity| + |gradient| |translate| |readUInt32!| |Si| |mergeDifference| |padecf| = + |isNot| |polyRicDE| |isOr| |dihedralGroup| |bat| |lflimitedint| + |print| |s17aef| |pToHdmp| |sh| |viewPosDefault| |bindings| + |principalIdeal| |goodPoint| |outputFloating| |resolve| |measure| + |rationalPoints| |binaryFunction| < |allRootsOf| |numberOfFactors| + |cap| |eulerPhi| |ReduceOrder| |cosh2sech| |f07fdf| |omError| + |trivialIdeal?| > |disjunction| |tan2trig| |localUnquote| + |getOperator| |dequeue| |e02adf| |upDateBranches| |setFieldInfo| + |acoshIfCan| <= |internalZeroSetSplit| |makeVariable| |push| + |anticoord| |routines| |supRittWu?| |setLegalFortranSourceExtensions| + |rk4f| |gderiv| >= |back| |unitCanonical| |changeVar| |setEpilogue!| + |readInt16!| |quasiRegular?| |prepareDecompose| + |brillhartIrreducible?| |outputSpacing| |operation| |vark| |mapUp!| + |PollardSmallFactor| |expIfCan| |setStatus| |radicalOfLeftTraceForm| + |leftUnit| |trigs2explogs| |acothIfCan| |useSingleFactorBound?| |inR?| + |varselect| |removeRedundantFactorsInContents| |interpret| + |fprindINFO| |encodingDirectory| |pdct| |associatedEquations| + + |critMonD1| |drawToScale| |dimensionsOf| |imagJ| |true| |close!| + |pile| |bivariatePolynomials| |removeDuplicates!| - |cn| + |approximants| |matrixDimensions| |lllip| |OMgetObject| |writeLine!| + |iiacoth| |updatD| |mantissa| |selectSumOfSquaresRoutines| / |lifting| + |primaryDecomp| |leftExtendedGcd| |eigenvectors| |lineColorDefault| + |unit| |branchPointAtInfinity?| |setMaxPoints| |exprToUPS| + |expressIdealMember| |Lazard| |quasiMonicPolynomials| |rischDE| + |category| |printingInfo?| |closed| |nil| |mapdiv| |create3Space| + |fullPartialFraction| |cardinality| |lfintegrate| |symmetricTensors| + |domain| |overlabel| |OMsupportsSymbol?| |bumprow| |curryRight| + |cAcsch| |uniform| |package| |expt| |elColumn2!| |multiple?| |subSet| + |asechIfCan| |numberOfImproperPartitions| |shift| |infLex?| + |multisect| |evaluateInverse| |rootPower| |basisOfLeftNucleus| |prem| + |approximate| |mapUnivariateIfCan| |fixedDivisor| |sylvesterSequence| + |stoseLastSubResultant| |powern| |numberOfMonomials| |nonLinearPart| + |complex| |OMputVariable| |removeCosSq| |readInt32!| |varList| + |univariate?| |color| |spherical| |lfextlimint| |irForm| |compBound| + |integralCoordinates| |sinh2csch| |show| |gbasis| |is?| |limit| + |stoseSquareFreePart| |dimensions| |property| + |constantCoefficientRicDE| |jordanAdmissible?| |doubleComplex?| + |primextintfrac| |arrayStack| |linearlyDependent?| |f01qdf| + |leastAffineMultiple| |OMputEndBind| |maximumExponent| |complexRoots| + |isConnected?| |trace| |rationalFunction| |ellipticCylindrical| + |reorder| |f02fjf| |normalizedDivide| |karatsubaDivide| |asinIfCan| + |iicot| |retract| |ParCond| |leader| |bezoutMatrix| |modTree| + |tubePlot| |units| |weight| |getMultiplicationMatrix| |delta| |imagj| + |typeLists| |rightFactorIfCan| |restorePrecision| |modularGcd| |less?| + |groebnerIdeal| |palgint0| |incrementKthElement| |root| |getCurve| + |viewport2D| |firstUncouplingMatrix| |pseudoRemainder| |splitLinear| + |resultantEuclideannaif| |rational?| |represents| |transpose| |key?| + |quadraticForm| |makingStats?| |decimal| |remove!| |s21bbf| |sin2csc| + |sequence| |linearDependence| |viewZoomDefault| |stFunc2| |wreath| + |typeForm| |f04adf| |leftRecip| |invertibleSet| |code| |exprex| + |insertionSort!| |mirror| |e02bbf| |dn| |leftTraceMatrix| |edf2fi| + |physicalLength!| |realZeros| |tryFunctionalDecomposition?| + |upperBound| |even?| |formula| |pmComplexintegrate| |concat!| + |hexDigit| |relationsIdeal| |c02aff| |e04ycf| |listYoungTableaus| + |showArrayValues| |setClipValue| |lambda| |diagonal?| |chebyshevT| + |toseInvertibleSet| |notelem| |selectODEIVPRoutines| |setRealSteps| + RF2UTS |paraboloidal| |plus| |uncouplingMatrices| |normalDenom| + |stiffnessAndStabilityOfODEIF| |viewDefaults| |shanksDiscLogAlgorithm| + |chvar| |mix| |curve| |insertMatch| |extractPoint| |bat1| |morphism| + |e01saf| |squareFreeFactors| |dom| |OMputString| |cAtanh| + |removeSuperfluousQuasiComponents| |llprop| |approxSqrt| |linSolve| + |OMUnknownCD?| |nrows| |subNodeOf?| |sum| |clearFortranOutputStack| + |datalist| |pmintegrate| |leftOne| |pointColorDefault| |coth2tanh| + |atom?| |supersub| |sinhIfCan| |ncols| |generalizedEigenvector| + |palglimint| |FormatArabic| |hconcat| |increase| |rotatey| |xCoord| + |times| |iicosh| |BasicMethod| |setButtonValue| |noLinearFactor?| + |tubePoints| |ocf2ocdf| |setMinPoints3D| |s17dcf| |symbolTable| + |separateFactors| |linear| |removeConstantTerm| |LyndonBasis| + |constantOperator| |corrPoly| |isPower| |top| |gramschmidt| + |coercePreimagesImages| |complexForm| |exponent| |lp| |systemCommand| + |complexZeros| |factorSquareFree| |mainVariable| |invmultisect| + |summation| |pushFortranOutputStack| |scalarTypeOf| + |numberOfComputedEntries| |stoseInvertible?reg| |title| |comp| + |getOrder| |polynomial| |clipWithRanges| |stiffnessAndStabilityFactor| + |linear?| |factorGroebnerBasis| |point| |selectAndPolynomials| + |toScale| |popFortranOutputStack| |eisensteinIrreducible?| + |monicLeftDivide| |external?| |monom| |node| |options| + |nextPrimitiveNormalPoly| |nilFactor| |generalPosition| |exponential| + |satisfy?| |continue| |sort| |semiLastSubResultantEuclidean| |orbit| + |outputAsFortran| |children| |iisqrt2| |normal| |iiabs| |redPol| + |primlimitedint| |myDegree| |graphs| + |rewriteIdealWithQuasiMonicGenerators| |e| |makeTerm| |moebius| + |mappingAst| |closedCurve?| |ip4Address| |unravel| |symbolIfCan| + |possiblyInfinite?| |totalDegree| |terms| |listLoops| |series| + |prologue| |list| |OMgetEndBind| |OMunhandledSymbol| |pol| + |coordinates| |fortranDouble| |common| |inHallBasis?| |string| + |distFact| |lazyPremWithDefault| |linearMatrix| |cross| |d01ajf| + |wrregime| |car| |isobaric?| |convergents| |exists?| |fTable| |ksec| + |unvectorise| |quadratic?| |e04ucf| |distribute| |f04arf| |random| + |cdr| |normalizedAssociate| |reduction| |normalizeIfCan| + |supDimElseRittWu?| |d02raf| |FormatRoman| |leftRankPolynomial| + |computeBasis| |functionIsFracPolynomial?| |setDifference| |e04mbf| + |delete!| |cCoth| |isAbsolutelyIrreducible?| |createPrimitivePoly| + |randomR| |definingEquations| |f07fef| |min| |zero?| |setIntersection| + |smith| |constantOpIfCan| |c06ebf| |createZechTable| |sizeLess?| + |e04jaf| |unit?| |solve| |factors| |setUnion| |insertRoot!| |fi2df| + |OMsetEncoding| |scan| |parabolicCylindrical| |stronglyReduce| + |coerceImages| |interpretString| |sPol| |indicialEquationAtInfinity| + |apply| |inverse| |bipolarCylindrical| |moreAlgebraic?| |dmpToP| + |elRow1!| |OMgetVariable| |iiacosh| |strongGenerators| |redPo| + |characteristic| |divisorCascade| |makeEq| |curryLeft| + |getButtonValue| |zero| |pushuconst| |coleman| |cothIfCan| |getGraph| + |harmonic| |size| |trace2PowMod| |resetAttributeButtons| |rubiksGroup| + |style| |makeGraphImage| |explimitedint| |d01bbf| |rightGcd| |width| + |algebraicSort| |minimalPolynomial| |cSech| |rightScalarTimes!| + |elem?| |And| |setProperties| |reindex| |enqueue!| |algDsolve| + |equation| |polynomialZeros| |charthRoot| |makeResult| |initials| + |vector| |tensorProduct| |Or| |decrease| |enterInCache| |factorList| + |fortranTypeOf| |slash| |first| |normFactors| |lazyPseudoRemainder| + |eulerE| |differentiate| |chineseRemainder| |Not| |bezoutResultant| + |getRef| |complex?| |characteristicPolynomial| |components| |rest| + |UP2ifCan| |indicialEquations| |removeIrreducibleRedundantFactors| + |parents| |maxrow| |numeric| |iiasech| |pow| |besselJ| |nonQsign| + |fixedPointExquo| |substitute| |univariatePolynomial| |cExp| + |discriminant| |weights| |radical| |partialNumerators| + |fortranDoubleComplex| |listOfLists| |logical?| |hash| |rdregime| + |removeDuplicates| |binding| |iExquo| |linearPolynomials| |maxint| + |count| |intPatternMatch| |normalized?| |LyndonCoordinates| + |countRealRootsMultiple| |atanIfCan| |top!| |squareFreeLexTriangular| + |mr| |LowTriBddDenomInv| |algintegrate| + |rightCharacteristicPolynomial| |writable?| |super| |showTheFTable| + |endSubProgram| |name| |optional| |gethi| |bipolar| |mainForm| |ode1| + |rischNormalize| |explicitlyFinite?| |pascalTriangle| |zeroDimPrime?| + |frobenius| |d03edf| |lift| |body| |subQuasiComponent?| |inc| + |viewDeltaXDefault| |addBadValue| |prime?| |numericalIntegration| + |badNum| |iidprod| |s13adf| |permanent| |reduce| |findBinding| + |setPoly| |parts| |OMputEndAttr| |hasSolution?| |nextsubResultant2| + |OMreadStr| |resultantnaif| |hostPlatform| |extension| |airyBi| |pop!| + |rightNorm| |s17agf| |certainlySubVariety?| |pseudoDivide| |randomLC| + |every?| |primextendedint| |splitDenominator| |intChoose| |coerceS| + |extract!| |constantLeft| |tanintegrate| |bitTruth| |rspace| + |nonSingularModel| |univariatePolynomialsGcds| |isPlus| + |OMParseError?| |OMputAtp| |nthFractionalTerm| |reducedForm| |bounds| + |clipBoolean| |green| FG2F |quoted?| |figureUnits| |floor| |reseed| + |cos2sec| SEGMENT |conical| |error| |setLabelValue| |iprint| + |singular?| |extendedIntegrate| |safetyMargin| |port| |rightTrace| + |d01asf| |critBonD| |leftNorm| |d02bhf| |rightOne| |assert| |tower| + |totalfract| |leastMonomial| |symmetricRemainder| + |lastSubResultantEuclidean| |minordet| |inputOutputBinaryFile| + |remainder| |nodeOf?| |mapBivariate| |problemPoints| + |createMultiplicationMatrix| |tab1| |e02ddf| |t| |yellow| |entries| + |reify| |root?| |lepol| |tanNa| LODO2FUN |nextSubsetGray| |direction| + |loadNativeModule| |viewport3D| |collectUpper| |clearTable!| + |bivariate?| |intermediateResultsIF| |coefChoose| |knownInfBasis| + |algebraicVariables| |palgRDE0| |unaryFunction| + |generalizedContinuumHypothesisAssumed| |pomopo!| |gcdPrimitive| |hex| + |printInfo!| |s19adf| |constant| |nextSublist| |monicRightFactorIfCan| + |critM| |complexNumeric| |fortranLogical| |infiniteProduct| + |leviCivitaSymbol| |showAllElements| |pointColor| |space| |iiasin| + |roughUnitIdeal?| |byte| |predicate| |wholeRagits| |quasiRegular| + |conjugates| |padicallyExpand| |sup| |unknownEndian| |child?| + |changeNameToObjf| |kernels| |numberOfPrimitivePoly| |thetaCoord| + |getGoodPrime| |associatedSystem| |select!| + |createPrimitiveNormalPoly| |swap| |operator| |singularAtInfinity?| + |cons| |e02bdf| |idealSimplify| |iiacsch| |setAdaptive3D| |prevPrime| + |associator| |semiResultantReduitEuclidean| + |stoseIntegralLastSubResultant| |iomode| |mathieu24| |critB| |step| + |taylorQuoByVar| |yCoord| |besselI| |split| |univariate| |zeroDim?| + |viewDeltaYDefault| |listBranches| |makeMulti| |complexNormalize| + |clearTheSymbolTable| |comment| |chiSquare1| |palgLODE0| + |univariateSolve| |element?| |extendedResultant| |rootSplit| + |mkIntegral| |userOrdered?| |subresultantSequence| |iiacos| + |complexLimit| |iifact| |commutative?| |integralDerivationMatrix| + |ode2| |fixedPoint| |coerce| |identityMatrix| |factor| |algint| + |lazyResidueClass| |Nul| |completeHensel| |stoseInvertible?sqfreg| + |int| |fortranLinkerArgs| |firstNumer| |acschIfCan| |construct| + |float?| |overlap| |sqrt| |OMconnectTCP| |source| |cyclic?| |mkcomm| + |OMgetEndObject| |qelt| |controlPanel| |parameters| |real| |cCos| + |purelyAlgebraicLeadingMonomial?| |frst| |c06eaf| |lazyVariations| + |f02abf| |setref| |qsetelt| |flexible?| |imag| |vspace| + |zeroSetSplitIntoTriangularSystems| |compiledFunction| |child| + |meatAxe| |hypergeometric0F1| |Vectorise| |xRange| + |expandTrigProducts| |directProduct| |palgextint| |oddInfiniteProduct| + |curveColor| |outputMeasure| |exteriorDifferential| |rroot| |create| + |swap!| |indiceSubResultant| |OMgetApp| |hostByteOrder| |totolex| + |chainSubResultants| |scopes| |antiCommutator| |groebnerFactorize| + |complexEigenvectors| |brace| |OMputEndObject| |target| |ptree| + |integralMatrixAtInfinity| |generators| |argumentList!| + |rewriteSetWithReduction| |rowEchLocal| |e01sef| + |associatorDependence| |qinterval| |destruct| |internalIntegrate| + |makeprod| |genericRightTrace| |evenlambert| |e02bcf| |rightDivide| + |nodes| |stoseInvertible?| |generalizedContinuumHypothesisAssumed?| + |curveColorPalette| |whatInfinity| |s19abf| |symmetricDifference| + |kind| |internalInfRittWu?| |stoseInvertibleSetreg| |besselK| + |expenseOfEvaluation| |polCase| |s17ajf| |dioSolve| |generalTwoFactor| + |nthExponent| |op| |cRationalPower| |acosIfCan| |makeSUP| |cAtan| + |useEisensteinCriterion| |positive?| |separant| |f02aff| |mappingMode| + |mainVariable?| |mkPrim| |open?| |oblateSpheroidal| |ravel| |monomial| + |simplifyExp| |quoByVar| |OMencodingXML| |nextPartition| |coerceL| + |iicoth| |rightTraceMatrix| |infix| |ran| |sumOfKthPowerDivisors| + |reshape| |squareFreePolynomial| |rename| |cosSinInfo| + |toseLastSubResultant| |arguments| |assign| |coordinate| |isList| + |setelt| |whileLoop| |triangulate| |constant?| |retractable?| + |buildSyntax| |fglmIfCan| |index?| |setPosition| |schema| |rischDEsys| + |alphabetic| |Frobenius| |limitedint| |linearlyDependentOverZ?| + |addMatch| |purelyTranscendental?| |OMopenString| |stFunc1| |copy| + |mapmult| |tValues| |Aleph| |selectFiniteRoutines| |euclideanGroebner| + |setTopPredicate| |reciprocalPolynomial| |union| |mapMatrixIfCan| + |putProperties| |infinityNorm| |setEmpty!| |selectfirst| |bigEndian| + |mindeg| |d02cjf| |semiIndiceSubResultantEuclidean| |mathieu23| + |dihedral| |graphImage| |fractRagits| |numerators| |doublyTransitive?| + |idealiser| |isImplies| |update| |modifyPointData| |adjoint| + |multMonom| |wordInStrongGenerators| |polygon| |autoCoerce| |opeval| + |unmakeSUP| |setrest!| |setLength!| |primitivePart| |trim| + |subtractIfCan| |implies| |readLineIfCan!| |composites| |alphabetic?| + |sinhcosh| |multiEuclideanTree| |rightMult| |number?| |just| + |hexDigit?| |leftRemainder| |bfKeys| |createPrimitiveElement| |sort!| + |drawStyle| |rank| |psolve| |monomials| |unary?| |OMreadFile| + |changeMeasure| |imagE| |jordanAlgebra?| |split!| |GospersMethod| + |legendre| |loopPoints| |startPolynomial| |normal?| |prefixRagits| + |digit?| |rightRemainder| |appendPoint| |lyndon?| |s17dgf| + |cyclePartition| |position| |contours| |lowerCase?| |randnum| + |difference| |minPoly| |tracePowMod| |powerAssociative?| |match?| + |in?| |e02def| |leadingSupport| |variable?| |linearPart| + |repeatUntilLoop| |lyndonIfCan| |fortranLiteral| |monic?| |zeroOf| + |exQuo| |roughEqualIdeals?| |OMlistSymbols| |curry| + |lazyPseudoQuotient| |outlineRender| |uniform01| |aQuadratic| |polar| + |move| |numberOfHues| |product| |rk4| |rewriteIdealWithHeadRemainder| + |s19aaf| |capacity| |declare| |cycleSplit!| |inGroundField?| |trunc| + |parametersOf| |janko2| |findCycle| |viewSizeDefault| |inrootof| + |permutation| |leftScalarTimes!| |iisqrt3| |infieldint| |setOfMinN| + |selectNonFiniteRoutines| |categoryFrame| |showTheSymbolTable| + |primes| |basisOfMiddleNucleus| |voidMode| |denomLODE| |polygamma| + |univcase| |collectQuasiMonic| |basisOfLeftNucloid| |minrank| + |swapRows!| |rowEchelon| |invertibleElseSplit?| |listexp| |simplify| + |writeByte!| |polarCoordinates| |arg1| |iiasec| |reducedQPowers| + |f02bbf| |tanQ| |lazyIntegrate| |basisOfLeftAnnihilator| + |balancedFactorisation| |stFuncN| |useSingleFactorBound| |palgint| + |arg2| |sech| |member?| |boundOfCauchy| |blue| |rur| |rightLcm| + |radicalRoots| |diag| |ignore?| |airyAi| |csch| |leftQuotient| + |acscIfCan| |putProperty| |e02gaf| |close| + |semiSubResultantGcdEuclidean2| |cscIfCan| |genericLeftTrace| + |innerEigenvectors| |conditions| |bumptab| |asinh| |connect| + |coshIfCan| |kmax| |minRowIndex| |palginfieldint| |monomialIntegrate| + |diophantineSystem| |setAttributeButtonStep| |inverseIntegralMatrix| + |match| |acosh| |ListOfTerms| |colorDef| |mainKernel| |stop| |e02bef| + |abelianGroup| |display| |autoReduced?| |bright| |ord| + |rationalApproximation| |precision| |cosIfCan| |atanh| + |LagrangeInterpolation| |mapDown!| |integerBound| |octon| |cAcos| + |OMserve| |presuper| |li| |acoth| |mapSolve| |subset?| |henselFact| + |mightHaveRoots| |genericLeftMinimalPolynomial| |lazyGintegrate| + |setleaves!| |linearAssociatedExp| |leadingCoefficientRicDE| + |basisOfCenter| |s18aff| |goto| |asech| |transcendentalDecompose| + |extractBottom!| |listConjugateBases| |simpsono| |badValues| |s18def| + |xn| |elseBranch| |palgintegrate| |ef2edf| |character?| |deriv| + |rootPoly| |BumInSepFFE| |plus!| |multiple| |generalLambert| + |trapezoidalo| |subspace| |reducedSystem| |input| |minPoints| + |currentSubProgram| |realElementary| |headReduce| |magnitude| + |environment| |f07aef| |applyQuote| |constantKernel| |sn| |infinite?| + |library| |s17akf| |radicalEigenvectors| |differentialVariables| + |dimensionOfIrreducibleRepresentation| |separateDegrees| |hasoln| + |totalLex| |gcdPolynomial| |skewSFunction| |alphanumeric| + |mapUnivariate| |someBasis| |nil?| |sumOfDivisors| |collectUnder| + |subscriptedVariables| |decompose| |idealiserMatrix| |powmod| |cAsec| + |explicitEntries?| |besselY| |numericIfCan| |lookupFunction| |d02bbf| + |ruleset| |removeRoughlyRedundantFactorsInPol| |copies| |f01qef| + |OMreceive| |LyndonWordsList1| |tubePointsDefault| |baseRDE| |c06gbf| + |box| |plotPolar| |orthonormalBasis| |binomThmExpt| |s20acf| |set| + |Beta| |partitions| |generalSqFr| |square?| |clearTheFTable| + |stoseInternalLastSubResultant| |nativeModuleExtension| |elliptic?| + |test| |createLowComplexityNormalBasis| |id| |numFunEvals3D| + |insertTop!| |factorAndSplit| |palgRDE| |edf2df| |d03faf| + |exprToGenUPS| |suchThat| |testModulus| |normDeriv2| |compose| + |OMReadError?| |eigenMatrix| |s17acf| |finiteBound| |iilog| + |palglimint0| |c06fqf| |table| |RittWuCompare| |var1StepsDefault| + |component| |setCondition!| |showRegion| |any| |clip| |module| + |polyPart| |expintegrate| |insert| |new| |hdmpToDmp| |branchIfCan| + |generalInfiniteProduct| |createMultiplicationTable| |torsionIfCan| + |obj| |lfinfieldint| |structuralConstants| |f02wef| |addPointLast| + |size?| |showTheRoutinesTable| |solveLinearlyOverQ| |eq| |readLine!| + |OMgetBVar| |c06fuf| |prefix| |zeroDimPrimary?| |cache| + |selectMultiDimensionalRoutines| |callForm?| |iipow| |iter| |f01brf| + |subMatrix| |c06gqf| |sparsityIF| |startTableInvSet!| + |setScreenResolution3D| |resultant| |order| |OMgetSymbol| + |setProperty| |delete| |OMputError| |signature| |exponential1| + |OMputAttr| |signAround| |extractSplittingLeaf| |connectTo| + |quasiComponent| |subst| |double?| |normalise| |exp1| |OMlistCDs| + |sech2cosh| |zeroVector| |cSinh| |LiePolyIfCan| |calcRanges| + |fortranInteger| |one?| |exprHasLogarithmicWeights| |OMgetError| + |areEquivalent?| |fortranCharacter| |s17def| |csch2sinh| |normalDeriv| + |principal?| |drawCurves| |fractRadix| |LazardQuotient| |conjunction| + |e04fdf| |expandPower| |directory| |script| |antiAssociative?| + |squareFreePart| |factorial| |cycleTail| |lazyIrreducibleFactors| + |setMaxPoints3D| |directSum| |radicalSimplify| |any?| |central?| + |readUInt8!| |sorted?| |headRemainder| |weierstrass| + |exponentialOrder| |setOrder| |ref| |retractIfCan| |rk4qc| + |rightExactQuotient| |exactQuotient!| |flatten| |aspFilename| + |selectPDERoutines| |exp| |equality| |removeRedundantFactors| |c06ekf| + |commutator| |coHeight| |objects| |tex| |sign| |localIntegralBasis| + |left| |s18aef| |numer| |particularSolution| |ddFact| |factorFraction| + |leadingBasisTerm| |rightRankPolynomial| |genericRightTraceForm| + |base| |/\\| |f01rdf| |pushNewContour| |right| |setnext!| |outputList| + |denom| |droot| |setPredicates| |semiDiscriminantEuclidean| + |resultantReduitEuclidean| |viewWriteDefault| |setRow!| |\\/| |redmat| + |minimumExponent| |reduceLODE| F2FG |separate| |createNormalElement| + |universe| |conditionP| |jacobi| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index beb0fe8d..af30144d 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,152 +1,152 @@ -(3228596 . 3480761546) -((-3699 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-2107 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3932 ((|#2| $ (-570) |#2|) NIL) ((|#2| $ (-1244 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T) ((-458) -2892 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-499) |has| |#1| (-1212)) ((-520 (-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((-520 |#1| |#1|) |has| |#1| (-313 |#1|)) ((-562) -2892 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-652 #0#) -2892 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) -2892 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) -2892 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-646 |#1|) . T) ((-646 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) -2892 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-723 |#1|) . T) ((-723 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-730 |#1| #1#) . T) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) |has| |#1| (-893 (-384))) ((-893 (-570)) |has| |#1| (-893 (-570))) ((-891 |#1|) . T) ((-916) -12 (|has| |#1| (-311)) (|has| |#1| (-916))) ((-927) -2892 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-1011) -12 (|has| |#1| (-1011)) (|has| |#1| (-1212))) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1060 #0#) -2892 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1060 |#1|) . T) ((-1060 $) . T) ((-1065 #0#) -2892 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1065 |#1|) . T) ((-1065 $) . T) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-354)) ((-1212) |has| |#1| (-1212)) ((-1215) |has| |#1| (-1212)) ((-1227) . 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T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2892 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2892 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2892 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2892 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2892 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2892 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2892 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-2336 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-3625 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1356 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2336 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3625 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1356 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-1356 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-3625 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-2336 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-111 #0# #0#) |has| |#1| (-562)) ((-111 |#1| |#1|) |has| |#1| (-174)) ((-111 $ $) |has| |#1| (-562)) ((-132) -2892 (|has| |#1| (-1058)) (|has| |#1| (-562)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-21))) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #0#) -2892 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-562))) ((-622 #1=(-413 (-959 |#1|))) |has| |#1| (-562)) ((-622 (-570)) -2892 (|has| |#1| (-1058)) (|has| |#1| (-1047 (-570))) (|has| |#1| (-562)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-622 #2=(-618 $)) . T) ((-622 #3=(-959 |#1|)) |has| |#1| (-1058)) ((-622 #4=(-1186)) . T) ((-622 |#1|) . T) ((-622 $) |has| |#1| (-562)) ((-619 (-868)) . T) ((-174) |has| |#1| (-562)) ((-620 (-542)) |has| |#1| (-620 (-542))) ((-620 (-899 (-384))) |has| |#1| (-620 (-899 (-384)))) ((-620 (-899 (-570))) |has| |#1| (-620 (-899 (-570)))) ((-245) |has| |#1| (-562)) ((-294) |has| |#1| (-562)) ((-311) |has| |#1| (-562)) ((-313 $) . T) ((-306) . T) ((-368) |has| |#1| (-562)) ((-382 |#1|) |has| |#1| (-1058)) ((-406 |#1|) . T) ((-417 |#1|) . T) ((-458) |has| |#1| (-562)) ((-479) |has| |#1| (-479)) ((-520 (-618 $) $) . T) ((-520 $ $) . T) ((-562) |has| |#1| (-562)) ((-652 #0#) |has| |#1| (-562)) ((-652 (-570)) -2892 (|has| |#1| (-1058)) (|has| |#1| (-562)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-21))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2892 (|has| |#1| (-1058)) (|has| |#1| (-562)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-654 #0#) |has| |#1| (-562)) ((-654 |#1|) |has| |#1| (-174)) ((-654 $) -2892 (|has| |#1| (-1058)) (|has| |#1| (-562)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-646 #0#) |has| |#1| (-562)) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) |has| |#1| (-562)) ((-645 (-570)) -12 (|has| |#1| (-645 (-570))) (|has| |#1| (-1058))) ((-645 |#1|) |has| |#1| (-1058)) ((-723 #0#) |has| |#1| (-562)) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) |has| |#1| (-562)) ((-732) -2892 (|has| |#1| (-1121)) (|has| |#1| (-1058)) (|has| |#1| (-562)) (|has| |#1| (-479)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-907 (-1186)) |has| |#1| (-1058)) ((-893 (-384)) |has| |#1| (-893 (-384))) ((-893 (-570)) |has| |#1| (-893 (-570))) ((-891 |#1|) . 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T) ((-107 #0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((-102) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-1109)) ((-619 (-868)) -2892 (|has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-1109)) (|has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-619 (-868)))) ((-152 #0#) . T) ((-620 (-542)) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-620 (-542))) ((-231 #0#) . T) ((-237 #0#) . T) ((-313 #0#) -12 (|has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)))) (|has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-1109))) ((-495 #0#) . T) ((-520 #0# #0#) -12 (|has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)))) (|has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-1109))) ((-1109) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-1109)) ((-1227) . 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(*1 *1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-618 *3)) (-4 *3 (-1109)))) (-3413 (*1 *2 *1) (|partial| -12 (-5 *2 (-1186)) (-5 *1 (-618 *3)) (-4 *3 (-1109)))) (-3190 (*1 *2 *1 *3) (-12 (-5 *3 (-115)) (-5 *2 (-112)) (-5 *1 (-618 *4)) (-4 *4 (-1109)))) (-3190 (*1 *2 *1 *3) (-12 (-5 *3 (-1186)) (-5 *2 (-112)) (-5 *1 (-618 *4)) (-4 *4 (-1109))))) +(-13 (-133) (-856) (-891 |#1|) (-10 -8 (-15 -3756 ((-115) $)) (-15 -1905 ((-650 |#1|) $)) (-15 -1444 ((-777) $)) (-15 -1365 ($ (-115) (-650 |#1|) (-777))) (-15 -1365 ($ (-1186))) (-15 -3413 ((-3 (-1186) "failed") $)) (-15 -3190 ((-112) $ (-115))) (-15 -3190 ((-112) $ (-1186))) (IF (|has| |#1| (-620 (-542))) (-6 (-620 (-542))) |%noBranch|))) ((-3799 ((|#1| $) 6))) (((-619 |#1|) (-141) (-1227)) (T -619)) ((-3799 (*1 *2 *1) (-12 (-4 *1 (-619 *2)) (-4 *2 (-1227))))) @@ -2507,18 +2507,18 @@ NIL (((-620 |#1|) (-141) (-1227)) (T -620)) ((-1425 (*1 *2 *1) (-12 (-4 *1 (-620 *2)) (-4 *2 (-1227))))) (-13 (-10 -8 (-15 -1425 (|t#1| $)))) -((-4375 (((-3 (-1182 (-413 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((-112) $ (|[\|\|]| -3106)))))) (T -623)) +((-1664 (*1 *1) (-5 *1 (-623))) (-1851 (*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -1954)) (-5 *2 (-112)) (-5 *1 (-623)))) (-1851 (*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -1664)) (-5 *2 (-112)) (-5 *1 (-623)))) (-1851 (*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3106)) (-5 *2 (-112)) (-5 *1 (-623))))) +(-13 (-976) (-10 -8 (-15 -1664 ($) -3725) (-15 -1851 ((-112) $ (|[\|\|]| -1954))) (-15 -1851 ((-112) $ (|[\|\|]| -1664))) (-15 -1851 ((-112) $ (|[\|\|]| -3106))))) ((-1425 (($ |#1|) 6))) (((-624 |#1|) (-141) (-1227)) (T -624)) ((-1425 (*1 *1 *2) (-12 (-4 *1 (-624 *2)) (-4 *2 (-1227))))) @@ -2527,478 +2527,478 @@ NIL (((-625 |#1| |#2|) (-10 -8 (-15 -3799 (|#1| |#2|)) (-15 -3799 (|#1| (-570))) (-15 -3799 ((-868) |#1|))) (-626 |#2|) (-1058)) (T -625)) NIL (-10 -8 (-15 -3799 (|#1| |#2|)) (-15 -3799 (|#1| (-570))) (-15 -3799 ((-868) |#1|))) -((-2557 (((-112) $ $) 7)) (-2959 (((-112) $) 17)) (-3800 (((-3 $ "failed") $ $) 20)) (-3317 (($) 18 T CONST)) (-2283 (((-3 $ 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T) ((-652 |#1|) . T) ((-652 |#2|) |has| |#1| (-368)) ((-652 $) . T) ((-654 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-654 |#1|) . T) ((-654 |#2|) |has| |#1| (-368)) ((-654 $) . T) ((-646 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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NIL NIL) (-1197 2873775 2874995 2876243 "TABLBUMP" 2877953 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872997 2873144 2873325 "SYSTEM" 2873616 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869456 2870155 2870938 "SYSSOLP" 2872248 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869254 2869411 2869442 "SYSPTR" 2869447 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868298 2868803 2868922 "SYSNNI" 2869108 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869193) (-1192 2867605 2868064 2868143 "SYSINT" 2868203 NIL SYSINT (NIL NIL) -8 NIL NIL 2868248) (-1191 2863937 2864883 2865593 "SYNTAX" 2866917 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861095 2861697 2862329 "SYMTAB" 2863327 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856344 2857246 2858229 "SYMS" 2860134 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853579 2855802 2856032 "SYMPOLY" 2856149 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853096 2853171 2853294 "SYMFUNC" 2853491 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849116 2850408 2851221 "SYMBOL" 2852305 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842655 2844344 2846064 "SWITCH" 2847418 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835889 2841476 2841779 "SUTS" 2842410 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827955 2835136 2835409 "SUPXS" 2835674 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819714 2827573 2827699 "SUP" 2827864 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818873 2819000 2819217 "SUPFRACF" 2819582 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818494 2818553 2818666 "SUP2" 2818808 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816942 2817216 2817572 "SUMRF" 2818193 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816277 2816343 2816535 "SUMFS" 2816863 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800244 2815454 2815705 "SULS" 2816084 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799846 2800066 2800136 "SUCHTAST" 2800196 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799141 2799371 2799511 "SUCH" 2799754 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2793008 2794047 2795006 "SUBSPACE" 2798229 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792438 2792528 2792692 "SUBRESP" 2792896 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785806 2787103 2788414 "STTF" 2791174 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779979 2781099 2782246 "STTFNC" 2784706 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771292 2773161 2774955 "STTAYLOR" 2778220 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764422 2771156 2771239 "STRTBL" 2771244 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759786 2764377 2764408 "STRING" 2764413 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754647 2759159 2759189 "STRICAT" 2759248 T STRICAT (NIL) -9 NIL 2759310 NIL) (-1166 2747400 2752266 2752877 "STREAM" 2754071 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746910 2746987 2747131 "STREAM3" 2747317 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745892 2746075 2746310 "STREAM2" 2746723 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745580 2745632 2745725 "STREAM1" 2745834 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744596 2744777 2745008 "STINPROD" 2745396 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744148 2744358 2744388 "STEP" 2744468 T STEP (NIL) -9 NIL 2744546 NIL) (-1160 2743335 2743637 2743785 "STEPAST" 2744022 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736767 2743234 2743311 "STBL" 2743316 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731893 2735988 2736031 "STAGG" 2736184 NIL STAGG (NIL T) -9 NIL 2736273 NIL) (-1157 2729595 2730197 2731069 "STAGG-" 2731074 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727742 2729365 2729457 "STACK" 2729538 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720437 2725883 2726339 "SREGSET" 2727372 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712862 2714231 2715744 "SRDCMPK" 2719043 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705779 2710302 2710332 "SRAGG" 2711635 T SRAGG (NIL) -9 NIL 2712243 NIL) (-1152 2704796 2705051 2705430 "SRAGG-" 2705435 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699256 2703743 2704164 "SQMATRIX" 2704422 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692941 2695974 2696701 "SPLTREE" 2698601 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688904 2689597 2690243 "SPLNODE" 2692367 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687951 2688184 2688214 "SPFCAT" 2688658 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686688 2686898 2687162 "SPECOUT" 2687709 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677798 2679670 2679700 "SPADXPT" 2684376 T SPADXPT (NIL) -9 NIL 2686540 NIL) (-1145 2677559 2677599 2677668 "SPADPRSR" 2677751 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675608 2677514 2677545 "SPADAST" 2677550 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667553 2669326 2669369 "SPACEC" 2673742 NIL SPACEC (NIL T) -9 NIL 2675558 NIL) (-1142 2665683 2667485 2667534 "SPACE3" 2667539 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664435 2664606 2664897 "SORTPAK" 2665488 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662527 2662830 2663242 "SOLVETRA" 2664099 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661577 2661799 2662060 "SOLVESER" 2662300 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656881 2657769 2658764 "SOLVERAD" 2660629 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652696 2653305 2654034 "SOLVEFOR" 2656248 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646966 2652045 2652142 "SNTSCAT" 2652147 NIL SNTSCAT (NIL T T T T) -9 NIL 2652217 NIL) (-1135 2641072 2645289 2645680 "SMTS" 2646656 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635757 2640960 2641037 "SMP" 2641042 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633916 2634217 2634615 "SMITH" 2635454 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626629 2630825 2630928 "SMATCAT" 2632279 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632829 NIL) (-1131 2623569 2624392 2625570 "SMATCAT-" 2625575 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621235 2622805 2622848 "SKAGG" 2623109 NIL SKAGG (NIL T) -9 NIL 2623244 NIL) (-1129 2617561 2620708 2620892 "SINT" 2621044 T SINT (NIL) -8 NIL NIL 2621206) (-1128 2617333 2617371 2617437 "SIMPAN" 2617517 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616612 2616868 2617008 "SIG" 2617215 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615450 2615671 2615946 "SIGNRF" 2616371 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614283 2614434 2614718 "SIGNEF" 2615279 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613589 2613866 2613990 "SIGAST" 2614181 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611279 2611733 2612239 "SHP" 2613130 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605131 2611180 2611256 "SHDP" 2611261 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604704 2604896 2604926 "SGROUP" 2605019 T SGROUP (NIL) -9 NIL 2605081 NIL) (-1120 2604562 2604588 2604661 "SGROUP-" 2604666 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601397 2602095 2602818 "SGCF" 2603861 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595765 2600844 2600941 "SFRTCAT" 2600946 NIL SFRTCAT (NIL T T T T) -9 NIL 2600985 NIL) (-1117 2589186 2590204 2591340 "SFRGCD" 2594748 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582312 2583385 2584571 "SFQCMPK" 2588119 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581932 2582021 2582132 "SFORT" 2582253 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2581050 2581772 2581893 "SEXOF" 2581898 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580157 2580931 2580999 "SEX" 2581004 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575670 2576385 2576480 "SEXCAT" 2579417 NIL SEXCAT (NIL T T T T T) -9 NIL 2579995 NIL) (-1111 2572823 2575604 2575652 "SET" 2575657 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2571047 2571536 2571841 "SETMN" 2572564 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570543 2570695 2570725 "SETCAT" 2570901 T SETCAT (NIL) -9 NIL 2571011 NIL) (-1108 2570235 2570313 2570443 "SETCAT-" 2570448 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566596 2568696 2568739 "SETAGG" 2569609 NIL SETAGG (NIL T) -9 NIL 2569949 NIL) (-1106 2566054 2566170 2566407 "SETAGG-" 2566412 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565497 2565750 2565851 "SEQAST" 2565975 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564696 2564990 2565051 "SEGXCAT" 2565337 NIL SEGXCAT (NIL T T) -9 NIL 2565457 NIL) (-1103 2563702 2564362 2564544 "SEG" 2564549 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562681 2562895 2562938 "SEGCAT" 2563460 NIL SEGCAT (NIL T) -9 NIL 2563681 NIL) (-1101 2561613 2562044 2562252 "SEGBIND" 2562508 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561234 2561293 2561406 "SEGBIND2" 2561548 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560807 2561035 2561112 "SEGAST" 2561179 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2560026 2560152 2560356 "SEG2" 2560651 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559436 2559961 2560008 "SDVAR" 2560013 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551963 2559206 2559336 "SDPOL" 2559341 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550556 2550822 2551141 "SCPKG" 2551678 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549720 2549892 2550084 "SCOPE" 2550386 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548940 2549074 2549253 "SCACHE" 2549575 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548586 2548772 2548802 "SASTCAT" 2548807 T SASTCAT (NIL) -9 NIL 2548820 NIL) (-1091 2548073 2548421 2548497 "SAOS" 2548532 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547638 2547673 2547846 "SAERFFC" 2548032 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541577 2547535 2547615 "SAE" 2547620 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541170 2541205 2541364 "SAEFACT" 2541536 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539491 2539805 2540206 "RURPK" 2540836 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538128 2538434 2538739 "RULESET" 2539325 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535351 2535881 2536339 "RULE" 2537809 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534963 2535145 2535228 "RULECOLD" 2535303 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534753 2534781 2534852 "RTVALUE" 2534914 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534224 2534470 2534564 "RSTRCAST" 2534681 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2529072 2529867 2530787 "RSETGCD" 2533423 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518302 2523381 2523478 "RSETCAT" 2527597 NIL RSETCAT (NIL T T T T) -9 NIL 2528694 NIL) (-1079 2516229 2516768 2517592 "RSETCAT-" 2517597 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508615 2509991 2511511 "RSDCMPK" 2514828 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506594 2507061 2507135 "RRCC" 2508221 NIL RRCC (NIL T T) -9 NIL 2508565 NIL) (-1076 2505945 2506119 2506398 "RRCC-" 2506403 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505388 2505641 2505742 "RPTAST" 2505866 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479234 2488593 2488660 "RPOLCAT" 2499326 NIL RPOLCAT (NIL T T T) -9 NIL 2502486 NIL) (-1073 2470732 2473072 2476194 "RPOLCAT-" 2476199 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461663 2468943 2469425 "ROUTINE" 2470272 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458461 2461289 2461429 "ROMAN" 2461545 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456705 2457321 2457581 "ROIRC" 2458266 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452937 2455221 2455251 "RNS" 2455555 T RNS (NIL) -9 NIL 2455829 NIL) (-1068 2451446 2451829 2452363 "RNS-" 2452438 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450849 2451257 2451287 "RNG" 2451292 T RNG (NIL) -9 NIL 2451313 NIL) (-1066 2449852 2450214 2450416 "RNGBIND" 2450700 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449251 2449639 2449682 "RMODULE" 2449687 NIL RMODULE (NIL T) -9 NIL 2449714 NIL) (-1064 2448087 2448181 2448517 "RMCAT2" 2449152 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444937 2447433 2447730 "RMATRIX" 2447849 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437764 2440024 2440139 "RMATCAT" 2443498 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444480 NIL) (-1061 2437139 2437286 2437593 "RMATCAT-" 2437598 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436540 2436761 2436804 "RLINSET" 2436998 NIL RLINSET (NIL T) -9 NIL 2437089 NIL) (-1059 2436107 2436182 2436310 "RINTERP" 2436459 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435165 2435719 2435749 "RING" 2435805 T RING (NIL) -9 NIL 2435897 NIL) (-1057 2434957 2435001 2435098 "RING-" 2435103 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433798 2434035 2434293 "RIDIST" 2434721 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425087 2433266 2433472 "RGCHAIN" 2433646 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424437 2424843 2424884 "RGBCSPC" 2424942 NIL RGBCSPC (NIL T) -9 NIL 2424994 NIL) (-1053 2423595 2423976 2424017 "RGBCMDL" 2424249 NIL RGBCMDL (NIL T) -9 NIL 2424363 NIL) (-1052 2420589 2421203 2421873 "RF" 2422959 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420235 2420298 2420401 "RFFACTOR" 2420520 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419960 2419995 2420092 "RFFACT" 2420194 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418077 2418441 2418823 "RFDIST" 2419600 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417530 2417622 2417785 "RETSOL" 2417979 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417166 2417246 2417289 "RETRACT" 2417422 NIL RETRACT (NIL T) -9 NIL 2417509 NIL) (-1046 2417015 2417040 2417127 "RETRACT-" 2417132 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416617 2416837 2416907 "RETAST" 2416967 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409355 2416270 2416397 "RESULT" 2416512 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407946 2408624 2408823 "RESRING" 2409258 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407582 2407631 2407729 "RESLATC" 2407883 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407287 2407322 2407429 "REPSQ" 2407541 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404709 2405289 2405891 "REP" 2406707 T REP (NIL) -7 NIL NIL NIL) (-1039 2404406 2404441 2404552 "REPDB" 2404668 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398306 2399695 2400918 "REP2" 2403218 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394683 2395364 2396172 "REP1" 2397533 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387379 2392824 2393280 "REGSET" 2394313 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386144 2386527 2386777 "REF" 2387164 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385521 2385624 2385791 "REDORDER" 2386028 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381489 2384734 2384961 "RECLOS" 2385349 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380541 2380722 2380937 "REALSOLV" 2381296 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380387 2380428 2380458 "REAL" 2380463 T REAL (NIL) -9 NIL 2380498 NIL) (-1030 2376870 2377672 2378556 "REAL0Q" 2379552 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372471 2373459 2374520 "REAL0" 2375851 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371942 2372188 2372282 "RDUCEAST" 2372399 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2371347 2371419 2371626 "RDIV" 2371864 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2370415 2370589 2370802 "RDIST" 2371169 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2369012 2369299 2369671 "RDETRS" 2370123 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366824 2367278 2367816 "RDETR" 2368554 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2365449 2365727 2366124 "RDEEFS" 2366540 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363958 2364264 2364689 "RDEEF" 2365137 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2358019 2360939 2360969 "RCFIELD" 2362264 T RCFIELD (NIL) -9 NIL 2362995 NIL) (-1020 2356083 2356587 2357283 "RCFIELD-" 2357358 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2352352 2354184 2354227 "RCAGG" 2355311 NIL RCAGG (NIL T) -9 NIL 2355776 NIL) (-1018 2351980 2352074 2352237 "RCAGG-" 2352242 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2351315 2351427 2351592 "RATRET" 2351864 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350868 2350935 2351056 "RATFACT" 2351243 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2350176 2350296 2350448 "RANDSRC" 2350738 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349910 2349954 2350027 "RADUTIL" 2350125 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2343024 2348741 2349052 "RADIX" 2349633 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2334643 2342866 2342996 "RADFF" 2343001 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2334290 2334365 2334395 "RADCAT" 2334555 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2334072 2334120 2334220 "RADCAT-" 2334225 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2332170 2333842 2333934 "QUEUE" 2334015 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328707 2332103 2332151 "QUAT" 2332156 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2328338 2328381 2328512 "QUATCT2" 2328658 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321787 2325132 2325174 "QUATCAT" 2325965 NIL QUATCAT (NIL T) -9 NIL 2326731 NIL) (-1005 2317926 2318963 2320353 "QUATCAT-" 2320449 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2315391 2317002 2317045 "QUAGG" 2317426 NIL QUAGG (NIL T) -9 NIL 2317601 NIL) (-1003 2314993 2315213 2315283 "QQUTAST" 2315343 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313886 2314386 2314560 "QFORM" 2314865 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304879 2310118 2310160 "QFCAT" 2310828 NIL QFCAT (NIL T) -9 NIL 2311829 NIL) (-1000 2300446 2301647 2303241 "QFCAT-" 2303337 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2300080 2300123 2300252 "QFCAT2" 2300397 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2299540 2299650 2299780 "QEQUAT" 2299970 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292686 2293759 2294943 "QCMPACK" 2298473 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2290235 2290683 2291111 "QALGSET" 2292341 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2289480 2289654 2289886 "QALGSET2" 2290055 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2288170 2288394 2288711 "PWFFINTB" 2289253 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2286352 2286520 2286874 "PUSHVAR" 2287984 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2282270 2283324 2283365 "PTRANFN" 2285249 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280672 2280963 2281285 "PTPACK" 2281981 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2280304 2280361 2280470 "PTFUNC2" 2280609 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274781 2279176 2279217 "PTCAT" 2279513 NIL PTCAT (NIL T) -9 NIL 2279666 NIL) (-988 2274439 2274474 2274598 "PSQFR" 2274740 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2273034 2273332 2273666 "PSEUDLIN" 2274137 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259797 2262168 2264492 "PSETPK" 2270794 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) 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NIL NIL) (-878 2030596 2035985 2036180 "PADICRC" 2036582 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023823 2029940 2030125 "PADICRAT" 2030443 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2022138 2023760 2023805 "PADIC" 2023810 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2019248 2020812 2020852 "PADICCT" 2021433 NIL PADICCT (NIL NIL) -9 NIL 2021715 NIL) (-874 2018205 2018405 2018673 "PADEPAC" 2019035 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017417 2017550 2017756 "PADE" 2018067 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015804 2016625 2016905 "OWP" 2017221 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015297 2015510 2015607 "OVERSET" 2015727 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014343 2014902 2015074 "OVAR" 2015165 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013607 2013728 2013889 "OUT" 2014202 T OUT (NIL) -7 NIL NIL NIL) (-868 2002479 2004716 2006916 "OUTFORM" 2011427 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001815 2002076 2002203 "OUTBFILE" 2002372 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2001122 2001287 2001315 "OUTBCON" 2001633 T OUTBCON (NIL) -9 NIL 2001799 NIL) (-865 2000723 2000835 2000992 "OUTBCON-" 2000997 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 2000103 2000452 2000541 "OSI" 2000654 T OSI (NIL) -8 NIL NIL NIL) (-863 1999633 1999971 1999999 "OSGROUP" 2000004 T OSGROUP (NIL) -9 NIL 2000026 NIL) (-862 1998378 1998605 1998890 "ORTHPOL" 1999380 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995929 1998213 1998334 "OREUP" 1998339 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993332 1995620 1995747 "ORESUP" 1995871 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990860 1991360 1991921 "OREPCTO" 1992821 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984546 1986747 1986788 "OREPCAT" 1989136 NIL OREPCAT (NIL T) -9 NIL 1990240 NIL) (-857 1981693 1982475 1983533 "OREPCAT-" 1983538 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980844 1981142 1981170 "ORDSET" 1981479 T ORDSET (NIL) -9 NIL 1981643 NIL) (-855 1980275 1980423 1980647 "ORDSET-" 1980652 NIL 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OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959543 1960723 1961227 "OP" 1961941 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958917 1959143 1959184 "OPERCAT" 1959396 NIL OPERCAT (NIL T) -9 NIL 1959493 NIL) (-840 1958672 1958728 1958845 "OPERCAT-" 1958850 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955485 1957469 1957838 "ONECOMP" 1958336 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954790 1954905 1955079 "ONECOMP2" 1955357 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954209 1954315 1954445 "OMSERVER" 1954680 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951071 1953649 1953689 "OMSAGG" 1953750 NIL OMSAGG (NIL T) -9 NIL 1953814 NIL) (-835 1949694 1949957 1950239 "OMPKG" 1950809 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949124 1949227 1949255 "OM" 1949554 T OM (NIL) -9 NIL NIL NIL) (-833 1947671 1948673 1948842 "OMLO" 1949005 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946631 1946778 1946998 "OMEXPR" 1947497 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945922 1946177 1946313 "OMERR" 1946515 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945073 1945343 1945503 "OMERRK" 1945782 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944524 1944750 1944858 "OMENC" 1944985 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938419 1939604 1940775 "OMDEV" 1943373 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937488 1937659 1937853 "OMCONN" 1938245 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936009 1936985 1937013 "OINTDOM" 1937018 T OINTDOM (NIL) -9 NIL 1937039 NIL) (-825 1933347 1934697 1935034 "OFMONOID" 1935704 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932758 1933284 1933329 "ODVAR" 1933334 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930181 1932503 1932658 "ODR" 1932663 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922762 1929957 1930083 "ODPOL" 1930088 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916584 1922634 1922739 "ODP" 1922744 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915350 1915565 1915840 "ODETOOLS" 1916358 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912317 1912975 1913691 "ODESYS" 1914683 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907199 1908107 1909132 "ODERTRIC" 1911392 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906625 1906707 1906901 "ODERED" 1907111 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903513 1904061 1904738 "ODERAT" 1906048 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900472 1900937 1901534 "ODEPRRIC" 1903042 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898415 1899011 1899497 "ODEPROB" 1900006 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894935 1895420 1896067 "ODEPRIM" 1897894 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894184 1894286 1894546 "ODEPAL" 1894827 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890346 1891137 1892001 "ODEPACK" 1893340 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889407 1889514 1889736 "ODEINT" 1890235 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883508 1884933 1886380 "ODEIFTBL" 1887980 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878906 1879692 1880644 "ODEEF" 1882667 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878255 1878344 1878567 "ODECONST" 1878811 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876380 1877041 1877069 "ODECAT" 1877674 T ODECAT (NIL) -9 NIL 1878205 NIL) (-805 1873235 1876085 1876207 "OCT" 1876290 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872873 1872916 1873043 "OCTCT2" 1873186 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867522 1869957 1869997 "OC" 1871094 NIL OC (NIL T) -9 NIL 1871952 NIL) (-802 1864749 1865497 1866487 "OC-" 1866581 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864101 1864569 1864597 "OCAMON" 1864602 T OCAMON (NIL) -9 NIL 1864623 NIL) (-800 1863632 1863973 1864001 "OASGP" 1864006 T OASGP (NIL) -9 NIL 1864026 NIL) (-799 1862893 1863382 1863410 "OAMONS" 1863450 T OAMONS (NIL) -9 NIL 1863493 NIL) (-798 1862307 1862740 1862768 "OAMON" 1862773 T OAMON (NIL) -9 NIL 1862793 NIL) (-797 1861565 1862083 1862111 "OAGROUP" 1862116 T OAGROUP (NIL) -9 NIL 1862136 NIL) (-796 1861255 1861305 1861393 "NUMTUBE" 1861509 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854828 1856346 1857882 "NUMQUAD" 1859739 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850584 1851572 1852597 "NUMODE" 1853823 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847939 1848819 1848847 "NUMINT" 1849770 T NUMINT (NIL) -9 NIL 1850534 NIL) (-792 1846887 1847084 1847302 "NUMFMT" 1847741 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833246 1836191 1838723 "NUMERIC" 1844394 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827616 1832695 1832790 "NTSCAT" 1832795 NIL NTSCAT (NIL T T T T) -9 NIL 1832834 NIL) (-789 1826810 1826975 1827168 "NTPOLFN" 1827455 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814887 1823635 1824447 "NSUP" 1826031 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814519 1814576 1814685 "NSUP2" 1814824 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804745 1814293 1814426 "NSMP" 1814431 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803177 1803478 1803835 "NREP" 1804433 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801768 1802020 1802378 "NPCOEF" 1802920 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800834 1800949 1801165 "NORMRETR" 1801649 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798875 1799165 1799574 "NORMPK" 1800542 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798560 1798588 1798712 "NORMMA" 1798841 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798360 1798517 1798546 "NONE" 1798551 T NONE (NIL) -8 NIL NIL NIL) (-779 1798149 1798178 1798247 "NONE1" 1798324 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797646 1797708 1797887 "NODE1" 1798081 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795931 1796782 1797037 "NNI" 1797384 T NNI (NIL) -8 NIL NIL 1797619) (-776 1794351 1794664 1795028 "NLINSOL" 1795599 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790592 1791587 1792486 "NIPROB" 1793472 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789349 1789583 1789885 "NFINTBAS" 1790354 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788523 1788999 1789040 "NETCLT" 1789212 NIL NETCLT (NIL T) -9 NIL 1789294 NIL) (-772 1787231 1787462 1787743 "NCODIV" 1788291 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786993 1787030 1787105 "NCNTFRAC" 1787188 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785173 1785537 1785957 "NCEP" 1786618 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784024 1784797 1784825 "NASRING" 1784935 T NASRING (NIL) -9 NIL 1785015 NIL) (-768 1783819 1783863 1783957 "NASRING-" 1783962 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782926 1783451 1783479 "NARNG" 1783596 T NARNG (NIL) -9 NIL 1783687 NIL) (-766 1782618 1782685 1782819 "NARNG-" 1782824 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781497 1781704 1781939 "NAGSP" 1782403 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772769 1774453 1776126 "NAGS" 1779844 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771317 1771625 1771956 "NAGF07" 1772458 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765855 1767146 1768453 "NAGF04" 1770030 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758823 1760437 1762070 "NAGF02" 1764242 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754047 1755147 1756264 "NAGF01" 1757726 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747675 1749241 1750826 "NAGE04" 1752482 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738844 1740965 1743095 "NAGE02" 1745565 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734797 1735744 1736708 "NAGE01" 1737900 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732592 1733126 1733684 "NAGD03" 1734259 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724342 1726270 1728224 "NAGD02" 1730658 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718153 1719578 1721018 "NAGD01" 1722922 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714362 1715184 1716021 "NAGC06" 1717336 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712827 1713159 1713515 "NAGC05" 1714026 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712203 1712322 1712466 "NAGC02" 1712703 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711162 1711745 1711785 "NAALG" 1711864 NIL NAALG (NIL T) -9 NIL 1711925 NIL) (-749 1710997 1711026 1711116 "NAALG-" 1711121 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704947 1706055 1707242 "MULTSQFR" 1709893 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704266 1704341 1704525 "MULTFACT" 1704859 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696990 1700903 1700956 "MTSCAT" 1702026 NIL MTSCAT (NIL T T) -9 NIL 1702541 NIL) (-745 1696702 1696756 1696848 "MTHING" 1696930 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696494 1696527 1696587 "MSYSCMD" 1696662 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692576 1695249 1695569 "MSET" 1696207 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689645 1692137 1692178 "MSETAGG" 1692183 NIL MSETAGG (NIL T) -9 NIL 1692217 NIL) (-741 1685487 1687024 1687769 "MRING" 1688945 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685053 1685120 1685251 "MRF2" 1685414 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684671 1684706 1684850 "MRATFAC" 1685012 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682283 1682578 1683009 "MPRFF" 1684376 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676580 1682137 1682234 "MPOLY" 1682239 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676070 1676105 1676313 "MPCPF" 1676539 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675584 1675627 1675811 "MPC3" 1676021 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674779 1674860 1675081 "MPC2" 1675499 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673080 1673417 1673807 "MONOTOOL" 1674439 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672305 1672622 1672650 "MONOID" 1672869 T MONOID (NIL) -9 NIL 1673016 NIL) (-731 1671851 1671970 1672151 "MONOID-" 1672156 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662326 1668277 1668336 "MONOGEN" 1669010 NIL MONOGEN (NIL T T) -9 NIL 1669466 NIL) (-729 1659544 1660279 1661279 "MONOGEN-" 1661398 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658377 1658823 1658851 "MONADWU" 1659243 T MONADWU (NIL) -9 NIL 1659481 NIL) (-727 1657749 1657908 1658156 "MONADWU-" 1658161 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657108 1657352 1657380 "MONAD" 1657587 T MONAD (NIL) -9 NIL 1657699 NIL) (-725 1656793 1656871 1657003 "MONAD-" 1657008 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655082 1655706 1655985 "MOEBIUS" 1656546 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654360 1654764 1654804 "MODULE" 1654809 NIL MODULE (NIL T) -9 NIL 1654848 NIL) (-722 1653928 1654024 1654214 "MODULE-" 1654219 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651608 1652292 1652619 "MODRING" 1653752 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648552 1649713 1650234 "MODOP" 1651137 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647140 1647619 1647896 "MODMONOM" 1648415 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637184 1645431 1645845 "MODMON" 1646777 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634340 1636028 1636304 "MODFIELD" 1637059 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633317 1633621 1633811 "MMLFORM" 1634170 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632843 1632886 1633065 "MMAP" 1633268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630922 1631689 1631730 "MLO" 1632153 NIL MLO (NIL T) -9 NIL 1632395 NIL) (-713 1628288 1628804 1629406 "MLIFT" 1630403 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627679 1627763 1627917 "MKUCFUNC" 1628199 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627278 1627348 1627471 "MKRECORD" 1627602 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626325 1626487 1626715 "MKFUNC" 1627089 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625713 1625817 1625973 "MKFLCFN" 1626208 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624990 1625092 1625277 "MKBCFUNC" 1625606 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621697 1624544 1624680 "MINT" 1624874 T MINT (NIL) -8 NIL NIL NIL) (-706 1620509 1620752 1621029 "MHROWRED" 1621452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615889 1619044 1619449 "MFLOAT" 1620124 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615246 1615322 1615493 "MFINFACT" 1615801 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611561 1612409 1613293 "MESH" 1614382 T MESH (NIL) -7 NIL NIL NIL) (-702 1609951 1610263 1610616 "MDDFACT" 1611248 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606746 1609110 1609151 "MDAGG" 1609406 NIL MDAGG (NIL T) -9 NIL 1609549 NIL) (-700 1596486 1606039 1606246 "MCMPLX" 1606559 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595623 1595769 1595970 "MCDEN" 1596335 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593513 1593783 1594163 "MCALCFN" 1595353 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592438 1592678 1592911 "MAYBE" 1593319 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590050 1590573 1591135 "MATSTOR" 1591909 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586007 1589422 1589670 "MATRIX" 1589835 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581773 1582480 1583216 "MATLIN" 1585364 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571879 1575065 1575142 "MATCAT" 1580022 NIL MATCAT (NIL T T T) -9 NIL 1581439 NIL) (-692 1568235 1569256 1570612 "MATCAT-" 1570617 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566829 1566982 1567315 "MATCAT2" 1568070 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564941 1565265 1565649 "MAPPKG3" 1566504 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563922 1564095 1564317 "MAPPKG2" 1564765 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562421 1562705 1563032 "MAPPKG1" 1563628 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561500 1561827 1562004 "MAPPAST" 1562264 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561111 1561169 1561292 "MAPHACK3" 1561436 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560703 1560764 1560878 "MAPHACK2" 1561043 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560141 1560244 1560386 "MAPHACK1" 1560594 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558220 1558841 1559145 "MAGMA" 1559869 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557699 1557944 1558035 "MACROAST" 1558149 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554117 1555938 1556399 "M3D" 1557271 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548223 1552486 1552527 "LZSTAGG" 1553309 NIL LZSTAGG (NIL T) -9 NIL 1553604 NIL) (-679 1544181 1545354 1546811 "LZSTAGG-" 1546816 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541268 1542072 1542559 "LWORD" 1543726 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540844 1541072 1541147 "LSTAST" 1541213 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534010 1540615 1540749 "LSQM" 1540754 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533234 1533373 1533601 "LSPP" 1533865 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531046 1531347 1531803 "LSMP" 1532923 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527825 1528499 1529229 "LSMP1" 1530348 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521702 1526992 1527033 "LSAGG" 1527095 NIL LSAGG (NIL T) -9 NIL 1527173 NIL) (-671 1518397 1519321 1520534 "LSAGG-" 1520539 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515996 1517541 1517790 "LPOLY" 1518192 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515578 1515663 1515786 "LPEFRAC" 1515905 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513899 1514672 1514925 "LO" 1515410 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513551 1513663 1513691 "LOGIC" 1513802 T LOGIC (NIL) -9 NIL 1513883 NIL) (-666 1513413 1513436 1513507 "LOGIC-" 1513512 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512606 1512746 1512939 "LODOOPS" 1513269 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510029 1512522 1512588 "LODO" 1512593 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508567 1508802 1509155 "LODOF" 1509776 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504785 1507216 1507257 "LODOCAT" 1507695 NIL LODOCAT (NIL T) -9 NIL 1507906 NIL) (-661 1504518 1504576 1504703 "LODOCAT-" 1504708 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501838 1504359 1504477 "LODO2" 1504482 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499273 1501775 1501820 "LODO1" 1501825 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498154 1498319 1498624 "LODEEF" 1499096 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493393 1496284 1496325 "LNAGG" 1497272 NIL LNAGG (NIL T) -9 NIL 1497716 NIL) (-656 1492540 1492754 1493096 "LNAGG-" 1493101 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488676 1489465 1490104 "LMOPS" 1491955 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488079 1488467 1488508 "LMODULE" 1488513 NIL LMODULE (NIL T) -9 NIL 1488539 NIL) (-653 1485277 1487724 1487847 "LMDICT" 1487989 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484683 1484904 1484945 "LLINSET" 1485136 NIL LLINSET (NIL T) -9 NIL 1485227 NIL) (-651 1484382 1484591 1484651 "LITERAL" 1484656 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477545 1483316 1483620 "LIST" 1484111 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477070 1477144 1477283 "LIST3" 1477465 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476077 1476255 1476483 "LIST2" 1476888 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474211 1474523 1474922 "LIST2MAP" 1475724 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473807 1474044 1474085 "LINSET" 1474090 NIL LINSET (NIL T) -9 NIL 1474124 NIL) (-645 1472468 1473138 1473179 "LINEXP" 1473434 NIL LINEXP (NIL T) -9 NIL 1473583 NIL) (-644 1471115 1471375 1471672 "LINDEP" 1472220 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467882 1468601 1469378 "LIMITRF" 1470370 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466185 1466481 1466890 "LIMITPS" 1467577 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460613 1465696 1465924 "LIE" 1466006 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459561 1460030 1460070 "LIECAT" 1460210 NIL LIECAT (NIL T) -9 NIL 1460361 NIL) (-639 1459402 1459429 1459517 "LIECAT-" 1459522 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451898 1458851 1459016 "LIB" 1459257 T LIB (NIL) -8 NIL NIL NIL) (-637 1447533 1448416 1449351 "LGROBP" 1451015 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445531 1445805 1446155 "LF" 1447254 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444371 1445063 1445091 "LFCAT" 1445298 T LFCAT (NIL) -9 NIL 1445437 NIL) (-634 1441273 1441903 1442591 "LEXTRIPK" 1443735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438017 1438843 1439346 "LEXP" 1440853 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437493 1437738 1437830 "LETAST" 1437945 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435891 1436204 1436605 "LEADCDET" 1437175 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435081 1435155 1435384 "LAZM3PK" 1435812 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429998 1433158 1433696 "LAUPOL" 1434593 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429577 1429621 1429782 "LAPLACE" 1429948 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427516 1428678 1428929 "LA" 1429410 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426510 1427094 1427135 "LALG" 1427197 NIL LALG (NIL T) -9 NIL 1427256 NIL) (-625 1426224 1426283 1426419 "LALG-" 1426424 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426059 1426083 1426124 "KVTFROM" 1426186 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424982 1425426 1425611 "KTVLOGIC" 1425894 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424817 1424841 1424882 "KRCFROM" 1424944 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423721 1423908 1424207 "KOVACIC" 1424617 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423556 1423580 1423621 "KONVERT" 1423683 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423391 1423415 1423456 "KOERCE" 1423518 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421221 1421984 1422361 "KERNEL" 1423047 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420717 1420798 1420930 "KERNEL2" 1421135 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414487 1419256 1419310 "KDAGG" 1419687 NIL KDAGG (NIL T T) -9 NIL 1419893 NIL) (-615 1414016 1414140 1414345 "KDAGG-" 1414350 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407164 1413677 1413832 "KAFILE" 1413894 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401592 1406675 1406903 "JORDAN" 1406985 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400971 1401241 1401362 "JOINAST" 1401491 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400817 1400876 1400931 "JAVACODE" 1400936 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397069 1399022 1399076 "IXAGG" 1400005 NIL IXAGG (NIL T T) -9 NIL 1400464 NIL) (-609 1395988 1396294 1396713 "IXAGG-" 1396718 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391518 1395910 1395969 "IVECTOR" 1395974 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390284 1390521 1390787 "ITUPLE" 1391285 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388786 1388963 1389258 "ITRIGMNP" 1390106 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387531 1387735 1388018 "ITFUN3" 1388562 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387163 1387220 1387329 "ITFUN2" 1387468 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386322 1386643 1386817 "ITFORM" 1387009 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384283 1385342 1385620 "ITAYLOR" 1386077 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373228 1378420 1379583 "ISUPS" 1383153 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372332 1372472 1372708 "ISUMP" 1373075 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367707 1372277 1372318 "ISTRING" 1372323 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367183 1367428 1367520 "ISAST" 1367635 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366392 1366474 1366690 "IRURPK" 1367097 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365328 1365529 1365769 "IRSN" 1366172 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363399 1363754 1364183 "IRRF2F" 1364966 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363146 1363184 1363260 "IRREDFFX" 1363355 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361761 1362020 1362319 "IROOT" 1362879 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358365 1359445 1360137 "IR" 1361101 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357570 1357858 1358009 "IRFORM" 1358234 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355183 1355678 1356244 "IR2" 1357048 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354283 1354396 1354610 "IR2F" 1355066 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354074 1354108 1354168 "IPRNTPK" 1354243 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350655 1353963 1354032 "IPF" 1354037 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348982 1350580 1350637 "IPADIC" 1350642 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348294 1348542 1348672 "IP4ADDR" 1348872 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347668 1347923 1348055 "IOMODE" 1348182 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346741 1347265 1347392 "IOBFILE" 1347561 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346229 1346645 1346673 "IOBCON" 1346678 T IOBCON (NIL) -9 NIL 1346699 NIL) (-581 1345740 1345798 1345981 "INVLAPLA" 1346165 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335388 1337742 1340128 "INTTR" 1343404 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331723 1332465 1333330 "INTTOOLS" 1334573 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331309 1331400 1331517 "INTSLPE" 1331626 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329262 1331232 1331291 "INTRVL" 1331296 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326864 1327376 1327951 "INTRF" 1328747 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326275 1326372 1326514 "INTRET" 1326762 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324272 1324661 1325131 "INTRAT" 1325883 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321535 1322118 1322737 "INTPM" 1323757 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318280 1318879 1319617 "INTPAF" 1320921 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313459 1314421 1315472 "INTPACK" 1317249 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310407 1313256 1313365 "INT" 1313370 T INT (NIL) -8 NIL NIL NIL) (-569 1309659 1309811 1310019 "INTHERTR" 1310249 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309098 1309178 1309366 "INTHERAL" 1309573 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306944 1307387 1307844 "INTHEORY" 1308661 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298350 1299971 1301743 "INTG0" 1305296 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278923 1283713 1288523 "INTFTBL" 1293560 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278172 1278310 1278483 "INTFACT" 1278782 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275599 1276045 1276602 "INTEF" 1277726 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273966 1274705 1274733 "INTDOM" 1275034 T INTDOM (NIL) -9 NIL 1275241 NIL) (-561 1273335 1273509 1273751 "INTDOM-" 1273756 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269723 1271651 1271705 "INTCAT" 1272504 NIL INTCAT (NIL T) -9 NIL 1272825 NIL) (-559 1269195 1269298 1269426 "INTBIT" 1269615 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267894 1268048 1268355 "INTALG" 1269040 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267377 1267467 1267624 "INTAF" 1267798 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260720 1267187 1267327 "INTABL" 1267332 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260061 1260527 1260592 "INT8" 1260626 T INT8 (NIL) -8 NIL NIL 1260671) (-554 1259401 1259867 1259932 "INT64" 1259966 T INT64 (NIL) -8 NIL NIL 1260011) (-553 1258741 1259207 1259272 "INT32" 1259306 T INT32 (NIL) -8 NIL NIL 1259351) (-552 1258081 1258547 1258612 "INT16" 1258646 T INT16 (NIL) -8 NIL NIL 1258691) (-551 1252991 1255704 1255732 "INS" 1256666 T INS (NIL) -9 NIL 1257331 NIL) (-550 1250231 1251002 1251976 "INS-" 1252049 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249006 1249233 1249531 "INPSIGN" 1249984 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248124 1248241 1248438 "INPRODPF" 1248886 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247018 1247135 1247372 "INPRODFF" 1248004 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246018 1246170 1246430 "INNMFACT" 1246854 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245215 1245312 1245500 "INMODGCD" 1245917 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243723 1243968 1244292 "INFSP" 1244960 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242907 1243024 1243207 "INFPROD0" 1243603 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239762 1240972 1241487 "INFORM" 1242400 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239372 1239432 1239530 "INFORM1" 1239697 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238895 1238984 1239098 "INFINITY" 1239278 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238071 1238615 1238716 "INETCLTS" 1238814 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236687 1236937 1237258 "INEP" 1237819 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235936 1236584 1236649 "INDE" 1236654 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235500 1235568 1235685 "INCRMAPS" 1235863 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234318 1234769 1234975 "INBFILE" 1235314 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229617 1230554 1231498 "INBFF" 1233406 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228525 1228794 1228822 "INBCON" 1229335 T INBCON (NIL) -9 NIL 1229601 NIL) (-532 1227777 1228000 1228276 "INBCON-" 1228281 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227256 1227501 1227592 "INAST" 1227706 T INAST (NIL) -8 NIL NIL NIL) (-530 1226683 1226935 1227041 "IMPTAST" 1227170 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223129 1226527 1226631 "IMATRIX" 1226636 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221837 1221960 1222276 "IMATQF" 1222985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220057 1220284 1220621 "IMATLIN" 1221593 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214635 1219981 1220039 "ILIST" 1220044 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212540 1214495 1214608 "IIARRAY2" 1214613 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207938 1212451 1212515 "IFF" 1212520 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207285 1207555 1207671 "IFAST" 1207842 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202280 1206577 1206765 "IFARRAY" 1207142 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201460 1202184 1202257 "IFAMON" 1202262 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201044 1201109 1201163 "IEVALAB" 1201370 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200719 1200787 1200947 "IEVALAB-" 1200952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200350 1200633 1200696 "IDPO" 1200701 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199600 1200239 1200314 "IDPOAMS" 1200319 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198907 1199489 1199564 "IDPOAM" 1199569 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197966 1198242 1198295 "IDPC" 1198708 NIL IDPC (NIL T T) -9 NIL 1198857 NIL) (-514 1197435 1197858 1197931 "IDPAM" 1197936 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196811 1197327 1197400 "IDPAG" 1197405 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196456 1196647 1196722 "IDENT" 1196756 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192711 1193559 1194454 "IDECOMP" 1195613 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185549 1186634 1187681 "IDEAL" 1191747 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184709 1184821 1185021 "ICDEN" 1185433 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183780 1184189 1184336 "ICARD" 1184582 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181840 1182153 1182558 "IBPTOOLS" 1183457 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177447 1181460 1181573 "IBITS" 1181759 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174170 1174746 1175441 "IBATOOL" 1176864 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171949 1172411 1172944 "IBACHIN" 1173705 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169778 1171795 1171898 "IARRAY2" 1171903 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165884 1169704 1169761 "IARRAY1" 1169766 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159993 1164296 1164777 "IAN" 1165423 T IAN (NIL) -8 NIL NIL NIL) (-500 1159504 1159561 1159734 "IALGFACT" 1159930 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159032 1159145 1159173 "HYPCAT" 1159380 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158570 1158687 1158873 "HYPCAT-" 1158878 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158165 1158365 1158448 "HOSTNAME" 1158507 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158010 1158047 1158088 "HOMOTOP" 1158093 NIL HOMOTOP (NIL T) -9 NIL 1158126 NIL) (-495 1154642 1156020 1156061 "HOAGG" 1157042 NIL HOAGG (NIL T) -9 NIL 1157721 NIL) (-494 1153236 1153635 1154161 "HOAGG-" 1154166 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147238 1152829 1152979 "HEXADEC" 1153106 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145986 1146208 1146471 "HEUGCD" 1147015 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145062 1145823 1145953 "HELLFDIV" 1145958 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143241 1144839 1144927 "HEAP" 1145006 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142504 1142793 1142927 "HEADAST" 1143127 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136370 1142419 1142481 "HDP" 1142486 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130358 1136005 1136157 "HDMP" 1136271 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129682 1129822 1129986 "HB" 1130214 T HB (NIL) -7 NIL NIL NIL) (-485 1123068 1129528 1129632 "HASHTBL" 1129637 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122544 1122789 1122881 "HASAST" 1122996 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120322 1122166 1122348 "HACKPI" 1122382 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115990 1120175 1120288 "GTSET" 1120293 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109405 1115868 1115966 "GSTBL" 1115971 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101683 1108436 1108701 "GSERIES" 1109196 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100824 1101241 1101269 "GROUP" 1101472 T GROUP (NIL) -9 NIL 1101606 NIL) (-478 1100190 1100349 1100600 "GROUP-" 1100605 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098557 1098878 1099265 "GROEBSOL" 1099867 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097471 1097759 1097810 "GRMOD" 1098339 NIL GRMOD (NIL T T) -9 NIL 1098507 NIL) (-475 1097239 1097275 1097403 "GRMOD-" 1097408 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092529 1093593 1094593 "GRIMAGE" 1096259 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090995 1091256 1091580 "GRDEF" 1092225 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090439 1090555 1090696 "GRAY" 1090874 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089626 1090032 1090083 "GRALG" 1090236 NIL GRALG (NIL T T) -9 NIL 1090329 NIL) (-470 1089287 1089360 1089523 "GRALG-" 1089528 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086064 1088872 1089050 "GPOLSET" 1089194 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085418 1085475 1085733 "GOSPER" 1086001 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081150 1081856 1082382 "GMODPOL" 1085117 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080155 1080339 1080577 "GHENSEL" 1080962 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074311 1075154 1076174 "GENUPS" 1079239 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074008 1074059 1074148 "GENUFACT" 1074254 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073420 1073497 1073662 "GENPGCD" 1073926 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072894 1072929 1073142 "GENMFACT" 1073379 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071460 1071717 1072024 "GENEEZ" 1072637 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065608 1071071 1071233 "GDMP" 1071383 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054951 1059379 1060485 "GCNAALG" 1064591 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053278 1054140 1054168 "GCDDOM" 1054423 T GCDDOM (NIL) -9 NIL 1054580 NIL) (-457 1052748 1052875 1053090 "GCDDOM-" 1053095 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051420 1051605 1051909 "GB" 1052527 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040036 1042366 1044758 "GBINTERN" 1049111 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037873 1038165 1038586 "GBF" 1039711 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036654 1036819 1037086 "GBEUCLID" 1037689 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036003 1036128 1036277 "GAUSSFAC" 1036525 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034370 1034672 1034986 "GALUTIL" 1035722 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032678 1032952 1033276 "GALPOLYU" 1034097 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030043 1030333 1030740 "GALFACTU" 1032375 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021849 1023348 1024956 "GALFACT" 1028475 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019237 1019895 1019923 "FVFUN" 1021079 T FVFUN (NIL) -9 NIL 1021799 NIL) (-446 1018503 1018685 1018713 "FVC" 1019004 T FVC (NIL) -9 NIL 1019187 NIL) (-445 1018146 1018328 1018396 "FUNDESC" 1018455 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017761 1017943 1018024 "FUNCTION" 1018098 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015505 1016083 1016549 "FT" 1017315 T FT (NIL) -8 NIL NIL NIL) (-442 1014296 1014806 1015009 "FTEM" 1015322 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012587 1012876 1013273 "FSUPFACT" 1013987 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010984 1011273 1011605 "FST" 1012275 T FST (NIL) -8 NIL NIL NIL) (-439 1010183 1010289 1010477 "FSRED" 1010866 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008882 1009138 1009485 "FSPRMELT" 1009898 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006188 1006626 1007112 "FSPECF" 1008445 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987826 996157 996198 "FS" 1000082 NIL FS (NIL T) -9 NIL 1002371 NIL) (-435 976469 979462 983519 "FS-" 983819 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975997 976051 976221 "FSINT" 976410 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974289 974990 975293 "FSERIES" 975776 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973331 973447 973671 "FSCINT" 974169 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969539 972275 972316 "FSAGG" 972686 NIL FSAGG (NIL T) -9 NIL 972945 NIL) (-430 967301 967902 968698 "FSAGG-" 968793 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966343 966486 966713 "FSAGG2" 967154 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964025 964305 964852 "FS2UPS" 966061 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963659 963702 963831 "FS2" 963976 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962537 962708 963010 "FS2EXPXP" 963484 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961963 962078 962230 "FRUTIL" 962417 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953376 957458 958816 "FR" 960637 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948345 951019 951059 "FRNAALG" 952455 NIL FRNAALG (NIL T) -9 NIL 953062 NIL) (-422 944018 945094 946369 "FRNAALG-" 947119 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943656 943699 943826 "FRNAAF2" 943969 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942031 942505 942801 "FRMOD" 943468 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939774 940406 940724 "FRIDEAL" 941822 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938965 939052 939343 "FRIDEAL2" 939681 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938098 938512 938553 "FRETRCT" 938558 NIL FRETRCT (NIL T) -9 NIL 938734 NIL) (-416 937210 937441 937792 "FRETRCT-" 937797 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934298 935508 935567 "FRAMALG" 936449 NIL FRAMALG (NIL T T) -9 NIL 936741 NIL) (-414 932432 932887 933517 "FRAMALG-" 933740 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926351 931905 932182 "FRAC" 932187 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925987 926044 926151 "FRAC2" 926288 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925623 925680 925787 "FR2" 925924 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920136 923029 923057 "FPS" 924176 T FPS (NIL) -9 NIL 924733 NIL) (-409 919585 919694 919858 "FPS-" 920004 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916887 918556 918584 "FPC" 918809 T FPC (NIL) -9 NIL 918951 NIL) (-407 916680 916720 916817 "FPC-" 916822 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915470 916168 916209 "FPATMAB" 916214 NIL FPATMAB (NIL T) -9 NIL 916366 NIL) (-405 913143 913646 914072 "FPARFRAC" 915107 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908537 909035 909717 "FORTRAN" 912575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906253 906753 907292 "FORT" 908018 T FORT (NIL) -7 NIL NIL NIL) (-402 903929 904491 904519 "FORTFN" 905579 T FORTFN (NIL) -9 NIL 906203 NIL) (-401 903693 903743 903771 "FORTCAT" 903830 T FORTCAT (NIL) -9 NIL 903892 NIL) (-400 901799 902309 902699 "FORMULA" 903323 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901587 901617 901686 "FORMULA1" 901763 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901110 901162 901335 "FORDER" 901529 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900206 900370 900563 "FOP" 900937 T FOP (NIL) -7 NIL NIL NIL) (-396 898787 899486 899660 "FNLA" 900088 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897516 897931 897959 "FNCAT" 898419 T FNCAT (NIL) -9 NIL 898679 NIL) (-394 897055 897475 897503 "FNAME" 897508 T FNAME (NIL) -8 NIL NIL NIL) (-393 895618 896581 896609 "FMTC" 896614 T FMTC (NIL) -9 NIL 896650 NIL) (-392 894364 895554 895600 "FMONOID" 895605 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891192 892360 892401 "FMONCAT" 893618 NIL FMONCAT (NIL T) -9 NIL 894223 NIL) (-390 890384 890934 891083 "FM" 891088 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887808 888454 888482 "FMFUN" 889626 T FMFUN (NIL) -9 NIL 890334 NIL) (-388 887077 887258 887286 "FMC" 887576 T FMC (NIL) -9 NIL 887758 NIL) (-387 884156 885016 885070 "FMCAT" 886265 NIL FMCAT (NIL T T) -9 NIL 886760 NIL) (-386 883022 883922 884022 "FM1" 884101 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880796 881212 881706 "FLOATRP" 882573 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874374 878525 879146 "FLOAT" 880195 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871812 872312 872890 "FLOATCP" 873841 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870552 871390 871431 "FLINEXP" 871436 NIL FLINEXP (NIL T) -9 NIL 871529 NIL) (-381 869706 869941 870269 "FLINEXP-" 870274 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868782 868926 869150 "FLASORT" 869558 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865898 866766 866818 "FLALG" 868045 NIL FLALG (NIL T T) -9 NIL 868512 NIL) (-378 859634 863384 863425 "FLAGG" 864687 NIL FLAGG (NIL T) -9 NIL 865339 NIL) (-377 858360 858699 859189 "FLAGG-" 859194 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857402 857545 857772 "FLAGG2" 858213 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854253 855261 855320 "FINRALG" 856448 NIL FINRALG (NIL T T) -9 NIL 856956 NIL) (-374 853413 853642 853981 "FINRALG-" 853986 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852793 853032 853060 "FINITE" 853256 T FINITE (NIL) -9 NIL 853363 NIL) (-372 845150 847337 847377 "FINAALG" 851044 NIL FINAALG (NIL T) -9 NIL 852497 NIL) (-371 840482 841532 842676 "FINAALG-" 844055 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839850 840237 840340 "FILE" 840412 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838508 838846 838900 "FILECAT" 839584 NIL FILECAT (NIL T T) -9 NIL 839800 NIL) (-368 836224 837752 837780 "FIELD" 837820 T FIELD (NIL) -9 NIL 837900 NIL) (-367 834844 835229 835740 "FIELD-" 835745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832694 833479 833826 "FGROUP" 834530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831784 831948 832168 "FGLMICPK" 832526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827616 831709 831766 "FFX" 831771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827217 827278 827413 "FFSLPE" 827549 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823207 823989 824785 "FFPOLY" 826453 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822711 822747 822956 "FFPOLY2" 823165 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818557 822630 822693 "FFP" 822698 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813955 818468 818532 "FF" 818537 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809081 813298 813488 "FFNBX" 813809 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804009 808216 808474 "FFNBP" 808935 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798642 803293 803504 "FFNB" 803842 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797474 797672 797987 "FFINTBAS" 798439 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793543 795763 795791 "FFIELDC" 796411 T FFIELDC (NIL) -9 NIL 796787 NIL) (-353 792205 792576 793073 "FFIELDC-" 793078 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791774 791820 791944 "FFHOM" 792147 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789469 789956 790473 "FFF" 791289 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785087 789211 789312 "FFCGX" 789412 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780709 784819 784926 "FFCGP" 785030 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775892 780436 780544 "FFCG" 780645 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757288 766369 766455 "FFCAT" 771620 NIL FFCAT (NIL T T T) -9 NIL 773071 NIL) (-346 752485 753533 754847 "FFCAT-" 756077 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751896 751939 752174 "FFCAT2" 752436 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741219 744868 746088 "FEXPR" 750748 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740219 740654 740695 "FEVALAB" 740779 NIL FEVALAB (NIL T) -9 NIL 741040 NIL) (-342 739378 739588 739926 "FEVALAB-" 739931 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737944 738761 738964 "FDIV" 739277 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734964 735705 735820 "FDIVCAT" 737388 NIL FDIVCAT (NIL T T T T) -9 NIL 737825 NIL) (-339 734726 734753 734923 "FDIVCAT-" 734928 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733946 734033 734310 "FDIV2" 734633 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732920 733241 733443 "FCTRDATA" 733764 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731606 731865 732154 "FCPAK1" 732651 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730705 731106 731247 "FCOMP" 731497 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714410 717855 721393 "FC" 727187 T FC (NIL) -8 NIL NIL NIL) (-333 706773 710801 710841 "FAXF" 712643 NIL FAXF (NIL T) -9 NIL 713335 NIL) (-332 704050 704707 705532 "FAXF-" 705997 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699102 703426 703602 "FARRAY" 703907 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693996 696063 696116 "FAMR" 697139 NIL FAMR (NIL T T) -9 NIL 697599 NIL) (-329 692886 693188 693623 "FAMR-" 693628 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692055 692808 692861 "FAMONOID" 692866 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689841 690551 690604 "FAMONC" 691545 NIL FAMONC (NIL T T) -9 NIL 691931 NIL) (-326 688505 689595 689732 "FAGROUP" 689737 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686300 686619 687022 "FACUTIL" 688186 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685399 685584 685806 "FACTFUNC" 686110 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677821 684702 684901 "EXPUPXS" 685255 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675304 675844 676430 "EXPRTUBE" 677255 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671575 672167 672897 "EXPRODE" 674643 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657060 670224 670653 "EXPR" 671179 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651614 652201 653007 "EXPR2UPS" 656358 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651246 651303 651412 "EXPR2" 651551 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642634 650397 650688 "EXPEXPAN" 651082 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642434 642591 642620 "EXIT" 642625 T EXIT (NIL) -8 NIL NIL NIL) (-315 641914 642158 642249 "EXITAST" 642363 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641541 641603 641716 "EVALCYC" 641846 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641082 641200 641241 "EVALAB" 641411 NIL EVALAB (NIL T) -9 NIL 641515 NIL) (-312 640563 640685 640906 "EVALAB-" 640911 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637931 639233 639261 "EUCDOM" 639816 T EUCDOM (NIL) -9 NIL 640166 NIL) (-310 636336 636778 637368 "EUCDOM-" 637373 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623875 626634 629384 "ESTOOLS" 633606 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623507 623564 623673 "ESTOOLS2" 623812 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623258 623300 623380 "ESTOOLS1" 623459 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617295 618903 618931 "ES" 621699 T ES (NIL) -9 NIL 623109 NIL) (-305 612242 613529 615346 "ES-" 615510 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608616 609377 610157 "ESCONT" 611482 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608361 608393 608475 "ESCONT1" 608578 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608036 608086 608186 "ES2" 608305 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607666 607724 607833 "ES1" 607972 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606882 607011 607187 "ERROR" 607510 T ERROR (NIL) -7 NIL NIL NIL) (-299 600274 606741 606832 "EQTBL" 606837 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592777 595588 597037 "EQ" 598858 NIL -2199 (NIL T) -8 NIL NIL NIL) (-297 592409 592466 592575 "EQ2" 592714 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587700 588747 589840 "EP" 591348 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586300 586591 586897 "ENV" 587414 T ENV (NIL) -8 NIL NIL NIL) (-294 585394 585948 585976 "ENTIRER" 585981 T ENTIRER (NIL) -9 NIL 586027 NIL) (-293 581861 583349 583719 "EMR" 585193 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581005 581190 581244 "ELTAGG" 581624 NIL ELTAGG (NIL T T) -9 NIL 581835 NIL) (-291 580724 580786 580927 "ELTAGG-" 580932 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580513 580542 580596 "ELTAB" 580680 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579639 579785 579984 "ELFUTS" 580364 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579381 579437 579465 "ELEMFUN" 579570 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579251 579272 579340 "ELEMFUN-" 579345 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574095 577351 577392 "ELAGG" 578332 NIL ELAGG (NIL T) -9 NIL 578795 NIL) (-285 572380 572814 573477 "ELAGG-" 573482 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571692 571829 571985 "ELABOR" 572244 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570353 570632 570926 "ELABEXPR" 571418 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563217 565020 565847 "EFUPXS" 569629 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556667 558468 559278 "EFULS" 562493 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554152 554510 554982 "EFSTRUC" 556299 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543943 545509 547057 "EF" 552667 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543017 543428 543577 "EAB" 543814 T EAB (NIL) -8 NIL NIL NIL) (-277 542199 542976 543004 "E04UCFA" 543009 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541381 542158 542186 "E04NAFA" 542191 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540563 541340 541368 "E04MBFA" 541373 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539745 540522 540550 "E04JAFA" 540555 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538929 539704 539732 "E04GCFA" 539737 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538113 538888 538916 "E04FDFA" 538921 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537295 538072 538100 "E04DGFA" 538105 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531468 532820 534184 "E04AGNT" 535951 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530148 530654 530694 "DVARCAT" 531169 NIL DVARCAT (NIL T) -9 NIL 531368 NIL) (-268 529352 529564 529878 "DVARCAT-" 529883 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522489 529151 529280 "DSMP" 529285 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517270 518434 519502 "DROPT" 521441 T DROPT (NIL) -8 NIL NIL NIL) (-265 516935 516994 517092 "DROPT1" 517205 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512050 513176 514313 "DROPT0" 515818 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510395 510720 511106 "DRAWPT" 511684 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504982 505905 506984 "DRAW" 509369 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504615 504668 504786 "DRAWHACK" 504923 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503346 503615 503906 "DRAWCX" 504344 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502861 502930 503081 "DRAWCURV" 503272 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493329 495291 497406 "DRAWCFUN" 500766 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490093 492022 492063 "DQAGG" 492692 NIL DQAGG (NIL T) -9 NIL 492966 NIL) (-256 478217 484686 484769 "DPOLCAT" 486621 NIL DPOLCAT (NIL T T T T) -9 NIL 487166 NIL) (-255 473054 474402 476360 "DPOLCAT-" 476365 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466176 472915 473013 "DPMO" 473018 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459201 465956 466123 "DPMM" 466128 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458679 458893 458991 "DOMTMPLT" 459123 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458112 458481 458561 "DOMCTOR" 458619 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457324 457592 457743 "DOMAIN" 457981 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451312 456959 457111 "DMP" 457225 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450912 450968 451112 "DLP" 451250 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444734 450239 450429 "DLIST" 450754 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441531 443587 443628 "DLAGG" 444178 NIL DLAGG (NIL T) -9 NIL 444408 NIL) (-245 440207 440871 440899 "DIVRING" 440991 T DIVRING (NIL) -9 NIL 441074 NIL) (-244 439444 439634 439934 "DIVRING-" 439939 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437546 437903 438309 "DISPLAY" 439058 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431434 437460 437523 "DIRPROD" 437528 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430282 430485 430750 "DIRPROD2" 431227 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419057 425063 425116 "DIRPCAT" 425526 NIL DIRPCAT (NIL NIL T) -9 NIL 426366 NIL) (-239 416383 417025 417906 "DIRPCAT-" 418243 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415670 415830 416016 "DIOSP" 416217 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412325 414582 414623 "DIOPS" 415057 NIL DIOPS (NIL T) -9 NIL 415286 NIL) (-236 411874 411988 412179 "DIOPS-" 412184 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410697 411325 411353 "DIFRING" 411540 T DIFRING (NIL) -9 NIL 411650 NIL) (-234 410343 410420 410572 "DIFRING-" 410577 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408079 409351 409392 "DIFEXT" 409755 NIL DIFEXT (NIL T) -9 NIL 410049 NIL) (-232 406364 406792 407458 "DIFEXT-" 407463 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403639 405896 405937 "DIAGG" 405942 NIL DIAGG (NIL T) -9 NIL 405962 NIL) (-230 403023 403180 403432 "DIAGG-" 403437 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398440 401982 402259 "DHMATRIX" 402792 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394052 394961 395971 "DFSFUN" 397450 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389131 392983 393295 "DFLOAT" 393760 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387394 387675 388064 "DFINTTLS" 388839 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384423 385415 385815 "DERHAM" 387060 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382224 384198 384287 "DEQUEUE" 384367 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381478 381611 381794 "DEGRED" 382086 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377908 378653 379499 "DEFINTRF" 380706 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375463 375932 376524 "DEFINTEF" 377427 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374813 375083 375198 "DEFAST" 375368 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368815 374406 374556 "DECIMAL" 374683 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366327 366785 367291 "DDFACT" 368359 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365923 365966 366117 "DBLRESP" 366278 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363795 364156 364516 "DBASE" 365690 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363037 363275 363421 "DATAARY" 363694 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362143 362996 363024 "D03FAFA" 363029 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361250 362102 362130 "D03EEFA" 362135 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359200 359666 360155 "D03AGNT" 360781 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358489 359159 359187 "D02EJFA" 359192 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357778 358448 358476 "D02CJFA" 358481 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357067 357737 357765 "D02BHFA" 357770 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356356 357026 357054 "D02BBFA" 357059 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349553 351142 352748 "D02AGNT" 354770 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347321 347844 348390 "D01WGTS" 349027 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346388 347280 347308 "D01TRNS" 347313 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345456 346347 346375 "D01GBFA" 346380 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344524 345415 345443 "D01FCFA" 345448 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343592 344483 344511 "D01ASFA" 344516 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342660 343551 343579 "D01AQFA" 343584 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341728 342619 342647 "D01APFA" 342652 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340796 341687 341715 "D01ANFA" 341720 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339864 340755 340783 "D01AMFA" 340788 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338932 339823 339851 "D01ALFA" 339856 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338000 338891 338919 "D01AKFA" 338924 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337068 337959 337987 "D01AJFA" 337992 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330363 331916 333477 "D01AGNT" 335527 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329700 329828 329980 "CYCLOTOM" 330231 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326434 327148 327875 "CYCLES" 328993 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325746 325880 326051 "CVMP" 326295 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323587 323845 324214 "CTRIGMNP" 325474 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323023 323381 323454 "CTOR" 323534 T CTOR (NIL) -8 NIL NIL NIL) (-188 322532 322754 322855 "CTORKIND" 322942 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321823 322139 322167 "CTORCAT" 322349 T CTORCAT (NIL) -9 NIL 322462 NIL) (-186 321421 321532 321691 "CTORCAT-" 321696 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320883 321095 321203 "CTORCALL" 321345 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320257 320356 320509 "CSTTOOLS" 320780 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316056 316713 317471 "CRFP" 319569 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315531 315777 315869 "CRCEAST" 315984 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314578 314763 314991 "CRAPACK" 315335 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313962 314063 314267 "CPMATCH" 314454 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313687 313715 313821 "CPIMA" 313928 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310035 310707 311426 "COORDSYS" 313022 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309447 309568 309710 "CONTOUR" 309913 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305338 307450 307942 "CONTFRAC" 308987 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305218 305239 305267 "CONDUIT" 305304 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304306 304860 304888 "COMRING" 304893 T COMRING (NIL) -9 NIL 304945 NIL) (-173 303360 303664 303848 "COMPPROP" 304142 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303021 303056 303184 "COMPLPAT" 303319 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293312 302830 302939 "COMPLEX" 302944 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292948 293005 293112 "COMPLEX2" 293249 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292287 292408 292568 "COMPILER" 292808 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292005 292040 292138 "COMPFACT" 292246 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276085 286079 286119 "COMPCAT" 287123 NIL COMPCAT (NIL T) -9 NIL 288471 NIL) (-166 265597 268524 272151 "COMPCAT-" 272507 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265326 265354 265457 "COMMUPC" 265563 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265120 265154 265213 "COMMONOP" 265287 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264676 264871 264958 "COMM" 265053 T COMM (NIL) -8 NIL NIL NIL) (-162 264252 264480 264555 "COMMAAST" 264621 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263501 263695 263723 "COMBOPC" 264061 T COMBOPC (NIL) -9 NIL 264236 NIL) (-160 262397 262607 262849 "COMBINAT" 263291 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258854 259428 260055 "COMBF" 261819 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257612 257970 258205 "COLOR" 258639 T COLOR (NIL) -8 NIL NIL NIL) (-157 257088 257333 257425 "COLONAST" 257540 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256728 256775 256900 "CMPLXRT" 257035 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256176 256428 256527 "CLLCTAST" 256649 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251678 252706 253786 "CLIP" 255116 T CLIP (NIL) -7 NIL NIL NIL) (-153 250019 250779 251019 "CLIF" 251505 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246194 248165 248206 "CLAGG" 249135 NIL CLAGG (NIL T) -9 NIL 249671 NIL) (-151 244616 245073 245656 "CLAGG-" 245661 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244160 244245 244385 "CINTSLPE" 244525 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241661 242132 242680 "CHVAR" 243688 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240835 241389 241417 "CHARZ" 241422 T CHARZ (NIL) -9 NIL 241437 NIL) (-147 240589 240629 240707 "CHARPOL" 240789 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239647 240234 240262 "CHARNZ" 240309 T CHARNZ (NIL) -9 NIL 240365 NIL) (-145 237553 238301 238654 "CHAR" 239314 T CHAR (NIL) -8 NIL NIL NIL) (-144 237279 237340 237368 "CFCAT" 237479 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236520 236631 236814 "CDEN" 237163 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232485 235673 235953 "CCLASS" 236260 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231736 231893 232070 "CATEGORY" 232328 T -10 (NIL) -8 NIL NIL NIL) (-140 231309 231655 231703 "CATCTOR" 231708 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230760 231012 231110 "CATAST" 231231 T CATAST (NIL) -8 NIL NIL NIL) (-138 230236 230481 230573 "CASEAST" 230688 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225246 226265 227018 "CARTEN" 229539 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224354 224502 224723 "CARTEN2" 225093 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222670 223504 223761 "CARD" 224117 T CARD (NIL) -8 NIL NIL NIL) (-134 222246 222474 222549 "CAPSLAST" 222615 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221750 221958 221986 "CACHSET" 222118 T CACHSET (NIL) -9 NIL 222196 NIL) (-132 221220 221542 221570 "CABMON" 221620 T CABMON (NIL) -9 NIL 221676 NIL) (-131 220693 220924 221034 "BYTEORD" 221130 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219675 220227 220369 "BYTE" 220532 T BYTE (NIL) -8 NIL NIL 220654) (-129 215025 219180 219352 "BYTEBUF" 219523 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212534 214717 214824 "BTREE" 214951 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209983 212182 212304 "BTOURN" 212444 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207353 209453 209494 "BTCAT" 209562 NIL BTCAT (NIL T) -9 NIL 209639 NIL) (-125 207020 207100 207249 "BTCAT-" 207254 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202430 206309 206337 "BTAGG" 206451 T BTAGG (NIL) -9 NIL 206561 NIL) (-123 201920 202045 202251 "BTAGG-" 202256 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198915 201198 201413 "BSTREE" 201737 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198053 198179 198363 "BRILL" 198771 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194705 196779 196820 "BRAGG" 197469 NIL BRAGG (NIL T) -9 NIL 197727 NIL) (-119 193234 193640 194195 "BRAGG-" 194200 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186461 192578 192763 "BPADICRT" 193081 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184776 186398 186443 "BPADIC" 186448 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184474 184504 184618 "BOUNDZRO" 184740 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179702 180900 181812 "BOP" 183582 T BOP (NIL) -8 NIL NIL NIL) (-114 177483 177887 178362 "BOP1" 179260 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177184 177245 177273 "BOOLE" 177384 T BOOLE (NIL) -9 NIL 177466 NIL) (-112 176009 176758 176907 "BOOLEAN" 177055 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175288 175692 175746 "BMODULE" 175751 NIL BMODULE (NIL T T) -9 NIL 175816 NIL) (-110 171089 175086 175159 "BITS" 175235 T BITS (NIL) -8 NIL NIL NIL) (-109 170510 170629 170769 "BINDING" 170969 T BINDING (NIL) -8 NIL NIL NIL) (-108 164515 170105 170254 "BINARY" 170381 T BINARY (NIL) -8 NIL NIL NIL) (-107 162295 163770 163811 "BGAGG" 164071 NIL BGAGG (NIL T) -9 NIL 164208 NIL) (-106 162126 162158 162249 "BGAGG-" 162254 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161197 161510 161715 "BFUNCT" 161941 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159887 160065 160353 "BEZOUT" 161021 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156356 158739 159069 "BBTREE" 159590 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156090 156143 156171 "BASTYPE" 156290 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155942 155971 156044 "BASTYPE-" 156049 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155376 155452 155604 "BALFACT" 155853 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154232 154791 154977 "AUTOMOR" 155221 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153958 153963 153989 "ATTREG" 153994 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152210 152655 153007 "ATTRBUT" 153624 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151818 152038 152104 "ATTRAST" 152162 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151354 151467 151493 "ATRIG" 151694 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151163 151204 151291 "ATRIG-" 151296 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150808 150994 151020 "ASTCAT" 151025 T ASTCAT (NIL) -9 NIL 151055 NIL) (-92 150535 150594 150713 "ASTCAT-" 150718 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148684 150311 150399 "ASTACK" 150478 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147189 147486 147851 "ASSOCEQ" 148366 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146221 146848 146972 "ASP9" 147096 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145984 146169 146208 "ASP8" 146213 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144852 145589 145731 "ASP80" 145873 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143750 144487 144619 "ASP7" 144751 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142704 143427 143545 "ASP78" 143663 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141673 142384 142501 "ASP77" 142618 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140585 141311 141442 "ASP74" 141573 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139485 140220 140352 "ASP73" 140484 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138589 139311 139411 "ASP6" 139416 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137536 138266 138384 "ASP55" 138502 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136485 137210 137329 "ASP50" 137448 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135573 136186 136296 "ASP4" 136406 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134661 135274 135384 "ASP49" 135494 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133445 134200 134368 "ASP42" 134550 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132222 132978 133148 "ASP41" 133332 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131172 131899 132017 "ASP35" 132135 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130937 131120 131159 "ASP34" 131164 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130674 130741 130817 "ASP33" 130892 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129568 130309 130441 "ASP31" 130573 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129333 129516 129555 "ASP30" 129560 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129068 129137 129213 "ASP29" 129288 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128833 129016 129055 "ASP28" 129060 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128598 128781 128820 "ASP27" 128825 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127682 128296 128407 "ASP24" 128518 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126759 127484 127596 "ASP20" 127601 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125847 126460 126570 "ASP1" 126680 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124790 125521 125640 "ASP19" 125759 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124527 124594 124670 "ASP12" 124745 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123379 124126 124270 "ASP10" 124414 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121230 123223 123314 "ARRAY2" 123319 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116995 120878 120992 "ARRAY1" 121147 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116027 116200 116421 "ARRAY12" 116818 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110339 112257 112332 "ARR2CAT" 114962 NIL ARR2CAT (NIL T T T) -9 NIL 115720 NIL) (-56 107773 108517 109471 "ARR2CAT-" 109476 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107090 107400 107525 "ARITY" 107666 T ARITY (NIL) -8 NIL NIL NIL) (-54 105866 106018 106317 "APPRULE" 106926 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105517 105565 105684 "APPLYORE" 105812 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104871 105110 105230 "ANY" 105415 T ANY (NIL) -8 NIL NIL NIL) (-51 104149 104272 104429 "ANY1" 104745 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101679 102586 102913 "ANTISYM" 103873 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101171 101386 101482 "ANON" 101601 T ANON (NIL) -8 NIL NIL NIL) (-48 95420 99710 100164 "AN" 100735 T AN (NIL) -8 NIL NIL NIL) (-47 91318 92706 92757 "AMR" 93505 NIL AMR (NIL T T) -9 NIL 94105 NIL) (-46 90430 90651 91014 "AMR-" 91019 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74869 90347 90408 "ALIST" 90413 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71674 74463 74632 "ALGSC" 74787 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68230 68784 69391 "ALGPKG" 71114 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67507 67608 67792 "ALGMFACT" 68116 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64121 64715 "ALGMANIP" 67091 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3228552 3228557 3228562 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228537 3228542 3228547 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228522 3228527 3228532 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228507 3228512 3228517 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1305 3227650 3228382 3228459 "ZMOD" 3228464 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1304 3226760 3226924 3227133 "ZLINDEP" 3227482 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1303 3216060 3217828 3219800 "ZDSOLVE" 3224890 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1302 3215306 3215447 3215636 "YSTREAM" 3215906 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1301 3213080 3214607 3214811 "XRPOLY" 3215149 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3209633 3210951 3211526 "XPR" 3212552 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3207354 3208964 3209168 "XPOLY" 3209464 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3205007 3206375 3206430 "XPOLYC" 3206718 NIL XPOLYC (NIL T T) -9 NIL 3206831 NIL) (-1297 3201383 3203524 3203912 "XPBWPOLY" 3204665 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3197078 3199373 3199415 "XF" 3200036 NIL XF (NIL T) -9 NIL 3200436 NIL) (-1295 3196699 3196787 3196956 "XF-" 3196961 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191895 3193184 3193239 "XFALG" 3195411 NIL XFALG (NIL T T) -9 NIL 3196200 NIL) (-1293 3191028 3191132 3191337 "XEXPPKG" 3191787 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3189137 3190878 3190974 "XDPOLY" 3190979 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187944 3188544 3188587 "XALG" 3188592 NIL XALG (NIL T) -9 NIL 3188703 NIL) (-1290 3181386 3185921 3186415 "WUTSET" 3187536 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179642 3180438 3180761 "WP" 3181197 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3179244 3179464 3179534 "WHILEAST" 3179594 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178716 3178961 3179055 "WHEREAST" 3179172 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3177602 3177800 3178095 "WFFINTBS" 3178513 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3175506 3175933 3176395 "WEIER" 3177174 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3174552 3175002 3175044 "VSPACE" 3175180 NIL VSPACE (NIL T) -9 NIL 3175254 NIL) (-1283 3174390 3174417 3174508 "VSPACE-" 3174513 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3174199 3174241 3174309 "VOID" 3174344 T VOID (NIL) -8 NIL NIL NIL) (-1281 3172335 3172694 3173100 "VIEW" 3173815 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168759 3169398 3170135 "VIEWDEF" 3171620 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3158063 3160307 3162480 "VIEW3D" 3166608 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3150314 3151974 3153553 "VIEW2D" 3156506 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145667 3150084 3150176 "VECTOR" 3150257 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3144244 3144503 3144821 "VECTOR2" 3145397 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137718 3142025 3142068 "VECTCAT" 3143063 NIL VECTCAT (NIL T) -9 NIL 3143650 NIL) (-1274 3136732 3136986 3137376 "VECTCAT-" 3137381 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3136186 3136383 3136503 "VARIABLE" 3136647 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3136119 3136124 3136154 "UTYPE" 3136159 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134949 3135103 3135365 "UTSODETL" 3135945 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3132389 3132849 3133373 "UTSODE" 3134490 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3124227 3130015 3130504 "UTS" 3131958 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3115101 3120468 3120511 "UTSCAT" 3121623 NIL UTSCAT (NIL T) -9 NIL 3122381 NIL) (-1267 3112449 3113171 3114160 "UTSCAT-" 3114165 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3112076 3112119 3112252 "UTS2" 3112400 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3106302 3108914 3108957 "URAGG" 3111027 NIL URAGG (NIL T) -9 NIL 3111750 NIL) (-1264 3103241 3104104 3105227 "URAGG-" 3105232 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098950 3101876 3102341 "UPXSSING" 3102905 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3091016 3098197 3098470 "UPXS" 3098735 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3084089 3090920 3090992 "UPXSCONS" 3090997 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073834 3080627 3080689 "UPXSCCA" 3081263 NIL UPXSCCA (NIL T T) -9 NIL 3081496 NIL) (-1259 3073472 3073557 3073731 "UPXSCCA-" 3073736 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3063069 3069635 3069678 "UPXSCAT" 3070326 NIL UPXSCAT (NIL T) -9 NIL 3070935 NIL) (-1257 3062499 3062578 3062757 "UPXS2" 3062984 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3061153 3061406 3061757 "UPSQFREE" 3062242 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3054574 3057631 3057686 "UPSCAT" 3058847 NIL UPSCAT (NIL T T) -9 NIL 3059621 NIL) (-1254 3053778 3053985 3054312 "UPSCAT-" 3054317 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3039433 3047201 3047244 "UPOLYC" 3049345 NIL UPOLYC (NIL T) -9 NIL 3050566 NIL) (-1252 3030761 3033187 3036334 "UPOLYC-" 3036339 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3030388 3030431 3030564 "UPOLYC2" 3030712 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3022199 3030071 3030200 "UP" 3030307 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3021538 3021645 3021809 "UPMP" 3022088 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3021091 3021172 3021311 "UPDIVP" 3021451 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3019659 3019908 3020224 "UPDECOMP" 3020840 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018890 3019002 3019188 "UPCDEN" 3019543 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3018409 3018478 3018627 "UP2" 3018815 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016876 3017613 3017890 "UNISEG" 3018167 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3016091 3016218 3016423 "UNISEG2" 3016719 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3015151 3015331 3015557 "UNIFACT" 3015907 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2999083 3014328 3014579 "ULS" 3014958 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2987081 2998987 2999059 "ULSCONS" 2999064 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2969098 2981083 2981145 "ULSCCAT" 2981783 NIL ULSCCAT (NIL T T) -9 NIL 2982072 NIL) (-1238 2968148 2968393 2968781 "ULSCCAT-" 2968786 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2957522 2964002 2964045 "ULSCAT" 2964908 NIL ULSCAT (NIL T) -9 NIL 2965639 NIL) (-1236 2956952 2957031 2957210 "ULS2" 2957437 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2956079 2956589 2956696 "UINT8" 2956807 T UINT8 (NIL) -8 NIL NIL 2956892) (-1234 2955205 2955715 2955822 "UINT64" 2955933 T UINT64 (NIL) -8 NIL NIL 2956018) (-1233 2954331 2954841 2954948 "UINT32" 2955059 T UINT32 (NIL) -8 NIL NIL 2955144) (-1232 2953457 2953967 2954074 "UINT16" 2954185 T UINT16 (NIL) -8 NIL NIL 2954270) (-1231 2951760 2952717 2952747 "UFD" 2952959 T UFD (NIL) -9 NIL 2953073 NIL) (-1230 2951554 2951600 2951695 "UFD-" 2951700 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2950636 2950819 2951035 "UDVO" 2951360 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2948452 2948861 2949332 "UDPO" 2950200 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2948385 2948390 2948420 "TYPE" 2948425 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2948145 2948340 2948371 "TYPEAST" 2948376 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2947116 2947318 2947558 "TWOFACT" 2947939 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2946139 2946525 2946760 "TUPLE" 2946916 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943830 2944349 2944888 "TUBETOOL" 2945622 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2942679 2942884 2943125 "TUBE" 2943623 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2937408 2941651 2941934 "TS" 2942431 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2926048 2930167 2930264 "TSETCAT" 2935533 NIL TSETCAT (NIL T T T T) -9 NIL 2937064 NIL) (-1219 2920780 2922380 2924271 "TSETCAT-" 2924276 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2915419 2916266 2917195 "TRMANIP" 2919916 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914860 2914923 2915086 "TRIMAT" 2915351 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2912726 2912963 2913320 "TRIGMNIP" 2914609 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2912246 2912359 2912389 "TRIGCAT" 2912602 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911915 2911994 2912135 "TRIGCAT-" 2912140 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908760 2910773 2911054 "TREE" 2911669 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2908034 2908562 2908592 "TRANFUN" 2908627 T TRANFUN (NIL) -9 NIL 2908693 NIL) (-1211 2907313 2907504 2907784 "TRANFUN-" 2907789 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2907117 2907149 2907210 "TOPSP" 2907274 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2906465 2906580 2906734 "TOOLSIGN" 2906998 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2905099 2905642 2905881 "TEXTFILE" 2906248 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2903011 2903552 2903981 "TEX" 2904692 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902792 2902823 2902895 "TEX1" 2902974 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2902440 2902503 2902593 "TEMUTL" 2902724 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2900594 2900874 2901199 "TBCMPPK" 2902163 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2892371 2898754 2898810 "TBAGG" 2899210 NIL TBAGG (NIL T T) -9 NIL 2899421 NIL) (-1202 2887441 2888929 2890683 "TBAGG-" 2890688 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886825 2886932 2887077 "TANEXP" 2887330 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2886336 2886600 2886690 "TALGOP" 2886770 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2879726 2886193 2886286 "TABLE" 2886291 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879138 2879237 2879375 "TABLEAU" 2879623 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873746 2874966 2876214 "TABLBUMP" 2877924 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872968 2873115 2873296 "SYSTEM" 2873587 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869427 2870126 2870909 "SYSSOLP" 2872219 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869225 2869382 2869413 "SYSPTR" 2869418 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868269 2868774 2868893 "SYSNNI" 2869079 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869164) (-1192 2867576 2868035 2868114 "SYSINT" 2868174 NIL SYSINT (NIL NIL) -8 NIL NIL 2868219) (-1191 2863908 2864854 2865564 "SYNTAX" 2866888 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861066 2861668 2862300 "SYMTAB" 2863298 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856315 2857217 2858200 "SYMS" 2860105 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853550 2855773 2856003 "SYMPOLY" 2856120 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853067 2853142 2853265 "SYMFUNC" 2853462 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849087 2850379 2851192 "SYMBOL" 2852276 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842626 2844315 2846035 "SWITCH" 2847389 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835860 2841447 2841750 "SUTS" 2842381 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827926 2835107 2835380 "SUPXS" 2835645 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819685 2827544 2827670 "SUP" 2827835 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818844 2818971 2819188 "SUPFRACF" 2819553 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818465 2818524 2818637 "SUP2" 2818779 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816913 2817187 2817543 "SUMRF" 2818164 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816248 2816314 2816506 "SUMFS" 2816834 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800215 2815425 2815676 "SULS" 2816055 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799817 2800037 2800107 "SUCHTAST" 2800167 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799112 2799342 2799482 "SUCH" 2799725 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792979 2794018 2794977 "SUBSPACE" 2798200 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792409 2792499 2792663 "SUBRESP" 2792867 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785777 2787074 2788385 "STTF" 2791145 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779950 2781070 2782217 "STTFNC" 2784677 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771263 2773132 2774926 "STTAYLOR" 2778191 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764393 2771127 2771210 "STRTBL" 2771215 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759757 2764348 2764379 "STRING" 2764384 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754618 2759130 2759160 "STRICAT" 2759219 T STRICAT (NIL) -9 NIL 2759281 NIL) (-1166 2747371 2752237 2752848 "STREAM" 2754042 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746881 2746958 2747102 "STREAM3" 2747288 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745863 2746046 2746281 "STREAM2" 2746694 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745551 2745603 2745696 "STREAM1" 2745805 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744567 2744748 2744979 "STINPROD" 2745367 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744119 2744329 2744359 "STEP" 2744439 T STEP (NIL) -9 NIL 2744517 NIL) (-1160 2743306 2743608 2743756 "STEPAST" 2743993 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736738 2743205 2743282 "STBL" 2743287 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731864 2735959 2736002 "STAGG" 2736155 NIL STAGG (NIL T) -9 NIL 2736244 NIL) (-1157 2729566 2730168 2731040 "STAGG-" 2731045 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727713 2729336 2729428 "STACK" 2729509 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720408 2725854 2726310 "SREGSET" 2727343 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712833 2714202 2715715 "SRDCMPK" 2719014 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705750 2710273 2710303 "SRAGG" 2711606 T SRAGG (NIL) -9 NIL 2712214 NIL) (-1152 2704767 2705022 2705401 "SRAGG-" 2705406 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699227 2703714 2704135 "SQMATRIX" 2704393 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692912 2695945 2696672 "SPLTREE" 2698572 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688875 2689568 2690214 "SPLNODE" 2692338 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687922 2688155 2688185 "SPFCAT" 2688629 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686659 2686869 2687133 "SPECOUT" 2687680 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677769 2679641 2679671 "SPADXPT" 2684347 T SPADXPT (NIL) -9 NIL 2686511 NIL) (-1145 2677530 2677570 2677639 "SPADPRSR" 2677722 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675579 2677485 2677516 "SPADAST" 2677521 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667524 2669297 2669340 "SPACEC" 2673713 NIL SPACEC (NIL T) -9 NIL 2675529 NIL) (-1142 2665654 2667456 2667505 "SPACE3" 2667510 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664406 2664577 2664868 "SORTPAK" 2665459 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662498 2662801 2663213 "SOLVETRA" 2664070 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661548 2661770 2662031 "SOLVESER" 2662271 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656852 2657740 2658735 "SOLVERAD" 2660600 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652667 2653276 2654005 "SOLVEFOR" 2656219 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646937 2652016 2652113 "SNTSCAT" 2652118 NIL SNTSCAT (NIL T T T T) -9 NIL 2652188 NIL) (-1135 2641043 2645260 2645651 "SMTS" 2646627 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635728 2640931 2641008 "SMP" 2641013 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633887 2634188 2634586 "SMITH" 2635425 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626600 2630796 2630899 "SMATCAT" 2632250 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632800 NIL) (-1131 2623540 2624363 2625541 "SMATCAT-" 2625546 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621206 2622776 2622819 "SKAGG" 2623080 NIL SKAGG (NIL T) -9 NIL 2623215 NIL) (-1129 2617532 2620679 2620863 "SINT" 2621015 T SINT (NIL) -8 NIL NIL 2621177) (-1128 2617304 2617342 2617408 "SIMPAN" 2617488 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616583 2616839 2616979 "SIG" 2617186 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615421 2615642 2615917 "SIGNRF" 2616342 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614254 2614405 2614689 "SIGNEF" 2615250 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613560 2613837 2613961 "SIGAST" 2614152 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611250 2611704 2612210 "SHP" 2613101 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605102 2611151 2611227 "SHDP" 2611232 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604675 2604867 2604897 "SGROUP" 2604990 T SGROUP (NIL) -9 NIL 2605052 NIL) (-1120 2604533 2604559 2604632 "SGROUP-" 2604637 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601324 2602022 2602745 "SGCF" 2603832 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595692 2600771 2600868 "SFRTCAT" 2600873 NIL SFRTCAT (NIL T T T T) -9 NIL 2600912 NIL) (-1117 2589113 2590131 2591267 "SFRGCD" 2594675 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582239 2583312 2584498 "SFQCMPK" 2588046 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581859 2581948 2582059 "SFORT" 2582180 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580977 2581699 2581820 "SEXOF" 2581825 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580084 2580858 2580926 "SEX" 2580931 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575597 2576312 2576407 "SEXCAT" 2579344 NIL SEXCAT (NIL T T T T T) -9 NIL 2579922 NIL) (-1111 2572750 2575531 2575579 "SET" 2575584 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570974 2571463 2571768 "SETMN" 2572491 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570470 2570622 2570652 "SETCAT" 2570828 T SETCAT (NIL) -9 NIL 2570938 NIL) (-1108 2570162 2570240 2570370 "SETCAT-" 2570375 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566523 2568623 2568666 "SETAGG" 2569536 NIL SETAGG (NIL T) -9 NIL 2569876 NIL) (-1106 2565981 2566097 2566334 "SETAGG-" 2566339 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565424 2565677 2565778 "SEQAST" 2565902 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564623 2564917 2564978 "SEGXCAT" 2565264 NIL SEGXCAT (NIL T T) -9 NIL 2565384 NIL) (-1103 2563629 2564289 2564471 "SEG" 2564476 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562608 2562822 2562865 "SEGCAT" 2563387 NIL SEGCAT (NIL T) -9 NIL 2563608 NIL) (-1101 2561540 2561971 2562179 "SEGBIND" 2562435 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561161 2561220 2561333 "SEGBIND2" 2561475 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560734 2560962 2561039 "SEGAST" 2561106 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559953 2560079 2560283 "SEG2" 2560578 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559363 2559888 2559935 "SDVAR" 2559940 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551890 2559133 2559263 "SDPOL" 2559268 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550483 2550749 2551068 "SCPKG" 2551605 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549647 2549819 2550011 "SCOPE" 2550313 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548867 2549001 2549180 "SCACHE" 2549502 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548513 2548699 2548729 "SASTCAT" 2548734 T SASTCAT (NIL) -9 NIL 2548747 NIL) (-1091 2548000 2548348 2548424 "SAOS" 2548459 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547565 2547600 2547773 "SAERFFC" 2547959 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541504 2547462 2547542 "SAE" 2547547 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541097 2541132 2541291 "SAEFACT" 2541463 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539418 2539732 2540133 "RURPK" 2540763 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538055 2538361 2538666 "RULESET" 2539252 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535278 2535808 2536266 "RULE" 2537736 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534890 2535072 2535155 "RULECOLD" 2535230 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534680 2534708 2534779 "RTVALUE" 2534841 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534151 2534397 2534491 "RSTRCAST" 2534608 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528999 2529794 2530714 "RSETGCD" 2533350 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518229 2523308 2523405 "RSETCAT" 2527524 NIL RSETCAT (NIL T T T T) -9 NIL 2528621 NIL) (-1079 2516156 2516695 2517519 "RSETCAT-" 2517524 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508542 2509918 2511438 "RSDCMPK" 2514755 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506521 2506988 2507062 "RRCC" 2508148 NIL RRCC (NIL T T) -9 NIL 2508492 NIL) (-1076 2505872 2506046 2506325 "RRCC-" 2506330 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505315 2505568 2505669 "RPTAST" 2505793 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479161 2488520 2488587 "RPOLCAT" 2499253 NIL RPOLCAT (NIL T T T) -9 NIL 2502413 NIL) (-1073 2470659 2472999 2476121 "RPOLCAT-" 2476126 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461590 2468870 2469352 "ROUTINE" 2470199 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458388 2461216 2461356 "ROMAN" 2461472 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456632 2457248 2457508 "ROIRC" 2458193 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452864 2455148 2455178 "RNS" 2455482 T RNS (NIL) -9 NIL 2455756 NIL) (-1068 2451373 2451756 2452290 "RNS-" 2452365 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450776 2451184 2451214 "RNG" 2451219 T RNG (NIL) -9 NIL 2451240 NIL) (-1066 2449779 2450141 2450343 "RNGBIND" 2450627 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449178 2449566 2449609 "RMODULE" 2449614 NIL RMODULE (NIL T) -9 NIL 2449641 NIL) (-1064 2448014 2448108 2448444 "RMCAT2" 2449079 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444864 2447360 2447657 "RMATRIX" 2447776 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437691 2439951 2440066 "RMATCAT" 2443425 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444407 NIL) (-1061 2437066 2437213 2437520 "RMATCAT-" 2437525 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436467 2436688 2436731 "RLINSET" 2436925 NIL RLINSET (NIL T) -9 NIL 2437016 NIL) (-1059 2436034 2436109 2436237 "RINTERP" 2436386 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435092 2435646 2435676 "RING" 2435732 T RING (NIL) -9 NIL 2435824 NIL) (-1057 2434884 2434928 2435025 "RING-" 2435030 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433725 2433962 2434220 "RIDIST" 2434648 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425014 2433193 2433399 "RGCHAIN" 2433573 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424364 2424770 2424811 "RGBCSPC" 2424869 NIL RGBCSPC (NIL T) -9 NIL 2424921 NIL) (-1053 2423522 2423903 2423944 "RGBCMDL" 2424176 NIL RGBCMDL (NIL T) -9 NIL 2424290 NIL) (-1052 2420516 2421130 2421800 "RF" 2422886 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420162 2420225 2420328 "RFFACTOR" 2420447 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419887 2419922 2420019 "RFFACT" 2420121 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418004 2418368 2418750 "RFDIST" 2419527 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417457 2417549 2417712 "RETSOL" 2417906 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417093 2417173 2417216 "RETRACT" 2417349 NIL RETRACT (NIL T) -9 NIL 2417436 NIL) (-1046 2416942 2416967 2417054 "RETRACT-" 2417059 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416544 2416764 2416834 "RETAST" 2416894 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409282 2416197 2416324 "RESULT" 2416439 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407873 2408551 2408750 "RESRING" 2409185 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407509 2407558 2407656 "RESLATC" 2407810 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407214 2407249 2407356 "REPSQ" 2407468 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404636 2405216 2405818 "REP" 2406634 T REP (NIL) -7 NIL NIL NIL) (-1039 2404333 2404368 2404479 "REPDB" 2404595 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398233 2399622 2400845 "REP2" 2403145 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394610 2395291 2396099 "REP1" 2397460 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387306 2392751 2393207 "REGSET" 2394240 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386071 2386454 2386704 "REF" 2387091 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385448 2385551 2385718 "REDORDER" 2385955 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381416 2384661 2384888 "RECLOS" 2385276 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380468 2380649 2380864 "REALSOLV" 2381223 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380314 2380355 2380385 "REAL" 2380390 T REAL (NIL) -9 NIL 2380425 NIL) (-1030 2376797 2377599 2378483 "REAL0Q" 2379479 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372398 2373386 2374447 "REAL0" 2375778 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371869 2372115 2372209 "RDUCEAST" 2372326 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2371274 2371346 2371553 "RDIV" 2371791 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2370342 2370516 2370729 "RDIST" 2371096 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368939 2369226 2369598 "RDETRS" 2370050 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366751 2367205 2367743 "RDETR" 2368481 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2365376 2365654 2366051 "RDEEFS" 2366467 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363885 2364191 2364616 "RDEEF" 2365064 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357946 2360866 2360896 "RCFIELD" 2362191 T RCFIELD (NIL) -9 NIL 2362922 NIL) (-1020 2356010 2356514 2357210 "RCFIELD-" 2357285 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2352279 2354111 2354154 "RCAGG" 2355238 NIL RCAGG (NIL T) -9 NIL 2355703 NIL) (-1018 2351907 2352001 2352164 "RCAGG-" 2352169 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2351242 2351354 2351519 "RATRET" 2351791 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350795 2350862 2350983 "RATFACT" 2351170 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2350103 2350223 2350375 "RANDSRC" 2350665 T RANDSRC (NIL) -7 NIL NIL NIL) 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2281212 "PTPACK" 2281908 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2280231 2280288 2280397 "PTFUNC2" 2280536 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274708 2279103 2279144 "PTCAT" 2279440 NIL PTCAT (NIL T) -9 NIL 2279593 NIL) (-988 2274366 2274401 2274525 "PSQFR" 2274667 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272961 2273259 2273593 "PSEUDLIN" 2274064 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259724 2262095 2264419 "PSETPK" 2270721 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252742 2255482 2255578 "PSETCAT" 2258599 NIL PSETCAT (NIL T T T T) -9 NIL 2259413 NIL) (-984 2250578 2251212 2252033 "PSETCAT-" 2252038 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249927 2250092 2250120 "PSCURVE" 2250388 T PSCURVE (NIL) -9 NIL 2250555 NIL) (-982 2245925 2247441 2247506 "PSCAT" 2248350 NIL PSCAT (NIL T T T) -9 NIL 2248590 NIL) (-981 2244988 2245204 2245604 "PSCAT-" 2245609 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2243797 2244420 2244599 "PRTITION" 2244829 T PRTITION 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NIL) (-860 1993332 1995620 1995747 "ORESUP" 1995871 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990860 1991360 1991921 "OREPCTO" 1992821 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984546 1986747 1986788 "OREPCAT" 1989136 NIL OREPCAT (NIL T) -9 NIL 1990240 NIL) (-857 1981693 1982475 1983533 "OREPCAT-" 1983538 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980844 1981142 1981170 "ORDSET" 1981479 T ORDSET (NIL) -9 NIL 1981643 NIL) (-855 1980275 1980423 1980647 "ORDSET-" 1980652 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978840 1979631 1979659 "ORDRING" 1979861 T ORDRING (NIL) -9 NIL 1979986 NIL) (-853 1978485 1978579 1978723 "ORDRING-" 1978728 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977865 1978328 1978356 "ORDMON" 1978361 T ORDMON (NIL) -9 NIL 1978382 NIL) (-851 1977027 1977174 1977369 "ORDFUNS" 1977714 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976365 1976784 1976812 "ORDFIN" 1976877 T ORDFIN (NIL) -9 NIL 1976951 NIL) (-849 1972924 1974951 1975360 "ORDCOMP" 1975989 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1972190 1972317 1972503 "ORDCOMP2" 1972784 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968771 1969681 1970495 "OPTPROB" 1971396 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965573 1966212 1966916 "OPTPACK" 1968087 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963260 1964026 1964054 "OPTCAT" 1964873 T OPTCAT (NIL) -9 NIL 1965523 NIL) (-844 1962644 1962937 1963042 "OPSIG" 1963175 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962412 1962451 1962517 "OPQUERY" 1962598 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959543 1960723 1961227 "OP" 1961941 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958917 1959143 1959184 "OPERCAT" 1959396 NIL OPERCAT (NIL T) -9 NIL 1959493 NIL) (-840 1958672 1958728 1958845 "OPERCAT-" 1958850 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955485 1957469 1957838 "ONECOMP" 1958336 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954790 1954905 1955079 "ONECOMP2" 1955357 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954209 1954315 1954445 "OMSERVER" 1954680 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951071 1953649 1953689 "OMSAGG" 1953750 NIL OMSAGG (NIL T) -9 NIL 1953814 NIL) (-835 1949694 1949957 1950239 "OMPKG" 1950809 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949124 1949227 1949255 "OM" 1949554 T OM (NIL) -9 NIL NIL NIL) (-833 1947671 1948673 1948842 "OMLO" 1949005 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946631 1946778 1946998 "OMEXPR" 1947497 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945922 1946177 1946313 "OMERR" 1946515 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945073 1945343 1945503 "OMERRK" 1945782 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944524 1944750 1944858 "OMENC" 1944985 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938419 1939604 1940775 "OMDEV" 1943373 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937488 1937659 1937853 "OMCONN" 1938245 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936009 1936985 1937013 "OINTDOM" 1937018 T OINTDOM (NIL) -9 NIL 1937039 NIL) (-825 1933347 1934697 1935034 "OFMONOID" 1935704 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932758 1933284 1933329 "ODVAR" 1933334 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930181 1932503 1932658 "ODR" 1932663 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922762 1929957 1930083 "ODPOL" 1930088 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916584 1922634 1922739 "ODP" 1922744 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915350 1915565 1915840 "ODETOOLS" 1916358 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912317 1912975 1913691 "ODESYS" 1914683 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907199 1908107 1909132 "ODERTRIC" 1911392 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906625 1906707 1906901 "ODERED" 1907111 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903513 1904061 1904738 "ODERAT" 1906048 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900472 1900937 1901534 "ODEPRRIC" 1903042 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898415 1899011 1899497 "ODEPROB" 1900006 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894935 1895420 1896067 "ODEPRIM" 1897894 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894184 1894286 1894546 "ODEPAL" 1894827 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890346 1891137 1892001 "ODEPACK" 1893340 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889407 1889514 1889736 "ODEINT" 1890235 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883508 1884933 1886380 "ODEIFTBL" 1887980 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878906 1879692 1880644 "ODEEF" 1882667 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878255 1878344 1878567 "ODECONST" 1878811 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876380 1877041 1877069 "ODECAT" 1877674 T ODECAT (NIL) -9 NIL 1878205 NIL) (-805 1873235 1876085 1876207 "OCT" 1876290 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872873 1872916 1873043 "OCTCT2" 1873186 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867522 1869957 1869997 "OC" 1871094 NIL OC (NIL T) -9 NIL 1871952 NIL) (-802 1864749 1865497 1866487 "OC-" 1866581 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864101 1864569 1864597 "OCAMON" 1864602 T OCAMON (NIL) -9 NIL 1864623 NIL) (-800 1863632 1863973 1864001 "OASGP" 1864006 T OASGP (NIL) -9 NIL 1864026 NIL) (-799 1862893 1863382 1863410 "OAMONS" 1863450 T OAMONS (NIL) -9 NIL 1863493 NIL) (-798 1862307 1862740 1862768 "OAMON" 1862773 T OAMON (NIL) -9 NIL 1862793 NIL) (-797 1861565 1862083 1862111 "OAGROUP" 1862116 T OAGROUP (NIL) -9 NIL 1862136 NIL) (-796 1861255 1861305 1861393 "NUMTUBE" 1861509 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854828 1856346 1857882 "NUMQUAD" 1859739 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850584 1851572 1852597 "NUMODE" 1853823 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847939 1848819 1848847 "NUMINT" 1849770 T NUMINT (NIL) -9 NIL 1850534 NIL) (-792 1846887 1847084 1847302 "NUMFMT" 1847741 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833246 1836191 1838723 "NUMERIC" 1844394 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827616 1832695 1832790 "NTSCAT" 1832795 NIL NTSCAT (NIL T T T T) -9 NIL 1832834 NIL) (-789 1826810 1826975 1827168 "NTPOLFN" 1827455 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814887 1823635 1824447 "NSUP" 1826031 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814519 1814576 1814685 "NSUP2" 1814824 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804745 1814293 1814426 "NSMP" 1814431 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803177 1803478 1803835 "NREP" 1804433 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801768 1802020 1802378 "NPCOEF" 1802920 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800834 1800949 1801165 "NORMRETR" 1801649 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798875 1799165 1799574 "NORMPK" 1800542 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798560 1798588 1798712 "NORMMA" 1798841 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798360 1798517 1798546 "NONE" 1798551 T NONE (NIL) -8 NIL NIL NIL) (-779 1798149 1798178 1798247 "NONE1" 1798324 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797646 1797708 1797887 "NODE1" 1798081 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795931 1796782 1797037 "NNI" 1797384 T NNI (NIL) -8 NIL NIL 1797619) (-776 1794351 1794664 1795028 "NLINSOL" 1795599 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790592 1791587 1792486 "NIPROB" 1793472 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789349 1789583 1789885 "NFINTBAS" 1790354 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788523 1788999 1789040 "NETCLT" 1789212 NIL NETCLT (NIL T) -9 NIL 1789294 NIL) (-772 1787231 1787462 1787743 "NCODIV" 1788291 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786993 1787030 1787105 "NCNTFRAC" 1787188 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785173 1785537 1785957 "NCEP" 1786618 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784024 1784797 1784825 "NASRING" 1784935 T NASRING (NIL) -9 NIL 1785015 NIL) (-768 1783819 1783863 1783957 "NASRING-" 1783962 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782926 1783451 1783479 "NARNG" 1783596 T NARNG (NIL) -9 NIL 1783687 NIL) (-766 1782618 1782685 1782819 "NARNG-" 1782824 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781497 1781704 1781939 "NAGSP" 1782403 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772769 1774453 1776126 "NAGS" 1779844 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771317 1771625 1771956 "NAGF07" 1772458 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765855 1767146 1768453 "NAGF04" 1770030 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758823 1760437 1762070 "NAGF02" 1764242 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754047 1755147 1756264 "NAGF01" 1757726 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747675 1749241 1750826 "NAGE04" 1752482 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738844 1740965 1743095 "NAGE02" 1745565 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734797 1735744 1736708 "NAGE01" 1737900 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732592 1733126 1733684 "NAGD03" 1734259 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724342 1726270 1728224 "NAGD02" 1730658 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718153 1719578 1721018 "NAGD01" 1722922 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714362 1715184 1716021 "NAGC06" 1717336 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712827 1713159 1713515 "NAGC05" 1714026 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712203 1712322 1712466 "NAGC02" 1712703 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711162 1711745 1711785 "NAALG" 1711864 NIL NAALG (NIL T) -9 NIL 1711925 NIL) (-749 1710997 1711026 1711116 "NAALG-" 1711121 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704947 1706055 1707242 "MULTSQFR" 1709893 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704266 1704341 1704525 "MULTFACT" 1704859 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696990 1700903 1700956 "MTSCAT" 1702026 NIL MTSCAT (NIL T T) -9 NIL 1702541 NIL) (-745 1696702 1696756 1696848 "MTHING" 1696930 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696494 1696527 1696587 "MSYSCMD" 1696662 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692576 1695249 1695569 "MSET" 1696207 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689645 1692137 1692178 "MSETAGG" 1692183 NIL MSETAGG (NIL T) -9 NIL 1692217 NIL) (-741 1685487 1687024 1687769 "MRING" 1688945 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685053 1685120 1685251 "MRF2" 1685414 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684671 1684706 1684850 "MRATFAC" 1685012 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682283 1682578 1683009 "MPRFF" 1684376 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676580 1682137 1682234 "MPOLY" 1682239 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676070 1676105 1676313 "MPCPF" 1676539 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675584 1675627 1675811 "MPC3" 1676021 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674779 1674860 1675081 "MPC2" 1675499 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673080 1673417 1673807 "MONOTOOL" 1674439 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672305 1672622 1672650 "MONOID" 1672869 T MONOID (NIL) -9 NIL 1673016 NIL) (-731 1671851 1671970 1672151 "MONOID-" 1672156 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662326 1668277 1668336 "MONOGEN" 1669010 NIL MONOGEN (NIL T T) -9 NIL 1669466 NIL) (-729 1659544 1660279 1661279 "MONOGEN-" 1661398 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658377 1658823 1658851 "MONADWU" 1659243 T MONADWU (NIL) -9 NIL 1659481 NIL) (-727 1657749 1657908 1658156 "MONADWU-" 1658161 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657108 1657352 1657380 "MONAD" 1657587 T MONAD (NIL) -9 NIL 1657699 NIL) (-725 1656793 1656871 1657003 "MONAD-" 1657008 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655082 1655706 1655985 "MOEBIUS" 1656546 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654360 1654764 1654804 "MODULE" 1654809 NIL MODULE (NIL T) -9 NIL 1654848 NIL) (-722 1653928 1654024 1654214 "MODULE-" 1654219 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651608 1652292 1652619 "MODRING" 1653752 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648552 1649713 1650234 "MODOP" 1651137 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647140 1647619 1647896 "MODMONOM" 1648415 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637184 1645431 1645845 "MODMON" 1646777 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634340 1636028 1636304 "MODFIELD" 1637059 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633317 1633621 1633811 "MMLFORM" 1634170 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632843 1632886 1633065 "MMAP" 1633268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630922 1631689 1631730 "MLO" 1632153 NIL MLO (NIL T) -9 NIL 1632395 NIL) (-713 1628288 1628804 1629406 "MLIFT" 1630403 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627679 1627763 1627917 "MKUCFUNC" 1628199 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627278 1627348 1627471 "MKRECORD" 1627602 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626325 1626487 1626715 "MKFUNC" 1627089 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625713 1625817 1625973 "MKFLCFN" 1626208 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624990 1625092 1625277 "MKBCFUNC" 1625606 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621697 1624544 1624680 "MINT" 1624874 T MINT (NIL) -8 NIL NIL NIL) (-706 1620509 1620752 1621029 "MHROWRED" 1621452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615889 1619044 1619449 "MFLOAT" 1620124 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615246 1615322 1615493 "MFINFACT" 1615801 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611561 1612409 1613293 "MESH" 1614382 T MESH (NIL) -7 NIL NIL NIL) (-702 1609951 1610263 1610616 "MDDFACT" 1611248 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606746 1609110 1609151 "MDAGG" 1609406 NIL MDAGG (NIL T) -9 NIL 1609549 NIL) (-700 1596486 1606039 1606246 "MCMPLX" 1606559 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595623 1595769 1595970 "MCDEN" 1596335 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593513 1593783 1594163 "MCALCFN" 1595353 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592438 1592678 1592911 "MAYBE" 1593319 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590050 1590573 1591135 "MATSTOR" 1591909 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586007 1589422 1589670 "MATRIX" 1589835 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581773 1582480 1583216 "MATLIN" 1585364 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571879 1575065 1575142 "MATCAT" 1580022 NIL MATCAT (NIL T T T) -9 NIL 1581439 NIL) (-692 1568235 1569256 1570612 "MATCAT-" 1570617 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566829 1566982 1567315 "MATCAT2" 1568070 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564941 1565265 1565649 "MAPPKG3" 1566504 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563922 1564095 1564317 "MAPPKG2" 1564765 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562421 1562705 1563032 "MAPPKG1" 1563628 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561500 1561827 1562004 "MAPPAST" 1562264 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561111 1561169 1561292 "MAPHACK3" 1561436 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560703 1560764 1560878 "MAPHACK2" 1561043 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560141 1560244 1560386 "MAPHACK1" 1560594 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558220 1558841 1559145 "MAGMA" 1559869 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557699 1557944 1558035 "MACROAST" 1558149 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554117 1555938 1556399 "M3D" 1557271 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548223 1552486 1552527 "LZSTAGG" 1553309 NIL LZSTAGG (NIL T) -9 NIL 1553604 NIL) (-679 1544181 1545354 1546811 "LZSTAGG-" 1546816 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541268 1542072 1542559 "LWORD" 1543726 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540844 1541072 1541147 "LSTAST" 1541213 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534010 1540615 1540749 "LSQM" 1540754 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533234 1533373 1533601 "LSPP" 1533865 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531046 1531347 1531803 "LSMP" 1532923 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527825 1528499 1529229 "LSMP1" 1530348 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521702 1526992 1527033 "LSAGG" 1527095 NIL LSAGG (NIL T) -9 NIL 1527173 NIL) (-671 1518397 1519321 1520534 "LSAGG-" 1520539 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515996 1517541 1517790 "LPOLY" 1518192 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515578 1515663 1515786 "LPEFRAC" 1515905 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513899 1514672 1514925 "LO" 1515410 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513551 1513663 1513691 "LOGIC" 1513802 T LOGIC (NIL) -9 NIL 1513883 NIL) (-666 1513413 1513436 1513507 "LOGIC-" 1513512 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512606 1512746 1512939 "LODOOPS" 1513269 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510029 1512522 1512588 "LODO" 1512593 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508567 1508802 1509155 "LODOF" 1509776 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504785 1507216 1507257 "LODOCAT" 1507695 NIL LODOCAT (NIL T) -9 NIL 1507906 NIL) (-661 1504518 1504576 1504703 "LODOCAT-" 1504708 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501838 1504359 1504477 "LODO2" 1504482 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499273 1501775 1501820 "LODO1" 1501825 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498154 1498319 1498624 "LODEEF" 1499096 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493393 1496284 1496325 "LNAGG" 1497272 NIL LNAGG (NIL T) -9 NIL 1497716 NIL) (-656 1492540 1492754 1493096 "LNAGG-" 1493101 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488676 1489465 1490104 "LMOPS" 1491955 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488079 1488467 1488508 "LMODULE" 1488513 NIL LMODULE (NIL T) -9 NIL 1488539 NIL) (-653 1485277 1487724 1487847 "LMDICT" 1487989 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484683 1484904 1484945 "LLINSET" 1485136 NIL LLINSET (NIL T) -9 NIL 1485227 NIL) (-651 1484382 1484591 1484651 "LITERAL" 1484656 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477545 1483316 1483620 "LIST" 1484111 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477070 1477144 1477283 "LIST3" 1477465 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476077 1476255 1476483 "LIST2" 1476888 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474211 1474523 1474922 "LIST2MAP" 1475724 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473807 1474044 1474085 "LINSET" 1474090 NIL LINSET (NIL T) -9 NIL 1474124 NIL) (-645 1472468 1473138 1473179 "LINEXP" 1473434 NIL LINEXP (NIL T) -9 NIL 1473583 NIL) (-644 1471115 1471375 1471672 "LINDEP" 1472220 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467882 1468601 1469378 "LIMITRF" 1470370 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466185 1466481 1466890 "LIMITPS" 1467577 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460613 1465696 1465924 "LIE" 1466006 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459561 1460030 1460070 "LIECAT" 1460210 NIL LIECAT (NIL T) -9 NIL 1460361 NIL) (-639 1459402 1459429 1459517 "LIECAT-" 1459522 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451898 1458851 1459016 "LIB" 1459257 T LIB (NIL) -8 NIL NIL NIL) (-637 1447533 1448416 1449351 "LGROBP" 1451015 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445531 1445805 1446155 "LF" 1447254 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444371 1445063 1445091 "LFCAT" 1445298 T LFCAT (NIL) -9 NIL 1445437 NIL) (-634 1441273 1441903 1442591 "LEXTRIPK" 1443735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438017 1438843 1439346 "LEXP" 1440853 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437493 1437738 1437830 "LETAST" 1437945 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435891 1436204 1436605 "LEADCDET" 1437175 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435081 1435155 1435384 "LAZM3PK" 1435812 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429998 1433158 1433696 "LAUPOL" 1434593 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429577 1429621 1429782 "LAPLACE" 1429948 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427516 1428678 1428929 "LA" 1429410 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426510 1427094 1427135 "LALG" 1427197 NIL LALG (NIL T) -9 NIL 1427256 NIL) (-625 1426224 1426283 1426419 "LALG-" 1426424 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426059 1426083 1426124 "KVTFROM" 1426186 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424982 1425426 1425611 "KTVLOGIC" 1425894 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424817 1424841 1424882 "KRCFROM" 1424944 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423721 1423908 1424207 "KOVACIC" 1424617 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423556 1423580 1423621 "KONVERT" 1423683 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423391 1423415 1423456 "KOERCE" 1423518 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421221 1421984 1422361 "KERNEL" 1423047 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420717 1420798 1420930 "KERNEL2" 1421135 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414487 1419256 1419310 "KDAGG" 1419687 NIL KDAGG (NIL T T) -9 NIL 1419893 NIL) (-615 1414016 1414140 1414345 "KDAGG-" 1414350 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407164 1413677 1413832 "KAFILE" 1413894 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401592 1406675 1406903 "JORDAN" 1406985 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400971 1401241 1401362 "JOINAST" 1401491 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400817 1400876 1400931 "JAVACODE" 1400936 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397069 1399022 1399076 "IXAGG" 1400005 NIL IXAGG (NIL T T) -9 NIL 1400464 NIL) (-609 1395988 1396294 1396713 "IXAGG-" 1396718 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391518 1395910 1395969 "IVECTOR" 1395974 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390284 1390521 1390787 "ITUPLE" 1391285 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388786 1388963 1389258 "ITRIGMNP" 1390106 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387531 1387735 1388018 "ITFUN3" 1388562 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387163 1387220 1387329 "ITFUN2" 1387468 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386322 1386643 1386817 "ITFORM" 1387009 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384283 1385342 1385620 "ITAYLOR" 1386077 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373228 1378420 1379583 "ISUPS" 1383153 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372332 1372472 1372708 "ISUMP" 1373075 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367707 1372277 1372318 "ISTRING" 1372323 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367183 1367428 1367520 "ISAST" 1367635 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366392 1366474 1366690 "IRURPK" 1367097 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365328 1365529 1365769 "IRSN" 1366172 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363399 1363754 1364183 "IRRF2F" 1364966 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363146 1363184 1363260 "IRREDFFX" 1363355 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361761 1362020 1362319 "IROOT" 1362879 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358365 1359445 1360137 "IR" 1361101 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357570 1357858 1358009 "IRFORM" 1358234 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355183 1355678 1356244 "IR2" 1357048 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354283 1354396 1354610 "IR2F" 1355066 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354074 1354108 1354168 "IPRNTPK" 1354243 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350655 1353963 1354032 "IPF" 1354037 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348982 1350580 1350637 "IPADIC" 1350642 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348294 1348542 1348672 "IP4ADDR" 1348872 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347668 1347923 1348055 "IOMODE" 1348182 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346741 1347265 1347392 "IOBFILE" 1347561 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346229 1346645 1346673 "IOBCON" 1346678 T IOBCON (NIL) -9 NIL 1346699 NIL) (-581 1345740 1345798 1345981 "INVLAPLA" 1346165 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335388 1337742 1340128 "INTTR" 1343404 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331723 1332465 1333330 "INTTOOLS" 1334573 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331309 1331400 1331517 "INTSLPE" 1331626 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329262 1331232 1331291 "INTRVL" 1331296 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326864 1327376 1327951 "INTRF" 1328747 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326275 1326372 1326514 "INTRET" 1326762 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324272 1324661 1325131 "INTRAT" 1325883 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321535 1322118 1322737 "INTPM" 1323757 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318280 1318879 1319617 "INTPAF" 1320921 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313459 1314421 1315472 "INTPACK" 1317249 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310407 1313256 1313365 "INT" 1313370 T INT (NIL) -8 NIL NIL NIL) (-569 1309659 1309811 1310019 "INTHERTR" 1310249 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309098 1309178 1309366 "INTHERAL" 1309573 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306944 1307387 1307844 "INTHEORY" 1308661 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298350 1299971 1301743 "INTG0" 1305296 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278923 1283713 1288523 "INTFTBL" 1293560 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278172 1278310 1278483 "INTFACT" 1278782 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275599 1276045 1276602 "INTEF" 1277726 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273966 1274705 1274733 "INTDOM" 1275034 T INTDOM (NIL) -9 NIL 1275241 NIL) (-561 1273335 1273509 1273751 "INTDOM-" 1273756 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269723 1271651 1271705 "INTCAT" 1272504 NIL INTCAT (NIL T) -9 NIL 1272825 NIL) (-559 1269195 1269298 1269426 "INTBIT" 1269615 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267894 1268048 1268355 "INTALG" 1269040 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267377 1267467 1267624 "INTAF" 1267798 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260720 1267187 1267327 "INTABL" 1267332 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260061 1260527 1260592 "INT8" 1260626 T INT8 (NIL) -8 NIL NIL 1260671) (-554 1259401 1259867 1259932 "INT64" 1259966 T INT64 (NIL) -8 NIL NIL 1260011) (-553 1258741 1259207 1259272 "INT32" 1259306 T INT32 (NIL) -8 NIL NIL 1259351) (-552 1258081 1258547 1258612 "INT16" 1258646 T INT16 (NIL) -8 NIL NIL 1258691) (-551 1252991 1255704 1255732 "INS" 1256666 T INS (NIL) -9 NIL 1257331 NIL) (-550 1250231 1251002 1251976 "INS-" 1252049 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249006 1249233 1249531 "INPSIGN" 1249984 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248124 1248241 1248438 "INPRODPF" 1248886 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247018 1247135 1247372 "INPRODFF" 1248004 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246018 1246170 1246430 "INNMFACT" 1246854 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245215 1245312 1245500 "INMODGCD" 1245917 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243723 1243968 1244292 "INFSP" 1244960 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242907 1243024 1243207 "INFPROD0" 1243603 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239762 1240972 1241487 "INFORM" 1242400 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239372 1239432 1239530 "INFORM1" 1239697 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238895 1238984 1239098 "INFINITY" 1239278 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238071 1238615 1238716 "INETCLTS" 1238814 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236687 1236937 1237258 "INEP" 1237819 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235936 1236584 1236649 "INDE" 1236654 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235500 1235568 1235685 "INCRMAPS" 1235863 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234318 1234769 1234975 "INBFILE" 1235314 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229617 1230554 1231498 "INBFF" 1233406 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228525 1228794 1228822 "INBCON" 1229335 T INBCON (NIL) -9 NIL 1229601 NIL) (-532 1227777 1228000 1228276 "INBCON-" 1228281 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227256 1227501 1227592 "INAST" 1227706 T INAST (NIL) -8 NIL NIL NIL) (-530 1226683 1226935 1227041 "IMPTAST" 1227170 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223129 1226527 1226631 "IMATRIX" 1226636 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221837 1221960 1222276 "IMATQF" 1222985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220057 1220284 1220621 "IMATLIN" 1221593 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214635 1219981 1220039 "ILIST" 1220044 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212540 1214495 1214608 "IIARRAY2" 1214613 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207938 1212451 1212515 "IFF" 1212520 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207285 1207555 1207671 "IFAST" 1207842 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202280 1206577 1206765 "IFARRAY" 1207142 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201460 1202184 1202257 "IFAMON" 1202262 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201044 1201109 1201163 "IEVALAB" 1201370 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200719 1200787 1200947 "IEVALAB-" 1200952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200350 1200633 1200696 "IDPO" 1200701 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199600 1200239 1200314 "IDPOAMS" 1200319 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198907 1199489 1199564 "IDPOAM" 1199569 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197966 1198242 1198295 "IDPC" 1198708 NIL IDPC (NIL T T) -9 NIL 1198857 NIL) (-514 1197435 1197858 1197931 "IDPAM" 1197936 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196811 1197327 1197400 "IDPAG" 1197405 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196456 1196647 1196722 "IDENT" 1196756 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192711 1193559 1194454 "IDECOMP" 1195613 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185549 1186634 1187681 "IDEAL" 1191747 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184709 1184821 1185021 "ICDEN" 1185433 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183780 1184189 1184336 "ICARD" 1184582 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181840 1182153 1182558 "IBPTOOLS" 1183457 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177447 1181460 1181573 "IBITS" 1181759 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174170 1174746 1175441 "IBATOOL" 1176864 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171949 1172411 1172944 "IBACHIN" 1173705 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169778 1171795 1171898 "IARRAY2" 1171903 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165884 1169704 1169761 "IARRAY1" 1169766 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159993 1164296 1164777 "IAN" 1165423 T IAN (NIL) -8 NIL NIL NIL) (-500 1159504 1159561 1159734 "IALGFACT" 1159930 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159032 1159145 1159173 "HYPCAT" 1159380 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158570 1158687 1158873 "HYPCAT-" 1158878 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158165 1158365 1158448 "HOSTNAME" 1158507 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158010 1158047 1158088 "HOMOTOP" 1158093 NIL HOMOTOP (NIL T) -9 NIL 1158126 NIL) (-495 1154642 1156020 1156061 "HOAGG" 1157042 NIL HOAGG (NIL T) -9 NIL 1157721 NIL) (-494 1153236 1153635 1154161 "HOAGG-" 1154166 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147238 1152829 1152979 "HEXADEC" 1153106 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145986 1146208 1146471 "HEUGCD" 1147015 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145062 1145823 1145953 "HELLFDIV" 1145958 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143241 1144839 1144927 "HEAP" 1145006 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142504 1142793 1142927 "HEADAST" 1143127 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136370 1142419 1142481 "HDP" 1142486 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130358 1136005 1136157 "HDMP" 1136271 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129682 1129822 1129986 "HB" 1130214 T HB (NIL) -7 NIL NIL NIL) (-485 1123068 1129528 1129632 "HASHTBL" 1129637 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122544 1122789 1122881 "HASAST" 1122996 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120322 1122166 1122348 "HACKPI" 1122382 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115990 1120175 1120288 "GTSET" 1120293 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109405 1115868 1115966 "GSTBL" 1115971 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101683 1108436 1108701 "GSERIES" 1109196 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100824 1101241 1101269 "GROUP" 1101472 T GROUP (NIL) -9 NIL 1101606 NIL) (-478 1100190 1100349 1100600 "GROUP-" 1100605 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098557 1098878 1099265 "GROEBSOL" 1099867 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097471 1097759 1097810 "GRMOD" 1098339 NIL GRMOD (NIL T T) -9 NIL 1098507 NIL) (-475 1097239 1097275 1097403 "GRMOD-" 1097408 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092529 1093593 1094593 "GRIMAGE" 1096259 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090995 1091256 1091580 "GRDEF" 1092225 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090439 1090555 1090696 "GRAY" 1090874 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089626 1090032 1090083 "GRALG" 1090236 NIL GRALG (NIL T T) -9 NIL 1090329 NIL) (-470 1089287 1089360 1089523 "GRALG-" 1089528 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086064 1088872 1089050 "GPOLSET" 1089194 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085418 1085475 1085733 "GOSPER" 1086001 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081150 1081856 1082382 "GMODPOL" 1085117 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080155 1080339 1080577 "GHENSEL" 1080962 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074311 1075154 1076174 "GENUPS" 1079239 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074008 1074059 1074148 "GENUFACT" 1074254 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073420 1073497 1073662 "GENPGCD" 1073926 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072894 1072929 1073142 "GENMFACT" 1073379 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071460 1071717 1072024 "GENEEZ" 1072637 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065608 1071071 1071233 "GDMP" 1071383 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054951 1059379 1060485 "GCNAALG" 1064591 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053278 1054140 1054168 "GCDDOM" 1054423 T GCDDOM (NIL) -9 NIL 1054580 NIL) (-457 1052748 1052875 1053090 "GCDDOM-" 1053095 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051420 1051605 1051909 "GB" 1052527 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040036 1042366 1044758 "GBINTERN" 1049111 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037873 1038165 1038586 "GBF" 1039711 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036654 1036819 1037086 "GBEUCLID" 1037689 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036003 1036128 1036277 "GAUSSFAC" 1036525 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034370 1034672 1034986 "GALUTIL" 1035722 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032678 1032952 1033276 "GALPOLYU" 1034097 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030043 1030333 1030740 "GALFACTU" 1032375 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021849 1023348 1024956 "GALFACT" 1028475 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019237 1019895 1019923 "FVFUN" 1021079 T FVFUN (NIL) -9 NIL 1021799 NIL) (-446 1018503 1018685 1018713 "FVC" 1019004 T FVC (NIL) -9 NIL 1019187 NIL) (-445 1018146 1018328 1018396 "FUNDESC" 1018455 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017761 1017943 1018024 "FUNCTION" 1018098 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015505 1016083 1016549 "FT" 1017315 T FT (NIL) -8 NIL NIL NIL) (-442 1014296 1014806 1015009 "FTEM" 1015322 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012587 1012876 1013273 "FSUPFACT" 1013987 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010984 1011273 1011605 "FST" 1012275 T FST (NIL) -8 NIL NIL NIL) (-439 1010183 1010289 1010477 "FSRED" 1010866 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008882 1009138 1009485 "FSPRMELT" 1009898 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006188 1006626 1007112 "FSPECF" 1008445 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987826 996157 996198 "FS" 1000082 NIL FS (NIL T) -9 NIL 1002371 NIL) (-435 976469 979462 983519 "FS-" 983819 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975997 976051 976221 "FSINT" 976410 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974289 974990 975293 "FSERIES" 975776 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973331 973447 973671 "FSCINT" 974169 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969539 972275 972316 "FSAGG" 972686 NIL FSAGG (NIL T) -9 NIL 972945 NIL) (-430 967301 967902 968698 "FSAGG-" 968793 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966343 966486 966713 "FSAGG2" 967154 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964025 964305 964852 "FS2UPS" 966061 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963659 963702 963831 "FS2" 963976 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962537 962708 963010 "FS2EXPXP" 963484 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961963 962078 962230 "FRUTIL" 962417 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953376 957458 958816 "FR" 960637 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948345 951019 951059 "FRNAALG" 952455 NIL FRNAALG (NIL T) -9 NIL 953062 NIL) (-422 944018 945094 946369 "FRNAALG-" 947119 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943656 943699 943826 "FRNAAF2" 943969 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942031 942505 942801 "FRMOD" 943468 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939774 940406 940724 "FRIDEAL" 941822 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938965 939052 939343 "FRIDEAL2" 939681 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938098 938512 938553 "FRETRCT" 938558 NIL FRETRCT (NIL T) -9 NIL 938734 NIL) (-416 937210 937441 937792 "FRETRCT-" 937797 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934298 935508 935567 "FRAMALG" 936449 NIL FRAMALG (NIL T T) -9 NIL 936741 NIL) (-414 932432 932887 933517 "FRAMALG-" 933740 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926351 931905 932182 "FRAC" 932187 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925987 926044 926151 "FRAC2" 926288 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925623 925680 925787 "FR2" 925924 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920136 923029 923057 "FPS" 924176 T FPS (NIL) -9 NIL 924733 NIL) (-409 919585 919694 919858 "FPS-" 920004 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916887 918556 918584 "FPC" 918809 T FPC (NIL) -9 NIL 918951 NIL) (-407 916680 916720 916817 "FPC-" 916822 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915470 916168 916209 "FPATMAB" 916214 NIL FPATMAB (NIL T) -9 NIL 916366 NIL) (-405 913143 913646 914072 "FPARFRAC" 915107 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908537 909035 909717 "FORTRAN" 912575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906253 906753 907292 "FORT" 908018 T FORT (NIL) -7 NIL NIL NIL) (-402 903929 904491 904519 "FORTFN" 905579 T FORTFN (NIL) -9 NIL 906203 NIL) (-401 903693 903743 903771 "FORTCAT" 903830 T FORTCAT (NIL) -9 NIL 903892 NIL) (-400 901799 902309 902699 "FORMULA" 903323 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901587 901617 901686 "FORMULA1" 901763 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901110 901162 901335 "FORDER" 901529 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900206 900370 900563 "FOP" 900937 T FOP (NIL) -7 NIL NIL NIL) (-396 898787 899486 899660 "FNLA" 900088 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897516 897931 897959 "FNCAT" 898419 T FNCAT (NIL) -9 NIL 898679 NIL) (-394 897055 897475 897503 "FNAME" 897508 T FNAME (NIL) -8 NIL NIL NIL) (-393 895618 896581 896609 "FMTC" 896614 T FMTC (NIL) -9 NIL 896650 NIL) (-392 894364 895554 895600 "FMONOID" 895605 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891192 892360 892401 "FMONCAT" 893618 NIL FMONCAT (NIL T) -9 NIL 894223 NIL) (-390 890384 890934 891083 "FM" 891088 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887808 888454 888482 "FMFUN" 889626 T FMFUN (NIL) -9 NIL 890334 NIL) (-388 887077 887258 887286 "FMC" 887576 T FMC (NIL) -9 NIL 887758 NIL) (-387 884156 885016 885070 "FMCAT" 886265 NIL FMCAT (NIL T T) -9 NIL 886760 NIL) (-386 883022 883922 884022 "FM1" 884101 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880796 881212 881706 "FLOATRP" 882573 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874374 878525 879146 "FLOAT" 880195 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871812 872312 872890 "FLOATCP" 873841 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870552 871390 871431 "FLINEXP" 871436 NIL FLINEXP (NIL T) -9 NIL 871529 NIL) (-381 869706 869941 870269 "FLINEXP-" 870274 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868782 868926 869150 "FLASORT" 869558 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865898 866766 866818 "FLALG" 868045 NIL FLALG (NIL T T) -9 NIL 868512 NIL) (-378 859634 863384 863425 "FLAGG" 864687 NIL FLAGG (NIL T) -9 NIL 865339 NIL) (-377 858360 858699 859189 "FLAGG-" 859194 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857402 857545 857772 "FLAGG2" 858213 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854253 855261 855320 "FINRALG" 856448 NIL FINRALG (NIL T T) -9 NIL 856956 NIL) (-374 853413 853642 853981 "FINRALG-" 853986 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852793 853032 853060 "FINITE" 853256 T FINITE (NIL) -9 NIL 853363 NIL) (-372 845150 847337 847377 "FINAALG" 851044 NIL FINAALG (NIL T) -9 NIL 852497 NIL) (-371 840482 841532 842676 "FINAALG-" 844055 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839850 840237 840340 "FILE" 840412 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838508 838846 838900 "FILECAT" 839584 NIL FILECAT (NIL T T) -9 NIL 839800 NIL) (-368 836224 837752 837780 "FIELD" 837820 T FIELD (NIL) -9 NIL 837900 NIL) (-367 834844 835229 835740 "FIELD-" 835745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832694 833479 833826 "FGROUP" 834530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831784 831948 832168 "FGLMICPK" 832526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827616 831709 831766 "FFX" 831771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827217 827278 827413 "FFSLPE" 827549 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823207 823989 824785 "FFPOLY" 826453 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822711 822747 822956 "FFPOLY2" 823165 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818557 822630 822693 "FFP" 822698 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813955 818468 818532 "FF" 818537 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809081 813298 813488 "FFNBX" 813809 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804009 808216 808474 "FFNBP" 808935 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798642 803293 803504 "FFNB" 803842 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797474 797672 797987 "FFINTBAS" 798439 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793543 795763 795791 "FFIELDC" 796411 T FFIELDC (NIL) -9 NIL 796787 NIL) (-353 792205 792576 793073 "FFIELDC-" 793078 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791774 791820 791944 "FFHOM" 792147 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789469 789956 790473 "FFF" 791289 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785087 789211 789312 "FFCGX" 789412 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780709 784819 784926 "FFCGP" 785030 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775892 780436 780544 "FFCG" 780645 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757288 766369 766455 "FFCAT" 771620 NIL FFCAT (NIL T T T) -9 NIL 773071 NIL) (-346 752485 753533 754847 "FFCAT-" 756077 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751896 751939 752174 "FFCAT2" 752436 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741219 744868 746088 "FEXPR" 750748 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740219 740654 740695 "FEVALAB" 740779 NIL FEVALAB (NIL T) -9 NIL 741040 NIL) (-342 739378 739588 739926 "FEVALAB-" 739931 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737944 738761 738964 "FDIV" 739277 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734964 735705 735820 "FDIVCAT" 737388 NIL FDIVCAT (NIL T T T T) -9 NIL 737825 NIL) (-339 734726 734753 734923 "FDIVCAT-" 734928 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733946 734033 734310 "FDIV2" 734633 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732920 733241 733443 "FCTRDATA" 733764 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731606 731865 732154 "FCPAK1" 732651 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730705 731106 731247 "FCOMP" 731497 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714410 717855 721393 "FC" 727187 T FC (NIL) -8 NIL NIL NIL) (-333 706773 710801 710841 "FAXF" 712643 NIL FAXF (NIL T) -9 NIL 713335 NIL) (-332 704050 704707 705532 "FAXF-" 705997 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699102 703426 703602 "FARRAY" 703907 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693996 696063 696116 "FAMR" 697139 NIL FAMR (NIL T T) -9 NIL 697599 NIL) (-329 692886 693188 693623 "FAMR-" 693628 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692055 692808 692861 "FAMONOID" 692866 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689841 690551 690604 "FAMONC" 691545 NIL FAMONC (NIL T T) -9 NIL 691931 NIL) (-326 688505 689595 689732 "FAGROUP" 689737 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686300 686619 687022 "FACUTIL" 688186 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685399 685584 685806 "FACTFUNC" 686110 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677821 684702 684901 "EXPUPXS" 685255 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675304 675844 676430 "EXPRTUBE" 677255 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671575 672167 672897 "EXPRODE" 674643 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657060 670224 670653 "EXPR" 671179 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651614 652201 653007 "EXPR2UPS" 656358 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651246 651303 651412 "EXPR2" 651551 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642634 650397 650688 "EXPEXPAN" 651082 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642434 642591 642620 "EXIT" 642625 T EXIT (NIL) -8 NIL NIL NIL) (-315 641914 642158 642249 "EXITAST" 642363 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641541 641603 641716 "EVALCYC" 641846 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641082 641200 641241 "EVALAB" 641411 NIL EVALAB (NIL T) -9 NIL 641515 NIL) (-312 640563 640685 640906 "EVALAB-" 640911 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637931 639233 639261 "EUCDOM" 639816 T EUCDOM (NIL) -9 NIL 640166 NIL) (-310 636336 636778 637368 "EUCDOM-" 637373 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623875 626634 629384 "ESTOOLS" 633606 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623507 623564 623673 "ESTOOLS2" 623812 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623258 623300 623380 "ESTOOLS1" 623459 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617295 618903 618931 "ES" 621699 T ES (NIL) -9 NIL 623109 NIL) (-305 612242 613529 615346 "ES-" 615510 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608616 609377 610157 "ESCONT" 611482 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608361 608393 608475 "ESCONT1" 608578 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608036 608086 608186 "ES2" 608305 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607666 607724 607833 "ES1" 607972 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606882 607011 607187 "ERROR" 607510 T ERROR (NIL) -7 NIL NIL NIL) (-299 600274 606741 606832 "EQTBL" 606837 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592777 595588 597037 "EQ" 598858 NIL -2199 (NIL T) -8 NIL NIL NIL) (-297 592409 592466 592575 "EQ2" 592714 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587700 588747 589840 "EP" 591348 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586300 586591 586897 "ENV" 587414 T ENV (NIL) -8 NIL NIL NIL) (-294 585394 585948 585976 "ENTIRER" 585981 T ENTIRER (NIL) -9 NIL 586027 NIL) (-293 581861 583349 583719 "EMR" 585193 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581005 581190 581244 "ELTAGG" 581624 NIL ELTAGG (NIL T T) -9 NIL 581835 NIL) (-291 580724 580786 580927 "ELTAGG-" 580932 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580513 580542 580596 "ELTAB" 580680 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579639 579785 579984 "ELFUTS" 580364 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579381 579437 579465 "ELEMFUN" 579570 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579251 579272 579340 "ELEMFUN-" 579345 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574095 577351 577392 "ELAGG" 578332 NIL ELAGG (NIL T) -9 NIL 578795 NIL) (-285 572380 572814 573477 "ELAGG-" 573482 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571692 571829 571985 "ELABOR" 572244 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570353 570632 570926 "ELABEXPR" 571418 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563217 565020 565847 "EFUPXS" 569629 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556667 558468 559278 "EFULS" 562493 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554152 554510 554982 "EFSTRUC" 556299 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543943 545509 547057 "EF" 552667 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543017 543428 543577 "EAB" 543814 T EAB (NIL) -8 NIL NIL NIL) (-277 542199 542976 543004 "E04UCFA" 543009 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541381 542158 542186 "E04NAFA" 542191 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540563 541340 541368 "E04MBFA" 541373 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539745 540522 540550 "E04JAFA" 540555 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538929 539704 539732 "E04GCFA" 539737 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538113 538888 538916 "E04FDFA" 538921 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537295 538072 538100 "E04DGFA" 538105 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531468 532820 534184 "E04AGNT" 535951 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530148 530654 530694 "DVARCAT" 531169 NIL DVARCAT (NIL T) -9 NIL 531368 NIL) (-268 529352 529564 529878 "DVARCAT-" 529883 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522489 529151 529280 "DSMP" 529285 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517270 518434 519502 "DROPT" 521441 T DROPT (NIL) -8 NIL NIL NIL) (-265 516935 516994 517092 "DROPT1" 517205 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512050 513176 514313 "DROPT0" 515818 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510395 510720 511106 "DRAWPT" 511684 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504982 505905 506984 "DRAW" 509369 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504615 504668 504786 "DRAWHACK" 504923 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503346 503615 503906 "DRAWCX" 504344 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502861 502930 503081 "DRAWCURV" 503272 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493329 495291 497406 "DRAWCFUN" 500766 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490093 492022 492063 "DQAGG" 492692 NIL DQAGG (NIL T) -9 NIL 492966 NIL) (-256 478217 484686 484769 "DPOLCAT" 486621 NIL DPOLCAT (NIL T T T T) -9 NIL 487166 NIL) (-255 473054 474402 476360 "DPOLCAT-" 476365 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466176 472915 473013 "DPMO" 473018 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459201 465956 466123 "DPMM" 466128 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458679 458893 458991 "DOMTMPLT" 459123 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458112 458481 458561 "DOMCTOR" 458619 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457324 457592 457743 "DOMAIN" 457981 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451312 456959 457111 "DMP" 457225 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450912 450968 451112 "DLP" 451250 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444734 450239 450429 "DLIST" 450754 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441531 443587 443628 "DLAGG" 444178 NIL DLAGG (NIL T) -9 NIL 444408 NIL) (-245 440207 440871 440899 "DIVRING" 440991 T DIVRING (NIL) -9 NIL 441074 NIL) (-244 439444 439634 439934 "DIVRING-" 439939 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437546 437903 438309 "DISPLAY" 439058 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431434 437460 437523 "DIRPROD" 437528 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430282 430485 430750 "DIRPROD2" 431227 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419057 425063 425116 "DIRPCAT" 425526 NIL DIRPCAT (NIL NIL T) -9 NIL 426366 NIL) (-239 416383 417025 417906 "DIRPCAT-" 418243 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415670 415830 416016 "DIOSP" 416217 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412325 414582 414623 "DIOPS" 415057 NIL DIOPS (NIL T) -9 NIL 415286 NIL) (-236 411874 411988 412179 "DIOPS-" 412184 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410697 411325 411353 "DIFRING" 411540 T DIFRING (NIL) -9 NIL 411650 NIL) (-234 410343 410420 410572 "DIFRING-" 410577 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408079 409351 409392 "DIFEXT" 409755 NIL DIFEXT (NIL T) -9 NIL 410049 NIL) (-232 406364 406792 407458 "DIFEXT-" 407463 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403639 405896 405937 "DIAGG" 405942 NIL DIAGG (NIL T) -9 NIL 405962 NIL) (-230 403023 403180 403432 "DIAGG-" 403437 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398440 401982 402259 "DHMATRIX" 402792 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394052 394961 395971 "DFSFUN" 397450 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389131 392983 393295 "DFLOAT" 393760 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387394 387675 388064 "DFINTTLS" 388839 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384423 385415 385815 "DERHAM" 387060 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382224 384198 384287 "DEQUEUE" 384367 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381478 381611 381794 "DEGRED" 382086 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377908 378653 379499 "DEFINTRF" 380706 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375463 375932 376524 "DEFINTEF" 377427 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374813 375083 375198 "DEFAST" 375368 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368815 374406 374556 "DECIMAL" 374683 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366327 366785 367291 "DDFACT" 368359 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365923 365966 366117 "DBLRESP" 366278 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363795 364156 364516 "DBASE" 365690 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363037 363275 363421 "DATAARY" 363694 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362143 362996 363024 "D03FAFA" 363029 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361250 362102 362130 "D03EEFA" 362135 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359200 359666 360155 "D03AGNT" 360781 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358489 359159 359187 "D02EJFA" 359192 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357778 358448 358476 "D02CJFA" 358481 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357067 357737 357765 "D02BHFA" 357770 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356356 357026 357054 "D02BBFA" 357059 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349553 351142 352748 "D02AGNT" 354770 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347321 347844 348390 "D01WGTS" 349027 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346388 347280 347308 "D01TRNS" 347313 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345456 346347 346375 "D01GBFA" 346380 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344524 345415 345443 "D01FCFA" 345448 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343592 344483 344511 "D01ASFA" 344516 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342660 343551 343579 "D01AQFA" 343584 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341728 342619 342647 "D01APFA" 342652 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340796 341687 341715 "D01ANFA" 341720 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339864 340755 340783 "D01AMFA" 340788 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338932 339823 339851 "D01ALFA" 339856 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338000 338891 338919 "D01AKFA" 338924 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337068 337959 337987 "D01AJFA" 337992 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330363 331916 333477 "D01AGNT" 335527 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329700 329828 329980 "CYCLOTOM" 330231 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326434 327148 327875 "CYCLES" 328993 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325746 325880 326051 "CVMP" 326295 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323587 323845 324214 "CTRIGMNP" 325474 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323023 323381 323454 "CTOR" 323534 T CTOR (NIL) -8 NIL NIL NIL) (-188 322532 322754 322855 "CTORKIND" 322942 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321823 322139 322167 "CTORCAT" 322349 T CTORCAT (NIL) -9 NIL 322462 NIL) (-186 321421 321532 321691 "CTORCAT-" 321696 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320883 321095 321203 "CTORCALL" 321345 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320257 320356 320509 "CSTTOOLS" 320780 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316056 316713 317471 "CRFP" 319569 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315531 315777 315869 "CRCEAST" 315984 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314578 314763 314991 "CRAPACK" 315335 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313962 314063 314267 "CPMATCH" 314454 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313687 313715 313821 "CPIMA" 313928 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310035 310707 311426 "COORDSYS" 313022 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309447 309568 309710 "CONTOUR" 309913 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305338 307450 307942 "CONTFRAC" 308987 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305218 305239 305267 "CONDUIT" 305304 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304306 304860 304888 "COMRING" 304893 T COMRING (NIL) -9 NIL 304945 NIL) (-173 303360 303664 303848 "COMPPROP" 304142 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303021 303056 303184 "COMPLPAT" 303319 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293312 302830 302939 "COMPLEX" 302944 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292948 293005 293112 "COMPLEX2" 293249 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292287 292408 292568 "COMPILER" 292808 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292005 292040 292138 "COMPFACT" 292246 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276085 286079 286119 "COMPCAT" 287123 NIL COMPCAT (NIL T) -9 NIL 288471 NIL) (-166 265597 268524 272151 "COMPCAT-" 272507 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265326 265354 265457 "COMMUPC" 265563 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265120 265154 265213 "COMMONOP" 265287 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264676 264871 264958 "COMM" 265053 T COMM (NIL) -8 NIL NIL NIL) (-162 264252 264480 264555 "COMMAAST" 264621 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263501 263695 263723 "COMBOPC" 264061 T COMBOPC (NIL) -9 NIL 264236 NIL) (-160 262397 262607 262849 "COMBINAT" 263291 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258854 259428 260055 "COMBF" 261819 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257612 257970 258205 "COLOR" 258639 T COLOR (NIL) -8 NIL NIL NIL) (-157 257088 257333 257425 "COLONAST" 257540 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256728 256775 256900 "CMPLXRT" 257035 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256176 256428 256527 "CLLCTAST" 256649 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251678 252706 253786 "CLIP" 255116 T CLIP (NIL) -7 NIL NIL NIL) (-153 250019 250779 251019 "CLIF" 251505 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246194 248165 248206 "CLAGG" 249135 NIL CLAGG (NIL T) -9 NIL 249671 NIL) (-151 244616 245073 245656 "CLAGG-" 245661 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244160 244245 244385 "CINTSLPE" 244525 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241661 242132 242680 "CHVAR" 243688 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240835 241389 241417 "CHARZ" 241422 T CHARZ (NIL) -9 NIL 241437 NIL) (-147 240589 240629 240707 "CHARPOL" 240789 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239647 240234 240262 "CHARNZ" 240309 T CHARNZ (NIL) -9 NIL 240365 NIL) (-145 237553 238301 238654 "CHAR" 239314 T CHAR (NIL) -8 NIL NIL NIL) (-144 237279 237340 237368 "CFCAT" 237479 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236520 236631 236814 "CDEN" 237163 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232485 235673 235953 "CCLASS" 236260 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231736 231893 232070 "CATEGORY" 232328 T -10 (NIL) -8 NIL NIL NIL) (-140 231309 231655 231703 "CATCTOR" 231708 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230760 231012 231110 "CATAST" 231231 T CATAST (NIL) -8 NIL NIL NIL) (-138 230236 230481 230573 "CASEAST" 230688 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225246 226265 227018 "CARTEN" 229539 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224354 224502 224723 "CARTEN2" 225093 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222670 223504 223761 "CARD" 224117 T CARD (NIL) -8 NIL NIL NIL) (-134 222246 222474 222549 "CAPSLAST" 222615 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221750 221958 221986 "CACHSET" 222118 T CACHSET (NIL) -9 NIL 222196 NIL) (-132 221220 221542 221570 "CABMON" 221620 T CABMON (NIL) -9 NIL 221676 NIL) (-131 220693 220924 221034 "BYTEORD" 221130 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219675 220227 220369 "BYTE" 220532 T BYTE (NIL) -8 NIL NIL 220654) (-129 215025 219180 219352 "BYTEBUF" 219523 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212534 214717 214824 "BTREE" 214951 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209983 212182 212304 "BTOURN" 212444 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207353 209453 209494 "BTCAT" 209562 NIL BTCAT (NIL T) -9 NIL 209639 NIL) (-125 207020 207100 207249 "BTCAT-" 207254 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202430 206309 206337 "BTAGG" 206451 T BTAGG (NIL) -9 NIL 206561 NIL) (-123 201920 202045 202251 "BTAGG-" 202256 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198915 201198 201413 "BSTREE" 201737 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198053 198179 198363 "BRILL" 198771 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194705 196779 196820 "BRAGG" 197469 NIL BRAGG (NIL T) -9 NIL 197727 NIL) (-119 193234 193640 194195 "BRAGG-" 194200 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186461 192578 192763 "BPADICRT" 193081 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184776 186398 186443 "BPADIC" 186448 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184474 184504 184618 "BOUNDZRO" 184740 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179702 180900 181812 "BOP" 183582 T BOP (NIL) -8 NIL NIL NIL) (-114 177483 177887 178362 "BOP1" 179260 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177184 177245 177273 "BOOLE" 177384 T BOOLE (NIL) -9 NIL 177466 NIL) (-112 176009 176758 176907 "BOOLEAN" 177055 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175288 175692 175746 "BMODULE" 175751 NIL BMODULE (NIL T T) -9 NIL 175816 NIL) (-110 171089 175086 175159 "BITS" 175235 T BITS (NIL) -8 NIL NIL NIL) (-109 170510 170629 170769 "BINDING" 170969 T BINDING (NIL) -8 NIL NIL NIL) (-108 164515 170105 170254 "BINARY" 170381 T BINARY (NIL) -8 NIL NIL NIL) (-107 162295 163770 163811 "BGAGG" 164071 NIL BGAGG (NIL T) -9 NIL 164208 NIL) (-106 162126 162158 162249 "BGAGG-" 162254 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161197 161510 161715 "BFUNCT" 161941 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159887 160065 160353 "BEZOUT" 161021 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156356 158739 159069 "BBTREE" 159590 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156090 156143 156171 "BASTYPE" 156290 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155942 155971 156044 "BASTYPE-" 156049 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155376 155452 155604 "BALFACT" 155853 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154232 154791 154977 "AUTOMOR" 155221 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153958 153963 153989 "ATTREG" 153994 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152210 152655 153007 "ATTRBUT" 153624 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151818 152038 152104 "ATTRAST" 152162 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151354 151467 151493 "ATRIG" 151694 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151163 151204 151291 "ATRIG-" 151296 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150808 150994 151020 "ASTCAT" 151025 T ASTCAT (NIL) -9 NIL 151055 NIL) (-92 150535 150594 150713 "ASTCAT-" 150718 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148684 150311 150399 "ASTACK" 150478 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147189 147486 147851 "ASSOCEQ" 148366 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146221 146848 146972 "ASP9" 147096 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145984 146169 146208 "ASP8" 146213 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144852 145589 145731 "ASP80" 145873 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143750 144487 144619 "ASP7" 144751 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142704 143427 143545 "ASP78" 143663 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141673 142384 142501 "ASP77" 142618 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140585 141311 141442 "ASP74" 141573 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139485 140220 140352 "ASP73" 140484 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138589 139311 139411 "ASP6" 139416 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137536 138266 138384 "ASP55" 138502 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136485 137210 137329 "ASP50" 137448 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135573 136186 136296 "ASP4" 136406 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134661 135274 135384 "ASP49" 135494 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133445 134200 134368 "ASP42" 134550 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132222 132978 133148 "ASP41" 133332 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131172 131899 132017 "ASP35" 132135 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130937 131120 131159 "ASP34" 131164 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130674 130741 130817 "ASP33" 130892 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129568 130309 130441 "ASP31" 130573 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129333 129516 129555 "ASP30" 129560 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129068 129137 129213 "ASP29" 129288 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128833 129016 129055 "ASP28" 129060 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128598 128781 128820 "ASP27" 128825 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127682 128296 128407 "ASP24" 128518 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126759 127484 127596 "ASP20" 127601 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125847 126460 126570 "ASP1" 126680 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124790 125521 125640 "ASP19" 125759 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124527 124594 124670 "ASP12" 124745 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123379 124126 124270 "ASP10" 124414 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121230 123223 123314 "ARRAY2" 123319 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116995 120878 120992 "ARRAY1" 121147 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116027 116200 116421 "ARRAY12" 116818 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110339 112257 112332 "ARR2CAT" 114962 NIL ARR2CAT (NIL T T T) -9 NIL 115720 NIL) (-56 107773 108517 109471 "ARR2CAT-" 109476 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107090 107400 107525 "ARITY" 107666 T ARITY (NIL) -8 NIL NIL NIL) (-54 105866 106018 106317 "APPRULE" 106926 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105517 105565 105684 "APPLYORE" 105812 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104871 105110 105230 "ANY" 105415 T ANY (NIL) -8 NIL NIL NIL) (-51 104149 104272 104429 "ANY1" 104745 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101679 102586 102913 "ANTISYM" 103873 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101171 101386 101482 "ANON" 101601 T ANON (NIL) -8 NIL NIL NIL) (-48 95420 99710 100164 "AN" 100735 T AN (NIL) -8 NIL NIL NIL) (-47 91318 92706 92757 "AMR" 93505 NIL AMR (NIL T T) -9 NIL 94105 NIL) (-46 90430 90651 91014 "AMR-" 91019 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74869 90347 90408 "ALIST" 90413 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71674 74463 74632 "ALGSC" 74787 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68230 68784 69391 "ALGPKG" 71114 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67507 67608 67792 "ALGMFACT" 68116 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64121 64715 "ALGMANIP" 67091 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 3ef76f94..a9808ba4 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,90 +1,55 @@ -(733547 . 3480761526) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-400)))) - ((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1207))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-868))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3684 *8))) - (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-997 *4 *5 *6 *7 *8)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3684 *8))) - (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-1116 *4 *5 *6 *7 *8))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -1452 *3) (|:| |gap| (-777)) (|:| -4077 (-788 *3)) - (|:| -2766 (-788 *3)))) - (-5 *1 (-788 *3)) (-4 *3 (-1058)))) - ((*1 *2 *1 *1 *3) - (-12 (-4 *4 (-1058)) (-4 *5 (-799)) (-4 *3 (-856)) - (-5 *2 - (-2 (|:| -1452 *1) (|:| |gap| (-777)) (|:| -4077 *1) - (|:| -2766 *1))) - (-4 *1 (-1074 *4 *5 *3)))) +(733597 . 3480886513) +(((*1 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-695 *1)) (-4 *1 (-354)) (-5 *2 (-1277 *1)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-695 *1)) (-4 *1 (-146)) (-4 *1 (-916)) + (-5 *2 (-1277 *1))))) +(((*1 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-373)) (-4 *2 (-1109))))) +(((*1 *1) (-12 (-4 *1 (-333 *2)) (-4 *2 (-373)) (-4 *2 (-368))))) +(((*1 *2 *3) + (-12 (-4 *4 (-368)) (-4 *4 (-562)) (-4 *5 (-1253 *4)) + (-5 *2 (-2 (|:| -4288 (-629 *4 *5)) (|:| -1338 (-413 *5)))) + (-5 *1 (-629 *4 *5)) (-5 *3 (-413 *5)))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 (-1174 *3 *4))) (-5 *1 (-1174 *3 *4)) + (-14 *3 (-928)) (-4 *4 (-1058)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 - (-2 (|:| -1452 *1) (|:| |gap| (-777)) (|:| -4077 *1) - (|:| -2766 *1))) - (-4 *1 (-1074 *3 *4 *5))))) + (-12 (-4 *3 (-458)) (-4 *3 (-1058)) + (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) + (-4 *1 (-1253 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-562)) (-4 *2 (-13 (-436 (-171 *4)) (-1011) (-1212))) + (-5 *1 (-606 *4 *3 *2)) (-4 *3 (-13 (-436 *4) (-1011) (-1212)))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-1109)) (-4 *3 (-907 *5)) (-5 *2 (-695 *3)) - (-5 *1 (-698 *5 *3 *6 *4)) (-4 *6 (-378 *3)) - (-4 *4 (-13 (-378 *5) (-10 -7 (-6 -4449))))))) -(((*1 *1 *1 *2) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) - (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *3 (-1074 *4 *5 *6)) - (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -3684 *1)))) - (-4 *1 (-1080 *4 *5 *6 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-980)) (-5 *1 (-912 *3)) (-4 *3 (-1109))))) -(((*1 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-551)))) - ((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-980))))) -(((*1 *2 *3 *4 *5 *6 *7 *7 *8) - (-12 - (-5 *3 - (-2 (|:| |det| *12) (|:| |rows| (-650 (-570))) - (|:| |cols| (-650 (-570))))) - (-5 *4 (-695 *12)) (-5 *5 (-650 (-413 (-959 *9)))) - (-5 *6 (-650 (-650 *12))) (-5 *7 (-777)) (-5 *8 (-570)) - (-4 *9 (-13 (-311) (-148))) (-4 *12 (-956 *9 *11 *10)) - (-4 *10 (-13 (-856) (-620 (-1186)))) (-4 *11 (-799)) - (-5 *2 - (-2 (|:| |eqzro| (-650 *12)) (|:| |neqzro| (-650 *12)) - (|:| |wcond| (-650 (-959 *9))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1277 (-413 (-959 *9)))) - (|:| -4169 (-650 (-1277 (-413 (-959 *9))))))))) - (-5 *1 (-931 *9 *10 *11 *12))))) + (-12 (-4 *5 (-368)) (-4 *7 (-1253 *5)) (-4 *4 (-730 *5 *7)) + (-5 *2 (-2 (|:| -2415 (-695 *6)) (|:| |vec| (-1277 *5)))) + (-5 *1 (-817 *5 *6 *7 *4 *3)) (-4 *6 (-662 *5)) (-4 *3 (-662 *4))))) +(((*1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-705)))) + ((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-705))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-695 *7)) (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *6 *5)) + (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *1 (-931 *4 *5 *6 *7))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 (-570))) (-4 *3 (-1058)) (-5 *1 (-601 *3)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 (-570))) (-4 *1 (-1237 *3)) (-4 *3 (-1058)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 (-570))) (-4 *1 (-1268 *3)) (-4 *3 (-1058))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-570)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1227)) + (-4 *3 (-378 *4)) (-4 *5 (-378 *4))))) +(((*1 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1280)))) + ((*1 *2 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1280))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *4 (-562)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2407 *4))) + (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *2 *3) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3570 *4))) + (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-654 *3)) (-4 *3 (-1058)) - (-5 *1 (-720 *3 *4)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1058)) (-5 *1 (-842 *3))))) -(((*1 *2 *2 *3) (-12 (-5 *3 (-777)) (-5 *1 (-593 *2)) (-4 *2 (-551))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1253 *6)) - (-4 *6 (-13 (-27) (-436 *5))) (-4 *5 (-13 (-562) (-1047 (-570)))) - (-4 *8 (-1253 (-413 *7))) (-5 *2 (-592 *3)) - (-5 *1 (-558 *5 *6 *7 *8 *3)) (-4 *3 (-347 *6 *7 *8))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *4 *5 *6)) (-4 *4 (-311)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *1 (-453 *4 *5 *6 *2))))) + (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 *5)) (-4 *5 (-436 *4)) (-4 *4 (-562)) + (-5 *2 (-868)) (-5 *1 (-32 *4 *5))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-1001 *2)) (-4 *4 (-1253 *3)) (-4 *2 (-311)) @@ -101,7 +66,8 @@ (-5 *1 (-668 *3 *4 *2)) (-4 *3 (-723 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) (((*1 *2 *3) (-12 (-5 *3 (-650 (-52))) (-5 *2 (-1282)) (-5 *1 (-869))))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-124)))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4450)) (-4 *1 (-246 *2)) (-4 *2 (-1227))))) (((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -110,46 +76,54 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-1094))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1168)) (-5 *4 (-570)) (-5 *5 (-695 (-171 (-227)))) + (-5 *2 (-1044)) (-5 *1 (-760))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-650 (-1 (-112) *8))) (-4 *8 (-1074 *5 *6 *7)) - (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) - (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) - (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-695 *8)) (-4 *8 (-956 *5 *7 *6)) - (-4 *5 (-13 (-311) (-148))) (-4 *6 (-13 (-856) (-620 (-1186)))) - (-4 *7 (-799)) - (-5 *2 - (-650 - (-2 (|:| -4006 (-777)) - (|:| |eqns| - (-650 - (-2 (|:| |det| *8) (|:| |rows| (-650 (-570))) - (|:| |cols| (-650 (-570)))))) - (|:| |fgb| (-650 *8))))) - (-5 *1 (-931 *5 *6 *7 *8)) (-5 *4 (-777))))) (((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-31)))) ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) ((*1 *1) (-4 *1 (-551))) ((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705)))) ((*1 *2 *1) (-12 (-5 *2 (-650 *3)) (-5 *1 (-911 *3)) (-4 *3 (-1109))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-950 (-227))) (-5 *2 (-1282)) (-5 *1 (-474))))) -(((*1 *2 *2) (-12 (-5 *2 (-1166 (-650 (-570)))) (-5 *1 (-890))))) -(((*1 *1) (-12 (-5 *1 (-229 *2)) (-4 *2 (-13 (-368) (-1212)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) - (-4 *5 (-378 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(-1040))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856))))) + (-12 (-5 *3 (-413 (-959 *4))) (-4 *4 (-311)) + (-5 *2 (-413 (-424 (-959 *4)))) (-5 *1 (-1051 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-570)) (-5 *2 (-650 (-2 (|:| -3801 *3) (|:| -2130 *4)))) + (-5 *1 (-702 *3)) (-4 *3 (-1253 *4))))) +(((*1 *2 *3 *2) + (|partial| -12 (-5 *2 (-1277 *4)) (-5 *3 (-695 *4)) (-4 *4 (-368)) + (-5 *1 (-673 *4)))) + ((*1 *2 *3 *2) + (|partial| -12 (-4 *4 (-368)) + (-4 *5 (-13 (-378 *4) (-10 -7 (-6 -4450)))) + (-4 *2 (-13 (-378 *4) (-10 -7 (-6 -4450)))) + (-5 *1 (-674 *4 *5 *2 *3)) (-4 *3 (-693 *4 *5 *2)))) + ((*1 *2 *3 *2 *4 *5) + (|partial| -12 (-5 *4 (-650 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-368)) + (-5 *1 (-820 *2 *3)) (-4 *3 (-662 *2)))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) + (-5 *1 (-1137 *3 *2)) (-4 *3 (-1253 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) @@ -167,13 +141,7 @@ (-4 *4 (|SubsetCategory| (-732) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-777)) (-4 *5 (-1058)) (-5 *2 (-570)) - (-5 *1 (-449 *5 *3 *6)) (-4 *3 (-1253 *5)) - (-4 *6 (-13 (-410) (-1047 *5) (-368) (-1212) (-288))))) - ((*1 *2 *3) - (-12 (-4 *4 (-1058)) (-5 *2 (-570)) (-5 *1 (-449 *4 *3 *5)) - (-4 *3 (-1253 *4)) - (-4 *5 (-13 (-410) (-1047 *4) (-368) (-1212) (-288)))))) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) (((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -183,27 +151,91 @@ (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) (((*1 *2 *3) - (-12 (-5 *3 (-1186)) (-5 *2 (-1 *6 *5)) (-5 *1 (-712 *4 *5 *6)) - (-4 *4 (-620 (-542))) (-4 *5 (-1227)) (-4 *6 (-1227))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1277 *5)) (-4 *5 (-645 *4)) (-4 *4 (-562)) - (-5 *2 (-112)) (-5 *1 (-644 *4 *5))))) + (-12 (-4 *3 (-13 (-311) (-10 -8 (-15 -1652 ((-424 $) $))))) + (-4 *4 (-1253 *3)) + (-5 *2 + (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-695 *3)))) + (-5 *1 (-355 *3 *4 *5)) (-4 *5 (-415 *3 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-570)) (-4 *4 (-1253 *3)) + (-5 *2 + (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-695 *3)))) + (-5 *1 (-774 *4 *5)) (-4 *5 (-415 *3 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-354)) (-4 *3 (-1253 *4)) (-4 *5 (-1253 *3)) + (-5 *2 + (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-695 *3)))) + (-5 *1 (-994 *4 *3 *5 *6)) (-4 *6 (-730 *3 *5)))) + ((*1 *2 *3) + (-12 (-4 *4 (-354)) (-4 *3 (-1253 *4)) (-4 *5 (-1253 *3)) + (-5 *2 + (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-695 *3)))) + (-5 *1 (-1286 *4 *3 *5 *6)) (-4 *6 (-415 *3 *5))))) +(((*1 *2 *1) (-12 (-4 *1 (-854)) (-5 *2 (-570)))) + ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-912 *3)) (-4 *3 (-1109)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) + (-4 *3 (-1253 *4)) (-5 *2 (-570)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-13 (-562) (-1047 *2) (-645 *2) (-458))) + (-5 *2 (-570)) (-5 *1 (-1125 *4 *3)) + (-4 *3 (-13 (-27) (-1212) (-436 *4))))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-849 *3)) + (-4 *3 (-13 (-27) (-1212) (-436 *6))) + (-4 *6 (-13 (-562) (-1047 *2) (-645 *2) (-458))) (-5 *2 (-570)) + (-5 *1 (-1125 *6 *3)))) + ((*1 *2 *3 *4 *3 *5) + (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-1168)) + (-4 *6 (-13 (-562) (-1047 *2) (-645 *2) (-458))) (-5 *2 (-570)) + (-5 *1 (-1125 *6 *3)) (-4 *3 (-13 (-27) (-1212) (-436 *6))))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-413 (-959 *4))) (-4 *4 (-458)) (-5 *2 (-570)) + (-5 *1 (-1126 *4)))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-849 (-413 (-959 *6)))) + (-5 *3 (-413 (-959 *6))) (-4 *6 (-458)) (-5 *2 (-570)) + (-5 *1 (-1126 *6)))) + ((*1 *2 *3 *4 *3 *5) + (|partial| -12 (-5 *3 (-413 (-959 *6))) (-5 *4 (-1186)) + (-5 *5 (-1168)) (-4 *6 (-458)) (-5 *2 (-570)) (-5 *1 (-1126 *6)))) + ((*1 *2 *3) + (|partial| -12 (-5 *2 (-570)) (-5 *1 (-1209 *3)) (-4 *3 (-1058))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1207))))) (((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 - (-2 (|:| -1399 (-777)) (|:| |curves| (-777)) + (-2 (|:| -1981 (-777)) (|:| |curves| (-777)) (|:| |polygons| (-777)) (|:| |constructs| (-777))))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-334))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 (-112) *8)) (-4 *8 (-1074 *5 *6 *7)) (-4 *5 (-562)) - (-4 *6 (-799)) (-4 *7 (-856)) - (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) - (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-112)) (-5 *1 (-835))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-799)) + (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-4 *5 (-373)) + (-5 *2 (-777))))) +(((*1 *1 *1 *1) (-4 *1 (-479))) ((*1 *1 *1 *1) (-4 *1 (-767)))) +(((*1 *2 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-753))))) (((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-650 *3)) + (-5 *1 (-986 *4 *5 *6 *3)) (-4 *3 (-1074 *4 *5 *6)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-650 *3)) (-4 *3 (-1074 *4 *5 *6)) (-4 *4 (-562)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *1 (-986 *4 *5 *6 *3)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 (-650 *7) (-650 *7))) (-5 *2 (-650 *7)) + (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-562)) (-4 *5 (-799)) + (-4 *6 (-856)) (-5 *1 (-986 *4 *5 *6 *7))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-115) (-115))) (-5 *1 (-115))))) (((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-50 *3 *4)) (-4 *3 (-1058)) (-14 *4 (-650 (-1186))))) @@ -236,34 +268,31 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-1297 *3 *4)) (-4 *4 (-723 (-413 (-570)))) (-4 *3 (-856)) (-4 *4 (-174))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) - (-4 *4 (-1058))))) -(((*1 *2 *2) (|partial| -12 (-5 *1 (-564 *2)) (-4 *2 (-551))))) +(((*1 *1 *1) (-5 *1 (-1072)))) +(((*1 *2 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) (((*1 *1 *1) (-5 *1 (-542)))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-650 (-1226))) (-5 *3 (-1226)) (-5 *1 (-687))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *2)) (-5 *1 (-181 *2)) (-4 *2 (-311)))) - ((*1 *2 *3 *2) - (-12 (-5 *3 (-650 (-650 *4))) (-5 *2 (-650 *4)) (-4 *4 (-311)) - (-5 *1 (-181 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 *8)) - (-5 *4 - (-650 - (-2 (|:| -4169 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7))))) - (-5 *5 (-777)) (-4 *8 (-1253 *7)) (-4 *7 (-1253 *6)) (-4 *6 (-354)) - (-5 *2 - (-2 (|:| -4169 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7)))) - (-5 *1 (-504 *6 *7 *8)))) - ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1168)) - (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *2 (-112)) - (-5 *1 (-226 *4 *5)) (-4 *5 (-13 (-1212) (-29 *4)))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562))))) +(((*1 *1 *1 *1) + (|partial| -12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) +(((*1 *2 *3 *4 *5 *6 *5 *3 *7) + (-12 (-5 *4 (-570)) + (-5 *6 + (-2 (|:| |try| (-384)) (|:| |did| (-384)) (|:| -2158 (-384)))) + (-5 *7 (-1 (-1282) (-1277 *5) (-1277 *5) (-384))) + (-5 *3 (-1277 (-384))) (-5 *5 (-384)) (-5 *2 (-1282)) + (-5 *1 (-794)))) + ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) + (-12 (-5 *4 (-570)) + (-5 *6 + (-2 (|:| |try| (-384)) (|:| |did| (-384)) (|:| -2158 (-384)))) + (-5 *7 (-1 (-1282) (-1277 *5) (-1277 *5) (-384))) + (-5 *3 (-1277 (-384))) (-5 *5 (-384)) (-5 *2 (-1282)) + (-5 *1 (-794))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) @@ -341,24 +370,24 @@ ((*1 *1 *2) (|partial| -2892 (-12 (-5 *2 (-959 *3)) - (-12 (-1796 (-4 *3 (-38 (-413 (-570))))) - (-1796 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) + (-12 (-1795 (-4 *3 (-38 (-413 (-570))))) + (-1795 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1796 (-4 *3 (-551))) (-1796 (-4 *3 (-38 (-413 (-570))))) + (-12 (-1795 (-4 *3 (-551))) (-1795 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1796 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) + (-12 (-1795 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))))) ((*1 *1 *2) (|partial| -2892 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1796 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1795 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -368,379 +397,391 @@ (|partial| -12 (-5 *2 (-959 (-413 (-570)))) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-965 *3)) (-5 *1 (-1173 *4 *3)) - (-4 *3 (-1253 *4))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1277 *5)) (-4 *5 (-798)) (-5 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*2 *3) - (-12 (-5 *3 (-928)) (-4 *4 (-368)) (-5 *2 (-1277 *1)) - (-4 *1 (-333 *4)))) - ((*1 *2) (-12 (-4 *3 (-368)) (-5 *2 (-1277 *1)) (-4 *1 (-333 *3)))) - ((*1 *2) - (-12 (-4 *3 (-174)) (-4 *4 (-1253 *3)) (-5 *2 (-1277 *1)) - (-4 *1 (-415 *3 *4)))) - ((*1 *2 *1) - (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) - (-5 *2 (-1277 *6)) (-5 *1 (-419 *3 *4 *5 *6)) - (-4 *6 (-13 (-415 *4 *5) (-1047 *4))))) - ((*1 *2 *1) - (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) - (-5 *2 (-1277 *6)) (-5 *1 (-420 *3 *4 *5 *6 *7)) - (-4 *6 (-415 *4 *5)) (-14 *7 *2))) - ((*1 *2) (-12 (-4 *3 (-174)) (-5 *2 (-1277 *1)) (-4 *1 (-423 *3)))) - ((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1277 (-1277 *4))) (-5 *1 (-534 *4)) - (-4 *4 (-354))))) -(((*1 *2 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-1188 (-413 (-570)))) (-5 *1 (-192))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-1301 *3 *4)) (-4 *1 (-379 *3 *4)) (-4 *3 (-856)) - (-4 *4 (-174)))) - ((*1 *1 *1 *1) (|partial| -12 (-4 *1 (-391 *2)) (-4 *2 (-1109)))) - ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-825 *2)) (-4 *2 (-856)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1294 *2 *3)) (-4 *2 (-856)) (-4 *3 (-1058)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-825 *3)) (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) - (-4 *4 (-1058)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1294 *2 *3)) (-4 *2 (-856)) (-4 *3 (-1058))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-13 (-854) (-368))) (-5 *2 (-112)) (-5 *1 (-1070 *4 *3)) + (-4 *3 (-1253 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) + (-5 *2 + (-2 (|:| |contp| (-570)) + (|:| -3477 (-650 (-2 (|:| |irr| *3) (|:| -3563 (-570))))))) + (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) + (-5 *2 + (-2 (|:| |contp| (-570)) + (|:| -3477 (-650 (-2 (|:| |irr| *3) (|:| -3563 (-570))))))) + (-5 *1 (-1242 *3)) (-4 *3 (-1253 (-570)))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1107 *3)) (-4 *3 (-1109)) (-5 *2 (-112))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *5 *5)) + (-4 *5 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) + (-5 *2 + (-2 (|:| |solns| (-650 *5)) + (|:| |maps| (-650 (-2 (|:| |arg| *5) (|:| |res| *5)))))) + (-5 *1 (-1137 *3 *5)) (-4 *3 (-1253 *5))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1399,89 +1428,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *3 *4 *4) - (|partial| -12 (-5 *3 (-777)) (-4 *5 (-368)) (-5 *2 (-176 *6)) - (-5 *1 (-873 *5 *4 *6)) (-4 *4 (-1268 *5)) (-4 *6 (-1253 *5))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1212) (-1011)))))) (((*1 *1 *1) (-4 *1 (-635))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-650 - (-2 - (|:| -2106 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (|:| -2339 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1166 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -4043 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-565)))) - ((*1 *2 *1) - (-12 (-4 *1 (-610 *3 *4)) (-4 *3 (-1109)) (-4 *4 (-1227)) - (-5 *2 (-650 *4))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4020 *4))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-570)) (-4 *6 (-799)) (-4 *7 (-856)) (-4 *8 (-311)) - (-4 *9 (-956 *8 *6 *7)) - (-5 *2 (-2 (|:| -2560 (-1182 *9)) (|:| |polval| (-1182 *8)))) - (-5 *1 (-748 *6 *7 *8 *9)) (-5 *3 (-1182 *9)) (-5 *4 (-1182 *8))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4449)) (-4 *1 (-237 *3)) - (-4 *3 (-1109)))) - ((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4449)) (-4 *1 (-237 *2)) (-4 *2 (-1109)))) - ((*1 *1 *2 *1) - (-12 (-4 *1 (-286 *2)) (-4 *2 (-1227)) (-4 *2 (-1109)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-286 *3)) (-4 *3 (-1227)))) - ((*1 *2 *3 *1) - (|partial| -12 (-4 *1 (-616 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1109)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *2 (-1 (-112) *4)) (-5 *3 (-570)) (-4 *4 (-1109)) - (-5 *1 (-743 *4)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-570)) (-5 *1 (-743 *2)) (-4 *2 (-1109)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1149 *3 *4)) (-4 *3 (-13 (-1109) (-34))) - (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1150 *3 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) +(((*1 *1 *1 *1) (-5 *1 (-868)))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1129)) (-5 *2 (-1282)) (-5 *1 (-837))))) +(((*1 *1 *1) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) +(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) + (-12 (-4 *1 (-803 *2)) (-4 *2 (-174)))) + ((*1 *1 *2 *2) + (-12 (-5 *2 (-1008 *3)) (-4 *3 (-174)) (-5 *1 (-805 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *5 *6)) (-4 *6 (-620 (-1186))) - (-4 *4 (-368)) (-4 *5 (-799)) (-4 *6 (-856)) - (-5 *2 (-1175 (-650 (-959 *4)) (-650 (-298 (-959 *4))))) - (-5 *1 (-510 *4 *5 *6 *7))))) + (-12 (-4 *4 (-13 (-368) (-1047 (-413 *2)))) (-5 *2 (-570)) + (-5 *1 (-116 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 (-650 *2) *2 *2 *2)) (-4 *2 (-1109)) + (-5 *1 (-103 *2)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1109)) (-5 *1 (-103 *2))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-650 *4)) (-4 *4 (-368)) (-4 *2 (-1253 *4)) + (-5 *1 (-929 *4 *2))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1498,38 +1467,28 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1227))))) -(((*1 *2 *2 *3) - (-12 (-4 *4 (-799)) - (-4 *3 (-13 (-856) (-10 -8 (-15 -1425 ((-1186) $))))) (-4 *5 (-562)) - (-5 *1 (-738 *4 *3 *5 *2)) (-4 *2 (-956 (-413 (-959 *5)) *4 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *4 (-1058)) (-4 *5 (-799)) - (-4 *3 - (-13 (-856) - (-10 -8 (-15 -1425 ((-1186) $)) - (-15 -2799 ((-3 $ "failed") (-1186)))))) - (-5 *1 (-993 *4 *5 *3 *2)) (-4 *2 (-956 (-959 *4) *5 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-650 *6)) - (-4 *6 - (-13 (-856) - (-10 -8 (-15 -1425 ((-1186) $)) - (-15 -2799 ((-3 $ "failed") (-1186)))))) - (-4 *4 (-1058)) (-4 *5 (-799)) (-5 *1 (-993 *4 *5 *6 *2)) - (-4 *2 (-956 (-959 *4) *5 *6))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *2) (-12 (-5 *2 (-928)) (|has| *1 (-6 -4440)) (-4 *1 (-410)))) ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) ((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705)))) ((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1109)) (-5 *1 (-91 *3))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-227)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-227)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-384)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-384))))) +(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-145))))) (((*1 *2 *3) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-243)) (-5 *3 (-1168)))) ((*1 *2 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-243)))) ((*1 *1 *2) (-12 (-5 *2 (-158)) (-5 *1 (-880))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-949)) (-5 *3 (-570))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1 (-112) *7 (-650 *7))) (-4 *1 (-1220 *4 *5 *6 *7)) + (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-868) (-868))) (-5 *1 (-115)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-868) (-650 (-868)))) (-5 *1 (-115)))) ((*1 *2 *1) @@ -1538,8 +1497,8 @@ (-12 (-5 *2 (-1282)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-856) - (-10 -8 (-15 -1940 ((-1168) $ (-1186))) (-15 -4147 (*2 $)) - (-15 -3732 (*2 $))))))) + (-10 -8 (-15 -1941 ((-1168) $ (-1186))) (-15 -4147 (*2 $)) + (-15 -2176 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-400)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-400)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-508)))) @@ -1547,14 +1506,23 @@ ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1207)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-1207))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -4397 (-413 (-570))) (|:| -4410 (-413 (-570))))) - (-5 *2 (-413 (-570))) (-5 *1 (-1029 *4)) (-4 *4 (-1253 (-570)))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) + (-12 (-5 *3 (-650 (-928))) (-5 *2 (-911 (-570))) (-5 *1 (-924))))) +(((*1 *2 *3 *4 *5 *5 *5 *6 *4 *4 *4 *5 *4 *5 *7) + (-12 (-5 *3 (-1168)) (-5 *5 (-695 (-227))) (-5 *6 (-227)) + (-5 *7 (-695 (-570))) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-758))))) (((*1 *1) (-5 *1 (-334)))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-512)) (-5 *1 (-283))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-570))) (-5 *2 (-911 (-570))) (-5 *1 (-924)))) - ((*1 *2) (-12 (-5 *2 (-911 (-570))) (-5 *1 (-924))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-618 *1)) (-4 *1 (-306))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-158)) (-5 *2 (-1282)) (-5 *1 (-1279))))) +(((*1 *2 *1) + (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-1109)) + (-5 *2 (-650 (-2 (|:| |k| *4) (|:| |c| *3)))))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 (-2 (|:| |k| (-900 *3)) (|:| |c| *4)))) + (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) + (-4 *4 (-13 (-174) (-723 (-413 (-570))))) (-14 *5 (-928)))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 (-678 *3))) (-5 *1 (-900 *3)) (-4 *3 (-856))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1572,14 +1540,6 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) - (-5 *2 - (-2 (|:| -2307 *4) (|:| -3669 *4) (|:| |totalpts| (-570)) - (|:| |success| (-112)))) - (-5 *1 (-795)) (-5 *5 (-570))))) -(((*1 *2 *3 *4) (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 *6)) (-4 *5 (-1109)) (-4 *6 (-1227)) (-5 *2 (-1 *6 *5)) (-5 *1 (-647 *5 *6)))) ((*1 *2 *3 *4 *5) @@ -1598,32 +1558,38 @@ (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 *2)) (-5 *6 (-1 *2 *5)) (-4 *5 (-1109)) (-4 *2 (-1227)) (-5 *1 (-647 *5 *2)))) ((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1153)) (-5 *3 (-145)) (-5 *2 (-777))))) +(((*1 *2) + (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) + (-4 *5 (-1253 (-413 *4))) (-5 *2 (-695 (-413 *4)))))) +(((*1 *2 *2) (-12 (-5 *2 (-384)) (-5 *1 (-97))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-777)) (-5 *4 (-1277 *2)) (-4 *5 (-311)) - (-4 *6 (-1001 *5)) (-4 *2 (-13 (-415 *6 *7) (-1047 *6))) - (-5 *1 (-419 *5 *6 *7 *2)) (-4 *7 (-1253 *6))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-1058)) (-5 *1 (-450 *3 *2)) (-4 *2 (-1253 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) + (-12 (-4 *5 (-311)) (-4 *6 (-378 *5)) (-4 *4 (-378 *5)) + (-5 *2 + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1972 (-650 *4)))) + (-5 *1 (-1133 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *2) - (-12 + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) (-5 *2 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) - (|:| |xpnt| (-570)))) - (-4 *4 (-13 (-1253 *3) (-562) (-10 -8 (-15 -1942 ($ $ $))))) - (-4 *3 (-562)) (-5 *1 (-1256 *3 *4))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -3684 *4)))) - (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) -(((*1 *2 *3 *4 *4 *4 *5 *4 *6 *6 *3) - (-12 (-5 *4 (-695 (-227))) (-5 *5 (-695 (-570))) (-5 *6 (-227)) - (-5 *3 (-570)) (-5 *2 (-1044)) (-5 *1 (-757))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-1208))))) + (-2 (|:| |ir| (-592 (-413 *6))) (|:| |specpart| (-413 *6)) + (|:| |polypart| *6))) + (-5 *1 (-580 *5 *6)) (-5 *3 (-413 *6))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1253 *5)) + (-4 *5 (-13 (-27) (-436 *4))) (-4 *4 (-13 (-562) (-1047 (-570)))) + (-4 *7 (-1253 (-413 *6))) (-5 *1 (-558 *4 *5 *6 *7 *2)) + (-4 *2 (-347 *5 *6 *7))))) +(((*1 *2 *1) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *2 (-570)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) + (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-570))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 (-618 *5))) (-4 *4 (-1109)) (-5 *2 (-618 *5)) + (-5 *1 (-579 *4 *5)) (-4 *5 (-436 *4))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-928)) (-5 *4 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1640,36 +1606,40 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-650 (-650 (-650 *5)))) (-5 *3 (-1 (-112) *5 *5)) + (-5 *4 (-650 *5)) (-4 *5 (-856)) (-5 *1 (-1197 *5))))) (((*1 *2 *1) (-12 (-5 *2 (-650 *4)) (-5 *1 (-1150 *3 *4)) (-4 *3 (-13 (-1109) (-34))) (-4 *4 (-13 (-1109) (-34)))))) -(((*1 *1) - (|partial| -12 (-4 *1 (-372 *2)) (-4 *2 (-562)) (-4 *2 (-174))))) -(((*1 *1) - (|partial| -12 (-4 *1 (-372 *2)) 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*4) + (-12 (-5 *3 (-695 (-227))) (-5 *4 (-570)) (-5 *2 (-1044)) + (-5 *1 (-761))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-650 *5)) (-5 *4 (-570)) (-4 *5 (-854)) (-4 *5 (-368)) + (-5 *2 (-777)) (-5 *1 (-952 *5 *6)) (-4 *6 (-1253 *5))))) +(((*1 *2 *3 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-753))))) +(((*1 *2 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1227))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) + (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *1 *1) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) (((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-320 *4)) @@ -3295,16 +3082,10 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *1 (-1216 *3 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *3)))))) -(((*1 *2) - (-12 (-4 *3 (-562)) (-5 *2 (-650 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-423 *3))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -1942 (-788 *3)) (|:| |coef2| (-788 *3)))) - (-5 *1 (-788 *3)) (-4 *3 (-562)) (-4 *3 (-1058)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-562)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-2 (|:| -1942 *1) (|:| |coef2| *1))) - (-4 *1 (-1074 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-512))) (-5 *1 (-49)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-882))) (-5 *1 (-489))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1279))))) (((*1 *2 *1 *3 *3) (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-378 *2)) (-4 *5 (-378 *2)) (-4 *2 (-1227)))) @@ -3316,24 +3097,15 @@ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-570)) (-4 *1 (-1062 *4 *5 *2 *6 *7)) (-4 *6 (-240 *5 *2)) (-4 *7 (-240 *4 *2)) (-4 *2 (-1058))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) - (-5 *2 (-2 (|:| |k| (-825 *3)) (|:| |c| *4)))))) -(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) -(((*1 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(-5 *2 (-650 (-2 (|:| -1696 (-777)) (|:| -2288 *4) (|:| |num| *4)))) + (-5 *2 (-650 (-2 (|:| -3357 (-777)) (|:| -2288 *4) (|:| |num| *4)))) (-4 *4 (-1253 *3)) (-4 *3 (-13 (-368) (-148))) (-5 *1 (-405 *3 *4)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) @@ -3379,13 +3151,13 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-719 *2 *3 *4)) (-4 *2 (-856)) (-4 *3 (-1109)) (-14 *4 - (-1 (-112) (-2 (|:| -2266 *2) (|:| -1696 *3)) - (-2 (|:| -2266 *2) (|:| -1696 *3)))))) + (-1 (-112) (-2 (|:| -2268 *2) (|:| -3357 *3)) + (-2 (|:| -2268 *2) (|:| -3357 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-844)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-879 *2 *3)) (-4 *2 (-1227)) (-4 *3 (-1227)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -2106 (-1186)) (|:| -2339 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -2106 (-1186)) (|:| -2340 *4)))) (-4 *4 (-1109)) (-5 *1 (-896 *3 *4)) (-4 *3 (-1109)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-650 *5)) (-4 *5 (-13 (-1109) (-34))) @@ -3419,13 +3191,9 @@ (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1150 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1175 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-1109))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-777)) (-4 *5 (-562)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-978 *5 *3)) (-4 *3 (-1253 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-413 (-570))) (-5 *1 (-108)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-542))) (-5 *1 (-542))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *1) (-12 (-5 *1 (-921 *2)) (-4 *2 (-311))))) +(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) @@ -3434,31 +3202,28 @@ ((*1 *1 *1) (-5 *1 (-868))) ((*1 *2 *3) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-1170 *3)) (-4 *3 (-1058))))) -(((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-777)) (-5 *1 (-788 *3)) (-4 *3 (-1058)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *1 (-970 *3 *2)) (-4 *2 (-132)) (-4 *3 (-562)) - (-4 *3 (-1058)) (-4 *2 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|bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-565)))) ((*1 *2 *1) + (-12 (-4 *1 (-610 *3 *4)) (-4 *3 (-1109)) (-4 *4 (-1227)) + (-5 *2 (-650 *4))))) +(((*1 *1) (-5 *1 (-158)))) +(((*1 *2 *3) (-12 (-5 *3 (-777)) (-5 *2 (-1 (-384))) (-5 *1 (-1049))))) +(((*1 *2 *3 *4 *5 *5 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *4) + (-12 (-5 *3 (-1168)) (-5 *4 (-570)) (-5 *5 (-695 (-227))) + (-5 *6 (-227)) (-5 *2 (-1044)) (-5 *1 (-758))))) +(((*1 *2 *3) + (-12 (-4 *4 (-856)) (-5 *2 (-650 (-650 (-650 *4)))) + (-5 *1 (-1197 *4)) (-5 *3 (-650 (-650 *4)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1277 (-650 (-2 (|:| -2308 *4) (|:| -2268 (-1129)))))) + (-4 *4 (-354)) (-5 *2 (-695 *4)) (-5 *1 (-351 *4))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-320 (-227))) (-5 *4 (-1186)) + (-5 *5 (-1103 (-849 (-227)))) (-5 *2 (-650 (-227))) (-5 *1 (-194)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-320 (-227))) (-5 *4 (-1186)) + (-5 *5 (-1103 (-849 (-227)))) (-5 *2 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(-5 *5 (-384)) (-5 *2 (-1282)) - (-5 *1 (-794))))) +(((*1 *2) + (-12 (-4 *2 (-13 (-436 *3) (-1011))) (-5 *1 (-279 *3 *2)) + (-4 *3 (-562))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1227)) (-5 *2 (-650 *1)) (-4 *1 (-1019 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 (-1174 *3 *4))) (-5 *1 (-1174 *3 *4)) + (-14 *3 (-928)) (-4 *4 (-1058))))) (((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-62 *3)) (-14 *3 (-1186)))) ((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-69 *3)) (-14 *3 (-1186)))) ((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-72 *3)) (-14 *3 (-1186)))) @@ -6218,18 +6198,20 @@ ((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1282)) (-5 *1 (-1147)))) ((*1 *2 *3) (-12 (-5 *3 (-650 (-868))) (-5 *2 (-1282)) (-5 *1 (-1147))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-777)) (-4 *6 (-1109)) (-4 *3 (-907 *6)) - (-5 *2 (-695 *3)) (-5 *1 (-698 *6 *3 *7 *4)) (-4 *7 (-378 *3)) - (-4 *4 (-13 (-378 *6) (-10 -7 (-6 -4449))))))) -(((*1 *2 *1) - (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-650 *6)) - (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 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(-5 *2 (-2 (|:| |under| *1) (|:| -2516 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3665 *1) (|:| |upper| *1))) (-4 *1 (-985 *4 *5 *3 *6))))) (((*1 *1 *2) (-12 (-5 *2 (-1129)) (-5 *1 (-334))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-695 (-171 (-413 (-570))))) (-5 *2 (-650 (-171 *4))) - (-5 *1 (-770 *4)) (-4 *4 (-13 (-368) (-854)))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1166 *3)) (-4 *3 (-1058)) (-5 *1 (-1170 *3))))) -(((*1 *2 *1) - (|partial| -12 (-5 *2 (-1186)) (-5 *1 (-618 *3)) (-4 *3 (-1109))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-1277 *4)) (-5 *3 (-1129)) (-4 *4 (-354)) - (-5 *1 (-534 *4))))) +(((*1 *2 *1 *3) + (|partial| -12 (-5 *3 (-899 *4)) (-4 *4 (-1109)) (-5 *2 (-112)) + (-5 *1 (-896 *4 *5)) (-4 *5 (-1109)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-899 *5)) (-4 *5 (-1109)) (-5 *2 (-112)) + (-5 *1 (-897 *5 *3)) (-4 *3 (-1227)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *6)) (-5 *4 (-899 *5)) (-4 *5 (-1109)) + (-4 *6 (-1227)) (-5 *2 (-112)) (-5 *1 (-897 *5 *6))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1262 *3 *4 *5)) (-4 *3 (-368)) (-14 *4 (-1186)) + (-14 *5 *3) (-5 *1 (-323 *3 *4 *5)))) + ((*1 *2 *3) (-12 (-5 *2 (-1 (-384))) (-5 *1 (-1049)) (-5 *3 (-384))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-650 *6)) (-4 *6 (-856)) (-4 *4 (-368)) (-4 *5 (-799)) + (-5 *2 + (-2 (|:| |mval| (-695 *4)) (|:| |invmval| (-695 *4)) + (|:| |genIdeal| (-510 *4 *5 *6 *7)))) + (-5 *1 (-510 *4 *5 *6 *7)) (-4 *7 (-956 *4 *5 *6))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) (((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) + (|partial| -12 (-5 *2 (-1182 *3)) (-4 *3 (-354)) (-5 *1 (-362 *3))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-266))) (-5 *1 (-1278)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-266))) (-5 *1 (-1278)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-266))) (-5 *1 (-1279)))) @@ -6267,24 +6258,25 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-825 *4)) (-4 *4 (-856)) (-4 *1 (-1294 *4 *3)) (-4 *3 (-1058))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 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*2) (-12 (-5 *2 (-1282)) (-5 *1 (-397))))) -(((*1 *1) (-5 *1 (-142)))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-266))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-1 (-112) *8))) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) + (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) (((*1 *2 *1 *3 *4) (-12 (-5 *3 (-950 (-227))) (-5 *4 (-880)) (-5 *2 (-1282)) (-5 *1 (-474)))) @@ -6301,18 +6293,31 @@ (-12 (-5 *2 (-950 *3)) (-4 *1 (-1143 *3)) (-4 *3 (-1058)))) ((*1 *2 *3 *3 *3 *3) (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223)) (-5 *3 (-227))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-424 *5)) (-4 *5 (-562)) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-650 (-650 *7))) + (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) + (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) + (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 (-320 (-227)))) (-5 *2 (-112)) (-5 *1 (-270)))) + ((*1 *2 *3) (-12 (-5 *3 (-320 (-227))) (-5 *2 (-112)) (-5 *1 (-270)))) + ((*1 *2 *3) + (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-986 *4 *5 *6 *3)) (-4 *3 (-1074 *4 *5 *6))))) +(((*1 *2 *3) + (-12 (-5 *3 (-695 (-320 (-227)))) (-5 *2 - (-2 (|:| -1696 (-777)) (|:| -1452 *5) (|:| |radicand| (-650 *5)))) - (-5 *1 (-324 *5)) (-5 *4 (-777)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1011)) (-5 *2 (-570))))) -(((*1 *1 *1) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) + (-2 (|:| |stiffnessFactor| (-384)) (|:| |stabilityFactor| (-384)))) + (-5 *1 (-207))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *4 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(-695 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-415 *3 *4)) (-4 *3 (-174)) (-4 *4 (-1253 *3)) + (-5 *2 (-695 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1227)) (-5 *2 (-777)) (-5 *1 (-184 *4 *3)) + (-4 *3 (-680 *4))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1072))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1708 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -9254,39 +9574,59 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *2 *3) - (-12 - (-5 *2 - (-2 (|:| |partsol| (-1277 (-413 (-959 *4)))) - (|:| -4169 (-650 (-1277 (-413 (-959 *4))))))) - (-5 *3 (-650 *7)) (-4 *4 (-13 (-311) (-148))) - (-4 *7 (-956 *4 *6 *5)) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) (-5 *1 (-931 *4 *5 *6 *7))))) -(((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-934))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-879 (-928) 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*1 (-949)) (-5 *3 (-570))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-856)) (-5 *1 (-490 *3))))) +(((*1 *2 *3) + (|partial| -12 (-4 *5 (-1047 (-48))) + (-4 *4 (-13 (-562) (-1047 (-570)))) (-4 *5 (-436 *4)) + (-5 *2 (-424 (-1182 (-48)))) (-5 *1 (-441 *4 *5 *3)) + (-4 *3 (-1253 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-173))))) +(((*1 *2 *2) + (-12 (-4 *2 (-13 (-368) (-854))) (-5 *1 (-183 *2 *3)) + (-4 *3 (-1253 (-171 *2)))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-551)) + (-5 *2 (-413 (-570))))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-424 *3)) (-4 *3 (-551)) + (-4 *3 (-562)))) + ((*1 *2 *1) (|partial| -12 (-4 *1 (-551)) (-5 *2 (-413 (-570))))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-803 *3)) (-4 *3 (-174)) (-4 *3 (-551)) + (-5 *2 (-413 (-570))))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-839 *3)) (-4 *3 (-551)) + (-4 *3 (-1109)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-849 *3)) (-4 *3 (-551)) + (-4 *3 (-1109)))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-1006 *3)) (-4 *3 (-174)) (-4 *3 (-551)) + (-5 *2 (-413 (-570))))) + ((*1 *2 *3) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-1017 *3)) + (-4 *3 (-1047 *2))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) + (-12 (-5 *4 (-1186)) (-5 *2 (-1 (-227) (-227))) (-5 *1 (-709 *3)) + (-4 *3 (-620 (-542))))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-1186)) (-5 *2 (-1 (-227) (-227) (-227))) + (-5 *1 (-709 *3)) (-4 *3 (-620 (-542)))))) +(((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-928)) (-5 *1 (-792))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1708 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -9308,18 +9648,13 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-378 *2)) 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+9830,45 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-331 *3)) (-4 *3 (-1227)))) - ((*1 *2 *1) - (-12 (-5 *2 (-777)) (-5 *1 (-522 *3 *4)) (-4 *3 (-1227)) - (-14 *4 (-570))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-1168))) (-5 *2 (-1168)) (-5 *1 (-194)))) - ((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1277 *1)) (-5 *4 (-1 *5 *5)) (-4 *5 (-368)) - (-4 *1 (-730 *5 *6)) (-4 *5 (-174)) (-4 *6 (-1253 *5)) - (-5 *2 (-695 *5))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-650 (-283))) (-5 *1 (-283)))) - ((*1 *2 *1) (-12 (-5 *2 (-650 (-1191))) (-5 *1 (-1191))))) -(((*1 *2 *3 *2 *4) - (-12 (-5 *3 (-115)) (-5 *4 (-777)) - (-4 *5 (-13 (-458) (-1047 (-570)))) (-4 *5 (-562)) - (-5 *1 (-41 *5 *2)) (-4 *2 (-436 *5)) - (-4 *2 - (-13 (-368) (-306) - (-10 -8 (-15 -4399 ((-1134 *5 (-618 $)) $)) - (-15 -4413 ((-1134 *5 (-618 $)) $)) - (-15 -3799 ($ (-1134 *5 (-618 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+(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| -2415 (-695 (-413 (-959 *4)))) + (|:| |vec| (-650 (-413 (-959 *4)))) (|:| -4006 (-777)) + (|:| |rows| (-650 (-570))) (|:| |cols| (-650 (-570))))) + (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) + (-5 *2 + (-2 (|:| |partsol| (-1277 (-413 (-959 *4)))) + (|:| -1972 (-650 (-1277 (-413 (-959 *4))))))) + (-5 *1 (-931 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-176 *3)) (-4 *3 (-311))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-866)) (-5 *3 (-129)) (-5 *2 (-777))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) + (-5 *2 (-650 *4)) (-5 *1 (-1137 *3 *4)) (-4 *3 (-1253 *4)))) + ((*1 *2 *3 *3 *3) + (-12 (-4 *3 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) + (-5 *2 (-650 *3)) (-5 *1 (-1137 *4 *3)) (-4 *4 (-1253 *3))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-384)) (-5 *1 (-207))))) +(((*1 *2 *3) + (-12 (-4 *4 (-27)) + (-4 *4 (-13 (-368) (-148) (-1047 (-570)) (-1047 (-413 (-570))))) + (-4 *5 (-1253 *4)) (-5 *2 (-650 (-659 (-413 *5)))) + (-5 *1 (-663 *4 *5)) (-5 *3 (-659 (-413 *5)))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9535,53 +9885,58 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-650 (-650 *8))) (-5 *3 (-650 *8)) - (-4 *8 (-956 *5 *7 *6)) (-4 *5 (-13 (-311) (-148))) - (-4 *6 (-13 (-856) (-620 (-1186)))) (-4 *7 (-799)) (-5 *2 (-112)) - (-5 *1 (-931 *5 *6 *7 *8))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-695 *5)) (-5 *4 (-1277 *5)) (-4 *5 (-368)) - (-5 *2 (-112)) (-5 *1 (-673 *5)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4450)))) - (-4 *4 (-13 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(-1253 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-112)) + (-5 *1 (-190 *4 *3)) (-4 *3 (-13 (-27) (-1212) (-436 (-171 *4)))))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-440)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *2 (-112)) + (-5 *1 (-1216 *4 *3)) (-4 *3 (-13 (-27) (-1212) (-436 *4)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1112 *3 *4 *5 *6 *2)) (-4 *3 (-1109)) (-4 *4 (-1109)) + (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-1109))))) +(((*1 *2 *1) + (-12 (|has| *1 (-6 -4449)) (-4 *1 (-495 *3)) (-4 *3 (-1227)) + (-5 *2 (-650 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 *3)) (-5 *1 (-743 *3)) (-4 *3 (-1109)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-445))) (-5 *1 (-871))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9601,88 +9956,78 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *1) - (-12 (-4 *1 (-1112 *3 *4 *5 *6 *2)) (-4 *3 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-2521 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1044)) (-5 *1 (-309))))) (((*1 *2 *1) - (|partial| -12 (-4 *3 (-1121)) (-4 *3 (-1109)) (-5 *2 (-650 *1)) - (-4 *1 (-436 *3)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-650 (-899 *3))) (-5 *1 (-899 *3)) - (-4 *3 (-1109)))) - ((*1 *2 *1) - (|partial| -12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-650 *1)) (-4 *1 (-956 *3 *4 *5)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-1058)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-650 *3)) - (-5 *1 (-957 *4 *5 *6 *7 *3)) - (-4 *3 - (-13 (-368) - (-10 -8 (-15 -3799 ($ *7)) (-15 -4399 (*7 $)) - (-15 -4413 (*7 $)))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1277 (-695 *4))) (-4 *4 (-174)) - (-5 *2 (-1277 (-695 (-959 *4)))) (-5 *1 (-191 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*2 (-777)) (-5 *1 (-1154 *5 *6 *7 *8 *9))))) +(((*1 *1 *1) (-12 (-5 *1 (-921 *2)) (-4 *2 (-311))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) (-5 *2 (-112)) + (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) + (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -3684 *4)))) + (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *4 *5 *6)) (-4 *4 (-368)) + (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-5 *1 (-456 *4 *5 *6 *2)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-368)) + (-5 *2 + (-2 (|:| R (-695 *6)) (|:| A (-695 *6)) (|:| |Ainv| (-695 *6)))) + (-5 *1 (-987 *6)) (-5 *3 (-695 *6))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-777)) (-4 *3 (-1058)) (-4 *1 (-693 *3 *4 *5)) + (-4 *4 (-378 *3)) (-4 *5 (-378 *3)))) + ((*1 *1 *2) + (-12 (-4 *2 (-1058)) (-4 *1 (-1132 *3 *2 *4 *5)) (-4 *4 (-240 *3 *2)) + (-4 *5 (-240 *3 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9703,37 +10048,32 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *4 *4 *3 *5) - (-12 (-5 *4 (-618 *3)) (-5 *5 (-1182 *3)) - (-4 *3 (-13 (-436 *6) (-27) (-1212))) - (-4 *6 (-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) - (-5 *2 (-592 *3)) (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1109)))) - ((*1 *2 *3 *4 *4 *4 *3 *5) - (-12 (-5 *4 (-618 *3)) (-5 *5 (-413 (-1182 *3))) - (-4 *3 (-13 (-436 *6) (-27) (-1212))) - (-4 *6 (-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) - (-5 *2 (-592 *3)) (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1109))))) -(((*1 *2) - (-12 (-4 *3 (-562)) (-5 *2 (-650 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-423 *3))))) -(((*1 *2 *2) - (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1212) (-1011))) - (-5 *1 (-178 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -1942 *3))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-112)) (-5 *1 (-835))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-912 *4)) (-4 *4 (-1109)) (-5 *2 (-650 (-777))) + (-5 *1 (-911 *4))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1019 *3)) (-4 *3 (-1227)) (-5 *2 (-570))))) +(((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-409 *3)) (-4 *3 (-410)))) + ((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-409 *3)) (-4 *3 (-410)))) + ((*1 *2 *2) (-12 (-5 *2 (-928)) (|has| *1 (-6 -4440)) (-4 *1 (-410)))) + ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) + ((*1 *2 *1) (-12 (-4 *1 (-875 *3)) (-5 *2 (-1166 (-570)))))) +(((*1 *2 *3) + (|partial| -12 (-4 *4 (-13 (-562) (-148))) + (-5 *2 (-2 (|:| -4397 *3) (|:| -4410 *3))) (-5 *1 (-1247 *4 *3)) + (-4 *3 (-1253 *4))))) +(((*1 *1 *1) (-4 *1 (-551)))) (((*1 *2 *3 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) (-5 *1 (-266)))) @@ -9746,29 +10086,19 @@ ((*1 *2 *1 *3) (-12 (-5 *3 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) (-5 *2 (-1282)) (-5 *1 (-1279)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) (-5 *1 (-1279)))) ((*1 *2 *1 *3 *3 *3 *3 *3) (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279))))) -(((*1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *3 *3 *3 *4 *5) - (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1253 *6)) - (-4 *6 (-13 (-368) (-148) (-1047 *4))) (-5 *4 (-570)) - (-5 *2 - (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) - (|:| -4306 - (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) - (|:| |beta| *3))))) - (-5 *1 (-1024 *6 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9789,220 +10119,284 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1035 (-849 (-570)))) - (-5 *3 (-1166 (-2 (|:| |k| (-570)) (|:| |c| *4)))) (-4 *4 (-1058)) - (-5 *1 (-601 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-395)) (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-921 *3)) (-4 *3 (-311))))) -(((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-176 *3)) (-4 *3 (-311))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-413 (-570))) (-5 *4 (-570)) (-5 *2 (-52)) - (-5 *1 (-1014))))) +(((*1 *2 *1) (|partial| -12 (-5 *1 (-370 *2)) (-4 *2 (-1109)))) + ((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-1208))))) +(((*1 *2 *2 *3 *4 *5) + (-12 (-5 *2 (-650 *9)) (-5 *3 (-1 (-112) *9)) + (-5 *4 (-1 (-112) *9 *9)) (-5 *5 (-1 *9 *9 *9)) + (-4 *9 (-1074 *6 *7 *8)) (-4 *6 (-562)) (-4 *7 (-799)) + (-4 *8 (-856)) (-5 *1 (-986 *6 *7 *8 *9))))) +(((*1 *1 *2) + (-12 (-5 *2 (-650 (-510 *3 *4 *5 *6))) (-4 *3 (-368)) (-4 *4 (-799)) + (-4 *5 (-856)) (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5)))) + ((*1 *1 *1 *1) + (-12 (-4 *2 (-368)) (-4 *3 (-799)) (-4 *4 (-856)) + (-5 *1 (-510 *2 *3 *4 *5)) (-4 *5 (-956 *2 *3 *4)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-650 *1)) (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) + (-4 *5 (-799)) (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-650 *1)) (-5 *3 (-650 *7)) (-4 *1 (-1080 *4 *5 *6 *7)) + 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(-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) - (-5 *2 - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-566 *7 *3 *8)) (-4 *8 (-1109))))) -(((*1 *2 *1) (-12 (-5 *1 (-1222 *2)) (-4 *2 (-983))))) -(((*1 *2 *1) (-12 (-5 *2 (-830)) (-5 *1 (-831))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1111 *3)) (-5 *1 (-912 *3)) (-4 *3 (-373)) - (-4 *3 (-1109))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) + (-12 (-4 *3 (-562)) (-4 *4 (-1001 *3)) (-5 *1 (-1246 *3 *4 *2)) + (-4 *2 (-1253 *4))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-798)))) ((*1 *2 *1) (-12 (-4 *1 (-387 *3 *2)) (-4 *3 (-1058)) (-4 *2 (-1109)))) @@ -13607,8 +13990,8 @@ (-12 (-14 *3 (-650 (-1186))) (-4 *4 (-174)) (-4 *6 (-240 (-2569 *3) (-777))) (-14 *7 - (-1 (-112) (-2 (|:| -2266 *5) (|:| -1696 *6)) - (-2 (|:| -2266 *5) (|:| -1696 *6)))) + (-1 (-112) (-2 (|:| -2268 *5) (|:| -3357 *6)) + (-2 (|:| -2268 *5) (|:| -3357 *6)))) (-5 *2 (-719 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*1 (-1255 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-798)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1166 *3))))) -(((*1 *1) (-5 *1 (-565)))) (((*1 *2 *1) (-12 (-4 *1 (-246 *2)) (-4 *2 (-1227)))) ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1105)))) ((*1 *2 *1) @@ -14565,79 +14832,61 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *2 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-1189)))) - ((*1 *2 *3) (-12 (-5 *3 (-1186)) (-5 *2 (-1282)) (-5 *1 (-1189)))) - ((*1 *2 *3 *1) (-12 (-5 *3 (-1186)) (-5 *2 (-1282)) (-5 *1 (-1189))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-799)) (-4 *6 (-856)) (-4 *7 (-562)) - (-4 *3 (-956 *7 *5 *6)) - (-5 *2 - (-2 (|:| -1696 (-777)) (|:| -1452 *3) (|:| |radicand| (-650 *3)))) - (-5 *1 (-960 *5 *6 *7 *3 *8)) (-5 *4 (-777)) - (-4 *8 - (-13 (-368) - (-10 -8 (-15 -3799 ($ *3)) (-15 -4399 (*3 $)) (-15 -4413 (*3 $)))))))) +(((*1 *2 *3 *3 *3 *3 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) + (-5 *5 (-3 (|:| |fn| (-394)) (|:| |fp| (-64 -1708)))) + (-5 *2 (-1044)) (-5 *1 (-752))))) +(((*1 *2 *2 *2 *2 *3) + (-12 (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) (-4 *2 (-1253 *3))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) +(((*1 *2 *1) + (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) + (-4 *3 (-1253 *2))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) + (-4 *3 (-372 *4)))) + ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) + (-4 *3 (-372 *4)))) + ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-1168)) (-4 *1 (-369 *2 *4)) (-4 *2 (-1109)) (-4 *4 (-1109)))) ((*1 *1 *2) (-12 (-4 *1 (-369 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-1109))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *4 (-570))) (-5 *5 (-1 (-1166 *4))) (-4 *4 (-368)) - (-4 *4 (-1058)) (-5 *2 (-1166 *4)) (-5 *1 (-1170 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *2 *2)) 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((*1 *1 *1 *2) + (-12 (-5 *2 (-825 *3)) (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) + (-4 *4 (-1058)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1294 *2 *3)) (-4 *2 (-856)) (-4 *3 (-1058))))) +(((*1 *1 *2) + (-12 (-5 *2 (-650 (-650 *3))) (-4 *3 (-1109)) (-5 *1 (-1198 *3))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-562)) (-4 *2 (-1058)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) (-4 *2 (-1253 *3)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562)))) + ((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *3 (-1074 *4 *5 *6)) + (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -3684 *1)))) + (-4 *1 (-1080 *4 *5 *6 *3))))) +(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -3684 *4)))) (-5 *1 (-1150 *3 *4)) (-4 *3 (-13 (-1109) (-34))) (-4 *4 (-13 (-1109) (-34)))))) -(((*1 *1 *1 *1) (-5 *1 (-868)))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) (-5 *2 (-112)) - (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -3684 *4)))) - (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) +(((*1 *1) (-5 *1 (-1094)))) (((*1 *2 *3) (-12 (-5 *3 @@ -14673,43 +14922,61 @@ ((*1 *2 *3) (-12 (-5 *3 (-413 (-959 *4))) (-4 *4 (-562)) (-5 *2 (-650 (-1186))) (-5 *1 (-1052 *4))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-662 *2)) (-4 *2 (-1058)) (-4 *2 (-368)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-368)) (-5 *1 (-665 *4 *2)) + (-4 *2 (-662 *4))))) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-115)) (-5 *4 (-650 *2)) (-5 *1 (-114 *2)) - (-4 *2 (-1109)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 (-650 *4))) (-4 *4 (-1109)) - (-5 *1 (-114 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1109)) - (-5 *1 (-114 *4)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-115)) (-5 *2 (-1 *4 (-650 *4))) - (-5 *1 (-114 *4)) (-4 *4 (-1109)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-654 *3)) (-4 *3 (-1058)) - (-5 *1 (-720 *3 *4)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1058)) (-5 *1 (-842 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-413 (-570))) (-5 *1 (-493))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1109)) (-4 *4 (-13 (-1058) (-893 *3) (-620 (-899 *3)))) - (-5 *2 (-650 (-1186))) (-5 *1 (-1085 *3 *4 *5)) - (-4 *5 (-13 (-436 *4) (-893 *3) (-620 (-899 *3))))))) + (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 (-1 *6 (-650 *6)))) + (-4 *5 (-38 (-413 (-570)))) (-4 *6 (-1268 *5)) (-5 *2 (-650 *6)) + (-5 *1 (-1270 *5 *6))))) +(((*1 *2 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) (((*1 *1 *2 *3 *4) (-12 (-5 *2 (-1186)) (-5 *3 (-440)) (-4 *5 (-1109)) (-5 *1 (-1115 *5 *4)) (-4 *4 (-436 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1186)) + (-4 *5 (-13 (-1047 (-570)) (-458) (-645 (-570)))) + (-5 *2 (-2 (|:| 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(|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -4043 + (|:| -2521 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -15070,183 +15333,177 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-565))))) +(((*1 *2 *1 *3) + (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1072)) (-5 *3 (-1168))))) +(((*1 *2 *3 *3 *4 *4 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-758))))) (((*1 *2 *3) - (-12 (-5 *3 (-650 (-1186))) (-5 *2 (-1282)) (-5 *1 (-1229)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-650 (-1186))) (-5 *2 (-1282)) (-5 *1 (-1229))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) - (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) - (|:| |abserr| (-227)) (|:| |relerr| 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(-2 (|:| -2308 *4) (|:| -3670 *4) (|:| |totalpts| (-570)) + (|:| |success| (-112)))) + (-5 *1 (-795)) (-5 *5 (-570))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-112)) (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4)))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (-5 *2 (-570)) (-5 *1 (-206))))) -(((*1 *2 *1) - (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-4 *3 (-562)) - (-5 *2 (-1182 *3))))) + (-12 (-5 *3 (-777)) (-5 *2 (-695 (-959 *4))) (-5 *1 (-1037 *4)) + (-4 *4 (-1058))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-928)) (-4 *6 (-562)) (-5 *2 (-650 (-320 *6))) (-5 *1 (-223 *5 *6)) (-5 *3 (-320 *6)) (-4 *5 (-1058)))) @@ -16788,40 +16665,102 @@ ((*1 *2 *1) (-12 (-5 *2 (-1292 *3 *4)) (-5 *1 (-1301 *3 *4)) (-4 *3 (-856)) (-4 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(-5 *3 (-115)) (-5 *2 (-112)))) + ((*1 *2 *3) + (-12 (-5 *3 (-115)) (-4 *5 (-1109)) (-5 *2 (-112)) + (-5 *1 (-435 *4 *5)) (-4 *4 (-436 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) + (-5 *1 (-437 *4 *5)) (-4 *5 (-436 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) + (-5 *1 (-636 *4 *5)) (-4 *5 (-13 (-436 *4) (-1011) (-1212)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1227)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-856)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-856)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-570)) (-4 *1 (-286 *3)) (-4 *3 (-1227)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-570)) (-4 *1 (-286 *2)) (-4 *2 (-1227)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2106 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -2521 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -2340 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2521 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-565)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-4 *1 (-701 *2)) (-4 *2 (-1109)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2106 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (|:| -2340 + (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) + (|:| |expense| (-384)) (|:| |accuracy| (-384)) + (|:| |intermediateResults| (-384)))))) + (-5 *1 (-809)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-413 (-1182 (-320 *3)))) (-4 *3 (-562)) + (-5 *1 (-1139 *3))))) +(((*1 *2 *2) (|partial| -12 (-5 *1 (-593 *2)) (-4 *2 (-551))))) (((*1 *1 *2) - (-12 (-5 *2 (-777)) (-5 *1 (-681 *3)) (-4 *3 (-1058)) - (-4 *3 (-1109))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1188 (-413 (-570)))) (-5 *1 (-192))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1250 *5 *4)) (-4 *4 (-826)) (-14 *5 (-1186)) - (-5 *2 (-570)) (-5 *1 (-1123 *4 *5))))) -(((*1 *2 *3 *4 *5) - (-12 (-4 *6 (-1253 *9)) (-4 *7 (-799)) (-4 *8 (-856)) (-4 *9 (-311)) - (-4 *10 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(-384))) (-5 *5 (-650 (-266))) (-5 *2 (-1278)) (-5 *1 (-258)))) @@ -16919,107 +16858,111 @@ ((*1 *2 *3 *3 *3 *4) (-12 (-5 *3 (-650 (-227))) (-5 *4 (-650 (-266))) (-5 *2 (-1279)) (-5 *1 (-263))))) +(((*1 *2 *1) + (-12 (-5 *2 (-697 (-879 (-973 *3) (-973 *3)))) (-5 *1 (-973 *3)) + (-4 *3 (-1109))))) (((*1 *1 *1 *1) (-5 *1 (-130))) ((*1 *1 *1 *1) (-12 (-5 *1 (-1193 *2)) (-14 *2 (-928)))) ((*1 *1 *1 *1) (-5 *1 (-1232))) ((*1 *1 *1 *1) (-5 *1 (-1233))) ((*1 *1 *1 *1) (-5 *1 (-1234))) ((*1 *1 *1 *1) (-5 *1 (-1235)))) -(((*1 *2 *3 *2 *4) - (-12 (-5 *3 (-695 *2)) (-5 *4 (-777)) - (-4 *2 (-13 (-311) (-10 -8 (-15 -3417 ((-424 $) $))))) - (-4 *5 (-1253 *2)) (-5 *1 (-505 *2 *5 *6)) (-4 *6 (-415 *2 *5))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1227)) (-4 *3 (-1058)) (-5 *2 (-695 *3))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-662 *2)) (-4 *2 (-1058)) (-4 *2 (-368)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-368)) (-5 *1 (-665 *4 *2)) - (-4 *2 (-662 *4))))) -(((*1 *1 *2) - (-12 (-5 *2 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*2)) (-4 *2 (-436 *4)) (-4 *4 (-562)) - (-5 *1 (-32 *4 *2))))) +(((*1 *2) + (-12 + (-5 *2 (-2 (|:| -1458 (-650 (-1186))) (|:| -2762 (-650 (-1186))))) + (-5 *1 (-1229))))) (((*1 *2 *3) - (-12 (-5 *3 (-1277 *4)) (-4 *4 (-645 (-570))) (-5 *2 (-112)) - (-5 *1 (-1304 *4))))) + (|partial| -12 (-5 *2 (-570)) (-5 *1 (-575 *3)) (-4 *3 (-1047 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-1168)) (-5 *1 (-828))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-1226))) (-5 *1 (-530))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-650 - (-2 (|:| -4006 (-777)) - (|:| |eqns| - (-650 - (-2 (|:| |det| *7) (|:| |rows| (-650 (-570))) - (|:| |cols| (-650 (-570)))))) - (|:| |fgb| (-650 *7))))) - (-4 *7 (-956 *4 *6 *5)) (-4 *4 (-13 (-311) (-148))) - (-4 *5 (-13 (-856) (-620 (-1186)))) (-4 *6 (-799)) (-5 *2 (-777)) - (-5 *1 (-931 *4 *5 *6 *7))))) + (-12 (-5 *3 (-1250 *5 *4)) (-4 *4 (-826)) (-14 *5 (-1186)) + (-5 *2 (-570)) (-5 *1 (-1123 *4 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 *4)) (-4 *4 (-854)) (-4 *4 (-368)) (-5 *2 (-777)) + (-5 *1 (-952 *4 *5)) (-4 *5 (-1253 *4))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-798)))) @@ -17126,9 +17069,9 @@ (-4 *6 (-368)) (-5 *2 (-592 *6)) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -2318 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2616 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-368)) (-4 *6 (-368)) - (-5 *2 (-2 (|:| -2318 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2616 *6) (|:| |coeff| *6))) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -17264,7 +17207,7 @@ (-4 *6 (-13 (-856) (-10 -8 (-15 -1425 ((-1186) $)) - (-15 -2799 ((-3 $ "failed") (-1186)))))) + (-15 -2798 ((-3 $ "failed") (-1186)))))) (-5 *1 (-993 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-562)) (-4 *6 (-562)) @@ -17365,28 +17308,81 @@ ((*1 *2 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1227)) (-4 *2 (-1011)) (-4 *2 (-1058))))) -(((*1 *2 *3) (-12 (-5 *3 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\ No newline at end of file |