diff options
| -rw-r--r-- | src/ChangeLog | 6 | ||||
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 434 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 214 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1319 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8782 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29266 |
7 files changed, 20018 insertions, 20011 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 7e20ea09..3b240947 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,9 @@ +2009-05-28 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/boolean.spad.pamphlet (PropositionalLogic): Now export + `true' and `false'. + (Boolean): Ihenrit them. + 2009-05-27 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/newaux.lisp: Bot / and /\ are gliphs. diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index 0c9adbc6..f7cc1e9a 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -21,6 +21,10 @@ ++ Description: This category declares the connectives of ++ Propositional Logic. PropositionalLogic(): Category == SetCategory with + true: % + ++ true is a logical constant. + false: % + ++ false is a logical constant. not: % -> % ++ not p returns the logical negation of `p'. and: (%, %) -> % @@ -301,10 +305,6 @@ Logic: Category == BasicType with ++ true and false Boolean(): Join(OrderedFinite, Logic, PropositionalLogic, ConvertibleTo InputForm) with - true: % - ++ true is a logical constant. - false: % - ++ false is a logical constant. xor : (%, %) -> % ++ xor(a,b) returns the logical exclusive {\em or} ++ of Boolean \spad{a} and b. diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 56fb3245..7770fe19 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2282845 . 3452261758) +(2282845 . 3452516854) (-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 -2313) +(-32 R -2292) ((|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 -1034) (QUOTE (-564))))) @@ -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 -2313 UP UPUP -3807) +(-40 -2292 UP UPUP -2734) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2733 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2733 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2733 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -2313) +(-41 R -2292) ((|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 (-452))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|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."))) ((-4407 . T) (-4408 . T)) -((-2733 (-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|))))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|))))))) +((-2733 (-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|))))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|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 -2313) +(-54 |Base| R -2292) ((|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}."))) ((-4407 . T) (-4408 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-61 -2410) +(-61 -2531) ((|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 -2410) +(-62 -2531) ((|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 -2410) +(-63 -2531) ((|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 -2410) +(-64 -2531) ((|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 -2410) +(-65 -2531) ((|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 -2410) +(-66 -2531) ((|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 -2410) +(-67 -2531) ((|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 -2410) +(-68 -2531) ((|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 -2410) +(-69 -2531) ((|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 -2410) +(-70 -2531) ((|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 -2410) +(-71 -2531) ((|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 -2410) +(-72 -2531) ((|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 -2410) +(-73 -2531) ((|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 -2410) +(-74 -2531) ((|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 -2410) +(-77 -2531) ((|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 -2410) +(-78 -2531) ((|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 -2410) +(-79 -2531) ((|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 -2410) +(-80 -2531) ((|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 -2410) +(-81 -2531) ((|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 -2410) +(-82 -2531) ((|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 -2410) +(-83 -2531) ((|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 -2410) +(-84 -2531) ((|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 -2410) +(-85 -2531) ((|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 -2410) +(-86 -2531) ((|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 -2410) +(-87 -2531) ((|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 -2410) +(-88 -2531) ((|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 -2410) +(-89 -2531) ((|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 @@ -377,7 +377,7 @@ NIL ((-4402 . T) (-4401 . T)) NIL (-112) -((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) +((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) NIL NIL (-113 A) @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|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 -(-115 -2313 UP) +(-115 -2292 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 @@ -468,11 +468,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4409 "*") . T)) NIL -(-135 |minix| -3445 S T$) +(-135 |minix| -3503 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3445 R) +(-136 |minix| -3503 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4404 . T)) NIL -(-148 -2313 UP UPUP) +(-148 -2292 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 @@ -560,7 +560,7 @@ 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 -(-158 R -2313) +(-158 R -2292) ((|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 @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4400 -2733 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3591 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 -2733 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3564 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,7 +606,7 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4400 -2733 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3591 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 -2733 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3564 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2313) +(-188 R -2292) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,11 +788,11 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-215 -2313 UP UPUP R) +(-215 -2292 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 -(-216 -2313 FP) +(-216 -2292 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 @@ -804,7 +804,7 @@ 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 -(-219 R -2313) +(-219 R -2292) ((|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 @@ -824,13 +824,13 @@ 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}."))) ((-4404 . T)) NIL -(-224 R -2313) +(-224 R -2292) ((|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.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3553 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -876,19 +876,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -3445 R) +(-237 S -3503 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -3445 R) +(-238 -3503 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) NIL -(-239 -3445 A B) +(-239 -3503 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-240 -3445 R) +(-240 -3503 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) ((-2733 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST 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(QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-2733 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (|HasCategory| |#3| (QUOTE (-722))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2733 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (-2733 (|HasAttribute| |#3| (QUOTE -4404)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 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."))) @@ -1032,11 +1032,11 @@ 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 -(-276 R -2313) +(-276 R -2292) ((|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{\\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 -(-277 R -2313) +(-277 R -2292) ((|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{\\spad{ki}} was rewritten as \\spad{\\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 @@ -1084,7 +1084,7 @@ 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 -(-289 S R |Mod| -3379 -2994 |exactQuo|) +(-289 S R |Mod| -2689 -3893 |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"))) ((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1111,16 +1111,16 @@ NIL (-295 |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."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-296) ((|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 -(-297 -2313 S) +(-297 -2292 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 -(-298 E -2313) +(-298 E -2292) ((|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 @@ -1168,7 +1168,7 @@ 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 -(-310 -2313) +(-310 -2292) ((|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 @@ -1194,9 +1194,9 @@ NIL NIL (-316 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."))) -((-4404 -2733 (-2364 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2733 (-2364 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) +((-4404 -2733 (-2344 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2733 (-2344 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) ((-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2733 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2733 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2733 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) -(-317 R -2313) +(-317 R -2292) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1207,7 +1207,7 @@ NIL (-319 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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4284) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2403) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4059) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3757) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 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 @@ -1240,11 +1240,11 @@ 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."))) ((-4408 . T) (-4407 . T)) ((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -2313) +(-328 S -2292) ((|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 (-368)))) -(-329 -2313) +(-329 -2292) ((|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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1264,15 +1264,15 @@ 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 -(-334 S -2313 UP UPUP R) +(-334 S -2292 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 -(-335 -2313 UP UPUP R) +(-335 -2292 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 -(-336 -2313 UP UPUP R) +(-336 -2292 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 @@ -1292,11 +1292,11 @@ 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 -(-341 S -2313 UP UPUP) +(-341 S -2292 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(\\spad{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 (-368))) (|HasCategory| |#2| (QUOTE (-363)))) -(-342 -2313 UP UPUP) +(-342 -2292 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(\\spad{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."))) ((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1328,7 +1328,7 @@ 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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-350 R UP -2313) +(-350 R UP -2292) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1352,7 +1352,7 @@ 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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2313 GF) +(-356 -2292 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 @@ -1360,7 +1360,7 @@ 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 -(-358 -2313 FP FPP) +(-358 -2292 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4390 . T) (-4398 . T) (-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4390 . T) (-4398 . T) (-3553 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1496,7 +1496,7 @@ 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 -(-392 -2313 UP UPUP R) +(-392 -2292 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 @@ -1520,11 +1520,11 @@ 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 -(-398 -2410 |returnType| -2742 |symbols|) +(-398 -2531 |returnType| -2758 |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 -(-399 -2313 UP) +(-399 -2292 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#1| (QUOTE -4398))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3553 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-405 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1580,11 +1580,11 @@ 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 -(-413 R -2313 UP A) +(-413 R -2292 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)}."))) ((-4404 . T)) NIL -(-414 R -2313 UP A |ibasis|) +(-414 R -2292 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 -1034) (|devaluate| |#2|)))) @@ -1632,7 +1632,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4407 . T) (-4397 . T) (-4408 . T)) NIL -(-426 R -2313) +(-426 R -2292) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4394 -12 (|has| |#1| (-6 -4394)) (|has| |#2| (-6 -4394))) (-4401 . T) (-4402 . T) (-4404 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#2| (QUOTE -4394)))) -(-428 R -2313) +(-428 R -2292) ((|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 @@ -1652,15 +1652,15 @@ 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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}."))) ((-4404 -2733 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) NIL -(-431 R -2313) +(-431 R -2292) ((|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 -(-432 R -2313) +(-432 R -2292) ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-433 R -2313) +(-433 R -2292) ((|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 @@ -1668,7 +1668,7 @@ 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 -(-435 R -2313 UP) +(-435 R -2292 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 -1034) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ 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 -(-443 R UP -2313) +(-443 R UP -2292) ((|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 @@ -1812,7 +1812,7 @@ 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 -(-471 |lv| -2313 R) +(-471 |lv| -2292 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 @@ -1827,11 +1827,11 @@ NIL (-474 |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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4284) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2403) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4059) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3757) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-475 |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."))) ((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094)))) (-476 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)}"))) ((-4408 . T) (-4407 . T)) @@ -1847,7 +1847,7 @@ NIL (-479 |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."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-480) ((|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 @@ -1856,7 +1856,7 @@ NIL ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . 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(LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) @@ -1868,7 +1868,7 @@ 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}."))) ((-4407 . T) (-4408 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-485 -2313 UP UPUP R) +(-485 -2292 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 @@ -1904,7 +1904,7 @@ 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 -(-494 -2313 UP |AlExt| |AlPol|) +(-494 -2292 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 @@ -1924,7 +1924,7 @@ 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 -(-499 R UP -2313) +(-499 R UP -2292) ((|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{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\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{\\spad{mi}} is given by \\spad{\\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{\\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{\\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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -2313 |Expon| |VarSet| |DPoly|) +(-504 -2292 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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 -612) (QUOTE (-1170))))) @@ -2056,7 +2056,7 @@ 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 -(-532 K -2313 |Par|) +(-532 K -2292 |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 @@ -2080,7 +2080,7 @@ 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 -(-538 K -2313 |Par|) +(-538 K -2292 |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 @@ -2131,12 +2131,12 @@ NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) -(-551 R -2313) +((-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +(-551 R -2292) ((|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 -(-552 R0 -2313 UP UPUP R) +(-552 R0 -2292 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 @@ -2146,7 +2146,7 @@ NIL NIL (-554 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3583 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3553 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-555 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2156,7 +2156,7 @@ 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."))) ((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-557 R -2313) +(-557 R -2292) ((|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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{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 @@ -2168,7 +2168,7 @@ 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 -(-560 R -2313 L) +(-560 R -2292 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -652) (|devaluate| |#2|)))) @@ -2176,11 +2176,11 @@ 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 -(-562 -2313 UP UPUP R) +(-562 -2292 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 -(-563 -2313 UP) +(-563 -2292 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 @@ -2192,15 +2192,15 @@ 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 -(-566 R -2313 L) +(-566 R -2292 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -652) (|devaluate| |#2|)))) -(-567 R -2313) +(-567 R -2292) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -2313 UP) +(-568 -2292 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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{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 @@ -2208,27 +2208,27 @@ 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 -(-570 -2313) +(-570 -2292) ((|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,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 (-571 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-3583 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3553 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-572) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-573 R -2313) +(-573 R -2292) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -2313 UP) +(-574 -2292 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' + +/[\\spad{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(+,{}[\\spad{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(+,{}[\\spad{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 -(-575 R -2313) +(-575 R -2292) ((|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 @@ -2260,15 +2260,15 @@ 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 -(-583 R -2313) +(-583 R -2292) ((|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 -(-584 E -2313) +(-584 E -2292) ((|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 -(-585 -2313) +(-585 -2292) ((|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}."))) ((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170))))) @@ -2307,7 +2307,7 @@ NIL (-594 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |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.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2403) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4402 |has| |#1| (-556)) (-4401 |has| |#1| (-556)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4404 . T)) @@ -2320,7 +2320,7 @@ 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 -(-598 R -2313 FG) +(-598 R -2292 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{\\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{\\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 @@ -2350,12 +2350,12 @@ NIL NIL (-605 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)."))) -((-4404 -2733 (-2364 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) +((-4404 -2733 (-2344 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) ((-2733 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |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."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-607 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 @@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2313 UP) +(-613 -2292 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2408,7 +2408,7 @@ 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}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-844)))) -(-620 R -2313) +(-620 R -2292) ((|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 @@ -2440,18 +2440,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-628 R -2313) +(-628 R -2292) ((|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{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\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 -(-629 |lv| -2313) +(-629 |lv| -2292) ((|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 (-630) ((|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."))) ((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3683) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3736) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (QUOTE (-1094)))) (-631 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2462,7 +2462,7 @@ NIL NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4404 -2733 (-2364 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) +((-4404 -2733 (-2344 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) ((-2733 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-634 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))}."))) @@ -2475,7 +2475,7 @@ NIL (-636 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 -((-2354 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2334 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 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}."))) ((-4404 . T)) @@ -2520,7 +2520,7 @@ 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 -(-648 R -2313 L) +(-648 R -2292 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 @@ -2540,11 +2540,11 @@ 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}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-653 -2313 UP) +(-653 -2292 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)))) -(-654 A -1650) +(-654 A -3405) ((|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}}"))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) @@ -2580,11 +2580,11 @@ 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}."))) ((-4408 . T) (-4407 . T)) NIL -(-663 -2313) +(-663 -2292) ((|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 -(-664 -2313 |Row| |Col| M) +(-664 -2292 |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 @@ -2680,7 +2680,7 @@ 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 -(-688 S -2313 FLAF FLAS) +(-688 S -2292 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 @@ -2690,7 +2690,7 @@ NIL NIL (-690) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4400 . T) (-4405 |has| (-695) (-363)) (-4399 |has| (-695) (-363)) (-3591 . T) (-4406 |has| (-695) (-6 -4406)) (-4403 |has| (-695) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4405 |has| (-695) (-363)) (-4399 |has| (-695) (-363)) (-3564 . T) (-4406 |has| (-695) (-6 -4406)) (-4403 |has| (-695) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2733 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2733 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2733 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4406)) (|HasAttribute| (-695) (QUOTE -4403)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) @@ -2704,13 +2704,13 @@ 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 -(-694 OV E -2313 PG) +(-694 OV E -2292 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 (-695) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3553 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-696 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-702 S -3922 I) +(-702 S -3997 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2756,7 +2756,7 @@ 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 -(-707 R |Mod| -3379 -2994 |exactQuo|) +(-707 R |Mod| -2689 -3893 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -3379 -2994 |exactQuo|) +(-711 R |Mod| -2689 -3893 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4404 . T)) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4402 . T) (-4401 . T)) NIL -(-714 -2313) +(-714 -2292) ((|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]]}."))) ((-4404 . T)) NIL @@ -2820,7 +2820,7 @@ 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 -(-723 -2313 UP) +(-723 -2292 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 @@ -2972,11 +2972,11 @@ 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 -(-761 -2313) +(-761 -2292) ((|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 -(-762 P -2313) +(-762 P -2292) ((|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 @@ -2984,7 +2984,7 @@ NIL NIL NIL NIL -(-764 UP -2313) +(-764 UP -2292) ((|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{\\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{\\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{\\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{\\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{\\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{\\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 @@ -3000,7 +3000,7 @@ 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."))) (((-4409 "*") . T)) NIL -(-768 R -2313) +(-768 R -2292) ((|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 @@ -3020,7 +3020,7 @@ 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 -(-773 -2313 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2292 |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 @@ -3035,7 +3035,7 @@ NIL (-776 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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . 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|#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2334 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2334 (|HasCategory| |#1| (QUOTE (-545)))) (-2334 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2334 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564))))) (-2334 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2334 (|HasCategory| |#1| (LIST (QUOTE -988) (QUOTE (-564))))))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-777 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 @@ -3116,11 +3116,11 @@ 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 -(-797 R -2313 L) +(-797 R -2292 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{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-798 R -2313) +(-798 R -2292) ((|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 @@ -3128,7 +3128,7 @@ 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 -(-800 R -2313) +(-800 R -2292) ((|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 @@ -3136,11 +3136,11 @@ 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 -(-802 -2313 UP UPUP R) +(-802 -2292 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 -(-803 -2313 UP L LQ) +(-803 -2292 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 @@ -3148,31 +3148,31 @@ 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 -(-805 -2313 UP L LQ) +(-805 -2292 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^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{\\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{\\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 \\spad{ai}}} is \\spad{\\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 -(-806 -2313 UP) +(-806 -2292 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 -(-807 -2313 L UP A LO) +(-807 -2292 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 -(-808 -2313 UP) +(-808 -2292 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{\\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 \\spad{ai}}} is \\spad{\\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)))) -(-809 -2313 LO) +(-809 -2292 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 -(-810 -2313 LODO) +(-810 -2292 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(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-811 -3445 S |f|) +(-811 -3503 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) ((-2733 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST 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(LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) @@ -3292,7 +3292,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -3445 S) +(-841 -3503 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3328,11 +3328,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-850 R |sigma| -3707) +(-850 R |sigma| -2845) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-851 |x| R |sigma| -3707) +(-851 |x| R |sigma| -2845) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3463,7 +3463,7 @@ NIL (-883 |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 (-2354 (|HasCategory| |#2| (QUOTE (-1045)))) (-2354 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2354 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) +((-12 (-2334 (|HasCategory| |#2| (QUOTE (-1045)))) (-2334 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2334 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-884 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 @@ -3472,7 +3472,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-886 R -3922) +(-886 R -3997) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3496,7 +3496,7 @@ 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 -(-892 UP -2313) +(-892 UP -2292) ((|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 @@ -3556,7 +3556,7 @@ 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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-907 R0 -2313 UP UPUP R) +(-907 R0 -2292 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 @@ -3584,7 +3584,7 @@ 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(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{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 \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{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(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{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 -(-914 -2313) +(-914 -2292) ((|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 @@ -3600,11 +3600,11 @@ 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}."))) (((-4409 "*") . T)) NIL -(-918 -2313 P) +(-918 -2292 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -2313) +(-919 |xx| -2292) ((|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 @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-925 R -2313) +(-925 R -2292) ((|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 @@ -3640,7 +3640,7 @@ 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 -(-928 S R -2313) +(-928 S R -2292) ((|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 @@ -3660,11 +3660,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -882) (|devaluate| |#1|)))) -(-933 R -2313 -3922) +(-933 R -2292 -3997) ((|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 -(-934 -3922) +(-934 -3997) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3712,7 +3712,7 @@ 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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-946 E V R P -2313) +(-946 E V R P -2292) ((|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 @@ -3724,7 +3724,7 @@ 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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-905))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -2313) +(-949 E V R P -2292) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3752,7 +3752,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-956 -2313) +(-956 -2292) ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{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 @@ -3781,7 +3781,7 @@ NIL NIL NIL (-963) -((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}."))) +((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL (-964 S) @@ -3852,7 +3852,7 @@ 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 -(-981 K R UP -2313) +(-981 K R UP -2292) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3924,7 +3924,7 @@ 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 -(-999 -2313 UP UPUP |radicnd| |n|) +(-999 -2292 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2733 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2733 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2733 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) @@ -3964,19 +3964,19 @@ 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}}"))) ((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) NIL -(-1009 R -2313) +(-1009 R -2292) ((|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 -(-1010 R -2313) +(-1010 R -2292) ((|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 -(-1011 -2313 UP) +(-1011 -2292 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 -(-1012 -2313 UP) +(-1012 -2292 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 @@ -4012,7 +4012,7 @@ 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"))) ((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) ((-2733 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) -(-1021 -2313 L) +(-1021 -2292 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{\\spad{fi}} must satisfy \\spad{op \\spad{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 @@ -4048,14 +4048,14 @@ 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 -(-1030 -2313 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2292 |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"))) (((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1031) ((|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.}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3683) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3736) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1032) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4112,7 +4112,7 @@ 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."))) ((-4404 . T)) NIL -(-1046 |xx| -2313) +(-1046 |xx| -2292) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4159,7 +4159,7 @@ NIL (-1057) ((|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}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3683) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3736) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1058 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 @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -2313) +(-1070 |Base| R -2292) ((|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 -(-1071 |Base| R -2313) +(-1071 |Base| R -2292) ((|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 @@ -4368,7 +4368,7 @@ 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 -(-1110 R -2313) +(-1110 R -2292) ((|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 @@ -4416,7 +4416,7 @@ 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}"))) ((-4408 . T) (-4407 . T)) NIL -(-1122 UP -2313) +(-1122 UP -2292) ((|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 @@ -4507,7 +4507,7 @@ NIL (-1144 |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."))) ((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094)))) (-1145) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4543,7 +4543,7 @@ NIL (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#1|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#1|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1154 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |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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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 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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 @@ -4659,7 +4659,7 @@ NIL (-1182 |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}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1922) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3736) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1183 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4720,7 +4720,7 @@ 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 -(-1198 R -2313) +(-1198 R -2292) ((|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 @@ -4728,7 +4728,7 @@ 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 -(-1200 R -2313) +(-1200 R -2292) ((|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 -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) @@ -4756,7 +4756,7 @@ 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 (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-1207 -2313) +(-1207 -2292) ((|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 @@ -4819,11 +4819,11 @@ NIL (-1222 |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)}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . 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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 @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2326) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2403) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) @@ -4903,11 +4903,11 @@ NIL (-1243 |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)}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4284) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2403) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4059) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3757) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4284) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2403) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4059) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3757) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4409 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4400 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) @@ -4927,7 +4927,7 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4284) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3757) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4059) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) @@ -4935,12 +4935,12 @@ NIL (-1251 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4284) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2403) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4059) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3757) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1252 |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 -(-1253 -2313 UP L UTS) +(-1253 -2292 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 (-556)))) @@ -5000,7 +5000,7 @@ 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 -(-1268 K R UP -2313) +(-1268 K R UP -2292) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5036,11 +5036,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-1277 S -2313) +(-1277 S -2292) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -2313) +(-1278 -2292) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -5096,4 +5096,4 @@ NIL NIL NIL NIL -((-3 NIL 2282825 2282830 2282835 2282840) (-2 NIL 2282805 2282810 2282815 2282820) (-1 NIL 2282785 2282790 2282795 2282800) (0 NIL 2282765 2282770 2282775 2282780) (-1287 "ZMOD.spad" 2282574 2282587 2282703 2282760) (-1286 "ZLINDEP.spad" 2281618 2281629 2282564 2282569) (-1285 "ZDSOLVE.spad" 2271467 2271489 2281608 2281613) (-1284 "YSTREAM.spad" 2270960 2270971 2271457 2271462) (-1283 "XRPOLY.spad" 2270180 2270200 2270816 2270885) (-1282 "XPR.spad" 2267971 2267984 2269898 2269997) (-1281 "XPOLY.spad" 2267526 2267537 2267827 2267896) (-1280 "XPOLYC.spad" 2266843 2266859 2267452 2267521) (-1279 "XPBWPOLY.spad" 2265280 2265300 2266623 2266692) (-1278 "XF.spad" 2263741 2263756 2265182 2265275) (-1277 "XF.spad" 2262182 2262199 2263625 2263630) (-1276 "XFALG.spad" 2259206 2259222 2262108 2262177) (-1275 "XEXPPKG.spad" 2258457 2258483 2259196 2259201) (-1274 "XDPOLY.spad" 2258071 2258087 2258313 2258382) (-1273 "XALG.spad" 2257731 2257742 2258027 2258066) (-1272 "WUTSET.spad" 2253570 2253587 2257377 2257404) (-1271 "WP.spad" 2252769 2252813 2253428 2253495) (-1270 "WHILEAST.spad" 2252567 2252576 2252759 2252764) (-1269 "WHEREAST.spad" 2252238 2252247 2252557 2252562) (-1268 "WFFINTBS.spad" 2249801 2249823 2252228 2252233) (-1267 "WEIER.spad" 2248015 2248026 2249791 2249796) (-1266 "VSPACE.spad" 2247688 2247699 2247983 2248010) (-1265 "VSPACE.spad" 2247381 2247394 2247678 2247683) (-1264 "VOID.spad" 2247058 2247067 2247371 2247376) (-1263 "VIEW.spad" 2244680 2244689 2247048 2247053) (-1262 "VIEWDEF.spad" 2239877 2239886 2244670 2244675) (-1261 "VIEW3D.spad" 2223712 2223721 2239867 2239872) (-1260 "VIEW2D.spad" 2211449 2211458 2223702 2223707) (-1259 "VECTOR.spad" 2210124 2210135 2210375 2210402) (-1258 "VECTOR2.spad" 2208751 2208764 2210114 2210119) (-1257 "VECTCAT.spad" 2206651 2206662 2208719 2208746) (-1256 "VECTCAT.spad" 2204359 2204372 2206429 2206434) (-1255 "VARIABLE.spad" 2204139 2204154 2204349 2204354) (-1254 "UTYPE.spad" 2203783 2203792 2204129 2204134) (-1253 "UTSODETL.spad" 2203076 2203100 2203739 2203744) (-1252 "UTSODE.spad" 2201264 2201284 2203066 2203071) (-1251 "UTS.spad" 2196053 2196081 2199731 2199828) (-1250 "UTSCAT.spad" 2193504 2193520 2195951 2196048) (-1249 "UTSCAT.spad" 2190599 2190617 2193048 2193053) (-1248 "UTS2.spad" 2190192 2190227 2190589 2190594) (-1247 "URAGG.spad" 2184824 2184835 2190182 2190187) (-1246 "URAGG.spad" 2179420 2179433 2184780 2184785) (-1245 "UPXSSING.spad" 2177063 2177089 2178501 2178634) (-1244 "UPXS.spad" 2174211 2174239 2175195 2175344) (-1243 "UPXSCONS.spad" 2171968 2171988 2172343 2172492) (-1242 "UPXSCCA.spad" 2170533 2170553 2171814 2171963) (-1241 "UPXSCCA.spad" 2169240 2169262 2170523 2170528) (-1240 "UPXSCAT.spad" 2167821 2167837 2169086 2169235) (-1239 "UPXS2.spad" 2167362 2167415 2167811 2167816) (-1238 "UPSQFREE.spad" 2165774 2165788 2167352 2167357) (-1237 "UPSCAT.spad" 2163367 2163391 2165672 2165769) (-1236 "UPSCAT.spad" 2160666 2160692 2162973 2162978) (-1235 "UPOLYC.spad" 2155644 2155655 2160508 2160661) (-1234 "UPOLYC.spad" 2150514 2150527 2155380 2155385) (-1233 "UPOLYC2.spad" 2149983 2150002 2150504 2150509) (-1232 "UP.spad" 2147176 2147191 2147569 2147722) (-1231 "UPMP.spad" 2146066 2146079 2147166 2147171) (-1230 "UPDIVP.spad" 2145629 2145643 2146056 2146061) (-1229 "UPDECOMP.spad" 2143866 2143880 2145619 2145624) (-1228 "UPCDEN.spad" 2143073 2143089 2143856 2143861) (-1227 "UP2.spad" 2142435 2142456 2143063 2143068) (-1226 "UNISEG.spad" 2141788 2141799 2142354 2142359) (-1225 "UNISEG2.spad" 2141281 2141294 2141744 2141749) (-1224 "UNIFACT.spad" 2140382 2140394 2141271 2141276) (-1223 "ULS.spad" 2130934 2130962 2132027 2132456) (-1222 "ULSCONS.spad" 2123328 2123348 2123700 2123849) (-1221 "ULSCCAT.spad" 2121057 2121077 2123174 2123323) (-1220 "ULSCCAT.spad" 2118894 2118916 2121013 2121018) (-1219 "ULSCAT.spad" 2117110 2117126 2118740 2118889) (-1218 "ULS2.spad" 2116622 2116675 2117100 2117105) (-1217 "UINT8.spad" 2116499 2116508 2116612 2116617) (-1216 "UINT64.spad" 2116375 2116384 2116489 2116494) (-1215 "UINT32.spad" 2116251 2116260 2116365 2116370) (-1214 "UINT16.spad" 2116127 2116136 2116241 2116246) (-1213 "UFD.spad" 2115192 2115201 2116053 2116122) (-1212 "UFD.spad" 2114319 2114330 2115182 2115187) (-1211 "UDVO.spad" 2113166 2113175 2114309 2114314) (-1210 "UDPO.spad" 2110593 2110604 2113122 2113127) (-1209 "TYPE.spad" 2110525 2110534 2110583 2110588) (-1208 "TYPEAST.spad" 2110444 2110453 2110515 2110520) (-1207 "TWOFACT.spad" 2109094 2109109 2110434 2110439) (-1206 "TUPLE.spad" 2108578 2108589 2108993 2108998) (-1205 "TUBETOOL.spad" 2105415 2105424 2108568 2108573) (-1204 "TUBE.spad" 2104056 2104073 2105405 2105410) (-1203 "TS.spad" 2102645 2102661 2103621 2103718) (-1202 "TSETCAT.spad" 2089772 2089789 2102613 2102640) (-1201 "TSETCAT.spad" 2076885 2076904 2089728 2089733) (-1200 "TRMANIP.spad" 2071251 2071268 2076591 2076596) (-1199 "TRIMAT.spad" 2070210 2070235 2071241 2071246) (-1198 "TRIGMNIP.spad" 2068727 2068744 2070200 2070205) (-1197 "TRIGCAT.spad" 2068239 2068248 2068717 2068722) (-1196 "TRIGCAT.spad" 2067749 2067760 2068229 2068234) (-1195 "TREE.spad" 2066320 2066331 2067356 2067383) (-1194 "TRANFUN.spad" 2066151 2066160 2066310 2066315) (-1193 "TRANFUN.spad" 2065980 2065991 2066141 2066146) (-1192 "TOPSP.spad" 2065654 2065663 2065970 2065975) (-1191 "TOOLSIGN.spad" 2065317 2065328 2065644 2065649) (-1190 "TEXTFILE.spad" 2063874 2063883 2065307 2065312) (-1189 "TEX.spad" 2061006 2061015 2063864 2063869) (-1188 "TEX1.spad" 2060562 2060573 2060996 2061001) (-1187 "TEMUTL.spad" 2060117 2060126 2060552 2060557) (-1186 "TBCMPPK.spad" 2058210 2058233 2060107 2060112) (-1185 "TBAGG.spad" 2057246 2057269 2058190 2058205) (-1184 "TBAGG.spad" 2056290 2056315 2057236 2057241) (-1183 "TANEXP.spad" 2055666 2055677 2056280 2056285) (-1182 "TABLE.spad" 2054077 2054100 2054347 2054374) (-1181 "TABLEAU.spad" 2053558 2053569 2054067 2054072) (-1180 "TABLBUMP.spad" 2050341 2050352 2053548 2053553) (-1179 "SYSTEM.spad" 2049569 2049578 2050331 2050336) (-1178 "SYSSOLP.spad" 2047042 2047053 2049559 2049564) (-1177 "SYSNNI.spad" 2046222 2046233 2047032 2047037) (-1176 "SYSINT.spad" 2045626 2045637 2046212 2046217) (-1175 "SYNTAX.spad" 2041820 2041829 2045616 2045621) (-1174 "SYMTAB.spad" 2039876 2039885 2041810 2041815) (-1173 "SYMS.spad" 2035861 2035870 2039866 2039871) (-1172 "SYMPOLY.spad" 2034868 2034879 2034950 2035077) (-1171 "SYMFUNC.spad" 2034343 2034354 2034858 2034863) (-1170 "SYMBOL.spad" 2031770 2031779 2034333 2034338) (-1169 "SWITCH.spad" 2028527 2028536 2031760 2031765) (-1168 "SUTS.spad" 2025426 2025454 2026994 2027091) (-1167 "SUPXS.spad" 2022561 2022589 2023558 2023707) (-1166 "SUP.spad" 2019366 2019377 2020147 2020300) (-1165 "SUPFRACF.spad" 2018471 2018489 2019356 2019361) (-1164 "SUP2.spad" 2017861 2017874 2018461 2018466) (-1163 "SUMRF.spad" 2016827 2016838 2017851 2017856) (-1162 "SUMFS.spad" 2016460 2016477 2016817 2016822) (-1161 "SULS.spad" 2006999 2007027 2008105 2008534) (-1160 "SUCHTAST.spad" 2006768 2006777 2006989 2006994) (-1159 "SUCH.spad" 2006448 2006463 2006758 2006763) (-1158 "SUBSPACE.spad" 1998455 1998470 2006438 2006443) (-1157 "SUBRESP.spad" 1997615 1997629 1998411 1998416) (-1156 "STTF.spad" 1993714 1993730 1997605 1997610) (-1155 "STTFNC.spad" 1990182 1990198 1993704 1993709) (-1154 "STTAYLOR.spad" 1982580 1982591 1990063 1990068) (-1153 "STRTBL.spad" 1981085 1981102 1981234 1981261) (-1152 "STRING.spad" 1980494 1980503 1980508 1980535) (-1151 "STRICAT.spad" 1980282 1980291 1980462 1980489) (-1150 "STREAM.spad" 1977140 1977151 1979807 1979822) (-1149 "STREAM3.spad" 1976685 1976700 1977130 1977135) (-1148 "STREAM2.spad" 1975753 1975766 1976675 1976680) (-1147 "STREAM1.spad" 1975457 1975468 1975743 1975748) (-1146 "STINPROD.spad" 1974363 1974379 1975447 1975452) (-1145 "STEP.spad" 1973564 1973573 1974353 1974358) (-1144 "STBL.spad" 1972090 1972118 1972257 1972272) (-1143 "STAGG.spad" 1971165 1971176 1972080 1972085) (-1142 "STAGG.spad" 1970238 1970251 1971155 1971160) (-1141 "STACK.spad" 1969589 1969600 1969845 1969872) (-1140 "SREGSET.spad" 1967293 1967310 1969235 1969262) (-1139 "SRDCMPK.spad" 1965838 1965858 1967283 1967288) (-1138 "SRAGG.spad" 1960935 1960944 1965806 1965833) (-1137 "SRAGG.spad" 1956052 1956063 1960925 1960930) (-1136 "SQMATRIX.spad" 1953668 1953686 1954584 1954671) (-1135 "SPLTREE.spad" 1948220 1948233 1953104 1953131) (-1134 "SPLNODE.spad" 1944808 1944821 1948210 1948215) (-1133 "SPFCAT.spad" 1943585 1943594 1944798 1944803) (-1132 "SPECOUT.spad" 1942135 1942144 1943575 1943580) (-1131 "SPADXPT.spad" 1934274 1934283 1942125 1942130) (-1130 "spad-parser.spad" 1933739 1933748 1934264 1934269) (-1129 "SPADAST.spad" 1933440 1933449 1933729 1933734) (-1128 "SPACEC.spad" 1917453 1917464 1933430 1933435) (-1127 "SPACE3.spad" 1917229 1917240 1917443 1917448) (-1126 "SORTPAK.spad" 1916774 1916787 1917185 1917190) (-1125 "SOLVETRA.spad" 1914531 1914542 1916764 1916769) (-1124 "SOLVESER.spad" 1913051 1913062 1914521 1914526) (-1123 "SOLVERAD.spad" 1909061 1909072 1913041 1913046) (-1122 "SOLVEFOR.spad" 1907481 1907499 1909051 1909056) (-1121 "SNTSCAT.spad" 1907081 1907098 1907449 1907476) (-1120 "SMTS.spad" 1905341 1905367 1906646 1906743) (-1119 "SMP.spad" 1902816 1902836 1903206 1903333) (-1118 "SMITH.spad" 1901659 1901684 1902806 1902811) (-1117 "SMATCAT.spad" 1899769 1899799 1901603 1901654) (-1116 "SMATCAT.spad" 1897811 1897843 1899647 1899652) (-1115 "SKAGG.spad" 1896772 1896783 1897779 1897806) (-1114 "SINT.spad" 1895598 1895607 1896638 1896767) (-1113 "SIMPAN.spad" 1895326 1895335 1895588 1895593) (-1112 "SIG.spad" 1894654 1894663 1895316 1895321) (-1111 "SIGNRF.spad" 1893762 1893773 1894644 1894649) (-1110 "SIGNEF.spad" 1893031 1893048 1893752 1893757) (-1109 "SIGAST.spad" 1892412 1892421 1893021 1893026) (-1108 "SHP.spad" 1890330 1890345 1892368 1892373) (-1107 "SHDP.spad" 1880041 1880068 1880550 1880681) (-1106 "SGROUP.spad" 1879649 1879658 1880031 1880036) (-1105 "SGROUP.spad" 1879255 1879266 1879639 1879644) (-1104 "SGCF.spad" 1872136 1872145 1879245 1879250) (-1103 "SFRTCAT.spad" 1871064 1871081 1872104 1872131) (-1102 "SFRGCD.spad" 1870127 1870147 1871054 1871059) (-1101 "SFQCMPK.spad" 1864764 1864784 1870117 1870122) (-1100 "SFORT.spad" 1864199 1864213 1864754 1864759) (-1099 "SEXOF.spad" 1864042 1864082 1864189 1864194) (-1098 "SEX.spad" 1863934 1863943 1864032 1864037) (-1097 "SEXCAT.spad" 1861485 1861525 1863924 1863929) (-1096 "SET.spad" 1859785 1859796 1860906 1860945) (-1095 "SETMN.spad" 1858219 1858236 1859775 1859780) (-1094 "SETCAT.spad" 1857541 1857550 1858209 1858214) (-1093 "SETCAT.spad" 1856861 1856872 1857531 1857536) (-1092 "SETAGG.spad" 1853382 1853393 1856841 1856856) (-1091 "SETAGG.spad" 1849911 1849924 1853372 1853377) (-1090 "SEQAST.spad" 1849614 1849623 1849901 1849906) (-1089 "SEGXCAT.spad" 1848736 1848749 1849604 1849609) (-1088 "SEG.spad" 1848549 1848560 1848655 1848660) (-1087 "SEGCAT.spad" 1847456 1847467 1848539 1848544) (-1086 "SEGBIND.spad" 1846528 1846539 1847411 1847416) (-1085 "SEGBIND2.spad" 1846224 1846237 1846518 1846523) (-1084 "SEGAST.spad" 1845938 1845947 1846214 1846219) (-1083 "SEG2.spad" 1845363 1845376 1845894 1845899) (-1082 "SDVAR.spad" 1844639 1844650 1845353 1845358) (-1081 "SDPOL.spad" 1842065 1842076 1842356 1842483) (-1080 "SCPKG.spad" 1840144 1840155 1842055 1842060) (-1079 "SCOPE.spad" 1839293 1839302 1840134 1840139) (-1078 "SCACHE.spad" 1837975 1837986 1839283 1839288) (-1077 "SASTCAT.spad" 1837884 1837893 1837965 1837970) (-1076 "SAOS.spad" 1837756 1837765 1837874 1837879) (-1075 "SAERFFC.spad" 1837469 1837489 1837746 1837751) (-1074 "SAE.spad" 1835644 1835660 1836255 1836390) (-1073 "SAEFACT.spad" 1835345 1835365 1835634 1835639) (-1072 "RURPK.spad" 1832986 1833002 1835335 1835340) (-1071 "RULESET.spad" 1832427 1832451 1832976 1832981) (-1070 "RULE.spad" 1830631 1830655 1832417 1832422) (-1069 "RULECOLD.spad" 1830483 1830496 1830621 1830626) (-1068 "RTVALUE.spad" 1830216 1830225 1830473 1830478) (-1067 "RSTRCAST.spad" 1829933 1829942 1830206 1830211) (-1066 "RSETGCD.spad" 1826311 1826331 1829923 1829928) (-1065 "RSETCAT.spad" 1816095 1816112 1826279 1826306) (-1064 "RSETCAT.spad" 1805899 1805918 1816085 1816090) (-1063 "RSDCMPK.spad" 1804351 1804371 1805889 1805894) (-1062 "RRCC.spad" 1802735 1802765 1804341 1804346) (-1061 "RRCC.spad" 1801117 1801149 1802725 1802730) (-1060 "RPTAST.spad" 1800819 1800828 1801107 1801112) (-1059 "RPOLCAT.spad" 1780179 1780194 1800687 1800814) (-1058 "RPOLCAT.spad" 1759253 1759270 1779763 1779768) (-1057 "ROUTINE.spad" 1755116 1755125 1757900 1757927) (-1056 "ROMAN.spad" 1754444 1754453 1754982 1755111) (-1055 "ROIRC.spad" 1753524 1753556 1754434 1754439) (-1054 "RNS.spad" 1752427 1752436 1753426 1753519) (-1053 "RNS.spad" 1751416 1751427 1752417 1752422) (-1052 "RNG.spad" 1751151 1751160 1751406 1751411) (-1051 "RMODULE.spad" 1750789 1750800 1751141 1751146) (-1050 "RMCAT2.spad" 1750197 1750254 1750779 1750784) (-1049 "RMATRIX.spad" 1749021 1749040 1749364 1749403) (-1048 "RMATCAT.spad" 1744554 1744585 1748977 1749016) (-1047 "RMATCAT.spad" 1739977 1740010 1744402 1744407) (-1046 "RINTERP.spad" 1739865 1739885 1739967 1739972) (-1045 "RING.spad" 1739335 1739344 1739845 1739860) (-1044 "RING.spad" 1738813 1738824 1739325 1739330) (-1043 "RIDIST.spad" 1738197 1738206 1738803 1738808) (-1042 "RGCHAIN.spad" 1736776 1736792 1737682 1737709) (-1041 "RGBCSPC.spad" 1736557 1736569 1736766 1736771) (-1040 "RGBCMDL.spad" 1736087 1736099 1736547 1736552) (-1039 "RF.spad" 1733701 1733712 1736077 1736082) (-1038 "RFFACTOR.spad" 1733163 1733174 1733691 1733696) (-1037 "RFFACT.spad" 1732898 1732910 1733153 1733158) (-1036 "RFDIST.spad" 1731886 1731895 1732888 1732893) (-1035 "RETSOL.spad" 1731303 1731316 1731876 1731881) (-1034 "RETRACT.spad" 1730731 1730742 1731293 1731298) (-1033 "RETRACT.spad" 1730157 1730170 1730721 1730726) (-1032 "RETAST.spad" 1729969 1729978 1730147 1730152) (-1031 "RESULT.spad" 1728029 1728038 1728616 1728643) (-1030 "RESRING.spad" 1727376 1727423 1727967 1728024) (-1029 "RESLATC.spad" 1726700 1726711 1727366 1727371) (-1028 "REPSQ.spad" 1726429 1726440 1726690 1726695) (-1027 "REP.spad" 1723981 1723990 1726419 1726424) (-1026 "REPDB.spad" 1723686 1723697 1723971 1723976) (-1025 "REP2.spad" 1713258 1713269 1723528 1723533) (-1024 "REP1.spad" 1707248 1707259 1713208 1713213) (-1023 "REGSET.spad" 1705045 1705062 1706894 1706921) (-1022 "REF.spad" 1704374 1704385 1705000 1705005) (-1021 "REDORDER.spad" 1703550 1703567 1704364 1704369) (-1020 "RECLOS.spad" 1702333 1702353 1703037 1703130) (-1019 "REALSOLV.spad" 1701465 1701474 1702323 1702328) (-1018 "REAL.spad" 1701337 1701346 1701455 1701460) (-1017 "REAL0Q.spad" 1698619 1698634 1701327 1701332) (-1016 "REAL0.spad" 1695447 1695462 1698609 1698614) (-1015 "RDUCEAST.spad" 1695168 1695177 1695437 1695442) (-1014 "RDIV.spad" 1694819 1694844 1695158 1695163) (-1013 "RDIST.spad" 1694382 1694393 1694809 1694814) (-1012 "RDETRS.spad" 1693178 1693196 1694372 1694377) (-1011 "RDETR.spad" 1691285 1691303 1693168 1693173) (-1010 "RDEEFS.spad" 1690358 1690375 1691275 1691280) (-1009 "RDEEF.spad" 1689354 1689371 1690348 1690353) (-1008 "RCFIELD.spad" 1686540 1686549 1689256 1689349) (-1007 "RCFIELD.spad" 1683812 1683823 1686530 1686535) (-1006 "RCAGG.spad" 1681724 1681735 1683802 1683807) (-1005 "RCAGG.spad" 1679563 1679576 1681643 1681648) (-1004 "RATRET.spad" 1678923 1678934 1679553 1679558) (-1003 "RATFACT.spad" 1678615 1678627 1678913 1678918) (-1002 "RANDSRC.spad" 1677934 1677943 1678605 1678610) (-1001 "RADUTIL.spad" 1677688 1677697 1677924 1677929) (-1000 "RADIX.spad" 1674589 1674603 1676155 1676248) (-999 "RADFF.spad" 1673003 1673039 1673121 1673277) (-998 "RADCAT.spad" 1672597 1672605 1672993 1672998) (-997 "RADCAT.spad" 1672189 1672199 1672587 1672592) (-996 "QUEUE.spad" 1671532 1671542 1671796 1671823) (-995 "QUAT.spad" 1670114 1670124 1670456 1670521) (-994 "QUATCT2.spad" 1669733 1669751 1670104 1670109) (-993 "QUATCAT.spad" 1667898 1667908 1669663 1669728) (-992 "QUATCAT.spad" 1665814 1665826 1667581 1667586) (-991 "QUAGG.spad" 1664640 1664650 1665782 1665809) (-990 "QQUTAST.spad" 1664409 1664417 1664630 1664635) (-989 "QFORM.spad" 1663872 1663886 1664399 1664404) (-988 "QFCAT.spad" 1662575 1662585 1663774 1663867) (-987 "QFCAT.spad" 1660869 1660881 1662070 1662075) (-986 "QFCAT2.spad" 1660560 1660576 1660859 1660864) (-985 "QEQUAT.spad" 1660117 1660125 1660550 1660555) (-984 "QCMPACK.spad" 1654864 1654883 1660107 1660112) (-983 "QALGSET.spad" 1650939 1650971 1654778 1654783) (-982 "QALGSET2.spad" 1648935 1648953 1650929 1650934) (-981 "PWFFINTB.spad" 1646245 1646266 1648925 1648930) (-980 "PUSHVAR.spad" 1645574 1645593 1646235 1646240) (-979 "PTRANFN.spad" 1641700 1641710 1645564 1645569) (-978 "PTPACK.spad" 1638788 1638798 1641690 1641695) (-977 "PTFUNC2.spad" 1638609 1638623 1638778 1638783) (-976 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(-882 "PATMAB.spad" 1450539 1450549 1451104 1451109) (-881 "PATLRES.spad" 1449623 1449637 1450529 1450534) (-880 "PATAB.spad" 1449387 1449397 1449613 1449618) (-879 "PARTPERM.spad" 1446749 1446757 1449377 1449382) (-878 "PARSURF.spad" 1446177 1446205 1446739 1446744) (-877 "PARSU2.spad" 1445972 1445988 1446167 1446172) (-876 "script-parser.spad" 1445492 1445500 1445962 1445967) (-875 "PARSCURV.spad" 1444920 1444948 1445482 1445487) (-874 "PARSC2.spad" 1444709 1444725 1444910 1444915) (-873 "PARPCURV.spad" 1444167 1444195 1444699 1444704) (-872 "PARPC2.spad" 1443956 1443972 1444157 1444162) (-871 "PAN2EXPR.spad" 1443368 1443376 1443946 1443951) (-870 "PALETTE.spad" 1442338 1442346 1443358 1443363) (-869 "PAIR.spad" 1441321 1441334 1441926 1441931) (-868 "PADICRC.spad" 1438651 1438669 1439826 1439919) (-867 "PADICRAT.spad" 1436666 1436678 1436887 1436980) (-866 "PADIC.spad" 1436361 1436373 1436592 1436661) (-865 "PADICCT.spad" 1434902 1434914 1436287 1436356) (-864 "PADEPAC.spad" 1433581 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(-826 "OMSAGG.spad" 1376573 1376583 1376741 1376780) (-825 "OMPKG.spad" 1375185 1375193 1376563 1376568) (-824 "OM.spad" 1374150 1374158 1375175 1375180) (-823 "OMLO.spad" 1373575 1373587 1374036 1374075) (-822 "OMEXPR.spad" 1373409 1373419 1373565 1373570) (-821 "OMERR.spad" 1372952 1372960 1373399 1373404) (-820 "OMERRK.spad" 1371986 1371994 1372942 1372947) (-819 "OMENC.spad" 1371330 1371338 1371976 1371981) (-818 "OMDEV.spad" 1365619 1365627 1371320 1371325) (-817 "OMCONN.spad" 1365028 1365036 1365609 1365614) (-816 "OINTDOM.spad" 1364791 1364799 1364954 1365023) (-815 "OFMONOID.spad" 1360978 1360988 1364781 1364786) (-814 "ODVAR.spad" 1360239 1360249 1360968 1360973) (-813 "ODR.spad" 1359883 1359909 1360051 1360200) (-812 "ODPOL.spad" 1357265 1357275 1357605 1357732) (-811 "ODP.spad" 1347112 1347132 1347485 1347616) (-810 "ODETOOLS.spad" 1345695 1345714 1347102 1347107) (-809 "ODESYS.spad" 1343345 1343362 1345685 1345690) (-808 "ODERTRIC.spad" 1339286 1339303 1343302 1343307) 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1298645) (-788 "OAMON.spad" 1298031 1298039 1298160 1298165) (-787 "OAGROUP.spad" 1297893 1297901 1298021 1298026) (-786 "NUMTUBE.spad" 1297480 1297496 1297883 1297888) (-785 "NUMQUAD.spad" 1285342 1285350 1297470 1297475) (-784 "NUMODE.spad" 1276478 1276486 1285332 1285337) (-783 "NUMINT.spad" 1274036 1274044 1276468 1276473) (-782 "NUMFMT.spad" 1272876 1272884 1274026 1274031) (-781 "NUMERIC.spad" 1264948 1264958 1272681 1272686) (-780 "NTSCAT.spad" 1263450 1263466 1264916 1264943) (-779 "NTPOLFN.spad" 1262995 1263005 1263367 1263372) (-778 "NSUP.spad" 1256041 1256051 1260581 1260734) (-777 "NSUP2.spad" 1255433 1255445 1256031 1256036) (-776 "NSMP.spad" 1251664 1251683 1251972 1252099) (-775 "NREP.spad" 1250036 1250050 1251654 1251659) (-774 "NPCOEF.spad" 1249282 1249302 1250026 1250031) (-773 "NORMRETR.spad" 1248880 1248919 1249272 1249277) (-772 "NORMPK.spad" 1246782 1246801 1248870 1248875) (-771 "NORMMA.spad" 1246470 1246496 1246772 1246777) (-770 "NONE.spad" 1246211 1246219 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1017651 1020752 1020757) (-637 "LINEXP.spad" 1017071 1017081 1017619 1017634) (-636 "LINDEP.spad" 1015848 1015860 1016983 1016988) (-635 "LIMITRF.spad" 1013762 1013772 1015838 1015843) (-634 "LIMITPS.spad" 1012645 1012658 1013752 1013757) (-633 "LIE.spad" 1010659 1010671 1011935 1012080) (-632 "LIECAT.spad" 1010135 1010145 1010585 1010654) (-631 "LIECAT.spad" 1009639 1009651 1010091 1010096) (-630 "LIB.spad" 1007687 1007695 1008298 1008313) (-629 "LGROBP.spad" 1005040 1005059 1007677 1007682) (-628 "LF.spad" 1003959 1003975 1005030 1005035) (-627 "LFCAT.spad" 1002978 1002986 1003949 1003954) (-626 "LEXTRIPK.spad" 998481 998496 1002968 1002973) (-625 "LEXP.spad" 996484 996511 998461 998476) (-624 "LETAST.spad" 996183 996191 996474 996479) (-623 "LEADCDET.spad" 994567 994584 996173 996178) (-622 "LAZM3PK.spad" 993271 993293 994557 994562) (-621 "LAUPOL.spad" 991960 991973 992864 992933) (-620 "LAPLACE.spad" 991533 991549 991950 991955) (-619 "LA.spad" 990973 990987 991455 991494) (-618 "LALG.spad" 990749 990759 990953 990968) (-617 "LALG.spad" 990533 990545 990739 990744) (-616 "KVTFROM.spad" 990268 990278 990523 990528) (-615 "KTVLOGIC.spad" 989691 989699 990258 990263) (-614 "KRCFROM.spad" 989429 989439 989681 989686) (-613 "KOVACIC.spad" 988142 988159 989419 989424) (-612 "KONVERT.spad" 987864 987874 988132 988137) (-611 "KOERCE.spad" 987601 987611 987854 987859) (-610 "KERNEL.spad" 986136 986146 987385 987390) (-609 "KERNEL2.spad" 985839 985851 986126 986131) (-608 "KDAGG.spad" 984942 984964 985819 985834) (-607 "KDAGG.spad" 984053 984077 984932 984937) (-606 "KAFILE.spad" 983016 983032 983251 983278) (-605 "JORDAN.spad" 980843 980855 982306 982451) (-604 "JOINAST.spad" 980537 980545 980833 980838) (-603 "JAVACODE.spad" 980403 980411 980527 980532) (-602 "IXAGG.spad" 978526 978550 980393 980398) (-601 "IXAGG.spad" 976504 976530 978373 978378) (-600 "IVECTOR.spad" 975275 975290 975430 975457) (-599 "ITUPLE.spad" 974420 974430 975265 975270) (-598 "ITRIGMNP.spad" 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(-577 "IOBFILE.spad" 947591 947599 948220 948225) (-576 "IOBCON.spad" 947456 947464 947581 947586) (-575 "INVLAPLA.spad" 947101 947117 947446 947451) (-574 "INTTR.spad" 940347 940364 947091 947096) (-573 "INTTOOLS.spad" 938058 938074 939921 939926) (-572 "INTSLPE.spad" 937364 937372 938048 938053) (-571 "INTRVL.spad" 936930 936940 937278 937359) (-570 "INTRF.spad" 935294 935308 936920 936925) (-569 "INTRET.spad" 934726 934736 935284 935289) (-568 "INTRAT.spad" 933401 933418 934716 934721) (-567 "INTPM.spad" 931764 931780 933044 933049) (-566 "INTPAF.spad" 929532 929550 931696 931701) (-565 "INTPACK.spad" 919842 919850 929522 929527) (-564 "INT.spad" 919203 919211 919696 919837) (-563 "INTHERTR.spad" 918469 918486 919193 919198) (-562 "INTHERAL.spad" 918135 918159 918459 918464) (-561 "INTHEORY.spad" 914548 914556 918125 918130) (-560 "INTG0.spad" 908011 908029 914480 914485) (-559 "INTFTBL.spad" 902040 902048 908001 908006) (-558 "INTFACT.spad" 901099 901109 902030 902035) (-557 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879558 880479 880484) (-536 "INFORM.spad" 876700 876708 879529 879534) (-535 "INFORM1.spad" 876325 876335 876690 876695) (-534 "INFINITY.spad" 875877 875885 876315 876320) (-533 "INETCLTS.spad" 875854 875862 875867 875872) (-532 "INEP.spad" 874386 874408 875844 875849) (-531 "INDE.spad" 874115 874132 874376 874381) (-530 "INCRMAPS.spad" 873536 873546 874105 874110) (-529 "INBFILE.spad" 872608 872616 873526 873531) (-528 "INBFF.spad" 868378 868389 872598 872603) (-527 "INBCON.spad" 866666 866674 868368 868373) (-526 "INBCON.spad" 864952 864962 866656 866661) (-525 "INAST.spad" 864613 864621 864942 864947) (-524 "IMPTAST.spad" 864321 864329 864603 864608) (-523 "IMATRIX.spad" 863266 863292 863778 863805) (-522 "IMATQF.spad" 862360 862404 863222 863227) (-521 "IMATLIN.spad" 860965 860989 862316 862321) (-520 "ILIST.spad" 859621 859636 860148 860175) (-519 "IIARRAY2.spad" 859009 859047 859228 859255) (-518 "IFF.spad" 858419 858435 858690 858783) (-517 "IFAST.spad" 858033 858041 858409 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"FORMULA.spad" 645620 645628 648146 648151) (-393 "FORMULA1.spad" 645099 645109 645610 645615) (-392 "FORDER.spad" 644790 644814 645089 645094) (-391 "FOP.spad" 643991 643999 644780 644785) (-390 "FNLA.spad" 643415 643437 643959 643986) (-389 "FNCAT.spad" 642002 642010 643405 643410) (-388 "FNAME.spad" 641894 641902 641992 641997) (-387 "FMTC.spad" 641692 641700 641820 641889) (-386 "FMONOID.spad" 638747 638757 641648 641653) (-385 "FM.spad" 638442 638454 638681 638708) (-384 "FMFUN.spad" 635472 635480 638432 638437) (-383 "FMC.spad" 634524 634532 635462 635467) (-382 "FMCAT.spad" 632178 632196 634492 634519) (-381 "FM1.spad" 631535 631547 632112 632139) (-380 "FLOATRP.spad" 629256 629270 631525 631530) (-379 "FLOAT.spad" 622544 622552 629122 629251) (-378 "FLOATCP.spad" 619961 619975 622534 622539) (-377 "FLINEXP.spad" 619673 619683 619941 619956) (-376 "FLINEXP.spad" 619339 619351 619609 619614) (-375 "FLASORT.spad" 618659 618671 619329 619334) (-374 "FLALG.spad" 616305 616324 618585 618654) (-373 "FLAGG.spad" 613323 613333 616285 616300) (-372 "FLAGG.spad" 610242 610254 613206 613211) (-371 "FLAGG2.spad" 608923 608939 610232 610237) (-370 "FINRALG.spad" 606952 606965 608879 608918) (-369 "FINRALG.spad" 604907 604922 606836 606841) (-368 "FINITE.spad" 604059 604067 604897 604902) (-367 "FINAALG.spad" 593040 593050 604001 604054) (-366 "FINAALG.spad" 582033 582045 592996 593001) (-365 "FILE.spad" 581616 581626 582023 582028) (-364 "FILECAT.spad" 580134 580151 581606 581611) (-363 "FIELD.spad" 579540 579548 580036 580129) (-362 "FIELD.spad" 579032 579042 579530 579535) (-361 "FGROUP.spad" 577641 577651 579012 579027) (-360 "FGLMICPK.spad" 576428 576443 577631 577636) (-359 "FFX.spad" 575803 575818 576144 576237) (-358 "FFSLPE.spad" 575292 575313 575793 575798) (-357 "FFPOLY.spad" 566544 566555 575282 575287) (-356 "FFPOLY2.spad" 565604 565621 566534 566539) (-355 "FFP.spad" 565001 565021 565320 565413) (-354 "FF.spad" 564449 564465 564682 564775) (-353 "FFNBX.spad" 562961 562981 564165 564258) (-352 "FFNBP.spad" 561474 561491 562677 562770) (-351 "FFNB.spad" 559939 559960 561155 561248) (-350 "FFINTBAS.spad" 557353 557372 559929 559934) (-349 "FFIELDC.spad" 554928 554936 557255 557348) (-348 "FFIELDC.spad" 552589 552599 554918 554923) (-347 "FFHOM.spad" 551337 551354 552579 552584) (-346 "FFF.spad" 548772 548783 551327 551332) (-345 "FFCGX.spad" 547619 547639 548488 548581) (-344 "FFCGP.spad" 546508 546528 547335 547428) (-343 "FFCG.spad" 545300 545321 546189 546282) (-342 "FFCAT.spad" 538327 538349 545139 545295) (-341 "FFCAT.spad" 531433 531457 538247 538252) (-340 "FFCAT2.spad" 531178 531218 531423 531428) (-339 "FEXPR.spad" 522887 522933 530934 530973) (-338 "FEVALAB.spad" 522593 522603 522877 522882) (-337 "FEVALAB.spad" 522084 522096 522370 522375) (-336 "FDIV.spad" 521526 521550 522074 522079) (-335 "FDIVCAT.spad" 519568 519592 521516 521521) (-334 "FDIVCAT.spad" 517608 517634 519558 519563) (-333 "FDIV2.spad" 517262 517302 517598 517603) (-332 "FCPAK1.spad" 515815 515823 517252 517257) (-331 "FCOMP.spad" 515194 515204 515805 515810) (-330 "FC.spad" 505109 505117 515184 515189) (-329 "FAXF.spad" 498044 498058 505011 505104) (-328 "FAXF.spad" 491031 491047 498000 498005) (-327 "FARRAY.spad" 489177 489187 490214 490241) (-326 "FAMR.spad" 487297 487309 489075 489172) (-325 "FAMR.spad" 485401 485415 487181 487186) (-324 "FAMONOID.spad" 485051 485061 485355 485360) (-323 "FAMONC.spad" 483273 483285 485041 485046) (-322 "FAGROUP.spad" 482879 482889 483169 483196) (-321 "FACUTIL.spad" 481075 481092 482869 482874) (-320 "FACTFUNC.spad" 480251 480261 481065 481070) (-319 "EXPUPXS.spad" 477084 477107 478383 478532) (-318 "EXPRTUBE.spad" 474312 474320 477074 477079) (-317 "EXPRODE.spad" 471184 471200 474302 474307) (-316 "EXPR.spad" 466459 466469 467173 467580) (-315 "EXPR2UPS.spad" 462551 462564 466449 466454) (-314 "EXPR2.spad" 462254 462266 462541 462546) (-313 "EXPEXPAN.spad" 459192 459217 459826 459919) (-312 "EXIT.spad" 458863 458871 459182 459187) (-311 "EXITAST.spad" 458599 458607 458853 458858) (-310 "EVALCYC.spad" 458057 458071 458589 458594) (-309 "EVALAB.spad" 457621 457631 458047 458052) (-308 "EVALAB.spad" 457183 457195 457611 457616) (-307 "EUCDOM.spad" 454725 454733 457109 457178) (-306 "EUCDOM.spad" 452329 452339 454715 454720) (-305 "ESTOOLS.spad" 444169 444177 452319 452324) (-304 "ESTOOLS2.spad" 443770 443784 444159 444164) (-303 "ESTOOLS1.spad" 443455 443466 443760 443765) (-302 "ES.spad" 436002 436010 443445 443450) (-301 "ES.spad" 428455 428465 435900 435905) (-300 "ESCONT.spad" 425228 425236 428445 428450) (-299 "ESCONT1.spad" 424977 424989 425218 425223) (-298 "ES2.spad" 424472 424488 424967 424972) (-297 "ES1.spad" 424038 424054 424462 424467) (-296 "ERROR.spad" 421359 421367 424028 424033) (-295 "EQTBL.spad" 419831 419853 420040 420067) (-294 "EQ.spad" 414705 414715 417504 417616) (-293 "EQ2.spad" 414421 414433 414695 414700) (-292 "EP.spad" 410735 410745 414411 414416) (-291 "ENV.spad" 409387 409395 410725 410730) (-290 "ENTIRER.spad" 409055 409063 409331 409382) (-289 "EMR.spad" 408256 408297 408981 409050) (-288 "ELTAGG.spad" 406496 406515 408246 408251) (-287 "ELTAGG.spad" 404700 404721 406452 406457) (-286 "ELTAB.spad" 404147 404165 404690 404695) (-285 "ELFUTS.spad" 403526 403545 404137 404142) (-284 "ELEMFUN.spad" 403215 403223 403516 403521) (-283 "ELEMFUN.spad" 402902 402912 403205 403210) (-282 "ELAGG.spad" 400845 400855 402882 402897) (-281 "ELAGG.spad" 398725 398737 400764 400769) (-280 "ELABEXPR.spad" 397648 397656 398715 398720) (-279 "EFUPXS.spad" 394424 394454 397604 397609) (-278 "EFULS.spad" 391260 391283 394380 394385) (-277 "EFSTRUC.spad" 389215 389231 391250 391255) (-276 "EF.spad" 383981 383997 389205 389210) (-275 "EAB.spad" 382257 382265 383971 383976) (-274 "E04UCFA.spad" 381793 381801 382247 382252) (-273 "E04NAFA.spad" 381370 381378 381783 381788) (-272 "E04MBFA.spad" 380950 380958 381360 381365) (-271 "E04JAFA.spad" 380486 380494 380940 380945) (-270 "E04GCFA.spad" 380022 380030 380476 380481) (-269 "E04FDFA.spad" 379558 379566 380012 380017) (-268 "E04DGFA.spad" 379094 379102 379548 379553) (-267 "E04AGNT.spad" 374936 374944 379084 379089) (-266 "DVARCAT.spad" 371621 371631 374926 374931) (-265 "DVARCAT.spad" 368304 368316 371611 371616) (-264 "DSMP.spad" 365771 365785 366076 366203) (-263 "DROPT.spad" 359716 359724 365761 365766) (-262 "DROPT1.spad" 359379 359389 359706 359711) (-261 "DROPT0.spad" 354206 354214 359369 359374) (-260 "DRAWPT.spad" 352361 352369 354196 354201) (-259 "DRAW.spad" 344961 344974 352351 352356) (-258 "DRAWHACK.spad" 344269 344279 344951 344956) (-257 "DRAWCX.spad" 341711 341719 344259 344264) (-256 "DRAWCURV.spad" 341248 341263 341701 341706) (-255 "DRAWCFUN.spad" 330420 330428 341238 341243) (-254 "DQAGG.spad" 328588 328598 330388 330415) (-253 "DPOLCAT.spad" 323929 323945 328456 328583) (-252 "DPOLCAT.spad" 319356 319374 323885 323890) (-251 "DPMO.spad" 311582 311598 311720 312021) (-250 "DPMM.spad" 303821 303839 303946 304247) (-249 "DOMCTOR.spad" 303713 303721 303811 303816) (-248 "DOMAIN.spad" 302844 302852 303703 303708) (-247 "DMP.spad" 300102 300117 300674 300801) (-246 "DLP.spad" 299450 299460 300092 300097) (-245 "DLIST.spad" 298029 298039 298633 298660) (-244 "DLAGG.spad" 296440 296450 298019 298024) (-243 "DIVRING.spad" 295982 295990 296384 296435) (-242 "DIVRING.spad" 295568 295578 295972 295977) (-241 "DISPLAY.spad" 293748 293756 295558 295563) (-240 "DIRPROD.spad" 283328 283344 283968 284099) (-239 "DIRPROD2.spad" 282136 282154 283318 283323) (-238 "DIRPCAT.spad" 281078 281094 282000 282131) (-237 "DIRPCAT.spad" 279749 279767 280673 280678) (-236 "DIOSP.spad" 278574 278582 279739 279744) (-235 "DIOPS.spad" 277558 277568 278554 278569) (-234 "DIOPS.spad" 276516 276528 277514 277519) (-233 "DIFRING.spad" 275808 275816 276496 276511) (-232 "DIFRING.spad" 275108 275118 275798 275803) (-231 "DIFEXT.spad" 274267 274277 275088 275103) (-230 "DIFEXT.spad" 273343 273355 274166 274171) (-229 "DIAGG.spad" 272973 272983 273323 273338) (-228 "DIAGG.spad" 272611 272623 272963 272968) (-227 "DHMATRIX.spad" 270915 270925 272068 272095) (-226 "DFSFUN.spad" 264323 264331 270905 270910) (-225 "DFLOAT.spad" 261044 261052 264213 264318) (-224 "DFINTTLS.spad" 259253 259269 261034 261039) (-223 "DERHAM.spad" 257163 257195 259233 259248) (-222 "DEQUEUE.spad" 256481 256491 256770 256797) (-221 "DEGRED.spad" 256096 256110 256471 256476) (-220 "DEFINTRF.spad" 253621 253631 256086 256091) (-219 "DEFINTEF.spad" 252117 252133 253611 253616) (-218 "DEFAST.spad" 251485 251493 252107 252112) (-217 "DECIMAL.spad" 249591 249599 249952 250045) (-216 "DDFACT.spad" 247390 247407 249581 249586) (-215 "DBLRESP.spad" 246988 247012 247380 247385) (-214 "DBASE.spad" 245642 245652 246978 246983) (-213 "DATAARY.spad" 245104 245117 245632 245637) (-212 "D03FAFA.spad" 244932 244940 245094 245099) (-211 "D03EEFA.spad" 244752 244760 244922 244927) (-210 "D03AGNT.spad" 243832 243840 244742 244747) (-209 "D02EJFA.spad" 243294 243302 243822 243827) (-208 "D02CJFA.spad" 242772 242780 243284 243289) (-207 "D02BHFA.spad" 242262 242270 242762 242767) (-206 "D02BBFA.spad" 241752 241760 242252 242257) (-205 "D02AGNT.spad" 236556 236564 241742 241747) (-204 "D01WGTS.spad" 234875 234883 236546 236551) (-203 "D01TRNS.spad" 234852 234860 234865 234870) (-202 "D01GBFA.spad" 234374 234382 234842 234847) (-201 "D01FCFA.spad" 233896 233904 234364 234369) (-200 "D01ASFA.spad" 233364 233372 233886 233891) (-199 "D01AQFA.spad" 232810 232818 233354 233359) (-198 "D01APFA.spad" 232234 232242 232800 232805) (-197 "D01ANFA.spad" 231728 231736 232224 232229) (-196 "D01AMFA.spad" 231238 231246 231718 231723) (-195 "D01ALFA.spad" 230778 230786 231228 231233) (-194 "D01AKFA.spad" 230304 230312 230768 230773) (-193 "D01AJFA.spad" 229827 229835 230294 230299) (-192 "D01AGNT.spad" 225886 225894 229817 229822) (-191 "CYCLOTOM.spad" 225392 225400 225876 225881) (-190 "CYCLES.spad" 222224 222232 225382 225387) (-189 "CVMP.spad" 221641 221651 222214 222219) (-188 "CTRIGMNP.spad" 220131 220147 221631 221636) (-187 "CTOR.spad" 219822 219830 220121 220126) (-186 "CTORKIND.spad" 219425 219433 219812 219817) (-185 "CTORCAT.spad" 218674 218682 219415 219420) (-184 "CTORCAT.spad" 217921 217931 218664 218669) (-183 "CTORCALL.spad" 217501 217509 217911 217916) (-182 "CSTTOOLS.spad" 216744 216757 217491 217496) (-181 "CRFP.spad" 210448 210461 216734 216739) (-180 "CRCEAST.spad" 210168 210176 210438 210443) (-179 "CRAPACK.spad" 209211 209221 210158 210163) (-178 "CPMATCH.spad" 208711 208726 209136 209141) (-177 "CPIMA.spad" 208416 208435 208701 208706) (-176 "COORDSYS.spad" 203309 203319 208406 208411) (-175 "CONTOUR.spad" 202716 202724 203299 203304) (-174 "CONTFRAC.spad" 198328 198338 202618 202711) (-173 "CONDUIT.spad" 198086 198094 198318 198323) (-172 "COMRING.spad" 197760 197768 198024 198081) (-171 "COMPPROP.spad" 197274 197282 197750 197755) (-170 "COMPLPAT.spad" 197041 197056 197264 197269) (-169 "COMPLEX.spad" 191179 191189 191423 191684) (-168 "COMPLEX2.spad" 190892 190904 191169 191174) (-167 "COMPFACT.spad" 190494 190508 190882 190887) (-166 "COMPCAT.spad" 188562 188572 190228 190489) (-165 "COMPCAT.spad" 186359 186371 188027 188032) (-164 "COMMUPC.spad" 186105 186123 186349 186354) (-163 "COMMONOP.spad" 185638 185646 186095 186100) (-162 "COMM.spad" 185447 185455 185628 185633) (-161 "COMMAAST.spad" 185210 185218 185437 185442) (-160 "COMBOPC.spad" 184115 184123 185200 185205) (-159 "COMBINAT.spad" 182860 182870 184105 184110) (-158 "COMBF.spad" 180228 180244 182850 182855) (-157 "COLOR.spad" 179065 179073 180218 180223) (-156 "COLONAST.spad" 178731 178739 179055 179060) (-155 "CMPLXRT.spad" 178440 178457 178721 178726) (-154 "CLLCTAST.spad" 178102 178110 178430 178435) (-153 "CLIP.spad" 174194 174202 178092 178097) (-152 "CLIF.spad" 172833 172849 174150 174189) (-151 "CLAGG.spad" 169318 169328 172823 172828) (-150 "CLAGG.spad" 165674 165686 169181 169186) (-149 "CINTSLPE.spad" 164999 165012 165664 165669) (-148 "CHVAR.spad" 163077 163099 164989 164994) (-147 "CHARZ.spad" 162992 163000 163057 163072) (-146 "CHARPOL.spad" 162500 162510 162982 162987) (-145 "CHARNZ.spad" 162253 162261 162480 162495) (-144 "CHAR.spad" 160121 160129 162243 162248) (-143 "CFCAT.spad" 159437 159445 160111 160116) (-142 "CDEN.spad" 158595 158609 159427 159432) (-141 "CCLASS.spad" 156744 156752 158006 158045) (-140 "CATEGORY.spad" 155834 155842 156734 156739) (-139 "CATCTOR.spad" 155725 155733 155824 155829) (-138 "CATAST.spad" 155343 155351 155715 155720) (-137 "CASEAST.spad" 155057 155065 155333 155338) (-136 "CARTEN.spad" 150160 150184 155047 155052) (-135 "CARTEN2.spad" 149546 149573 150150 150155) (-134 "CARD.spad" 146835 146843 149520 149541) (-133 "CAPSLAST.spad" 146609 146617 146825 146830) (-132 "CACHSET.spad" 146231 146239 146599 146604) (-131 "CABMON.spad" 145784 145792 146221 146226) (-130 "BYTEORD.spad" 145459 145467 145774 145779) (-129 "BYTE.spad" 144884 144892 145449 145454) (-128 "BYTEBUF.spad" 142741 142749 144053 144080) (-127 "BTREE.spad" 141810 141820 142348 142375) (-126 "BTOURN.spad" 140813 140823 141417 141444) (-125 "BTCAT.spad" 140201 140211 140781 140808) (-124 "BTCAT.spad" 139609 139621 140191 140196) (-123 "BTAGG.spad" 138731 138739 139577 139604) (-122 "BTAGG.spad" 137873 137883 138721 138726) (-121 "BSTREE.spad" 136608 136618 137480 137507) (-120 "BRILL.spad" 134803 134814 136598 136603) (-119 "BRAGG.spad" 133727 133737 134793 134798) (-118 "BRAGG.spad" 132615 132627 133683 133688) (-117 "BPADICRT.spad" 130596 130608 130851 130944) (-116 "BPADIC.spad" 130260 130272 130522 130591) (-115 "BOUNDZRO.spad" 129916 129933 130250 130255) (-114 "BOP.spad" 124934 124942 129906 129911) (-113 "BOP1.spad" 122354 122364 124924 124929) (-112 "BOOLEAN.spad" 121678 121686 122344 122349) (-111 "BMODULE.spad" 121390 121402 121646 121673) (-110 "BITS.spad" 120809 120817 121026 121053) (-109 "BINDING.spad" 120220 120228 120799 120804) (-108 "BINARY.spad" 118331 118339 118687 118780) (-107 "BGAGG.spad" 117528 117538 118311 118326) (-106 "BGAGG.spad" 116733 116745 117518 117523) (-105 "BFUNCT.spad" 116297 116305 116713 116728) (-104 "BEZOUT.spad" 115431 115458 116247 116252) (-103 "BBTREE.spad" 112250 112260 115038 115065) (-102 "BASTYPE.spad" 111922 111930 112240 112245) (-101 "BASTYPE.spad" 111592 111602 111912 111917) (-100 "BALFACT.spad" 111031 111044 111582 111587) (-99 "AUTOMOR.spad" 110478 110487 111011 111026) (-98 "ATTREG.spad" 107197 107204 110230 110473) (-97 "ATTRBUT.spad" 103220 103227 107177 107192) (-96 "ATTRAST.spad" 102937 102944 103210 103215) (-95 "ATRIG.spad" 102407 102414 102927 102932) (-94 "ATRIG.spad" 101875 101884 102397 102402) (-93 "ASTCAT.spad" 101779 101786 101865 101870) (-92 "ASTCAT.spad" 101681 101690 101769 101774) (-91 "ASTACK.spad" 101014 101023 101288 101315) (-90 "ASSOCEQ.spad" 99814 99825 100970 100975) (-89 "ASP9.spad" 98895 98908 99804 99809) (-88 "ASP8.spad" 97938 97951 98885 98890) (-87 "ASP80.spad" 97260 97273 97928 97933) (-86 "ASP7.spad" 96420 96433 97250 97255) (-85 "ASP78.spad" 95871 95884 96410 96415) (-84 "ASP77.spad" 95240 95253 95861 95866) (-83 "ASP74.spad" 94332 94345 95230 95235) (-82 "ASP73.spad" 93603 93616 94322 94327) (-81 "ASP6.spad" 92470 92483 93593 93598) (-80 "ASP55.spad" 90979 90992 92460 92465) (-79 "ASP50.spad" 88796 88809 90969 90974) (-78 "ASP4.spad" 88091 88104 88786 88791) (-77 "ASP49.spad" 87090 87103 88081 88086) (-76 "ASP42.spad" 85497 85536 87080 87085) (-75 "ASP41.spad" 84076 84115 85487 85492) (-74 "ASP35.spad" 83064 83077 84066 84071) (-73 "ASP34.spad" 82365 82378 83054 83059) (-72 "ASP33.spad" 81925 81938 82355 82360) (-71 "ASP31.spad" 81065 81078 81915 81920) (-70 "ASP30.spad" 79957 79970 81055 81060) (-69 "ASP29.spad" 79423 79436 79947 79952) (-68 "ASP28.spad" 70696 70709 79413 79418) (-67 "ASP27.spad" 69593 69606 70686 70691) (-66 "ASP24.spad" 68680 68693 69583 69588) (-65 "ASP20.spad" 68144 68157 68670 68675) (-64 "ASP1.spad" 67525 67538 68134 68139) (-63 "ASP19.spad" 62211 62224 67515 67520) (-62 "ASP12.spad" 61625 61638 62201 62206) (-61 "ASP10.spad" 60896 60909 61615 61620) (-60 "ARRAY2.spad" 60256 60265 60503 60530) (-59 "ARRAY1.spad" 59091 59100 59439 59466) (-58 "ARRAY12.spad" 57760 57771 59081 59086) (-57 "ARR2CAT.spad" 53422 53443 57728 57755) (-56 "ARR2CAT.spad" 49104 49127 53412 53417) (-55 "ARITY.spad" 48476 48483 49094 49099) (-54 "APPRULE.spad" 47720 47742 48466 48471) (-53 "APPLYORE.spad" 47335 47348 47710 47715) (-52 "ANY.spad" 45677 45684 47325 47330) (-51 "ANY1.spad" 44748 44757 45667 45672) (-50 "ANTISYM.spad" 43187 43203 44728 44743) (-49 "ANON.spad" 42880 42887 43177 43182) (-48 "AN.spad" 41181 41188 42696 42789) (-47 "AMR.spad" 39360 39371 41079 41176) (-46 "AMR.spad" 37376 37389 39097 39102) (-45 "ALIST.spad" 34788 34809 35138 35165) (-44 "ALGSC.spad" 33911 33937 34660 34713) (-43 "ALGPKG.spad" 29620 29631 33867 33872) (-42 "ALGMFACT.spad" 28809 28823 29610 29615) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2282825 2282830 2282835 2282840) (-2 NIL 2282805 2282810 2282815 2282820) (-1 NIL 2282785 2282790 2282795 2282800) (0 NIL 2282765 2282770 2282775 2282780) (-1287 "ZMOD.spad" 2282574 2282587 2282703 2282760) (-1286 "ZLINDEP.spad" 2281618 2281629 2282564 2282569) (-1285 "ZDSOLVE.spad" 2271467 2271489 2281608 2281613) (-1284 "YSTREAM.spad" 2270960 2270971 2271457 2271462) (-1283 "XRPOLY.spad" 2270180 2270200 2270816 2270885) (-1282 "XPR.spad" 2267971 2267984 2269898 2269997) (-1281 "XPOLY.spad" 2267526 2267537 2267827 2267896) (-1280 "XPOLYC.spad" 2266843 2266859 2267452 2267521) (-1279 "XPBWPOLY.spad" 2265280 2265300 2266623 2266692) (-1278 "XF.spad" 2263741 2263756 2265182 2265275) (-1277 "XF.spad" 2262182 2262199 2263625 2263630) (-1276 "XFALG.spad" 2259206 2259222 2262108 2262177) (-1275 "XEXPPKG.spad" 2258457 2258483 2259196 2259201) (-1274 "XDPOLY.spad" 2258071 2258087 2258313 2258382) (-1273 "XALG.spad" 2257731 2257742 2258027 2258066) (-1272 "WUTSET.spad" 2253570 2253587 2257377 2257404) (-1271 "WP.spad" 2252769 2252813 2253428 2253495) (-1270 "WHILEAST.spad" 2252567 2252576 2252759 2252764) (-1269 "WHEREAST.spad" 2252238 2252247 2252557 2252562) (-1268 "WFFINTBS.spad" 2249801 2249823 2252228 2252233) (-1267 "WEIER.spad" 2248015 2248026 2249791 2249796) (-1266 "VSPACE.spad" 2247688 2247699 2247983 2248010) (-1265 "VSPACE.spad" 2247381 2247394 2247678 2247683) (-1264 "VOID.spad" 2247058 2247067 2247371 2247376) (-1263 "VIEW.spad" 2244680 2244689 2247048 2247053) (-1262 "VIEWDEF.spad" 2239877 2239886 2244670 2244675) (-1261 "VIEW3D.spad" 2223712 2223721 2239867 2239872) (-1260 "VIEW2D.spad" 2211449 2211458 2223702 2223707) (-1259 "VECTOR.spad" 2210124 2210135 2210375 2210402) (-1258 "VECTOR2.spad" 2208751 2208764 2210114 2210119) (-1257 "VECTCAT.spad" 2206651 2206662 2208719 2208746) (-1256 "VECTCAT.spad" 2204359 2204372 2206429 2206434) (-1255 "VARIABLE.spad" 2204139 2204154 2204349 2204354) (-1254 "UTYPE.spad" 2203783 2203792 2204129 2204134) (-1253 "UTSODETL.spad" 2203076 2203100 2203739 2203744) (-1252 "UTSODE.spad" 2201264 2201284 2203066 2203071) (-1251 "UTS.spad" 2196053 2196081 2199731 2199828) (-1250 "UTSCAT.spad" 2193504 2193520 2195951 2196048) (-1249 "UTSCAT.spad" 2190599 2190617 2193048 2193053) (-1248 "UTS2.spad" 2190192 2190227 2190589 2190594) (-1247 "URAGG.spad" 2184824 2184835 2190182 2190187) (-1246 "URAGG.spad" 2179420 2179433 2184780 2184785) (-1245 "UPXSSING.spad" 2177063 2177089 2178501 2178634) (-1244 "UPXS.spad" 2174211 2174239 2175195 2175344) (-1243 "UPXSCONS.spad" 2171968 2171988 2172343 2172492) (-1242 "UPXSCCA.spad" 2170533 2170553 2171814 2171963) (-1241 "UPXSCCA.spad" 2169240 2169262 2170523 2170528) (-1240 "UPXSCAT.spad" 2167821 2167837 2169086 2169235) (-1239 "UPXS2.spad" 2167362 2167415 2167811 2167816) (-1238 "UPSQFREE.spad" 2165774 2165788 2167352 2167357) (-1237 "UPSCAT.spad" 2163367 2163391 2165672 2165769) (-1236 "UPSCAT.spad" 2160666 2160692 2162973 2162978) (-1235 "UPOLYC.spad" 2155644 2155655 2160508 2160661) (-1234 "UPOLYC.spad" 2150514 2150527 2155380 2155385) (-1233 "UPOLYC2.spad" 2149983 2150002 2150504 2150509) (-1232 "UP.spad" 2147176 2147191 2147569 2147722) (-1231 "UPMP.spad" 2146066 2146079 2147166 2147171) (-1230 "UPDIVP.spad" 2145629 2145643 2146056 2146061) (-1229 "UPDECOMP.spad" 2143866 2143880 2145619 2145624) (-1228 "UPCDEN.spad" 2143073 2143089 2143856 2143861) (-1227 "UP2.spad" 2142435 2142456 2143063 2143068) (-1226 "UNISEG.spad" 2141788 2141799 2142354 2142359) (-1225 "UNISEG2.spad" 2141281 2141294 2141744 2141749) (-1224 "UNIFACT.spad" 2140382 2140394 2141271 2141276) (-1223 "ULS.spad" 2130934 2130962 2132027 2132456) (-1222 "ULSCONS.spad" 2123328 2123348 2123700 2123849) (-1221 "ULSCCAT.spad" 2121057 2121077 2123174 2123323) (-1220 "ULSCCAT.spad" 2118894 2118916 2121013 2121018) (-1219 "ULSCAT.spad" 2117110 2117126 2118740 2118889) (-1218 "ULS2.spad" 2116622 2116675 2117100 2117105) (-1217 "UINT8.spad" 2116499 2116508 2116612 2116617) (-1216 "UINT64.spad" 2116375 2116384 2116489 2116494) (-1215 "UINT32.spad" 2116251 2116260 2116365 2116370) (-1214 "UINT16.spad" 2116127 2116136 2116241 2116246) (-1213 "UFD.spad" 2115192 2115201 2116053 2116122) (-1212 "UFD.spad" 2114319 2114330 2115182 2115187) (-1211 "UDVO.spad" 2113166 2113175 2114309 2114314) (-1210 "UDPO.spad" 2110593 2110604 2113122 2113127) (-1209 "TYPE.spad" 2110525 2110534 2110583 2110588) (-1208 "TYPEAST.spad" 2110444 2110453 2110515 2110520) (-1207 "TWOFACT.spad" 2109094 2109109 2110434 2110439) (-1206 "TUPLE.spad" 2108578 2108589 2108993 2108998) (-1205 "TUBETOOL.spad" 2105415 2105424 2108568 2108573) (-1204 "TUBE.spad" 2104056 2104073 2105405 2105410) (-1203 "TS.spad" 2102645 2102661 2103621 2103718) (-1202 "TSETCAT.spad" 2089772 2089789 2102613 2102640) (-1201 "TSETCAT.spad" 2076885 2076904 2089728 2089733) (-1200 "TRMANIP.spad" 2071251 2071268 2076591 2076596) (-1199 "TRIMAT.spad" 2070210 2070235 2071241 2071246) (-1198 "TRIGMNIP.spad" 2068727 2068744 2070200 2070205) (-1197 "TRIGCAT.spad" 2068239 2068248 2068717 2068722) (-1196 "TRIGCAT.spad" 2067749 2067760 2068229 2068234) (-1195 "TREE.spad" 2066320 2066331 2067356 2067383) (-1194 "TRANFUN.spad" 2066151 2066160 2066310 2066315) (-1193 "TRANFUN.spad" 2065980 2065991 2066141 2066146) (-1192 "TOPSP.spad" 2065654 2065663 2065970 2065975) (-1191 "TOOLSIGN.spad" 2065317 2065328 2065644 2065649) (-1190 "TEXTFILE.spad" 2063874 2063883 2065307 2065312) (-1189 "TEX.spad" 2061006 2061015 2063864 2063869) (-1188 "TEX1.spad" 2060562 2060573 2060996 2061001) (-1187 "TEMUTL.spad" 2060117 2060126 2060552 2060557) (-1186 "TBCMPPK.spad" 2058210 2058233 2060107 2060112) (-1185 "TBAGG.spad" 2057246 2057269 2058190 2058205) (-1184 "TBAGG.spad" 2056290 2056315 2057236 2057241) (-1183 "TANEXP.spad" 2055666 2055677 2056280 2056285) (-1182 "TABLE.spad" 2054077 2054100 2054347 2054374) (-1181 "TABLEAU.spad" 2053558 2053569 2054067 2054072) (-1180 "TABLBUMP.spad" 2050341 2050352 2053548 2053553) (-1179 "SYSTEM.spad" 2049569 2049578 2050331 2050336) (-1178 "SYSSOLP.spad" 2047042 2047053 2049559 2049564) (-1177 "SYSNNI.spad" 2046222 2046233 2047032 2047037) (-1176 "SYSINT.spad" 2045626 2045637 2046212 2046217) (-1175 "SYNTAX.spad" 2041820 2041829 2045616 2045621) (-1174 "SYMTAB.spad" 2039876 2039885 2041810 2041815) (-1173 "SYMS.spad" 2035861 2035870 2039866 2039871) (-1172 "SYMPOLY.spad" 2034868 2034879 2034950 2035077) (-1171 "SYMFUNC.spad" 2034343 2034354 2034858 2034863) (-1170 "SYMBOL.spad" 2031770 2031779 2034333 2034338) (-1169 "SWITCH.spad" 2028527 2028536 2031760 2031765) (-1168 "SUTS.spad" 2025426 2025454 2026994 2027091) (-1167 "SUPXS.spad" 2022561 2022589 2023558 2023707) (-1166 "SUP.spad" 2019366 2019377 2020147 2020300) (-1165 "SUPFRACF.spad" 2018471 2018489 2019356 2019361) (-1164 "SUP2.spad" 2017861 2017874 2018461 2018466) (-1163 "SUMRF.spad" 2016827 2016838 2017851 2017856) (-1162 "SUMFS.spad" 2016460 2016477 2016817 2016822) (-1161 "SULS.spad" 2006999 2007027 2008105 2008534) (-1160 "SUCHTAST.spad" 2006768 2006777 2006989 2006994) (-1159 "SUCH.spad" 2006448 2006463 2006758 2006763) (-1158 "SUBSPACE.spad" 1998455 1998470 2006438 2006443) (-1157 "SUBRESP.spad" 1997615 1997629 1998411 1998416) (-1156 "STTF.spad" 1993714 1993730 1997605 1997610) (-1155 "STTFNC.spad" 1990182 1990198 1993704 1993709) (-1154 "STTAYLOR.spad" 1982580 1982591 1990063 1990068) (-1153 "STRTBL.spad" 1981085 1981102 1981234 1981261) (-1152 "STRING.spad" 1980494 1980503 1980508 1980535) (-1151 "STRICAT.spad" 1980282 1980291 1980462 1980489) (-1150 "STREAM.spad" 1977140 1977151 1979807 1979822) (-1149 "STREAM3.spad" 1976685 1976700 1977130 1977135) (-1148 "STREAM2.spad" 1975753 1975766 1976675 1976680) (-1147 "STREAM1.spad" 1975457 1975468 1975743 1975748) (-1146 "STINPROD.spad" 1974363 1974379 1975447 1975452) (-1145 "STEP.spad" 1973564 1973573 1974353 1974358) (-1144 "STBL.spad" 1972090 1972118 1972257 1972272) (-1143 "STAGG.spad" 1971165 1971176 1972080 1972085) (-1142 "STAGG.spad" 1970238 1970251 1971155 1971160) (-1141 "STACK.spad" 1969589 1969600 1969845 1969872) (-1140 "SREGSET.spad" 1967293 1967310 1969235 1969262) (-1139 "SRDCMPK.spad" 1965838 1965858 1967283 1967288) (-1138 "SRAGG.spad" 1960935 1960944 1965806 1965833) (-1137 "SRAGG.spad" 1956052 1956063 1960925 1960930) (-1136 "SQMATRIX.spad" 1953668 1953686 1954584 1954671) (-1135 "SPLTREE.spad" 1948220 1948233 1953104 1953131) (-1134 "SPLNODE.spad" 1944808 1944821 1948210 1948215) (-1133 "SPFCAT.spad" 1943585 1943594 1944798 1944803) (-1132 "SPECOUT.spad" 1942135 1942144 1943575 1943580) (-1131 "SPADXPT.spad" 1934274 1934283 1942125 1942130) (-1130 "spad-parser.spad" 1933739 1933748 1934264 1934269) (-1129 "SPADAST.spad" 1933440 1933449 1933729 1933734) (-1128 "SPACEC.spad" 1917453 1917464 1933430 1933435) (-1127 "SPACE3.spad" 1917229 1917240 1917443 1917448) (-1126 "SORTPAK.spad" 1916774 1916787 1917185 1917190) (-1125 "SOLVETRA.spad" 1914531 1914542 1916764 1916769) (-1124 "SOLVESER.spad" 1913051 1913062 1914521 1914526) (-1123 "SOLVERAD.spad" 1909061 1909072 1913041 1913046) (-1122 "SOLVEFOR.spad" 1907481 1907499 1909051 1909056) (-1121 "SNTSCAT.spad" 1907081 1907098 1907449 1907476) (-1120 "SMTS.spad" 1905341 1905367 1906646 1906743) (-1119 "SMP.spad" 1902816 1902836 1903206 1903333) (-1118 "SMITH.spad" 1901659 1901684 1902806 1902811) (-1117 "SMATCAT.spad" 1899769 1899799 1901603 1901654) (-1116 "SMATCAT.spad" 1897811 1897843 1899647 1899652) (-1115 "SKAGG.spad" 1896772 1896783 1897779 1897806) (-1114 "SINT.spad" 1895598 1895607 1896638 1896767) (-1113 "SIMPAN.spad" 1895326 1895335 1895588 1895593) (-1112 "SIG.spad" 1894654 1894663 1895316 1895321) (-1111 "SIGNRF.spad" 1893762 1893773 1894644 1894649) (-1110 "SIGNEF.spad" 1893031 1893048 1893752 1893757) (-1109 "SIGAST.spad" 1892412 1892421 1893021 1893026) (-1108 "SHP.spad" 1890330 1890345 1892368 1892373) (-1107 "SHDP.spad" 1880041 1880068 1880550 1880681) (-1106 "SGROUP.spad" 1879649 1879658 1880031 1880036) (-1105 "SGROUP.spad" 1879255 1879266 1879639 1879644) (-1104 "SGCF.spad" 1872136 1872145 1879245 1879250) (-1103 "SFRTCAT.spad" 1871064 1871081 1872104 1872131) (-1102 "SFRGCD.spad" 1870127 1870147 1871054 1871059) (-1101 "SFQCMPK.spad" 1864764 1864784 1870117 1870122) (-1100 "SFORT.spad" 1864199 1864213 1864754 1864759) (-1099 "SEXOF.spad" 1864042 1864082 1864189 1864194) (-1098 "SEX.spad" 1863934 1863943 1864032 1864037) (-1097 "SEXCAT.spad" 1861485 1861525 1863924 1863929) (-1096 "SET.spad" 1859785 1859796 1860906 1860945) (-1095 "SETMN.spad" 1858219 1858236 1859775 1859780) (-1094 "SETCAT.spad" 1857541 1857550 1858209 1858214) (-1093 "SETCAT.spad" 1856861 1856872 1857531 1857536) (-1092 "SETAGG.spad" 1853382 1853393 1856841 1856856) (-1091 "SETAGG.spad" 1849911 1849924 1853372 1853377) (-1090 "SEQAST.spad" 1849614 1849623 1849901 1849906) (-1089 "SEGXCAT.spad" 1848736 1848749 1849604 1849609) (-1088 "SEG.spad" 1848549 1848560 1848655 1848660) (-1087 "SEGCAT.spad" 1847456 1847467 1848539 1848544) (-1086 "SEGBIND.spad" 1846528 1846539 1847411 1847416) (-1085 "SEGBIND2.spad" 1846224 1846237 1846518 1846523) (-1084 "SEGAST.spad" 1845938 1845947 1846214 1846219) (-1083 "SEG2.spad" 1845363 1845376 1845894 1845899) (-1082 "SDVAR.spad" 1844639 1844650 1845353 1845358) (-1081 "SDPOL.spad" 1842065 1842076 1842356 1842483) (-1080 "SCPKG.spad" 1840144 1840155 1842055 1842060) (-1079 "SCOPE.spad" 1839293 1839302 1840134 1840139) (-1078 "SCACHE.spad" 1837975 1837986 1839283 1839288) (-1077 "SASTCAT.spad" 1837884 1837893 1837965 1837970) (-1076 "SAOS.spad" 1837756 1837765 1837874 1837879) (-1075 "SAERFFC.spad" 1837469 1837489 1837746 1837751) (-1074 "SAE.spad" 1835644 1835660 1836255 1836390) (-1073 "SAEFACT.spad" 1835345 1835365 1835634 1835639) (-1072 "RURPK.spad" 1832986 1833002 1835335 1835340) (-1071 "RULESET.spad" 1832427 1832451 1832976 1832981) (-1070 "RULE.spad" 1830631 1830655 1832417 1832422) (-1069 "RULECOLD.spad" 1830483 1830496 1830621 1830626) (-1068 "RTVALUE.spad" 1830216 1830225 1830473 1830478) (-1067 "RSTRCAST.spad" 1829933 1829942 1830206 1830211) (-1066 "RSETGCD.spad" 1826311 1826331 1829923 1829928) (-1065 "RSETCAT.spad" 1816095 1816112 1826279 1826306) (-1064 "RSETCAT.spad" 1805899 1805918 1816085 1816090) (-1063 "RSDCMPK.spad" 1804351 1804371 1805889 1805894) (-1062 "RRCC.spad" 1802735 1802765 1804341 1804346) (-1061 "RRCC.spad" 1801117 1801149 1802725 1802730) (-1060 "RPTAST.spad" 1800819 1800828 1801107 1801112) (-1059 "RPOLCAT.spad" 1780179 1780194 1800687 1800814) (-1058 "RPOLCAT.spad" 1759253 1759270 1779763 1779768) (-1057 "ROUTINE.spad" 1755116 1755125 1757900 1757927) (-1056 "ROMAN.spad" 1754444 1754453 1754982 1755111) (-1055 "ROIRC.spad" 1753524 1753556 1754434 1754439) (-1054 "RNS.spad" 1752427 1752436 1753426 1753519) (-1053 "RNS.spad" 1751416 1751427 1752417 1752422) (-1052 "RNG.spad" 1751151 1751160 1751406 1751411) (-1051 "RMODULE.spad" 1750789 1750800 1751141 1751146) (-1050 "RMCAT2.spad" 1750197 1750254 1750779 1750784) (-1049 "RMATRIX.spad" 1749021 1749040 1749364 1749403) (-1048 "RMATCAT.spad" 1744554 1744585 1748977 1749016) (-1047 "RMATCAT.spad" 1739977 1740010 1744402 1744407) (-1046 "RINTERP.spad" 1739865 1739885 1739967 1739972) (-1045 "RING.spad" 1739335 1739344 1739845 1739860) (-1044 "RING.spad" 1738813 1738824 1739325 1739330) (-1043 "RIDIST.spad" 1738197 1738206 1738803 1738808) (-1042 "RGCHAIN.spad" 1736776 1736792 1737682 1737709) (-1041 "RGBCSPC.spad" 1736557 1736569 1736766 1736771) (-1040 "RGBCMDL.spad" 1736087 1736099 1736547 1736552) (-1039 "RF.spad" 1733701 1733712 1736077 1736082) (-1038 "RFFACTOR.spad" 1733163 1733174 1733691 1733696) (-1037 "RFFACT.spad" 1732898 1732910 1733153 1733158) (-1036 "RFDIST.spad" 1731886 1731895 1732888 1732893) (-1035 "RETSOL.spad" 1731303 1731316 1731876 1731881) (-1034 "RETRACT.spad" 1730731 1730742 1731293 1731298) (-1033 "RETRACT.spad" 1730157 1730170 1730721 1730726) (-1032 "RETAST.spad" 1729969 1729978 1730147 1730152) (-1031 "RESULT.spad" 1728029 1728038 1728616 1728643) (-1030 "RESRING.spad" 1727376 1727423 1727967 1728024) (-1029 "RESLATC.spad" 1726700 1726711 1727366 1727371) (-1028 "REPSQ.spad" 1726429 1726440 1726690 1726695) (-1027 "REP.spad" 1723981 1723990 1726419 1726424) (-1026 "REPDB.spad" 1723686 1723697 1723971 1723976) (-1025 "REP2.spad" 1713258 1713269 1723528 1723533) (-1024 "REP1.spad" 1707248 1707259 1713208 1713213) (-1023 "REGSET.spad" 1705045 1705062 1706894 1706921) (-1022 "REF.spad" 1704374 1704385 1705000 1705005) (-1021 "REDORDER.spad" 1703550 1703567 1704364 1704369) (-1020 "RECLOS.spad" 1702333 1702353 1703037 1703130) (-1019 "REALSOLV.spad" 1701465 1701474 1702323 1702328) (-1018 "REAL.spad" 1701337 1701346 1701455 1701460) (-1017 "REAL0Q.spad" 1698619 1698634 1701327 1701332) (-1016 "REAL0.spad" 1695447 1695462 1698609 1698614) (-1015 "RDUCEAST.spad" 1695168 1695177 1695437 1695442) (-1014 "RDIV.spad" 1694819 1694844 1695158 1695163) (-1013 "RDIST.spad" 1694382 1694393 1694809 1694814) (-1012 "RDETRS.spad" 1693178 1693196 1694372 1694377) (-1011 "RDETR.spad" 1691285 1691303 1693168 1693173) (-1010 "RDEEFS.spad" 1690358 1690375 1691275 1691280) (-1009 "RDEEF.spad" 1689354 1689371 1690348 1690353) (-1008 "RCFIELD.spad" 1686540 1686549 1689256 1689349) (-1007 "RCFIELD.spad" 1683812 1683823 1686530 1686535) (-1006 "RCAGG.spad" 1681724 1681735 1683802 1683807) (-1005 "RCAGG.spad" 1679563 1679576 1681643 1681648) (-1004 "RATRET.spad" 1678923 1678934 1679553 1679558) (-1003 "RATFACT.spad" 1678615 1678627 1678913 1678918) (-1002 "RANDSRC.spad" 1677934 1677943 1678605 1678610) (-1001 "RADUTIL.spad" 1677688 1677697 1677924 1677929) (-1000 "RADIX.spad" 1674589 1674603 1676155 1676248) (-999 "RADFF.spad" 1673003 1673039 1673121 1673277) (-998 "RADCAT.spad" 1672597 1672605 1672993 1672998) (-997 "RADCAT.spad" 1672189 1672199 1672587 1672592) (-996 "QUEUE.spad" 1671532 1671542 1671796 1671823) (-995 "QUAT.spad" 1670114 1670124 1670456 1670521) (-994 "QUATCT2.spad" 1669733 1669751 1670104 1670109) (-993 "QUATCAT.spad" 1667898 1667908 1669663 1669728) (-992 "QUATCAT.spad" 1665814 1665826 1667581 1667586) (-991 "QUAGG.spad" 1664640 1664650 1665782 1665809) (-990 "QQUTAST.spad" 1664409 1664417 1664630 1664635) (-989 "QFORM.spad" 1663872 1663886 1664399 1664404) (-988 "QFCAT.spad" 1662575 1662585 1663774 1663867) (-987 "QFCAT.spad" 1660869 1660881 1662070 1662075) (-986 "QFCAT2.spad" 1660560 1660576 1660859 1660864) (-985 "QEQUAT.spad" 1660117 1660125 1660550 1660555) (-984 "QCMPACK.spad" 1654864 1654883 1660107 1660112) (-983 "QALGSET.spad" 1650939 1650971 1654778 1654783) (-982 "QALGSET2.spad" 1648935 1648953 1650929 1650934) (-981 "PWFFINTB.spad" 1646245 1646266 1648925 1648930) (-980 "PUSHVAR.spad" 1645574 1645593 1646235 1646240) (-979 "PTRANFN.spad" 1641700 1641710 1645564 1645569) (-978 "PTPACK.spad" 1638788 1638798 1641690 1641695) (-977 "PTFUNC2.spad" 1638609 1638623 1638778 1638783) (-976 "PTCAT.spad" 1637858 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1554141 1554168) (-938 "PNTHEORY.spad" 1550720 1550728 1554044 1554049) (-937 "PMTOOLS.spad" 1549477 1549491 1550710 1550715) (-936 "PMSYM.spad" 1549022 1549032 1549467 1549472) (-935 "PMQFCAT.spad" 1548609 1548623 1549012 1549017) (-934 "PMPRED.spad" 1548078 1548092 1548599 1548604) (-933 "PMPREDFS.spad" 1547522 1547544 1548068 1548073) (-932 "PMPLCAT.spad" 1546592 1546610 1547454 1547459) (-931 "PMLSAGG.spad" 1546173 1546187 1546582 1546587) (-930 "PMKERNEL.spad" 1545740 1545752 1546163 1546168) (-929 "PMINS.spad" 1545316 1545326 1545730 1545735) (-928 "PMFS.spad" 1544889 1544907 1545306 1545311) (-927 "PMDOWN.spad" 1544175 1544189 1544879 1544884) (-926 "PMASS.spad" 1543183 1543191 1544165 1544170) (-925 "PMASSFS.spad" 1542148 1542164 1543173 1543178) (-924 "PLOTTOOL.spad" 1541928 1541936 1542138 1542143) (-923 "PLOT.spad" 1536759 1536767 1541918 1541923) (-922 "PLOT3D.spad" 1533179 1533187 1536749 1536754) (-921 "PLOT1.spad" 1532320 1532330 1533169 1533174) (-920 "PLEQN.spad" 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1489905 1489920) (-900 "PERMGRP.spad" 1480492 1480502 1485746 1485751) (-899 "PERMCAT.spad" 1479044 1479054 1480472 1480487) (-898 "PERMAN.spad" 1477576 1477590 1479034 1479039) (-897 "PENDTREE.spad" 1476915 1476925 1477205 1477210) (-896 "PDRING.spad" 1475406 1475416 1476895 1476910) (-895 "PDRING.spad" 1473905 1473917 1475396 1475401) (-894 "PDEPROB.spad" 1472920 1472928 1473895 1473900) (-893 "PDEPACK.spad" 1466922 1466930 1472910 1472915) (-892 "PDECOMP.spad" 1466384 1466401 1466912 1466917) (-891 "PDECAT.spad" 1464738 1464746 1466374 1466379) (-890 "PCOMP.spad" 1464589 1464602 1464728 1464733) (-889 "PBWLB.spad" 1463171 1463188 1464579 1464584) (-888 "PATTERN.spad" 1457602 1457612 1463161 1463166) (-887 "PATTERN2.spad" 1457338 1457350 1457592 1457597) (-886 "PATTERN1.spad" 1455640 1455656 1457328 1457333) (-885 "PATRES.spad" 1453187 1453199 1455630 1455635) (-884 "PATRES2.spad" 1452849 1452863 1453177 1453182) (-883 "PATMATCH.spad" 1451006 1451037 1452557 1452562) (-882 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1433492 1434784 1434789) (-863 "PADE.spad" 1432213 1432229 1433463 1433468) (-862 "OWP.spad" 1431453 1431483 1432071 1432138) (-861 "OVERSET.spad" 1431026 1431034 1431443 1431448) (-860 "OVAR.spad" 1430807 1430830 1431016 1431021) (-859 "OUT.spad" 1429891 1429899 1430797 1430802) (-858 "OUTFORM.spad" 1419187 1419195 1429881 1429886) (-857 "OUTBFILE.spad" 1418605 1418613 1419177 1419182) (-856 "OUTBCON.spad" 1417603 1417611 1418595 1418600) (-855 "OUTBCON.spad" 1416599 1416609 1417593 1417598) (-854 "OSI.spad" 1416074 1416082 1416589 1416594) (-853 "OSGROUP.spad" 1415992 1416000 1416064 1416069) (-852 "ORTHPOL.spad" 1414453 1414463 1415909 1415914) (-851 "OREUP.spad" 1413906 1413934 1414133 1414172) (-850 "ORESUP.spad" 1413205 1413229 1413586 1413625) (-849 "OREPCTO.spad" 1411024 1411036 1413125 1413130) (-848 "OREPCAT.spad" 1405081 1405091 1410980 1411019) (-847 "OREPCAT.spad" 1399028 1399040 1404929 1404934) (-846 "ORDSET.spad" 1398194 1398202 1399018 1399023) (-845 "ORDSET.spad" 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(-826 "OMSAGG.spad" 1376465 1376475 1376633 1376672) (-825 "OMPKG.spad" 1375077 1375085 1376455 1376460) (-824 "OM.spad" 1374042 1374050 1375067 1375072) (-823 "OMLO.spad" 1373467 1373479 1373928 1373967) (-822 "OMEXPR.spad" 1373301 1373311 1373457 1373462) (-821 "OMERR.spad" 1372844 1372852 1373291 1373296) (-820 "OMERRK.spad" 1371878 1371886 1372834 1372839) (-819 "OMENC.spad" 1371222 1371230 1371868 1371873) (-818 "OMDEV.spad" 1365511 1365519 1371212 1371217) (-817 "OMCONN.spad" 1364920 1364928 1365501 1365506) (-816 "OINTDOM.spad" 1364683 1364691 1364846 1364915) (-815 "OFMONOID.spad" 1360870 1360880 1364673 1364678) (-814 "ODVAR.spad" 1360131 1360141 1360860 1360865) (-813 "ODR.spad" 1359775 1359801 1359943 1360092) (-812 "ODPOL.spad" 1357157 1357167 1357497 1357624) (-811 "ODP.spad" 1347004 1347024 1347377 1347508) (-810 "ODETOOLS.spad" 1345587 1345606 1346994 1346999) (-809 "ODESYS.spad" 1343237 1343254 1345577 1345582) (-808 "ODERTRIC.spad" 1339178 1339195 1343194 1343199) (-807 "ODERED.spad" 1338565 1338589 1339168 1339173) (-806 "ODERAT.spad" 1336116 1336133 1338555 1338560) (-805 "ODEPRRIC.spad" 1333007 1333029 1336106 1336111) (-804 "ODEPROB.spad" 1332264 1332272 1332997 1333002) (-803 "ODEPRIM.spad" 1329538 1329560 1332254 1332259) (-802 "ODEPAL.spad" 1328914 1328938 1329528 1329533) (-801 "ODEPACK.spad" 1315516 1315524 1328904 1328909) (-800 "ODEINT.spad" 1314947 1314963 1315506 1315511) (-799 "ODEIFTBL.spad" 1312342 1312350 1314937 1314942) (-798 "ODEEF.spad" 1307709 1307725 1312332 1312337) (-797 "ODECONST.spad" 1307228 1307246 1307699 1307704) (-796 "ODECAT.spad" 1305824 1305832 1307218 1307223) (-795 "OCT.spad" 1303962 1303972 1304678 1304717) (-794 "OCTCT2.spad" 1303606 1303627 1303952 1303957) (-793 "OC.spad" 1301380 1301390 1303562 1303601) (-792 "OC.spad" 1298879 1298891 1301063 1301068) (-791 "OCAMON.spad" 1298727 1298735 1298869 1298874) (-790 "OASGP.spad" 1298542 1298550 1298717 1298722) (-789 "OAMONS.spad" 1298062 1298070 1298532 1298537) (-788 "OAMON.spad" 1297923 1297931 1298052 1298057) (-787 "OAGROUP.spad" 1297785 1297793 1297913 1297918) (-786 "NUMTUBE.spad" 1297372 1297388 1297775 1297780) (-785 "NUMQUAD.spad" 1285234 1285242 1297362 1297367) (-784 "NUMODE.spad" 1276370 1276378 1285224 1285229) (-783 "NUMINT.spad" 1273928 1273936 1276360 1276365) (-782 "NUMFMT.spad" 1272768 1272776 1273918 1273923) (-781 "NUMERIC.spad" 1264840 1264850 1272573 1272578) (-780 "NTSCAT.spad" 1263342 1263358 1264808 1264835) (-779 "NTPOLFN.spad" 1262887 1262897 1263259 1263264) (-778 "NSUP.spad" 1255933 1255943 1260473 1260626) (-777 "NSUP2.spad" 1255325 1255337 1255923 1255928) (-776 "NSMP.spad" 1251556 1251575 1251864 1251991) (-775 "NREP.spad" 1249928 1249942 1251546 1251551) (-774 "NPCOEF.spad" 1249174 1249194 1249918 1249923) (-773 "NORMRETR.spad" 1248772 1248811 1249164 1249169) (-772 "NORMPK.spad" 1246674 1246693 1248762 1248767) (-771 "NORMMA.spad" 1246362 1246388 1246664 1246669) (-770 "NONE.spad" 1246103 1246111 1246352 1246357) (-769 "NONE1.spad" 1245779 1245789 1246093 1246098) (-768 "NODE1.spad" 1245248 1245264 1245769 1245774) (-767 "NNI.spad" 1244135 1244143 1245222 1245243) (-766 "NLINSOL.spad" 1242757 1242767 1244125 1244130) (-765 "NIPROB.spad" 1241298 1241306 1242747 1242752) (-764 "NFINTBAS.spad" 1238758 1238775 1241288 1241293) (-763 "NETCLT.spad" 1238732 1238743 1238748 1238753) (-762 "NCODIV.spad" 1236930 1236946 1238722 1238727) (-761 "NCNTFRAC.spad" 1236572 1236586 1236920 1236925) (-760 "NCEP.spad" 1234732 1234746 1236562 1236567) (-759 "NASRING.spad" 1234328 1234336 1234722 1234727) (-758 "NASRING.spad" 1233922 1233932 1234318 1234323) (-757 "NARNG.spad" 1233266 1233274 1233912 1233917) (-756 "NARNG.spad" 1232608 1232618 1233256 1233261) (-755 "NAGSP.spad" 1231681 1231689 1232598 1232603) (-754 "NAGS.spad" 1221206 1221214 1231671 1231676) (-753 "NAGF07.spad" 1219599 1219607 1221196 1221201) (-752 "NAGF04.spad" 1213831 1213839 1219589 1219594) (-751 "NAGF02.spad" 1207640 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"FORMULA.spad" 645512 645520 648038 648043) (-393 "FORMULA1.spad" 644991 645001 645502 645507) (-392 "FORDER.spad" 644682 644706 644981 644986) (-391 "FOP.spad" 643883 643891 644672 644677) (-390 "FNLA.spad" 643307 643329 643851 643878) (-389 "FNCAT.spad" 641894 641902 643297 643302) (-388 "FNAME.spad" 641786 641794 641884 641889) (-387 "FMTC.spad" 641584 641592 641712 641781) (-386 "FMONOID.spad" 638639 638649 641540 641545) (-385 "FM.spad" 638334 638346 638573 638600) (-384 "FMFUN.spad" 635364 635372 638324 638329) (-383 "FMC.spad" 634416 634424 635354 635359) (-382 "FMCAT.spad" 632070 632088 634384 634411) (-381 "FM1.spad" 631427 631439 632004 632031) (-380 "FLOATRP.spad" 629148 629162 631417 631422) (-379 "FLOAT.spad" 622436 622444 629014 629143) (-378 "FLOATCP.spad" 619853 619867 622426 622431) (-377 "FLINEXP.spad" 619565 619575 619833 619848) (-376 "FLINEXP.spad" 619231 619243 619501 619506) (-375 "FLASORT.spad" 618551 618563 619221 619226) (-374 "FLALG.spad" 616197 616216 618477 618546) (-373 "FLAGG.spad" 613215 613225 616177 616192) (-372 "FLAGG.spad" 610134 610146 613098 613103) (-371 "FLAGG2.spad" 608815 608831 610124 610129) (-370 "FINRALG.spad" 606844 606857 608771 608810) (-369 "FINRALG.spad" 604799 604814 606728 606733) (-368 "FINITE.spad" 603951 603959 604789 604794) (-367 "FINAALG.spad" 592932 592942 603893 603946) (-366 "FINAALG.spad" 581925 581937 592888 592893) (-365 "FILE.spad" 581508 581518 581915 581920) (-364 "FILECAT.spad" 580026 580043 581498 581503) (-363 "FIELD.spad" 579432 579440 579928 580021) (-362 "FIELD.spad" 578924 578934 579422 579427) (-361 "FGROUP.spad" 577533 577543 578904 578919) (-360 "FGLMICPK.spad" 576320 576335 577523 577528) (-359 "FFX.spad" 575695 575710 576036 576129) (-358 "FFSLPE.spad" 575184 575205 575685 575690) (-357 "FFPOLY.spad" 566436 566447 575174 575179) (-356 "FFPOLY2.spad" 565496 565513 566426 566431) (-355 "FFP.spad" 564893 564913 565212 565305) (-354 "FF.spad" 564341 564357 564574 564667) (-353 "FFNBX.spad" 562853 562873 564057 564150) (-352 "FFNBP.spad" 561366 561383 562569 562662) (-351 "FFNB.spad" 559831 559852 561047 561140) (-350 "FFINTBAS.spad" 557245 557264 559821 559826) (-349 "FFIELDC.spad" 554820 554828 557147 557240) (-348 "FFIELDC.spad" 552481 552491 554810 554815) (-347 "FFHOM.spad" 551229 551246 552471 552476) (-346 "FFF.spad" 548664 548675 551219 551224) (-345 "FFCGX.spad" 547511 547531 548380 548473) (-344 "FFCGP.spad" 546400 546420 547227 547320) (-343 "FFCG.spad" 545192 545213 546081 546174) (-342 "FFCAT.spad" 538219 538241 545031 545187) (-341 "FFCAT.spad" 531325 531349 538139 538144) (-340 "FFCAT2.spad" 531070 531110 531315 531320) (-339 "FEXPR.spad" 522779 522825 530826 530865) (-338 "FEVALAB.spad" 522485 522495 522769 522774) (-337 "FEVALAB.spad" 521976 521988 522262 522267) (-336 "FDIV.spad" 521418 521442 521966 521971) (-335 "FDIVCAT.spad" 519460 519484 521408 521413) (-334 "FDIVCAT.spad" 517500 517526 519450 519455) (-333 "FDIV2.spad" 517154 517194 517490 517495) (-332 "FCPAK1.spad" 515707 515715 517144 517149) (-331 "FCOMP.spad" 515086 515096 515697 515702) (-330 "FC.spad" 505001 505009 515076 515081) (-329 "FAXF.spad" 497936 497950 504903 504996) (-328 "FAXF.spad" 490923 490939 497892 497897) (-327 "FARRAY.spad" 489069 489079 490106 490133) (-326 "FAMR.spad" 487189 487201 488967 489064) (-325 "FAMR.spad" 485293 485307 487073 487078) (-324 "FAMONOID.spad" 484943 484953 485247 485252) (-323 "FAMONC.spad" 483165 483177 484933 484938) (-322 "FAGROUP.spad" 482771 482781 483061 483088) (-321 "FACUTIL.spad" 480967 480984 482761 482766) (-320 "FACTFUNC.spad" 480143 480153 480957 480962) (-319 "EXPUPXS.spad" 476976 476999 478275 478424) (-318 "EXPRTUBE.spad" 474204 474212 476966 476971) (-317 "EXPRODE.spad" 471076 471092 474194 474199) (-316 "EXPR.spad" 466351 466361 467065 467472) (-315 "EXPR2UPS.spad" 462443 462456 466341 466346) (-314 "EXPR2.spad" 462146 462158 462433 462438) (-313 "EXPEXPAN.spad" 459084 459109 459718 459811) (-312 "EXIT.spad" 458755 458763 459074 459079) (-311 "EXITAST.spad" 458491 458499 458745 458750) (-310 "EVALCYC.spad" 457949 457963 458481 458486) (-309 "EVALAB.spad" 457513 457523 457939 457944) (-308 "EVALAB.spad" 457075 457087 457503 457508) (-307 "EUCDOM.spad" 454617 454625 457001 457070) (-306 "EUCDOM.spad" 452221 452231 454607 454612) (-305 "ESTOOLS.spad" 444061 444069 452211 452216) (-304 "ESTOOLS2.spad" 443662 443676 444051 444056) (-303 "ESTOOLS1.spad" 443347 443358 443652 443657) (-302 "ES.spad" 435894 435902 443337 443342) (-301 "ES.spad" 428347 428357 435792 435797) (-300 "ESCONT.spad" 425120 425128 428337 428342) (-299 "ESCONT1.spad" 424869 424881 425110 425115) (-298 "ES2.spad" 424364 424380 424859 424864) (-297 "ES1.spad" 423930 423946 424354 424359) (-296 "ERROR.spad" 421251 421259 423920 423925) (-295 "EQTBL.spad" 419723 419745 419932 419959) (-294 "EQ.spad" 414597 414607 417396 417508) (-293 "EQ2.spad" 414313 414325 414587 414592) (-292 "EP.spad" 410627 410637 414303 414308) (-291 "ENV.spad" 409279 409287 410617 410622) (-290 "ENTIRER.spad" 408947 408955 409223 409274) (-289 "EMR.spad" 408148 408189 408873 408942) (-288 "ELTAGG.spad" 406388 406407 408138 408143) (-287 "ELTAGG.spad" 404592 404613 406344 406349) (-286 "ELTAB.spad" 404039 404057 404582 404587) (-285 "ELFUTS.spad" 403418 403437 404029 404034) (-284 "ELEMFUN.spad" 403107 403115 403408 403413) (-283 "ELEMFUN.spad" 402794 402804 403097 403102) (-282 "ELAGG.spad" 400737 400747 402774 402789) (-281 "ELAGG.spad" 398617 398629 400656 400661) (-280 "ELABEXPR.spad" 397540 397548 398607 398612) (-279 "EFUPXS.spad" 394316 394346 397496 397501) (-278 "EFULS.spad" 391152 391175 394272 394277) (-277 "EFSTRUC.spad" 389107 389123 391142 391147) (-276 "EF.spad" 383873 383889 389097 389102) (-275 "EAB.spad" 382149 382157 383863 383868) (-274 "E04UCFA.spad" 381685 381693 382139 382144) (-273 "E04NAFA.spad" 381262 381270 381675 381680) (-272 "E04MBFA.spad" 380842 380850 381252 381257) (-271 "E04JAFA.spad" 380378 380386 380832 380837) (-270 "E04GCFA.spad" 379914 379922 380368 380373) (-269 "E04FDFA.spad" 379450 379458 379904 379909) (-268 "E04DGFA.spad" 378986 378994 379440 379445) (-267 "E04AGNT.spad" 374828 374836 378976 378981) (-266 "DVARCAT.spad" 371513 371523 374818 374823) (-265 "DVARCAT.spad" 368196 368208 371503 371508) (-264 "DSMP.spad" 365663 365677 365968 366095) (-263 "DROPT.spad" 359608 359616 365653 365658) (-262 "DROPT1.spad" 359271 359281 359598 359603) (-261 "DROPT0.spad" 354098 354106 359261 359266) (-260 "DRAWPT.spad" 352253 352261 354088 354093) (-259 "DRAW.spad" 344853 344866 352243 352248) (-258 "DRAWHACK.spad" 344161 344171 344843 344848) (-257 "DRAWCX.spad" 341603 341611 344151 344156) (-256 "DRAWCURV.spad" 341140 341155 341593 341598) (-255 "DRAWCFUN.spad" 330312 330320 341130 341135) (-254 "DQAGG.spad" 328480 328490 330280 330307) (-253 "DPOLCAT.spad" 323821 323837 328348 328475) (-252 "DPOLCAT.spad" 319248 319266 323777 323782) (-251 "DPMO.spad" 311474 311490 311612 311913) (-250 "DPMM.spad" 303713 303731 303838 304139) (-249 "DOMCTOR.spad" 303605 303613 303703 303708) (-248 "DOMAIN.spad" 302736 302744 303595 303600) (-247 "DMP.spad" 299994 300009 300566 300693) (-246 "DLP.spad" 299342 299352 299984 299989) (-245 "DLIST.spad" 297921 297931 298525 298552) (-244 "DLAGG.spad" 296332 296342 297911 297916) (-243 "DIVRING.spad" 295874 295882 296276 296327) (-242 "DIVRING.spad" 295460 295470 295864 295869) (-241 "DISPLAY.spad" 293640 293648 295450 295455) (-240 "DIRPROD.spad" 283220 283236 283860 283991) (-239 "DIRPROD2.spad" 282028 282046 283210 283215) (-238 "DIRPCAT.spad" 280970 280986 281892 282023) (-237 "DIRPCAT.spad" 279641 279659 280565 280570) (-236 "DIOSP.spad" 278466 278474 279631 279636) (-235 "DIOPS.spad" 277450 277460 278446 278461) (-234 "DIOPS.spad" 276408 276420 277406 277411) (-233 "DIFRING.spad" 275700 275708 276388 276403) (-232 "DIFRING.spad" 275000 275010 275690 275695) (-231 "DIFEXT.spad" 274159 274169 274980 274995) (-230 "DIFEXT.spad" 273235 273247 274058 274063) (-229 "DIAGG.spad" 272865 272875 273215 273230) (-228 "DIAGG.spad" 272503 272515 272855 272860) (-227 "DHMATRIX.spad" 270807 270817 271960 271987) (-226 "DFSFUN.spad" 264215 264223 270797 270802) (-225 "DFLOAT.spad" 260936 260944 264105 264210) (-224 "DFINTTLS.spad" 259145 259161 260926 260931) (-223 "DERHAM.spad" 257055 257087 259125 259140) (-222 "DEQUEUE.spad" 256373 256383 256662 256689) (-221 "DEGRED.spad" 255988 256002 256363 256368) (-220 "DEFINTRF.spad" 253513 253523 255978 255983) (-219 "DEFINTEF.spad" 252009 252025 253503 253508) (-218 "DEFAST.spad" 251377 251385 251999 252004) (-217 "DECIMAL.spad" 249483 249491 249844 249937) (-216 "DDFACT.spad" 247282 247299 249473 249478) (-215 "DBLRESP.spad" 246880 246904 247272 247277) (-214 "DBASE.spad" 245534 245544 246870 246875) (-213 "DATAARY.spad" 244996 245009 245524 245529) (-212 "D03FAFA.spad" 244824 244832 244986 244991) (-211 "D03EEFA.spad" 244644 244652 244814 244819) (-210 "D03AGNT.spad" 243724 243732 244634 244639) (-209 "D02EJFA.spad" 243186 243194 243714 243719) (-208 "D02CJFA.spad" 242664 242672 243176 243181) (-207 "D02BHFA.spad" 242154 242162 242654 242659) (-206 "D02BBFA.spad" 241644 241652 242144 242149) (-205 "D02AGNT.spad" 236448 236456 241634 241639) (-204 "D01WGTS.spad" 234767 234775 236438 236443) (-203 "D01TRNS.spad" 234744 234752 234757 234762) (-202 "D01GBFA.spad" 234266 234274 234734 234739) (-201 "D01FCFA.spad" 233788 233796 234256 234261) (-200 "D01ASFA.spad" 233256 233264 233778 233783) (-199 "D01AQFA.spad" 232702 232710 233246 233251) (-198 "D01APFA.spad" 232126 232134 232692 232697) (-197 "D01ANFA.spad" 231620 231628 232116 232121) (-196 "D01AMFA.spad" 231130 231138 231610 231615) (-195 "D01ALFA.spad" 230670 230678 231120 231125) (-194 "D01AKFA.spad" 230196 230204 230660 230665) (-193 "D01AJFA.spad" 229719 229727 230186 230191) (-192 "D01AGNT.spad" 225778 225786 229709 229714) (-191 "CYCLOTOM.spad" 225284 225292 225768 225773) (-190 "CYCLES.spad" 222116 222124 225274 225279) (-189 "CVMP.spad" 221533 221543 222106 222111) (-188 "CTRIGMNP.spad" 220023 220039 221523 221528) (-187 "CTOR.spad" 219714 219722 220013 220018) (-186 "CTORKIND.spad" 219317 219325 219704 219709) (-185 "CTORCAT.spad" 218566 218574 219307 219312) (-184 "CTORCAT.spad" 217813 217823 218556 218561) (-183 "CTORCALL.spad" 217393 217401 217803 217808) (-182 "CSTTOOLS.spad" 216636 216649 217383 217388) (-181 "CRFP.spad" 210340 210353 216626 216631) (-180 "CRCEAST.spad" 210060 210068 210330 210335) (-179 "CRAPACK.spad" 209103 209113 210050 210055) (-178 "CPMATCH.spad" 208603 208618 209028 209033) (-177 "CPIMA.spad" 208308 208327 208593 208598) (-176 "COORDSYS.spad" 203201 203211 208298 208303) (-175 "CONTOUR.spad" 202608 202616 203191 203196) (-174 "CONTFRAC.spad" 198220 198230 202510 202603) (-173 "CONDUIT.spad" 197978 197986 198210 198215) (-172 "COMRING.spad" 197652 197660 197916 197973) (-171 "COMPPROP.spad" 197166 197174 197642 197647) (-170 "COMPLPAT.spad" 196933 196948 197156 197161) (-169 "COMPLEX.spad" 191071 191081 191315 191576) (-168 "COMPLEX2.spad" 190784 190796 191061 191066) (-167 "COMPFACT.spad" 190386 190400 190774 190779) (-166 "COMPCAT.spad" 188454 188464 190120 190381) (-165 "COMPCAT.spad" 186251 186263 187919 187924) (-164 "COMMUPC.spad" 185997 186015 186241 186246) (-163 "COMMONOP.spad" 185530 185538 185987 185992) (-162 "COMM.spad" 185339 185347 185520 185525) (-161 "COMMAAST.spad" 185102 185110 185329 185334) (-160 "COMBOPC.spad" 184007 184015 185092 185097) (-159 "COMBINAT.spad" 182752 182762 183997 184002) (-158 "COMBF.spad" 180120 180136 182742 182747) (-157 "COLOR.spad" 178957 178965 180110 180115) (-156 "COLONAST.spad" 178623 178631 178947 178952) (-155 "CMPLXRT.spad" 178332 178349 178613 178618) (-154 "CLLCTAST.spad" 177994 178002 178322 178327) (-153 "CLIP.spad" 174086 174094 177984 177989) (-152 "CLIF.spad" 172725 172741 174042 174081) (-151 "CLAGG.spad" 169210 169220 172715 172720) (-150 "CLAGG.spad" 165566 165578 169073 169078) (-149 "CINTSLPE.spad" 164891 164904 165556 165561) (-148 "CHVAR.spad" 162969 162991 164881 164886) (-147 "CHARZ.spad" 162884 162892 162949 162964) (-146 "CHARPOL.spad" 162392 162402 162874 162879) (-145 "CHARNZ.spad" 162145 162153 162372 162387) (-144 "CHAR.spad" 160013 160021 162135 162140) (-143 "CFCAT.spad" 159329 159337 160003 160008) (-142 "CDEN.spad" 158487 158501 159319 159324) (-141 "CCLASS.spad" 156636 156644 157898 157937) (-140 "CATEGORY.spad" 155726 155734 156626 156631) (-139 "CATCTOR.spad" 155617 155625 155716 155721) (-138 "CATAST.spad" 155235 155243 155607 155612) (-137 "CASEAST.spad" 154949 154957 155225 155230) (-136 "CARTEN.spad" 150052 150076 154939 154944) (-135 "CARTEN2.spad" 149438 149465 150042 150047) (-134 "CARD.spad" 146727 146735 149412 149433) (-133 "CAPSLAST.spad" 146501 146509 146717 146722) (-132 "CACHSET.spad" 146123 146131 146491 146496) (-131 "CABMON.spad" 145676 145684 146113 146118) (-130 "BYTEORD.spad" 145351 145359 145666 145671) (-129 "BYTE.spad" 144776 144784 145341 145346) (-128 "BYTEBUF.spad" 142633 142641 143945 143972) (-127 "BTREE.spad" 141702 141712 142240 142267) (-126 "BTOURN.spad" 140705 140715 141309 141336) (-125 "BTCAT.spad" 140093 140103 140673 140700) (-124 "BTCAT.spad" 139501 139513 140083 140088) (-123 "BTAGG.spad" 138623 138631 139469 139496) (-122 "BTAGG.spad" 137765 137775 138613 138618) (-121 "BSTREE.spad" 136500 136510 137372 137399) (-120 "BRILL.spad" 134695 134706 136490 136495) (-119 "BRAGG.spad" 133619 133629 134685 134690) (-118 "BRAGG.spad" 132507 132519 133575 133580) (-117 "BPADICRT.spad" 130488 130500 130743 130836) (-116 "BPADIC.spad" 130152 130164 130414 130483) (-115 "BOUNDZRO.spad" 129808 129825 130142 130147) (-114 "BOP.spad" 124826 124834 129798 129803) (-113 "BOP1.spad" 122246 122256 124816 124821) (-112 "BOOLEAN.spad" 121678 121686 122236 122241) (-111 "BMODULE.spad" 121390 121402 121646 121673) (-110 "BITS.spad" 120809 120817 121026 121053) (-109 "BINDING.spad" 120220 120228 120799 120804) (-108 "BINARY.spad" 118331 118339 118687 118780) (-107 "BGAGG.spad" 117528 117538 118311 118326) (-106 "BGAGG.spad" 116733 116745 117518 117523) (-105 "BFUNCT.spad" 116297 116305 116713 116728) (-104 "BEZOUT.spad" 115431 115458 116247 116252) (-103 "BBTREE.spad" 112250 112260 115038 115065) (-102 "BASTYPE.spad" 111922 111930 112240 112245) (-101 "BASTYPE.spad" 111592 111602 111912 111917) (-100 "BALFACT.spad" 111031 111044 111582 111587) (-99 "AUTOMOR.spad" 110478 110487 111011 111026) (-98 "ATTREG.spad" 107197 107204 110230 110473) (-97 "ATTRBUT.spad" 103220 103227 107177 107192) (-96 "ATTRAST.spad" 102937 102944 103210 103215) (-95 "ATRIG.spad" 102407 102414 102927 102932) (-94 "ATRIG.spad" 101875 101884 102397 102402) (-93 "ASTCAT.spad" 101779 101786 101865 101870) (-92 "ASTCAT.spad" 101681 101690 101769 101774) (-91 "ASTACK.spad" 101014 101023 101288 101315) (-90 "ASSOCEQ.spad" 99814 99825 100970 100975) (-89 "ASP9.spad" 98895 98908 99804 99809) (-88 "ASP8.spad" 97938 97951 98885 98890) (-87 "ASP80.spad" 97260 97273 97928 97933) (-86 "ASP7.spad" 96420 96433 97250 97255) (-85 "ASP78.spad" 95871 95884 96410 96415) (-84 "ASP77.spad" 95240 95253 95861 95866) (-83 "ASP74.spad" 94332 94345 95230 95235) (-82 "ASP73.spad" 93603 93616 94322 94327) (-81 "ASP6.spad" 92470 92483 93593 93598) (-80 "ASP55.spad" 90979 90992 92460 92465) (-79 "ASP50.spad" 88796 88809 90969 90974) (-78 "ASP4.spad" 88091 88104 88786 88791) (-77 "ASP49.spad" 87090 87103 88081 88086) (-76 "ASP42.spad" 85497 85536 87080 87085) (-75 "ASP41.spad" 84076 84115 85487 85492) (-74 "ASP35.spad" 83064 83077 84066 84071) (-73 "ASP34.spad" 82365 82378 83054 83059) (-72 "ASP33.spad" 81925 81938 82355 82360) (-71 "ASP31.spad" 81065 81078 81915 81920) (-70 "ASP30.spad" 79957 79970 81055 81060) (-69 "ASP29.spad" 79423 79436 79947 79952) (-68 "ASP28.spad" 70696 70709 79413 79418) (-67 "ASP27.spad" 69593 69606 70686 70691) (-66 "ASP24.spad" 68680 68693 69583 69588) (-65 "ASP20.spad" 68144 68157 68670 68675) (-64 "ASP1.spad" 67525 67538 68134 68139) (-63 "ASP19.spad" 62211 62224 67515 67520) (-62 "ASP12.spad" 61625 61638 62201 62206) (-61 "ASP10.spad" 60896 60909 61615 61620) (-60 "ARRAY2.spad" 60256 60265 60503 60530) (-59 "ARRAY1.spad" 59091 59100 59439 59466) (-58 "ARRAY12.spad" 57760 57771 59081 59086) (-57 "ARR2CAT.spad" 53422 53443 57728 57755) (-56 "ARR2CAT.spad" 49104 49127 53412 53417) (-55 "ARITY.spad" 48476 48483 49094 49099) (-54 "APPRULE.spad" 47720 47742 48466 48471) (-53 "APPLYORE.spad" 47335 47348 47710 47715) (-52 "ANY.spad" 45677 45684 47325 47330) (-51 "ANY1.spad" 44748 44757 45667 45672) (-50 "ANTISYM.spad" 43187 43203 44728 44743) (-49 "ANON.spad" 42880 42887 43177 43182) (-48 "AN.spad" 41181 41188 42696 42789) (-47 "AMR.spad" 39360 39371 41079 41176) (-46 "AMR.spad" 37376 37389 39097 39102) (-45 "ALIST.spad" 34788 34809 35138 35165) (-44 "ALGSC.spad" 33911 33937 34660 34713) (-43 "ALGPKG.spad" 29620 29631 33867 33872) (-42 "ALGMFACT.spad" 28809 28823 29610 29615) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index b70e36df..a139019c 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,6 +1,6 @@ -(161804 . 3452261764) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(161804 . 3452516859) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) ((((-564)) . T) (($) -2733 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-564)) . T)) @@ -48,12 +48,12 @@ (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) (-2733 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (-2733 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(((|#2| (-482 (-2069 |#1|) (-767))) . T)) +(((|#2| (-482 (-2155 |#1|) (-767))) . T)) (((|#1| (-531 (-1170))) . T)) (((#0=(-866 |#1|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-1152)) . T) (((-954 (-129))) . T) (((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (|has| |#4| (-368)) (|has| |#3| (-368)) (((|#1|) . T)) @@ -70,7 +70,7 @@ ((((-564)) . T) (((-407 (-564))) -2733 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1034 (-407 (-564))))) ((|#2|) . T) (($) -2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) (-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) -((((-2 (|:| -2014 |#1|) (|:| -2531 |#2|))) . T)) +((((-2 (|:| -2068 |#1|) (|:| -2005 |#2|))) . T)) ((($) . T)) ((((-564)) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T) (($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1170)) . T)) ((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) @@ -114,7 +114,7 @@ (|has| |#1| (-368)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) (((|#1| |#2|) . T)) @@ -238,8 +238,8 @@ (((|#1|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (|has| |#1| (-556)) ((((-564)) -2733 (|has| |#4| (-172)) (|has| |#4| (-844)) (-12 (|has| |#4| (-1034 (-564))) (|has| |#4| (-1094))) (|has| |#4| (-1045))) ((|#4|) -2733 (|has| |#4| (-172)) (|has| |#4| (-1094))) (((-407 (-564))) -12 (|has| |#4| (-1034 (-407 (-564)))) (|has| |#4| (-1094)))) ((((-564)) -2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (-12 (|has| |#3| (-1034 (-564))) (|has| |#3| (-1094))) (|has| |#3| (-1045))) ((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-1094))) (((-407 (-564))) -12 (|has| |#3| (-1034 (-407 (-564)))) (|has| |#3| (-1094)))) @@ -266,11 +266,11 @@ ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) ((((-858)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2014 |#1|) (|:| -2531 |#2|))) . T) (((-858)) . T)) +((((-2 (|:| -2068 |#1|) (|:| -2005 |#2|))) . T) (((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564))))) (((|#4|) -2733 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1045))) (($) |has| |#4| (-172))) (((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045))) (($) |has| |#3| (-172))) -((((-2 (|:| -2014 |#1|) (|:| -2531 |#2|))) . T)) +((((-2 (|:| -2068 |#1|) (|:| -2005 |#2|))) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) @@ -278,7 +278,7 @@ (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) ((((-407 $) (-407 $)) |has| |#2| (-556)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-905)) ((((-1152) (-52)) . T)) @@ -314,7 +314,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1145)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -332,10 +332,10 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1045))) ((((-858)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (((|#1|) . T)) -((((-1259 (-339 (-2336) (-2336 (QUOTE X)) (-695)))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((#0=(-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) #0#) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))))) +((((-1259 (-339 (-2415) (-2415 (QUOTE X)) (-695)))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((#0=(-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) #0#) |has| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (-309 (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))))) ((((-858)) . T)) ((((-564) |#1|) . T)) ((((-536)) -12 (|has| |#1| (-612 (-536))) (|has| |#2| (-612 (-536)))) (((-888 (-379))) -12 (|has| |#1| (-612 (-888 (-379)))) (|has| |#2| (-612 (-888 (-379))))) (((-888 (-564))) -12 (|has| |#1| (-612 (-888 (-564)))) (|has| |#2| (-612 (-888 (-564)))))) @@ -431,11 +431,11 @@ ((((-144)) . T)) (((|#3|) |has| |#3| (-1094)) (((-564)) -12 (|has| |#3| (-1034 (-564))) (|has| |#3| (-1094))) (((-407 (-564))) -12 (|has| |#3| (-1034 (-407 (-564)))) (|has| |#3| (-1094)))) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1|) . T)) ((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) (|has| |#1| (-363)) ((((-1175)) . T)) (-2733 (|has| |#1| (-21)) (|has| |#1| (-844))) @@ -445,13 +445,13 @@ (|has| |#1| (-844)) (-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-536)) |has| |#1| (-612 (-536)))) (((|#1| |#2|) . T)) ((((-1170)) -12 (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))))) ((((-1152) |#1|) . T)) (((|#1| |#2| |#3| (-531 |#3|)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) @@ -655,7 +655,7 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (((|#2|) . T) (((-564)) |has| |#2| (-1034 (-564))) (((-407 (-564))) |has| |#2| (-1034 (-407 (-564))))) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((($) . T)) @@ -663,7 +663,7 @@ (((|#2|) . T)) (((|#3|) . T)) (-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (((|#2|) . T)) ((((-858)) -2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (((-564)) . T) (($) . T)) @@ -742,9 +742,9 @@ (-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-564) |#2|) . T)) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((($) -2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) ((((-564) |#1|) . T)) @@ -759,11 +759,11 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-858)) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-388) (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) (-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) @@ -959,7 +959,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-844)) -(((|#2| (-240 (-2069 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-240 (-2155 |#1|) (-767)) (-860 |#1|)) . T)) (|has| |#3| (-844)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -980,7 +980,7 @@ (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1045))) -(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (-2733 (|has| |#3| (-789)) (|has| |#3| (-844))) (-2733 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) @@ -1011,10 +1011,10 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-564)) -2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1045))) ((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094)))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) @@ -1023,8 +1023,8 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) |has| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (-309 (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))))) ((((-858)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1037,7 +1037,7 @@ (|has| |#1| (-1094)) (((|#2| |#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) (((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)))) -((((-564) (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T) ((|#1| |#2|) . T)) (((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) ((((-1175)) . T)) ((((-767)) . T)) @@ -1070,7 +1070,7 @@ (-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (-12 (|has| |#3| (-233)) (|has| |#3| (-1045))) (|has| |#2| (-1145)) -(((#0=(-52)) . T) (((-2 (|:| -3026 (-1170)) (|:| -3683 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1922 (-1170)) (|:| -3736 #0#))) . T)) (((|#1| |#2|) . T)) (-2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) (((|#1| (-564) (-1076)) . T)) @@ -1097,7 +1097,7 @@ ((((-564)) -2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (-12 (|has| |#3| (-1034 (-564))) (|has| |#3| (-1094))) (|has| |#3| (-1045))) ((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-1094))) (((-407 (-564))) -12 (|has| |#3| (-1034 (-407 (-564)))) (|has| |#3| (-1094)))) (((|#1|) . T)) (((|#4|) . T) (((-858)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (|has| |#1| (-556)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) @@ -1157,7 +1157,7 @@ (-12 (|has| |#1| (-789)) (|has| |#2| (-789))) (-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1187,7 +1187,7 @@ ((($) . T) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) (-2733 (|has| |#1| (-172)) (|has| |#1| (-556))) ((($) . T)) -(((#0=(-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) #0#) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) +(((#0=(-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) #0#) |has| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (-309 (-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))))) ((($) . T)) (((|#2|) |has| |#2| (-1094))) ((((-858)) -2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) @@ -1196,10 +1196,10 @@ ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-858)) . T)) ((((-906 |#1|)) . T)) (|has| |#1| (-363)) @@ -1226,7 +1226,7 @@ ((((-858)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) @@ -1240,7 +1240,7 @@ (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564))))) ((((-858)) . T)) -(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-506)) . T)) (|has| |#2| (-844)) ((((-506)) . T)) @@ -1269,7 +1269,7 @@ (((|#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-896 (-1170)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) @@ -1280,7 +1280,7 @@ (((|#2|) . T) (((-564)) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T) ((|#2|) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-1152) (-1170) (-564) (-225) (-858)) . T)) @@ -1369,7 +1369,7 @@ ((((-995 |#1|)) . T) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1377,7 +1377,7 @@ (|has| |#1| (-846)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) ((((-564) |#2|) . T)) ((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#2|) . T)) @@ -1392,7 +1392,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1427,7 +1427,7 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +(((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-846)) (((|#2| (-767) (-1076)) . T)) @@ -1471,7 +1471,7 @@ ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) -2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3026 (-1152)) (|:| -3683 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1922 (-1152)) (|:| -3736 #0#))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1500,7 +1500,7 @@ ((((-858)) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2069 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-482 (-2155 |#1|) (-767)) (-860 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1520,11 +1520,11 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) @@ -1570,11 +1570,11 @@ (|has| |#1| (-38 (-407 (-564)))) (-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-1170)) |has| |#1| (-896 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((#0=(-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) #0#) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))))) +(((#0=(-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) #0#) |has| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (-309 (-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-858)) . T) (((-1175)) . T)) @@ -1620,7 +1620,7 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((#0=(-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) #0#) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))))) +(((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((#0=(-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) #0#) |has| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (-309 (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))))) (-2733 (|has| |#2| (-452)) (|has| |#2| (-905))) (-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#1|) . T) (($) . T)) @@ -1645,7 +1645,7 @@ ((((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1713,7 +1713,7 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) @@ -1742,7 +1742,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-767)) . T)) (((|#1|) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1781,7 +1781,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1800,7 +1800,7 @@ (|has| |#1| (-844)) (((|#1| (-564) (-1076)) . T)) (-2733 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (|has| |#1| (-846)) @@ -1818,11 +1818,11 @@ (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) (-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) -((((-685 (-339 (-2336) (-2336 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +((((-685 (-339 (-2415) (-2415 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) ((((-858)) . T)) (|has| |#3| (-844)) ((((-858)) . T)) @@ -1836,9 +1836,9 @@ (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-846)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) |has| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (-309 (-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))))) (-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-858)) . T)) @@ -1888,7 +1888,7 @@ ((((-641 |#1|)) . T)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-1045))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1937,14 +1937,14 @@ ((((-112)) |has| |#1| (-1094)) (((-858)) -2733 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))) . T)) ((((-858)) . T)) ((((-564) |#1|) . T)) ((((-858)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) @@ -1961,7 +1961,7 @@ (|has| |#1| (-363)) ((((-1170)) |has| |#2| (-896 (-1170)))) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) @@ -1989,11 +1989,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-846)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2011,7 +2011,7 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#1| (-1018))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) (-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) @@ -2071,7 +2071,7 @@ ((((-948 |#1|)) . T) (((-858)) . T)) (((|#3|) . T)) (((|#1| |#1|) . T) (($ $) -2733 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) ((((-948 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) @@ -2111,7 +2111,7 @@ ((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))))) +((((-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))) |has| (-2 (|:| -1922 (-1152)) (|:| -3736 (-52))) (-309 (-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-844)) (|has| |#1| (-38 (-407 (-564)))) @@ -2154,10 +2154,10 @@ ((($) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-858)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) |has| (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|)) (-309 (-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (((|#1|) . T)) @@ -2198,7 +2198,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) (((|#1|) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) @@ -2226,7 +2226,7 @@ (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1|) . T)) (-2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((((-581 |#1|)) . T)) @@ -2344,14 +2344,14 @@ (|has| |#2| (-905)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) @@ -2373,7 +2373,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-187)) . T) (((-858)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2386,7 +2386,7 @@ ((((-858)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (|has| |#1| (-846)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2443,8 +2443,8 @@ (-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3026 (-1170)) (|:| -3683 #0#))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1922 (-1170)) (|:| -3736 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-858)) . T)) @@ -2521,7 +2521,7 @@ (|has| |#2| (-1018)) ((($) . T)) (|has| |#1| (-905)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2542,12 +2542,12 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-767) |#1|) . T)) -(((|#2| (-240 (-2069 |#1|) (-767))) . T)) +(((|#2| (-240 (-2155 |#1|) (-767))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) (-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-1152)) . T) (((-858)) . T)) -(((#0=(-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) #0#) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) +(((#0=(-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) #0#) |has| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (-309 (-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-905)) (|has| |#2| (-363)) @@ -2583,7 +2583,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2623,9 +2623,9 @@ (((|#2|) . T)) (((|#2|) . T)) (-2733 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -2748,7 +2748,7 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -2806,7 +2806,7 @@ ((($) -2733 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) (((|#1|) . T)) -((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -1922 (-1152)) (|:| -3736 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2923,7 +2923,7 @@ (((|#1|) . T)) ((((-858)) . T)) (|has| |#2| (-905)) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) ((((-858)) . T)) ((((-858)) . T)) @@ -2964,7 +2964,7 @@ ((((-407 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2069 |#1|) (-767))) . T)) +(((|#2| (-482 (-2155 |#1|) (-767))) . T)) ((((-564) |#1|) . T)) ((((-1152)) . T) (((-858)) . T)) (((|#2| |#2|) . T)) @@ -3020,7 +3020,7 @@ (((|#1|) . T)) (|has| |#1| (-233)) (((|#1| (-531 |#3|)) . T)) -(((|#2| (-240 (-2069 |#1|) (-767))) . T)) +(((|#2| (-240 (-2155 |#1|) (-767))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) @@ -3106,7 +3106,7 @@ ((((-1208)) . T) (((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) |has| (-2 (|:| -1922 (-1170)) (|:| -3736 (-52))) (-309 (-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))))) (-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((((-564) |#1|) . T)) ((((-564) |#1|) . T)) @@ -3298,7 +3298,7 @@ (-2733 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (-2733 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) @@ -3398,11 +3398,11 @@ ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-1134 |#1| |#2|)) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1018)) -(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) ((((-858)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#2| (-1018))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3456,7 +3456,7 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +((((-2 (|:| -1922 (-1170)) (|:| -3736 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3492,7 +3492,7 @@ (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -1922 |#1|) (|:| -3736 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3520,7 +3520,7 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1134 |#1| |#2|) #0#) |has| (-1134 |#1| |#2|) (-309 (-1134 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) #0#) |has| (-2 (|:| -1922 |#1|) (|:| -3736 |#2|)) (-309 (-2 (|:| -1922 |#1|) (|:| -3736 |#2|))))) (((#0=(-116 |#1|)) |has| #0# (-309 #0#))) ((($ $) . T)) (-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index e6db4ef2..f83f68fb 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3452261756) +(30 . 3452516853) (4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,661 +477,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |completeEval| |popFortranOutputStack| |sinh| - |conjugate| |whitePoint| |reduce| |s13aaf| |collectUnder| - |UnVectorise| |mainVariable?| |singleFactorBound| - |stoseInvertible?reg| |ncols| |tanintegrate| |cosh| |outputAsFortran| - |extractSplittingLeaf| |setTex!| |indiceSubResultant| |modTree| - |prepareDecompose| |unmakeSUP| |partialNumerators| - |certainlySubVariety?| |cscIfCan| |tanh| |bezoutDiscriminant| |gethi| - |pastel| |whileLoop| |minimalPolynomial| - |rewriteIdealWithHeadRemainder| |basisOfLeftAnnihilator| - |complexNormalize| |problemPoints| |coth| |integral?| - |OMencodingBinary| |deepCopy| |toScale| |characteristicPolynomial| - |shade| |printStats!| |euclideanGroebner| |symbolTable| |datalist| - |cAcsch| |sech| |label| |iidprod| |leftTrace| |generalizedEigenvector| - |setStatus| |iicosh| |regime| |cSec| |constantCoefficientRicDE| - |trivialIdeal?| |csch| |meshFun2Var| |froot| |zeroMatrix| - |clipWithRanges| |tail| |associatedSystem| |iicoth| |se2rfi| |bounds| - |minGbasis| |asinh| |host| |polyRDE| |validExponential| |subMatrix| - |Is| |subPolSet?| |createNormalElement| |rowEchelonLocal| |outputList| - |lowerCase| |acosh| |rules| |inrootof| |computeBasis| |totalfract| - |asinhIfCan| |clip| |imagK| |cPower| |sinhcosh| |hdmpToDmp| |leftOne| - |atanh| |equality| |toseSquareFreePart| |quartic| |unknown| |point| - |internalInfRittWu?| |idealiserMatrix| |currentCategoryFrame| - |directSum| |latex| |d01asf| |bfEntry| |shallowExpand| |acoth| - |previous| |hermiteH| |leader| |trueEqual| |startTableGcd!| - |reducedForm| |imagk| |horizConcat| |hasHi| |pascalTriangle| |asech| - |build| |contains?| |quasiComponent| |constructor| |complex?| - |completeHermite| |fmecg| |permutation| |reverseLex| |byte| |f02adf| - |subtractIfCan| |createThreeSpace| |pushuconst| |series| - |normalElement| |OMreadStr| |groebner?| |gcdPrimitive| |universe| - |option| |normInvertible?| |multiple| |splitSquarefree| |OMputEndBVar| - |makeSeries| |internalIntegrate| |subNode?| |reduced?| ** - |multinomial| |UpTriBddDenomInv| |edf2efi| |applyQuote| |f04atf| - |fortranReal| |nthExpon| |listOfMonoms| |df2st| |complexZeros| - |UP2ifCan| |makeSin| |zeroDim?| |coercePreimagesImages| |presub| - |expt| |int| |normDeriv2| |selectIntegrationRoutines| - |LagrangeInterpolation| |linearAssociatedExp| |simplifyExp| |ldf2lst| - |OMgetSymbol| |numFunEvals3D| |cyclicSubmodule| |e04dgf| |infinite?| - |rewriteSetByReducingWithParticularGenerators| |min| |splitNodeOf!| - |csch2sinh| |f02agf| |trim| |commutator| |resetAttributeButtons| - |escape| |drawCurves| |lastSubResultantEuclidean| |bottom!| |rotatez| - |ratpart| |unrankImproperPartitions0| |rightTrim| |mathieu24| |isPlus| - |dn| |credPol| |viewPhiDefault| |setRealSteps| |simpsono| |nand| - |leastAffineMultiple| |heap| |s19aaf| |leftTrim| |components| |zCoord| - |curryLeft| |d01anf| |power| |increment| |resultantReduit| - |rischNormalize| |reduceBasisAtInfinity| |symmetricProduct| |extend| - |iiasin| |localReal?| |positiveSolve| |cAsinh| |curveColor| |powmod| - |randnum| |algSplitSimple| |rdHack1| |OMputBind| - |showFortranOutputStack| |flagFactor| |resultantnaif| |getOrder| - |tryFunctionalDecomposition?| |mapBivariate| |symbolTableOf| |exists?| - |e02baf| |kind| |removeZero| |exprToUPS| |max| |mainSquareFreePart| - |perspective| |LazardQuotient| |opeval| |radicalOfLeftTraceForm| - |shufflein| |fixedDivisor| |mainContent| |checkPrecision| |op| - |vspace| |generalPosition| |isConnected?| |henselFact| |var1Steps| - |f02ajf| |readable?| |firstUncouplingMatrix| |test| |option?| |rk4qc| - |move| |rischDEsys| |orbits| |f2st| |copyInto!| |bat1| |testDim| - |logIfCan| |insertionSort!| |swap| |figureUnits| |sizePascalTriangle| - |exptMod| |rightPower| |fortranDoubleComplex| |plot| |hasSolution?| - |besselY| |setleft!| |isOr| |multisect| |pattern| |shiftLeft| - |generalTwoFactor| |replace| |setLength!| |extendedint| |node?| - |redPo| |wholeRadix| |quasiRegular| |resultant| |eq| |reducedQPowers| - |fi2df| |solveLinearPolynomialEquationByFractions| |rootNormalize| - |s15aef| |medialSet| |printInfo| |c06gsf| |cycle| - |setAttributeButtonStep| |intermediateResultsIF| |iter| |rotatex| - |inconsistent?| |errorInfo| |prefix| |functionIsContinuousAtEndPoints| - |isobaric?| |union| |generators| |commutative?| |f07fef| |d01amf| - |complementaryBasis| |complexForm| |isTerm| |polygon| |delete!| - |digamma| |e04fdf| |karatsuba| |strongGenerators| |message| - |removeSuperfluousCases| |d01bbf| |factorsOfDegree| |polyred| |primes| - |lookup| |readLine!| |parts| |extendedEuclidean| |cardinality| - |LazardQuotient2| |setTopPredicate| |leviCivitaSymbol| |f01rdf| - |setref| |writeUInt8!| |LowTriBddDenomInv| |packageCall| |cycleLength| - |reducedDiscriminant| |heapSort| |bivariateSLPEBR| |rightRemainder| - |roughUnitIdeal?| |splitDenominator| |queue| |internalAugment| - |d03faf| |prime| |cycleTail| |palgextint| |monicDivide| |d01aqf| - |diff| |OMputString| |backOldPos| |showTheFTable| |mat| - |algebraicSort| |close| |cotIfCan| |leftQuotient| |coordinate| - |removeConstantTerm| |members| |setMinPoints3D| |cExp| |airyBi| - |lazy?| |isTimes| |node| |stoseInternalLastSubResultant| - |setScreenResolution3D| |baseRDEsys| |complexNumericIfCan| - |setPredicates| |exp| |setright!| |checkForZero| |leftScalarTimes!| - |showTheSymbolTable| |cons| |OMputEndAttr| |singularAtInfinity?| - |display| |getDatabase| |rischDE| |systemSizeIF| |compBound| |cubic| - |points| |viewport3D| |belong?| |ScanRoman| |roughEqualIdeals?| - |subCase?| |clearTable!| |OMopenFile| |cothIfCan| |thetaCoord| - |charClass| |critBonD| |zeroDimensional?| |OMgetEndApp| |upperCase?| - |square?| |halfExtendedResultant1| |pointPlot| - |rightCharacteristicPolynomial| |outerProduct| |deleteRoutine!| - |iicsch| |showTheRoutinesTable| |imagI| |completeEchelonBasis| - |quoted?| |numberOfMonomials| |showClipRegion| |octon| |OMgetBVar| - |f04maf| |mergeFactors| |modularGcdPrimitive| |readInt32!| |tan2trig| - |coshIfCan| |nextPartition| |stronglyReduced?| |s21bbf| |listexp| - |interval| |unrankImproperPartitions1| |cyclicEqual?| |entries| - |shiftRight| |input| |c06fqf| |leftRemainder| |birth| |prinshINFO| - |screenResolution3D| |exponentialOrder| |complexLimit| |expint| - |source| |OMputError| |viewport2D| |library| |dmp2rfi| |sub| - |definingInequation| |exprHasWeightCosWXorSinWX| |triangSolve| - |axesColorDefault| |mathieu23| |var1StepsDefault| - |lazyIrreducibleFactors| |deref| |polygon?| |localUnquote| |tRange| - |exp1| |bracket| |range| |generalizedInverse| |binomial| - |realElementary| |branchIfCan| |ratDenom| |normal01| |viewpoint| - |laguerreL| |showScalarValues| |monic?| |knownInfBasis| |aromberg| - |fortranCarriageReturn| |createGenericMatrix| |taylorRep| |rootSimp| - |Lazard2| |returnTypeOf| |tanh2trigh| |dihedral| - |generalizedEigenvectors| |third| |deepExpand| |OMputObject| |c06ecf| - |pushdown| |signature| |totalDifferential| |f02xef| |set| |member?| - |central?| |addMatch| |leftZero| |separateFactors| |setVariableOrder| - |rotate| |makeViewport3D| |bernoulliB| |target| |mapExponents| - |reseed| |sum| |point?| |simpson| |numericIfCan| |tanh2coth| - |exponents| |extractTop!| |iisqrt3| |indicialEquation| - |characteristicSerie| |pushFortranOutputStack| |getProperty| |setPoly| - |permutationGroup| |radPoly| |OMUnknownSymbol?| |conjug| |cschIfCan| - |infLex?| |f04faf| |changeWeightLevel| |head| |subscriptedVariables| - |getPickedPoints| |setCondition!| |algDsolve| |vectorise| - |probablyZeroDim?| |cyclicEntries| |simpleBounds?| - |selectOptimizationRoutines| |stop| |void| |weighted| - |primitiveElement| |quotedOperators| |partition| |cyclePartition| - |epilogue| |even?| |trigs| |leftNorm| |traverse| |systemCommand| - |green| |brillhartIrreducible?| |squareFree| |freeOf?| |rootOf| - |mapExpon| |OMReadError?| |toseInvertibleSet| |lp| |gramschmidt| - |maxrow| |ravel| |lowerCase!| |close!| |kmax| |readUInt32!| - |internalSubQuasiComponent?| |fullPartialFraction| - |selectMultiDimensionalRoutines| |numberOfComposites| |mapCoef| - |nextNormalPoly| |reshape| |sech2cosh| |nextIrreduciblePoly| - |ridHack1| |generalizedContinuumHypothesisAssumed| |imports| - |minimize| |eulerPhi| |initiallyReduced?| |nthCoef| |schema| - |leftRankPolynomial| |normal| |signAround| |d01gaf| |iiacos| - |indiceSubResultantEuclidean| |upperCase| |f01mcf| |mpsode| - |sizeMultiplication| |leftMinimalPolynomial| |associates?| |ODESolve| - |dmpToP| |BasicMethod| |lexTriangular| |cartesian| |initials| - |numberOfFactors| |c06fpf| |iroot| |optimize| |tube| |iiacot| |parse| - |OMputApp| |semiResultantReduitEuclidean| |f02wef| |elements| - |kovacic| |OMgetFloat| |indicialEquationAtInfinity| |choosemon| - |OMgetType| |repeating?| |basicSet| |localAbs| |minRowIndex| |s19abf| - |makeop| |update| |cond| |moduleSum| |stoseLastSubResultant| - |readIfCan!| |badValues| |trace2PowMod| |vark| |pushNewContour| - |att2Result| |lifting1| |true| |collectUpper| |factorOfDegree| - |internalSubPolSet?| |dfRange| |sin?| |createLowComplexityNormalBasis| - |lintgcd| |fibonacci| |OMputInteger| |fixedPoints| - |definingPolynomial| |setAdaptive| |SturmHabichtCoefficients| |iidsum| - |primlimitedint| |rootKerSimp| |rarrow| |binding| |largest| |identity| - |dmpToHdmp| |tubePointsDefault| |child?| |symmetricRemainder| - |prevPrime| |e02dff| |leftFactorIfCan| |trigs2explogs| |stFuncN| - |clipParametric| |makeVariable| |box| |seriesSolve| |typeList| - |eulerE| |expintfldpoly| |resultantEuclidean| - |removeSuperfluousQuasiComponents| |unknownEndian| |represents| |nlde| - |cSinh| |linearDependence| F2FG |ksec| |block| |characteristic| - |pmComplexintegrate| |s19acf| |ef2edf| |ranges| |setOfMinN| |linear| - |writeBytes!| |nodes| |leadingIdeal| |logpart| - |createPrimitiveNormalPoly| |gradient| |lazyGintegrate| |rst| - |singRicDE| |useEisensteinCriterion?| |setelt!| |f02aaf| |generalSqFr| - |OMbindTCP| |tableau| |computeInt| |redmat| |multiplyExponents| - |polynomial| |univcase| |solveLinearlyOverQ| |simplifyPower| - |shellSort| |tanhIfCan| |factorSquareFree| |delete| |logical?| - |fullDisplay| |precision| |index| |firstNumer| |solveid| - |expenseOfEvaluationIF| |wordInStrongGenerators| |printingInfo?| - |overlabel| |expandPower| |cCosh| |partialDenominators| |abelianGroup| - |smith| |deleteProperty!| |makeTerm| |plenaryPower| |e04gcf| |arg1| - |connectTo| |lyndon| |purelyAlgebraic?| |determinant| |untab| - |integralCoordinates| |OMgetEndBVar| |deepestInitial| |arg2| |f07fdf| - |rootOfIrreduciblePoly| |super| |separate| |qqq| |pair| |schwerpunkt| - |external?| |OMencodingSGML| |getMeasure| |pleskenSplit| |negative?| - |goto| |setsubMatrix!| |particularSolution| |df2mf| |callForm?| - |operation| |nextNormalPrimitivePoly| |topPredicate| |pseudoRemainder| - |value| |hasTopPredicate?| |conditions| |subResultantsChain| - |lazyEvaluate| |f01qdf| |useSingleFactorBound| |graphImage| |#| - |approximants| |cyclotomicFactorization| |redpps| - |algebraicCoefficients?| |match| |reindex| |cyclotomic| EQ - |numericalIntegration| |top!| |antiCommutative?| |OMgetAttr| - |corrPoly| |cos2sec| |result| |basisOfCentroid| |iiacoth| |postfix| - |normalDenom| |compactFraction| |closeComponent| |makeSUP| - |flexibleArray| |youngGroup| |factorset| |mkcomm| |showRegion| - |OMconnInDevice| |zero?| |leadingExponent| |viewThetaDefault| - |getOperands| |sample| |testModulus| |reset| |coerceListOfPairs| - |removeZeroes| |sturmVariationsOf| |atrapezoidal| |internalIntegrate0| - |back| |monomialIntegrate| |decrease| |curve| |radicalSolve| - |newSubProgram| |hexDigit?| |linSolve| |doubleFloatFormat| - |coefficient| |rootBound| |write| |primextendedint| |findCycle| - |maxrank| |iCompose| |doublyTransitive?| |drawToScale| |c06fuf| - |cycleSplit!| |save| |gensym| |mapUp!| |errorKind| |rur| - |drawComplexVectorField| |yellow| |extractBottom!| |Vectorise| |color| - |log10| |solve| |any| |variationOfParameters| |closed?| |neglist| - |perfectNthPower?| |e02adf| |evenlambert| |bitand| |outputSpacing| - |prolateSpheroidal| |absolutelyIrreducible?| |adaptive3D?| - |alphabetic?| |rotate!| |abs| |alphabetic| |s21bcf| |bitior| - |changeMeasure| |setProperties!| |complete| |numeric| |jacobian| - |imagJ| |commutativeEquality| |algebraicDecompose| |s18aff| |insert!| - |balancedBinaryTree| |normalizeIfCan| |mesh| |radical| |nextColeman| - |lflimitedint| |makeSketch| |s17dlf| |symFunc| |bits| |sumSquares| - |selectOrPolynomials| |palgintegrate| |s14abf| |s17dhf| |maxPoints| - |generator| |Gamma| |dec| |loopPoints| |setImagSteps| |elColumn2!| - |subscript| |consnewpol| |FormatArabic| |OMputEndObject| - |semiIndiceSubResultantEuclidean| |multiplyCoefficients| |overbar| - |degreeSubResultant| |nor| |argument| |scalarTypeOf| |monomials| - |leastMonomial| |internalZeroSetSplit| |readBytes!| |nil?| |bsolve| - |sizeLess?| |indicialEquations| |sincos| |index?| |atoms| - |linearlyDependent?| |rquo| |maximumExponent| |B1solve| - |diagonalProduct| |revert| |insertMatch| |stosePrepareSubResAlgo| - |monomialIntPoly| |s17aef| |curry| |infiniteProduct| |pole?| |polar| - |s14baf| |isAnd| |rootSplit| |cot2trig| |cAcot| |expandTrigProducts| - |calcRanges| |mightHaveRoots| |search| |d02raf| |separant| - |outputBinaryFile| |genericRightDiscriminant| |swapColumns!| |prime?| - |connect| |cAcoth| |secIfCan| |outputFloating| |diag| - |monicRightFactorIfCan| |high| |droot| |matrix| |endSubProgram| - |tanAn| |numer| |trailingCoefficient| |duplicates| |mathieu22| - |gcdcofact| |rightFactorIfCan| |primlimintfrac| |conical| - |halfExtendedSubResultantGcd2| |makeCos| |denom| - |associatorDependence| |hitherPlane| |lighting| |OMParseError?| - |pointSizeDefault| |normalized?| |bipolar| |palgint| |s18def| - |dualSignature| |startTable!| |balancedFactorisation| |power!| - |charthRoot| |constantRight| Y |elliptic?| |pair?| |preprocess| |pi| - |extractIndex| |prologue| |selectAndPolynomials| |realZeros| - |minordet| |constantOpIfCan| |operations| |s18acf| |cross| |infinity| - |bivariatePolynomials| |coefChoose| |e01baf| |categories| - |univariatePolynomial| |s17ajf| |semiSubResultantGcdEuclidean1| - |doubleResultant| |mainMonomial| |normalise| |setEmpty!| |gbasis| - |stFunc1| |shift| |positive?| |subspace| |coleman| |length| F ~= - |completeSmith| |jacobiIdentity?| |palgRDE| - |purelyAlgebraicLeadingMonomial?| |intChoose| |rightGcd| - |setButtonValue| |principalAncestors| |countRealRootsMultiple| - |scripts| |curryRight| |coerce| |irreducible?| |rightUnit| |kernel| - |exprex| |stoseInvertible?sqfreg| |extensionDegree| - |jordanAdmissible?| |solveLinearPolynomialEquation| |showArrayValues| - |construct| |OMgetEndAttr| |draw| |rangePascalTriangle| |f02aff| - |saturate| |fractRadix| |null| |d02kef| |modularGcd| |cCoth| - |rightLcm| |midpoints| |intPatternMatch| - |removeRedundantFactorsInPols| |listOfLists| |mainVariable| - |stripCommentsAndBlanks| |not| |uniform01| |aLinear| |direction| - |exactQuotient| |objectOf| |factorPolynomial| |e01sef| |pureLex| - |finite?| |and| |parseString| |s21bdf| |resize| |viewSizeDefault| - |byteBuffer| |showSummary| |factorFraction| |stoseInvertibleSetsqfreg| - |nextsubResultant2| |characteristicSet| |or| |SturmHabicht| - |getMultiplicationTable| |whatInfinity| |pushucoef| |size?| |hexDigit| - |contract| |hessian| |constDsolve| |xor| |ellipticCylindrical| - |interactiveEnv| FG2F |bothWays| |obj| |iicot| |showAttributes| - |compdegd| |e01daf| |transpose| |OMputBVar| |case| |satisfy?| - |principal?| |coth2tanh| |approxNthRoot| |primintfldpoly| |lhs| |ode2| - |cache| |d01apf| |parent| |permutationRepresentation| |Zero| |name| - |normalForm| |f04mbf| |exponential1| |region| |rhs| |leadingBasisTerm| - |groebner| |modifyPoint| |mainCoefficients| RF2UTS |One| |body| - |solid| |graphState| |viewZoomDefault| |f01qef| |recip| |rspace| - |meatAxe| |degreePartition| |makeCrit| |groebSolve| |inspect| - |resultantReduitEuclidean| |convergents| |noLinearFactor?| - |LyndonBasis| |scripted?| |doubleRank| |e02bbf| |linearPart| - |tensorProduct| |intensity| |leftUnit| |ramified?| |cylindrical| - |c05pbf| |ord| |zeroDimPrimary?| |OMsetEncoding| - |rightMinimalPolynomial| |sh| |dflist| |accuracyIF| - |createMultiplicationTable| |newReduc| |symmetricDifference| |e01bef| - |sort| |linearPolynomials| |rombergo| |dominantTerm| |jordanAlgebra?| - |setelt| |randomR| |setMaxPoints3D| |more?| - |removeIrreducibleRedundantFactors| |stoseIntegralLastSubResultant| - |lllip| |leadingCoefficientRicDE| |OMsupportsCD?| |ratPoly| - |totalDegree| |kroneckerDelta| |c05nbf| |palgint0| |invertible?| - |port| LODO2FUN |phiCoord| |univariateSolve| |elliptic| - |invertibleSet| |torsionIfCan| |totalGroebner| |splitConstant| - |messagePrint| |companionBlocks| |augment| |addPoint2| - |radicalEigenvector| |splitLinear| |jacobi| |thenBranch| |bitCoef| - |random| |clearTheSymbolTable| |t| |linkToFortran| |exquo| |nilFactor| - |deriv| |virtualDegree| |error| |recur| |f01brf| |moduloP| - |getProperties| |ode1| |div| |stoseInvertibleSetreg| |clipBoolean| - |OMputAtp| |wordInGenerators| |assert| |csubst| |numberOfDivisors| - |cAtan| |semicolonSeparate| |bernoulli| |rightRegularRepresentation| - |quo| |lyndonIfCan| |numericalOptimization| |odd?| |declare| - |bringDown| |output| |bezoutMatrix| |exponent| |qPot| - |continuedFraction| |subset?| |iicsc| |setFieldInfo| |plotPolar| - |s17adf| |mkPrim| |OMserve| |submod| |ReduceOrder| |makeFR| |rem| - |partialFraction| |iteratedInitials| |primintegrate| - |cyclotomicDecomposition| |is?| |wordsForStrongGenerators| |setRow!| - |socf2socdf| |LiePolyIfCan| |rootProduct| |roughBase?| |rationalIfCan| - |rootRadius| |integralRepresents| |expenseOfEvaluation| |setrest!| - |mainPrimitivePart| |qelt| |differentialVariables| - |uncouplingMatrices| |content| |unitNormal| |call| |qsetelt| |redPol| - |LiePoly| |toseLastSubResultant| |pdf2df| |s17aff| |tracePowMod| - |shanksDiscLogAlgorithm| |semiDegreeSubResultantEuclidean| - |genericLeftNorm| |elementary| |reduceByQuasiMonic| |innerSolve| - |divideIfCan| |highCommonTerms| |xRange| |extension| |roman| |degree| - |f02axf| |basisOfMiddleNucleus| |iiexp| |solveInField| |OMreceive| - |entry?| |yRange| |hex| |alphanumeric| |printCode| - |SturmHabichtMultiple| |next| |getlo| |module| |stoseInvertible?| - |sin2csc| |in?| |zRange| |unitsColorDefault| |scaleRoots| - |leadingIndex| |alternative?| |createNormalPoly| |open?| |map!| - |OMlistCDs| |supersub| |doubleDisc| |updatF| |binaryTournament| - |numberOfOperations| |tValues| |qsetelt!| |LyndonWordsList1| |lllp| - |asecIfCan| |radicalEigenvalues| |iterationVar| |changeNameToObjf| - |degreeSubResultantEuclidean| |complexElementary| |weights| |li| - |csc2sin| |f02bjf| |ScanFloatIgnoreSpacesIfCan| |alternatingGroup| - |rootPower| |setEpilogue!| |sdf2lst| |OMputEndError| |superscript| - |overlap| |mvar| |bindings| |iisqrt2| |groebnerIdeal| - |zeroSquareMatrix| |updatD| |cAsin| |exteriorDifferential| - |maxPoints3D| |select!| |squareFreeFactors| |identityMatrix| |leaves| - |basisOfLeftNucloid| |aCubic| |denomRicDE| |round| |e01bhf| |leftRank| - |rightNorm| |meshPar1Var| |discreteLog| |rightMult| |acsch| BY |po| - |ParCondList| |countable?| |bitTruth| - |removeRoughlyRedundantFactorsInContents| |startStats!| - |zeroDimPrime?| |setMinPoints| |minIndex| |s18dcf| - |linearAssociatedLog| |rightZero| |hostPlatform| |lieAdmissible?| - |char| |OMlistSymbols| |middle| |outputFixed| |fractionFreeGauss!| - |triangulate| |readByte!| |repeatUntilLoop| |prindINFO| |partitions| - |stopTableInvSet!| |resetVariableOrder| |plusInfinity| |over| - |makeFloatFunction| |boundOfCauchy| |makeEq| |padicallyExpand| - |transcendent?| |zerosOf| |fortranLiteral| |minusInfinity| - |sqfrFactor| |lo| |iiasinh| |scopes| |chiSquare| - |integralMatrixAtInfinity| UTS2UP |multMonom| |realSolve| |chiSquare1| - |divide| |indices| |LyndonWordsList| |showTypeInOutput| |bat| - |writeLine!| |c06ebf| |incr| |cCot| |e02ahf| NOT |monomial?| |float| - |traceMatrix| |enterInCache| |computePowers| |f04axf| |real?| - |conditionP| |hi| |moebius| |extendIfCan| OR |processTemplate| - |summation| |bipolarCylindrical| |arrayStack| |s19adf| |implies| - |basisOfLeftNucleus| |quadraticNorm| |arguments| |getGraph| AND - |shuffle| |integerIfCan| |getRef| |bag| |type| |collect| - |eigenvectors| |normalDeriv| |eq?| |mask| |resolve| |sechIfCan| - |structuralConstants| |e02bcf| |OMencodingXML| |acothIfCan| - |singularitiesOf| |selectsecond| |powern| |flatten| |cAsec| - |relativeApprox| |addPointLast| |finiteBound| |divisor| |printHeader| - |isPower| |condition| |iomode| |principalIdeal| |coerceP| |zeroVector| - |numberOfNormalPoly| |rationalApproximation| |leftPower| |cyclic| - |superHeight| |reflect| |f01maf| |quickSort| - |rewriteIdealWithQuasiMonicGenerators| |representationType| - |bitLength| |OMgetEndObject| |scalarMatrix| |nonSingularModel| - |removeRedundantFactors| |const| |s17dgf| |matrixDimensions| - |divideExponents| |ignore?| |OMconnOutDevice| |acotIfCan| |flexible?| - |remainder| |increasePrecision| |rightRankPolynomial| - |rightScalarTimes!| |e02zaf| GE |complexExpand| |infix| - |bezoutResultant| |isOp| |digit| |pmintegrate| |e02ajf| - |triangularSystems| |iFTable| |makeYoungTableau| |comment| GT - |inverseIntegralMatrix| |solveLinear| |nullary?| |rightOne| - |raisePolynomial| |gderiv| |generateIrredPoly| |mainExpression| - |edf2ef| |viewWriteAvailable| LE |getStream| |acoshIfCan| |addmod| - |algebraicOf| |explicitlyEmpty?| |resetNew| |critB| |s01eaf| - |GospersMethod| |extractIfCan| |radicalSimplify| * LT |Ci| |listLoops| - |cCos| |laurentRep| |homogeneous?| |dot| |slash| |bandedHessian| - |hermite| |swap!| |mappingAst| |center| |evaluate| |mainVariables| - |toroidal| |tableForDiscreteLogarithm| |notelem| |blankSeparate| - |myDegree| |SturmHabichtSequence| |mapdiv| |makeGraphImage| - |irreducibleRepresentation| |normal?| |cyclicParents| - |explicitEntries?| |coHeight| |sign| |maxColIndex| |unitNormalize| - |modularFactor| |addMatchRestricted| |reverse!| |getExplanations| = - |cAcos| |cCsc| |startPolynomial| |isNot| |cap| |HenselLift| - |binomThmExpt| |intersect| |e01bff| |f01qcf| |basisOfRightNucloid| - |goodPoint| |e04jaf| |enumerate| |pile| |safetyMargin| |reorder| - |nextPrime| |f02bbf| |lprop| < |swapRows!| |c06frf| |fortran| - |useSingleFactorBound?| |possiblyNewVariety?| - |noncommutativeJordanAlgebra?| |product| |pol| |univariate?| |weight| - |makeprod| > |mapSolve| |currentSubProgram| |extract!| |generic?| - |realRoots| |moreAlgebraic?| |generalizedContinuumHypothesisAssumed?| - |resultantEuclideannaif| |doubleComplex?| |numberOfVariables| <= - |number?| |children| |rotatey| |lexico| |s17acf| |compile| - |removeRedundantFactorsInContents| |qinterval| |f02akf| |FormatRoman| - |gcdPolynomial| >= |fixedPoint| |s13adf| |property| |dequeue!| - |retract| |clikeUniv| |drawComplex| |rowEchelon| |tanIfCan| - |colorFunction| |mapUnivariateIfCan| |subResultantChain| - |headReduced?| |readInt8!| |cTan| |edf2fi| |internalLastSubResultant| - |vedf2vef| |commaSeparate| |numFunEvals| |genericPosition| |An| - |sumOfKthPowerDivisors| |setchildren!| |d02ejf| |totalLex| |e02aef| - |getCurve| |dAndcExp| |e01bgf| |OMclose| |ScanFloatIgnoreSpaces| - |endOfFile?| |bandedJacobian| |algebraicVariables| + |categoryFrame| - |identitySquareMatrix| |multiple?| |root| |units| |empty| |cosSinInfo| - |d01akf| |getBadValues| |asechIfCan| |forLoop| |lifting| - |f01ref| - |axes| |nextPrimitivePoly| |expIfCan| |rationalFunction| |coth2trigh| - |meshPar2Var| |argscript| |OMsend| |column| / |powerSum| |merge| - |parabolic| |character?| |OMputAttr| |bright| |removeSinSq| |rowEch| - |univariatePolynomialsGcds| |nextItem| |subresultantVector| - |musserTrials| |genericLeftMinimalPolynomial| |stFunc2| - |OMputVariable| |top| |c06ekf| |seriesToOutputForm| |nthRootIfCan| - |shallowCopy| |rationalPoints| |divideIfCan!| |quote| |minColIndex| - |divisorCascade| |d02cjf| |littleEndian| |code| |moebiusMu| - |argumentList!| |vconcat| |minPoints3D| |nextLatticePermutation| |key| - |inverseIntegralMatrixAtInfinity| |reverse| |plus| |function| |hasoln| - |list| |newTypeLists| |unitVector| |genericRightMinimalPolynomial| - |squareFreePrim| |cSech| |cyclicCopy| |getMultiplicationMatrix| - |eisensteinIrreducible?| |mapDown!| |tanQ| |conjugates| - |inputOutputBinaryFile| |car| |intcompBasis| |imaginary| |chebyshevT| - |powers| |addPoint| |filename| |before?| |leftLcm| |minrank| |eval| - |ricDsolve| |factorByRecursion| |cdr| |mr| |lazyPrem| - |selectPolynomials| |d01ajf| |infRittWu?| |fglmIfCan| |putGraph| - |iiperm| |getZechTable| |leftExtendedGcd| |setDifference| - |matrixConcat3D| |separateDegrees| |computeCycleLength| |bumptab| - |integralBasis| |hasPredicate?| |generalLambert| |decreasePrecision| - |times| |bytes| |symmetric?| |setIntersection| |s17agf| |f07aef| - |initial| |changeThreshhold| |factorAndSplit| |coordinates| |psolve| - |graphCurves| |createMultiplicationMatrix| |genericRightTraceForm| - |RemainderList| |associative?| |setUnion| |leftMult| |polynomialZeros| - |script| |copies| |iiGamma| |e02def| |dihedralGroup| |digit?| - |getCode| |HermiteIntegrate| |lquo| |derivationCoordinates| |apply| - |changeBase| |expextendedint| |d03edf| |evaluateInverse| |readUInt8!| - |e01saf| |logGamma| |showIntensityFunctions| |parametersOf| |truncate| - |normalize| |coerceS| |padicFraction| |leftTraceMatrix| |twoFactor| - |headAst| |monom| |fTable| |orbit| |c06gbf| |size| |var2Steps| - |vector| |tex| |mathieu11| |getConstant| |leftExactQuotient| |cAcsc| - |lazyVariations| |rule| |getGoodPrime| |symmetricGroup| - |removeRoughlyRedundantFactorsInPol| |subNodeOf?| |differentiate| - |iiacsch| |viewDeltaYDefault| |inHallBasis?| |e04mbf| |f04qaf| - |operator| |integer?| |enterPointData| |write!| |root?| - |taylorQuoByVar| |ptFunc| |listBranches| |basisOfCenter| - |beauzamyBound| |iipow| |stirling2| |common| |approxSqrt| |title| - |numberOfCycles| |first| |s18aef| |yCoord| |collectQuasiMonic| - |goodnessOfFit| |crushedSet| |hue| |lcm| |e02dcf| - |semiDiscriminantEuclidean| |viewDefaults| |euler| |rest| - |setPosition| |double?| |cycleEntry| |OMgetInteger| |squareFreePart| - |dark| |expr| |complement| |gcdcofactprim| |factorList| |substitute| - |OMputEndApp| |rootPoly| |iifact| |hyperelliptic| |initTable!| - |checkRur| |htrigs| |removeDuplicates| |e| |append| |rk4| |padecf| - |integralDerivationMatrix| |trapezoidalo| |domainOf| |exQuo| |failed| - |every?| |one?| |inRadical?| |constantIfCan| |gcd| |genericRightTrace| - |measure| |antiAssociative?| |rubiksGroup| |subResultantGcd| |s13acf| - |numerator| |c06gqf| UP2UTS |false| |lSpaceBasis| |airyAi| - |fortranDouble| |blue| |sayLength| |mix| |invmod| |magnitude| - |addBadValue| |variable| |sort!| |infinityNorm| |writeByte!| |critT| - |nothing| |iprint| |dimensionsOf| |legendreP| |setOrder| |setValue!| - |substring?| |baseRDE| |iterators| |setFormula!| |rational?| - |contours| |BumInSepFFE| |binarySearchTree| |firstDenom| - |createZechTable| |viewPosDefault| |invertibleElseSplit?| |oddlambert| - |innerEigenvectors| |plus!| |rightDiscriminant| |controlPanel| - |denominators| |poisson| |outputAsScript| |suffix?| |mdeg| |symbol?| - |isEquiv| |setClosed| |e04naf| |minPoints| |squareMatrix| |palglimint| - |primextintfrac| |divisors| |equiv| |inGroundField?| |f04jgf| - |monicModulo| |palgLODE0| |OMmakeConn| |complexSolve| |prefix?| - |repeating| |explogs2trigs| |replaceKthElement| |rightDivide| - |antiCommutator| |sinIfCan| |constantLeft| |subQuasiComponent?| - |KrullNumber| |totolex| |width| |numberOfImproperPartitions| - |semiResultantEuclideannaif| |externalList| |trunc| |mkAnswer| - |routines| |lyndon?| |f02awf| |s18adf| |increase| |constantOperator| - |outputMeasure| |topFortranOutputStack| |OMgetObject| |has?| - |binaryFunction| |headRemainder| |quasiAlgebraicSet| |properties| - |f04adf| |paraboloidal| |iisec| |applyRules| |light| |continue| - |monicRightDivide| |tab1| |lazyPseudoRemainder| |translate| - |tubePoints| |isList| |iExquo| |e02agf| |rename| |slex| |read!| - |listYoungTableaus| |tree| |permanent| |rightAlternative?| - |lfintegrate| |OMreadFile| |monomRDEsys| |ruleset| |autoReduced?| - |outlineRender| |mkIntegral| |leftAlternative?| |pade| - |monicLeftDivide| |infix?| |mesh?| |brillhartTrials| |tab| |midpoint| - |setlast!| |exprHasLogarithmicWeights| |terms| |aQuadratic| |sn| - |depth| |numberOfIrreduciblePoly| |createPrimitivePoly| |recolor| - |getVariableOrder| |measure2Result| |mulmod| |unvectorise| |reopen!| - |less?| |rightTrace| |genericLeftTraceForm| |minus!| |optional| - |readInt16!| |suchThat| |quoByVar| |harmonic| |radix| |showAll?| - |unary?| |besselK| |fortranLinkerArgs| |sequences| - |basisOfRightNucleus| |expPot| |linears| |mindeg| |infieldIntegrate| - |reduction| |badNum| |removeCoshSq| - |zeroSetSplitIntoTriangularSystems| |lexGroebner| |extractClosed| - |inR?| |integralMatrix| |cAcosh| |space| |uniform| |alphanumeric?| - |create3Space| |clearCache| |dimensionOfIrreducibleRepresentation| - |tanSum| |distribute| |relationsIdeal| |interpret| |hconcat| |stack| - |fillPascalTriangle| |elRow1!| |primitivePart| |limitPlus| - |roughSubIdeal?| |defineProperty| |mapMatrixIfCan| |branchPoint?| - |nullSpace| |reducedContinuedFraction| |removeCosSq| |integerBound| - |iflist2Result| |fortranInteger| |split!| |userOrdered?| - |rightTraceMatrix| |removeSinhSq| |linearMatrix| |tower| - |explimitedint| |permutations| |regularRepresentation| |generate| - |surface| |e02gaf| |quasiMonic?| |patternVariable| |sturmSequence| ~ - |genericRightNorm| |allRootsOf| |standardBasisOfCyclicSubmodule| - |extractProperty| SEGMENT |bigEndian| |OMunhandledSymbol| |directory| - |nthFlag| |ffactor| |f02abf| |log| |incrementBy| |getOperator| - |noKaratsuba| |dim| |palgLODE| |karatsubaDivide| |countRealRoots| - |positiveRemainder| |omError| |s14aaf| |list?| |iiatan| |open| - |putColorInfo| |extendedIntegrate| |Ei| |expand| |equation| |minPoly| - |finiteBasis| |fortranCompilerName| |OMputEndBind| |exactQuotient!| - |lieAlgebra?| |e02akf| |outputArgs| |sorted?| |filterWhile| - |limitedint| |physicalLength!| |stiffnessAndStabilityFactor| - |rightUnits| |optAttributes| |leftGcd| |polarCoordinates| - |nthExponent| |complexNumeric| |getMatch| |prinb| |filterUntil| - |wrregime| |branchPointAtInfinity?| |subresultantSequence| |inverse| - |polyPart| |maxIndex| |combineFeatureCompatibility| - |hypergeometric0F1| |composites| |unaryFunction| |select| - |complexEigenvectors| |karatsubaOnce| |aspFilename| |modifyPointData| - |withPredicates| |linear?| |kernels| |OMputSymbol| |fixPredicate| - |insertBottom!| |mainValue| |isExpt| |complexIntegrate| |e01sbf| - |optional?| |nary?| |functionIsFracPolynomial?| |nullary| |univariate| - |dimension| |movedPoints| |setMaxPoints| |partialQuotients| |aQuartic| - |maxdeg| |crest| |upDateBranches| |diagonals| |concat| |decimal| - |laplace| |mantissa| |ip4Address| |qroot| |atanhIfCan| |OMgetEndBind| - |useNagFunctions| |setAdaptive3D| |basisOfCommutingElements| - |exprToGenUPS| |innerint| |pointColorPalette| - |basisOfRightAnnihilator| |readUInt16!| |restorePrecision| |rightRank| - |fortranComplex| |nil| |bumprow| |semiResultantEuclidean1| - |oddintegers| |multiEuclidean| |patternMatch| |factor| |reify| - |factorSquareFreeByRecursion| |front| |outputForm| |shiftRoots| - |janko2| |binaryTree| |ratDsolve| |getIdentifier| |sqrt| |ref| - |orthonormalBasis| |makeRecord| |laguerre| |pop!| |pack!| - |normalizedDivide| |Frobenius| |startTableInvSet!| |status| |isOpen?| - |mainDefiningPolynomial| |wholePart| |refine| - |extendedSubResultantGcd| |real| |second| |stopMusserTrials| - |lfextendedint| |stiffnessAndStabilityOfODEIF| |overset?| |ipow| - |mapUnivariate| |SFunction| |integralAtInfinity?| |lastSubResultant| - |approximate| |irreducibleFactor| |charpol| |imag| |mindegTerm| - |leadingSupport| |zeroSetSplit| |exponential| |complex| - |selectFiniteRoutines| |nextPrimitiveNormalPoly| |updateStatus!| - |elem?| |empty?| |directProduct| |nthFactor| |rightFactorCandidate| - |rightExtendedGcd| |Hausdorff| |debug3D| |chebyshevU| |setProperty| - |roughBasicSet| |zeroOf| |mainForm| |merge!| |bumptab1| |newLine| - |graphs| |interReduce| |iiasech| |discriminantEuclidean| |d02bbf| - |usingTable?| |fracPart| |acosIfCan| |iisin| |OMencodingUnknown| - |brace| |printStatement| |appendPoint| |delay| |eigenvalues| - |OMgetEndError| |nextSubsetGray| |triangular?| |d02bhf| - |chainSubResultants| |createIrreduciblePoly| |pToDmp| |destruct| - |expressIdealMember| |llprop| |recoverAfterFail| |coerceImages| - |leftUnits| |key?| |fprindINFO| |tan2cot| |lastSubResultantElseSplit| - |OMgetString| |mapmult| |leftRegularRepresentation| |cfirst| - |closedCurve| |scanOneDimSubspaces| |comparison| |prefixRagits| - |lowerCase?| |OMputEndAtp| |lfunc| |remove| |rowEchLocal| - |idealSimplify| |pomopo!| |quotient| |pr2dmp| |inc| |eigenMatrix| - |sup| |extractPoint| |nthFractionalTerm| |localIntegralBasis| - |mergeDifference| |univariatePolynomials| |reciprocalPolynomial| - |s17dcf| |bubbleSort!| |OMconnectTCP| |initializeGroupForWordProblem| - |child| |leadingTerm| |selectNonFiniteRoutines| |last| |pushdterm| - |normFactors| |monomial| |iitan| |lowerPolynomial| - |createPrimitiveElement| |entry| |setleaves!| |s20acf| |zoom| - |qfactor| |rationalPower| |assoc| |writable?| |btwFact| |multivariate| - |scale| |lineColorDefault| |getButtonValue| |graeffe| |leftFactor| - |linearDependenceOverZ| |morphism| |integral| |basis| |variables| - |qualifier| |dictionary| |component| |tubeRadius| |delta| - |leftDiscriminant| |s15adf| |semiResultantEuclidean2| - |patternMatchTimes| |decompose| |iisech| |atom?| |critMonD1| |algint| - |specialTrigs| |wholeRagits| |rangeIsFinite| |polyRicDE| - |yCoordinates| |d02gbf| |returns| |palgextint0| |sequence| - |cycleRagits| |integralBasisAtInfinity| |subSet| |f04asf| - |denominator| |realEigenvalues| |primPartElseUnitCanonical!| |cn| - |leftRecip| |OMgetEndAtp| |ideal| |selectSumOfSquaresRoutines| - |factorGroebnerBasis| |category| |bivariate?| |unravel| - |findConstructor| |rectangularMatrix| |dimensions| |wreath| - |reducedSystem| |derivative| |OMgetVariable| |polCase| |domain| - |rightExactQuotient| |s20adf| |wronskianMatrix| |ceiling| - |invmultisect| |constantToUnaryFunction| |tablePow| |taylor| - |genericLeftTrace| |toseInvertible?| |rootsOf| |package| |nullity| - |Aleph| |makeViewport2D| |exportedOperators| |pointLists| |critM| - |cLog| |show| |laurent| |weierstrass| |extendedResultant| |copy| - |componentUpperBound| |f2df| |fractionPart| |difference| - |useEisensteinCriterion| |retractable?| |getSyntaxFormsFromFile| - |upperCase!| |puiseux| |leastPower| |compose| |f02aef| |lambda| - |physicalLength| |safeFloor| |imagi| |frobenius| |monomRDE| |trace| - |factorSFBRlcUnit| |tanNa| |mainKernel| |clipSurface| |bombieriNorm| - |typeLists| |mainCharacterization| |findBinding| |prod| - |primitivePart!| |inputBinaryFile| |fractRagits| |inv| |modulus| |low| - |autoCoerce| |rk4a| |simplify| |sortConstraints| |tubeRadiusDefault| - |asinIfCan| |fortranTypeOf| |ground?| |perfectSquare?| - |purelyTranscendental?| |invertIfCan| |viewWriteDefault| - |sylvesterSequence| |parents| |fixedPointExquo| |euclideanNormalForm| - |assign| |interpolate| |polygamma| |isMult| |ground| |critpOrder| - |makeUnit| |mathieu12| |Beta| |f02fjf| |makeResult| - |removeRoughlyRedundantFactorsInPols| |palglimint0| |lazyPseudoDivide| - |infieldint| |hcrf| |leadingMonomial| |style| |singular?| |torsion?| - |iiatanh| |s21baf| |prinpolINFO| |ScanArabic| |float?| |position| - |floor| |leadingCoefficient| |internalDecompose| - |numberOfFractionalTerms| |interpretString| |antisymmetric?| |match?| - 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|stronglyReduce| |pseudoDivide| |push| |clearTheFTable| |edf2df| - |integers| |nthr| |readLineIfCan!| |cCsch| |rootDirectory| |iiacsc| - |pointData| |d01gbf| |denomLODE| |functionIsOscillatory| |sncndn| - |prepareSubResAlgo| |outputAsTex| |Nul| |asimpson| |iilog| - |resetBadValues| |ramifiedAtInfinity?| |init| |halfExtendedResultant2| - |acscIfCan| |setLabelValue| |cup| |sumOfSquares| |lazyPseudoQuotient| - |d01fcf| |pToHdmp| |linearAssociatedOrder| |coord| |solveRetract| - |makingStats?| |groebgen| |unit| |graphStates| |quadratic?| - |removeSquaresIfCan| |maxint| |distance| |leaf?| |keys| |setClipValue| - |double| |lex| |operators| |semiLastSubResultantEuclidean| - |normalizeAtInfinity| |normalizedAssociate| |pquo| |stopTable!| - |safeCeiling| |makeMulti| |paren| |zero| |iiacosh| |solve1| - |stoseInvertibleSet| |nonLinearPart| |possiblyInfinite?| - |skewSFunction| |irreducibleFactors| |stopTableGcd!| |buildSyntax| - |generic| |unit?| |setfirst!| |distdfact| |symmetricSquare| |print| - |constant| |leftDivide| |realEigenvectors| |constant?| |pushup| |And| - |c02agf| |quasiMonicPolynomials| |reduceLODE| |rightQuotient| - |headReduce| |closedCurve?| |drawStyle| |Or| |setColumn!| |genus| - |argumentListOf| |cycles| |algebraic?| |laurentIfCan| |someBasis| - |presuper| |transcendenceDegree| |Not| |minimumExponent| - |squareFreePolynomial| |primeFactor| |anticoord| |stoseSquareFreePart| - |biRank| |setnext!| |iiabs| |OMgetApp| |constantKernel| |OMread| - |level| |anfactor| |eigenvector| |f01rcf| |declare!| |internal?| - |sparsityIF| |cosIfCan| |/\\| |isImplies| |fortranLogical| - |removeDuplicates!| |imagE| |contractSolve| |powerAssociative?| - |varselect| |\\/| |f04arf| |duplicates?| |rk4f| |cAsech| |prem| - |predicate| |sec2cos| |besselJ| |legendre| |matrixGcd| |s17ahf| - |setProperty!| |monicCompleteDecompose| |eyeDistance| |times!| - |curve?| |createNormalPrimitivePoly| |iibinom| |viewDeltaXDefault| - |ParCond| |lazyPquo| |id| |s17akf| |critMTonD1| |hMonic| |squareTop| - |lepol| |chvar| |changeVar| |primaryDecomp| |lfextlimint| - |firstSubsetGray| |listRepresentation| |quadraticForm| |diagonal| - |factorial| |rdregime| |signatureAst| |halfExtendedSubResultantGcd1| - |lazyIntegrate| |table| |weakBiRank| |ocf2ocdf| |d03eef| |rCoord| - |stirling1| |oblateSpheroidal| |tryFunctionalDecomposition| |insert| - |e02ddf| |new| |discriminant| |string?| |outputGeneral| |OMUnknownCD?| - |integralLastSubResultant| |segment| |computeCycleEntry| |pdf2ef| - |OMputFloat| |inf| |part?| |genericLeftDiscriminant| |varList| - |associatedEquations| |cycleElt| |explicitlyFinite?| |elRow2!| - |adjoint| |atanIfCan| |options| |besselI| |pseudoQuotient| |digits| - |clipPointsDefault| |coerceL| |mirror| |arity| |arbitrary| |ldf2vmf| - |primeFrobenius| |rightRecip| |setErrorBound| |tubePlot| |parameters| - |transcendentalDecompose| |completeHensel| |quasiRegular?| |nsqfree| - |geometric| |repSq| |supDimElseRittWu?| |divergence| |relerror| - |gcdprim| |rroot| |iitanh| |npcoef| |setScreenResolution| |string| - |exprHasAlgebraicWeight| |iiasec| |clearFortranOutputStack| |hclf| - |lazyResidueClass| |PollardSmallFactor| |palginfieldint| |cAtanh| - |order| |rename!| |coefficients| |c06gcf| - |unprotectedRemoveRedundantFactors| |capacity| |symbolIfCan| GF2FG - |clearTheIFTable| |minimumDegree| |subHeight| |optpair| - |isAbsolutelyIrreducible?| |retractIfCan| |compiledFunction| - |rewriteIdealWithRemainder| |c06eaf| |romberg| |mainMonomials| |xn| - |parabolicCylindrical| |setLegalFortranSourceExtensions| |Lazard| - |lagrange| |vertConcat| |distFact| |antisymmetricTensors| |check| - |selectPDERoutines| |iisinh| |var2StepsDefault| |element?| - |RittWuCompare| |erf| |numberOfComputedEntries| |c02aff| |hdmpToP| - |quotientByP| |ptree| |multiEuclideanTree| |changeName| - |conditionsForIdempotents| |OMgetError| |elseBranch| - |loadNativeModule| |diagonal?| |left| |shrinkable| |chineseRemainder| - |algintegrate| |clearDenominator| |printInfo!| |numberOfHues| - |fortranCharacter| |bit?| |screenResolution| |e01sff| |right| - |expintegrate| |quadratic| |composite| |OMcloseConn| - |linearlyDependentOverZ?| |ListOfTerms| |minset| |f01bsf| |nodeOf?| - |simplifyLog| |dilog| |generalInfiniteProduct| |idealiser| |norm| - |nextSublist| |PDESolve| |rank| |initiallyReduce| |colorDef| - |innerSolve1| |factors| |unitCanonical| |e04ycf| |sin| |OMopenString| - |ode| |euclideanSize| |areEquivalent?| |OMwrite| |symmetricTensors| - |oneDimensionalArray| |multiset| |comp| |isQuotient| |predicates| - |cos| |d01alf| |lambert| |identification| |factorials| |makeObject| - |ran| |Si| |nextsousResultant2| |log2| |map| |xCoord| |tan| |f04mcf| - |writeInt8!| |rational| |numberOfComponents| |symmetricPower| |ddFact| - |numberOfPrimitivePoly| |sPol| |currentEnv| |cot| |integrate| - |adaptive| |subTriSet?| |subst| |copy!| |e02bef| |coef| |cTanh| - |compound?| |imagj| |lazyPremWithDefault| |unparse| |sec| |any?| - |cRationalPower| |currentScope| |enqueue!| |palgRDE0| |s17def| |fill!| - |d02gaf| |addiag| |csc| |dequeue| |fortranLiteralLine| |linGenPos| - |OMgetBind| |factor1| |cot2tan| |setprevious!| |acschIfCan| |height| - |c05adf| |asin| |createRandomElement| |selectODEIVPRoutines| |iicos| - |trapezoidal| |semiSubResultantGcdEuclidean2| |lists| - |solveLinearPolynomialEquationByRecursion| |push!| |unexpand| - |convert| |cyclicGroup| |acos| |numberOfChildren| |cyclic?| |dom| - |df2ef| |bfKeys| |eof?| |find| |pointColor| |binary| |symbol| - |formula| |squareFreeLexTriangular| |atan| |setProperties| |row| - |limitedIntegrate| |randomLC| |sumOfDivisors| |pdct| |decomposeFunc| - |OMsupportsSymbol?| |expression| |complexEigenvalues| |acot| - |dioSolve| |radicalRoots| |diophantineSystem| |objects| |primitive?| - |e02bdf| |incrementKthElement| |elt| |evenInfiniteProduct| |minPol| - |integer| |asec| |nativeModuleExtension| |exprToXXP| - |pointColorDefault| |factorsOfCyclicGroupSize| |base| |inverseColeman| - |variable?| |listConjugateBases| |factorSquareFreePolynomial| - |fintegrate| |spherical| |setStatus!| |acsc| |lift| |diagonalMatrix| - |selectfirst| |leftCharacteristicPolynomial| |failed?| |taylorIfCan| - |frst| |seed| |nrows| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |branchPointAtInfinity?| |height| |f07aef| |imagK| + |highCommonTerms| |positiveSolve| |recip| |setFieldInfo| |lazyPquo| + |mainMonomials| |ldf2lst| |cAcoth| |singRicDE| |dihedralGroup| |lift| + |child| |maxdeg| |triangular?| |exactQuotient| |polyRDE| |convert| + |weights| |numberOfCycles| |fill!| |factorSquareFree| |midpoint| + |reduce| |setErrorBound| |box| |OMopenString| |rationalFunction| + |generalPosition| |redpps| |zeroSquareMatrix| |polyRicDE| |unit| + |monicDivide| |domainOf| |commutative?| |cAcsc| |adaptive3D?| + |iiasinh| |ideal| |radicalRoots| |reopen!| |isNot| |components| + |paraboloidal| |separate| |symbol| |viewPosDefault| |numeric| + |bombieriNorm| |hasSolution?| |fintegrate| |getProperty| + |rightFactorIfCan| |sturmVariationsOf| |linearAssociatedLog| + |linearlyDependent?| |bitLength| |expression| |radical| |branchIfCan| + |toScale| |setEmpty!| |LiePoly| |reorder| |f02fjf| |critM| + |bandedHessian| |integer| |hostByteOrder| |interactiveEnv| + |showTheRoutinesTable| |limitPlus| |shallowExpand| |pquo| |precision| + |implies| |objectOf| |readLineIfCan!| |leftNorm| |linearMatrix| + |squareFreePolynomial| |squareFreePrim| |eigenMatrix| |makeViewport3D| + |exponentialOrder| |f02wef| |leadingCoefficientRicDE| |mathieu23| + |curryRight| |tanIfCan| |e02bef| |dmpToHdmp| |rspace| |putColorInfo| + |d02bhf| |startTableInvSet!| |rightExtendedGcd| |yCoordinates| + |cosIfCan| |leadingTerm| |cAsinh| |declare| |crest| |s17akf| + |plotPolar| |xn| |deriv| |setchildren!| |csc2sin| |cap| |extension| + |tail| |coth2trigh| |ode| |OMputEndBVar| |complexZeros| |port| + |getCode| |diophantineSystem| |d02gaf| |graphStates| + |viewWriteDefault| |iisec| |lazyVariations| ** |alphabetic?| + |printInfo!| |byte| |logical?| |besselY| |primlimintfrac| |setPoly| + |OMputObject| |f07fef| |qqq| |isConnected?| |maxPoints| |t| + |outputList| |gbasis| |updatD| |label| |rules| |d01aqf| |hermiteH| + |error| |complexIntegrate| |rightZero| |rquo| |OMgetEndObject| + |replaceKthElement| |sup| |less?| |assert| |exponential1| |unknown| + |cCsch| |cLog| |invertibleElseSplit?| |groebnerFactorize| |ranges| + |powern| |nextPrime| |toseLastSubResultant| |int| |leader| |besselI| + |critMTonD1| |hermite| |hdmpToDmp| |solveLinear| |charClass| + |semiResultantEuclidean2| |cTanh| |stopTable!| |mathieu24| + |complexLimit| |elements| |monicDecomposeIfCan| |var1StepsDefault| + |setProperties| |gethi| |curveColor| |cSech| |mkcomm| |traverse| + |virtualDegree| |branchPoint?| |rischDE| |lSpaceBasis| + |tubePointsDefault| |OMputEndApp| |monomials| |cosSinInfo| + |OMsupportsCD?| |Hausdorff| |alphanumeric?| |subspace| |roman| + |findCycle| |any| |sylvesterMatrix| |computePowers| |leftTraceMatrix| + |li| |constructor| |isOpen?| |numberOfHues| |lazyResidueClass| |cross| + |quadratic?| |max| |selectNonFiniteRoutines| |sylvesterSequence| + |s01eaf| |connectTo| |parabolicCylindrical| |UP2ifCan| |setColumn!| + |OMbindTCP| |option| |c06ecf| |constantToUnaryFunction| |BasicMethod| + |makeSeries| |nullary?| |qinterval| |graphCurves| |diag| |sign| + |e01sbf| |fracPart| |po| |leftOne| |sinhIfCan| |computeCycleLength| + |cAsec| |pushNewContour| |terms| |region| |setProperty!| |lyndonIfCan| + |henselFact| |checkPrecision| |lazyIrreducibleFactors| |setOfMinN| + |setPrologue!| |comparison| |seriesToOutputForm| |pseudoQuotient| + |idealiser| |interval| |rightTrim| |recur| |critBonD| |tValues| + |rootRadius| |d03eef| |isPlus| |increase| |midpoints| + |selectOptimizationRoutines| |leftTrim| |debug3D| |pastel| + |patternMatchTimes| |moebiusMu| |rational| |rootPoly| |c06gsf| + |getOperator| |rombergo| |fortranCharacter| |nullSpace| |row| + |cardinality| |definingPolynomial| |showRegion| |insertRoot!| |d01akf| + |ratDsolve| |systemSizeIF| |makeSin| |coleman| |printInfo| |iicoth| + |calcRanges| |f04axf| |asinhIfCan| |leastMonomial| |minimumDegree| + |test| |write!| |PollardSmallFactor| |bivariatePolynomials| + |rightRemainder| |autoReduced?| |fixedPointExquo| |GospersMethod| + |lyndon| |createThreeSpace| |topPredicate| + |createMultiplicationMatrix| |create3Space| |sumOfSquares| + |aQuadratic| |pushdown| |lexTriangular| |twoFactor| |perspective| + |rightOne| |genus| |tableau| |maxColIndex| |monicRightFactorIfCan| + |leadingBasisTerm| |tablePow| |numericalOptimization| |baseRDE| + |att2Result| |f02akf| |adaptive?| |generate| |showTheIFTable| |close| + |rCoord| |eq| |optional?| |ParCondList| |acosIfCan| |closed?| |kind| + |deref| |writeBytes!| |relativeApprox| |integralRepresents| + |nthRootIfCan| |iter| |prefix| |digits| |norm| + |unrankImproperPartitions1| |whileLoop| |just| |incrementBy| |f01brf| + |pattern| |op| |display| |bumptab| |setAdaptive| |prefixRagits| + |flatten| |dn| |constantOperator| |intPatternMatch| |leftPower| + |zeroDimensional?| |chebyshevU| |LyndonWordsList1| |expand| + |numberOfComponents| |argumentList!| |iifact| |cycle| |noKaratsuba| + |weighted| |reducedContinuedFraction| |bit?| |unitNormalize| + |decompose| |filterWhile| |whitePoint| |getBadValues| |OMconnInDevice| + |internalZeroSetSplit| |length| |getIdentifier| |tracePowMod| + |zeroDim?| |limitedIntegrate| |completeSmith| |filterUntil| + |LazardQuotient2| |euclideanNormalForm| |extractIfCan| + |monicCompleteDecompose| |scripts| |dominantTerm| |compBound| + |palginfieldint| |root?| |message| |select| |mightHaveRoots| + |localIntegralBasis| |real?| |clip| |nonQsign| |pushuconst| + |computeInt| |pseudoRemainder| |sn| + |dimensionOfIrreducibleRepresentation| |input| |outlineRender| + |cartesian| |totalDifferential| |pushFortranOutputStack| |headAst| + |subHeight| |raisePolynomial| |genericRightTraceForm| |union| + |reductum| |library| |coefChoose| |lazyPseudoQuotient| + |roughUnitIdeal?| |exp| |nary?| |iisin| |purelyAlgebraic?| + |LazardQuotient| |subResultantGcdEuclidean| |minimalPolynomial| + |FormatRoman| |lifting1| |se2rfi| |countable?| |groebner| + |popFortranOutputStack| |odd?| |neglist| |polygon?| |OMgetEndApp| + |argumentListOf| |lowerCase?| |high| |qelt| |clipPointsDefault| + |genericLeftTrace| |nextSublist| |setFormula!| |setProperty| + |jacobiIdentity?| |nodes| |stirling1| |expenseOfEvaluation| + |outerProduct| |qsetelt| |credPol| |setAttributeButtonStep| + |cyclicEqual?| |cyclic| |cons| |symmetricPower| |makeRecord| |moduloP| + |removeCosSq| |integralBasis| |set| |shallowCopy| |xRange| + |hyperelliptic| |outputMeasure| |palgLODE| |setvalue!| + |screenResolution| |iisech| |cAtanh| |mkIntegral| |s13aaf| |yRange| + |zero?| |readBytes!| |removeRedundantFactorsInPols| |primitiveElement| + |coercePreimagesImages| |redmat| |lllp| |d02raf| |vconcat| |zRange| + |assign| |asechIfCan| |radicalSimplify| |jordanAlgebra?| + |taylorQuoByVar| |randomLC| |RemainderList| |setTopPredicate| + |SturmHabichtCoefficients| |map!| |conditionP| |cosh2sech| + |eyeDistance| |ref| |hasTopPredicate?| |OMputEndError| |cubic| + |shanksDiscLogAlgorithm| |modularFactor| |stop| |qsetelt!| |f02xef| + |fTable| |initials| |normalElement| |laplacian| |e01baf| |subSet| + |mergeDifference| |d01fcf| |functionIsFracPolynomial?| |second| + |bringDown| |determinant| |optpair| |gderiv| |upperCase?| |tanSum| + |collectUpper| |splitDenominator| |third| |modifyPoint| |bitTruth| + |OMencodingUnknown| |opeval| |localUnquote| |signature| |cycles| + |rewriteIdealWithHeadRemainder| |droot| |OMputEndAtp| |coerceL| + |PDESolve| |toseInvertible?| |perfectNthPower?| |e01sff| + |integerBound| |gcdPolynomial| |numberOfIrreduciblePoly| |setrest!| + |viewPhiDefault| |intermediateResultsIF| |entries| |rational?| + |presub| |leadingIdeal| |palgRDE| |oblateSpheroidal| |ddFact| |acsch| + |lhs| |leadingExponent| |topFortranOutputStack| |listOfLists| |limit| + |ptFunc| |optimize| |hasPredicate?| |order| |separant| + |rationalPoints| |rhs| |initTable!| |nil?| |karatsubaDivide| + |superHeight| |associative?| |subResultantsChain| |void| |asecIfCan| + |iidsum| |leftAlternative?| |moebius| |forLoop| |Ci| |quotedOperators| + |generateIrredPoly| |systemCommand| |atom?| |multiplyExponents| + |addMatchRestricted| |minPoints3D| |interpolate| |times!| + |stronglyReduce| |randomR| |deepestTail| |sumOfDivisors| |f04asf| + |pToHdmp| |semiDegreeSubResultantEuclidean| |member?| |rootsOf| + |numberOfFactors| |nextIrreduciblePoly| |orthonormalBasis| |tRange| + |superscript| |points| |factorOfDegree| |univariatePolynomials| + |nullary| |bezoutMatrix| |orbit| |thenBranch| + |isAbsolutelyIrreducible?| |basisOfLeftAnnihilator| |pushucoef| + |distribute| |normal| |createPrimitivePoly| |lfunc| |cSin| + |mainCoefficients| |printStatement| |untab| |OMreadStr| |square?| + |leftGcd| |univariatePolynomial| |queue| |mainPrimitivePart| |key| + |readUInt32!| |generalizedEigenvector| |mirror| |mr| |initiallyReduce| + |radicalOfLeftTraceForm| |expintegrate| |iflist2Result| |fixedPoint| + |numberOfPrimitivePoly| |endSubProgram| |irreducibleFactor| + |setRealSteps| |rotatex| |removeRoughlyRedundantFactorsInContents| + |reflect| |reduceBasisAtInfinity| |expt| + |purelyAlgebraicLeadingMonomial?| |algebraic?| |filename| + |primlimitedint| |splitConstant| |depth| |checkRur| |lifting| + |OMgetObject| |e02adf| |cond| |lazyEvaluate| |logpart| |rename!| + |outputBinaryFile| |nextLatticePermutation| |c02aff| + |viewThetaDefault| |bsolve| |shiftRight| |contours| + |reciprocalPolynomial| |leftMult| |generalLambert| |pade| |parse| + |perfectSqrt| |polygamma| |mainVariable| |listLoops| |OMgetAtp| + |critMonD1| |univcase| |linearAssociatedOrder| |genericLeftNorm| + |logIfCan| |extendIfCan| |countRealRoots| |pseudoDivide| |groebner?| + |overlap| |radicalEigenvalues| |goodPoint| |reverse!| |normalizeIfCan| + |central?| |c06fpf| |curve?| |partition| |pdct| |denominator| + |substring?| |iidprod| |internalAugment| |squareMatrix| + |integralCoordinates| |appendPoint| |setMaxPoints3D| + |halfExtendedResultant1| |viewport3D| |recolor| |internalSubPolSet?| + |rightScalarTimes!| |cycleEntry| |exponent| |c06gbf| |laguerre| + |relationsIdeal| |suffix?| |complexNormalize| |differentialVariables| + |tanAn| |call| |internalSubQuasiComponent?| |writeLine!| |setStatus| + |colorDef| |compiledFunction| |fortranInteger| |rowEchLocal| |s17ajf| + |super| |lex| |charpol| |tubeRadiusDefault| |inconsistent?| |nullity| + |shufflein| |lo| |rootKerSimp| |sPol| EQ |messagePrint| |Lazard2| + |has?| |startStats!| |BumInSepFFE| |number?| |exprToGenUPS| + |inverseIntegralMatrixAtInfinity| |symmetricProduct| |hdmpToP| + |linear?| |sizeLess?| |c06fqf| |evenlambert| |e02bbf| + |quasiMonicPolynomials| |elementary| |genericRightDiscriminant| + |palglimint| |ode2| |push| |positiveRemainder| |arg1| |twist| |iitanh| + |idealiserMatrix| |s17dcf| |monicLeftDivide| |associatedEquations| + |insertionSort!| |arg2| |f01maf| |block| |rootBound| |coord| |index| + |d03faf| |lcm| |e02zaf| |drawCurves| |insertTop!| |f02aff| |froot| + |c06gqf| |putGraph| |trailingCoefficient| |getExplanations| |mesh| + |OMgetInteger| |standardBasisOfCyclicSubmodule| |resultant| + |cyclePartition| |conditions| |dictionary| |ScanArabic| + |uncouplingMatrices| |getVariableOrder| |append| |associator| + |compactFraction| |externalList| |algebraicVariables| |pop!| |match| + |delete| |OMlistCDs| |structuralConstants| |pair| + |fullPartialFraction| |c06ebf| |gcd| |showIntensityFunctions| + |multiplyCoefficients| |value| |more?| |result| |eof?| + |prepareDecompose| |makeGraphImage| |f02aef| |companionBlocks| |false| + |asinIfCan| |abelianGroup| |acoshIfCan| |rewriteIdealWithRemainder| + |leftScalarTimes!| |roughEqualIdeals?| |bounds| |resetVariableOrder| + |mindegTerm| |returnTypeOf| |polCase| |subPolSet?| |gcdPrimitive| + |innerint| |inR?| |reset| |moduleSum| |writeUInt8!| |d01apf| + |quotientByP| |e01bhf| |mpsode| |linearPart| |selectAndPolynomials| + |setRow!| |stiffnessAndStabilityFactor| |swap| |OMputSymbol| + |categoryFrame| |csubst| |s18def| |completeHermite| |npcoef| + |reduceLODE| |write| |OMgetString| |SturmHabicht| |cycleElt| + |primextintfrac| |tan2trig| |#| |graphs| |sequences| |symbolTableOf| + |tree| |save| |primextendedint| |children| |Si| |rdregime| |cCot| + |nextColeman| |reducedQPowers| |saturate| |yellow| |makeprod| |dec| + |e02bcf| |currentCategoryFrame| |factorsOfDegree| |subresultantVector| + |complexRoots| |lastSubResultantEuclidean| |overbar| |extractProperty| + |critT| |buildSyntax| |nextPrimitiveNormalPoly| |iiperm| UP2UTS |sin?| + |s14baf| |RittWuCompare| |complexExpand| |closeComponent| |prem| + |trunc| |iomode| |eulerE| |characteristic| |float?| |divideIfCan!| + |listYoungTableaus| |bat1| |selectMultiDimensionalRoutines| + |squareFreePart| |addmod| |smith| |e04ucf| |addPoint| |jacobi| + |component| |unmakeSUP| |physicalLength| |irreducibleRepresentation| + |e04naf| |leadingSupport| |fortranTypeOf| |parametersOf| |expandLog| + |getlo| |algDsolve| |elseBranch| |pow| |supersub| |subCase?| |over| + |resetBadValues| |insert!| |leftRank| |augment| |tanh2trigh| + |createMultiplicationTable| |sizeMultiplication| |btwFact| |generator| + |find| |pointColorPalette| |minGbasis| |LowTriBddDenomInv| + |increasePrecision| |multiEuclideanTree| |comment| |fixPredicate| + |numberOfDivisors| |rightExactQuotient| |iicos| |front| |log10| + |tensorProduct| |showTheSymbolTable| |socf2socdf| + |getMultiplicationTable| |lfinfieldint| |figureUnits| |parent| + |bigEndian| |interReduce| |cExp| |unprotectedRemoveRedundantFactors| + |bitand| |integralMatrix| |setScreenResolution| |rightUnits| + |stoseLastSubResultant| |kmax| |level| |explicitlyFinite?| |minset| + |coshIfCan| |basisOfRightNucleus| |fmecg| |bitior| |OMencodingXML| + |realZeros| |musserTrials| |mapmult| |totalGroebner| |bottom!| |fi2df| + |identitySquareMatrix| |dualSignature| |extractBottom!| |rotatey| + |floor| |nextsousResultant2| |signatureAst| |lastSubResultant| |dark| + |mkAnswer| |fractRadix| |exists?| |generic| |partialNumerators| + |createLowComplexityNormalBasis| |rightQuotient| |polyred| F + |numberOfComputedEntries| |makeSUP| |degreeSubResultant| |sec2cos| + |iprint| |mapSolve| |symFunc| |getZechTable| |clearTable!| |quote| + |permanent| |basisOfNucleus| |open| |perfectSquare?| |matrix| + |deleteProperty!| |numer| |expintfldpoly| |hspace| |search| |digit| + |basisOfRightAnnihilator| |pmComplexintegrate| |safeFloor| |isAnd| + |null| |e02ahf| |algebraicOf| |truncate| |denom| |principalIdeal| + |before?| |tubeRadius| |intensity| |ramifiedAtInfinity?| + |makeFloatFunction| |dihedral| |leftMinimalPolynomial| |rightNorm| + |module| |newReduc| |not| |exprHasAlgebraicWeight| |doubleDisc| + |normal?| |packageCall| |insertBottom!| |iiasech| |s20adf| |vectorise| + |scale| |and| |pointColor| |useEisensteinCriterion?| |optAttributes| + |readIfCan!| |operations| |cAtan| |permutationRepresentation| |d02kef| + |trapezoidal| |outputForm| |or| |categories| |OMputEndAttr| + |changeThreshhold| |leftRegularRepresentation| |whatInfinity| + |capacity| |elRow2!| |f01bsf| |nextPartition| |airyBi| |xor| |cAcosh| + |acothIfCan| |genericLeftMinimalPolynomial| |LiePolyIfCan| + |permutation| |rotatez| |solveLinearPolynomialEquationByFractions| + |multiple?| |expPot| |case| |minordet| |internalDecompose| |log2| + |halfExtendedSubResultantGcd1| |nor| |complement| |e02baf| + |OMunhandledSymbol| |startTable!| |Zero| |lexico| + |certainlySubVariety?| |rootSplit| |lintgcd| |shift| |flexibleArray| + |unit?| |routines| |besselJ| |Vectorise| |One| |position!| + |OMopenFile| |headReduce| |rightAlternative?| |minColIndex| |coerce| Y + |purelyTranscendental?| |makeTerm| |explicitlyEmpty?| |dimensionsOf| + |currentSubProgram| |sech2cosh| |leftUnit| |s19acf| |imagi| |primes| + |construct| |monomial?| |normalize| |maxRowIndex| |coerceP| |leftLcm| + |readUInt16!| |leftExtendedGcd| |halfExtendedResultant2| + |boundOfCauchy| |generalizedEigenvectors| |associates?| |meshPar1Var| + |alternating| |resultantEuclidean| |iiasec| |leftDiscriminant| |infix| + |cyclicParents| |cycleLength| |shiftRoots| |normalForm| + |wronskianMatrix| |semicolonSeparate| |stoseInvertible?| |top| + |factorAndSplit| |updatF| |badValues| |parametric?| |lazyIntegrate| + |inc| |mainValue| |nthFlag| |discriminantEuclidean| |probablyZeroDim?| + |lineColorDefault| |testDim| |binary| |setelt!| |rootProduct| + |stFunc2| |showSummary| |adjoint| |semiSubResultantGcdEuclidean2| + |nodeOf?| |stronglyReduced?| |sort| |symmetricDifference| + |balancedBinaryTree| |constantOpIfCan| |singularitiesOf| + |divisorCascade| |cfirst| |obj| |rootNormalize| |ratpart| |continue| + |modularGcd| |symbolIfCan| |lazy?| |singularAtInfinity?| + |numberOfFractionalTerms| |fibonacci| |xCoord| |gcdcofactprim| + |showAttributes| |cache| |argument| |root| |balancedFactorisation| + |reverseLex| |space| |cscIfCan| |lookup| |makeEq| |lyndon?| + |youngGroup| |linears| |legendre| |list| |removeZero| |s17acf| + |cothIfCan| |lfintegrate| |frobenius| |extract!| |digit?| + |traceMatrix| |coerceS| |e02daf| |legendreP| |random| |car| + |ramified?| |closedCurve?| |reducedDiscriminant| |cot2trig| + |invertIfCan| |plenaryPower| |color| |resetNew| |cdr| |setfirst!| + |zeroSetSplit| |ef2edf| |restorePrecision| |explicitEntries?| + |secIfCan| |zeroVector| |deepExpand| |discreteLog| |ODESolve| + |setDifference| |minrank| |changeName| |name| + |clearFortranOutputStack| |matrixConcat3D| |acscIfCan| |setlast!| + |setIntersection| |f04mbf| |d02bbf| |ceiling| |quatern| + |removeSuperfluousQuasiComponents| |body| |binaryTournament| |f02aaf| + |weakBiRank| |trace2PowMod| |getButtonValue| |isExpt| |ffactor| + |bernoulli| |setUnion| |e01bef| |s15adf| |coordinates| |OMputVariable| + |roughBase?| |remove| |s21bbf| |atanIfCan| |apply| |simplifyLog| + |cyclicEntries| |sin2csc| |squareFreeLexTriangular| |selectsecond| + |d02cjf| |closedCurve| |factorList| |matrixGcd| |s15aef| + |solveLinearPolynomialEquationByRecursion| |janko2| |getDatabase| + |interpretString| |f04mcf| |OMputInteger| |last| |scalarTypeOf| + |unrankImproperPartitions0| |cCoth| GF2FG |isTimes| |size| + |bezoutDiscriminant| |s18acf| |cAcot| |padicallyExpand| |assoc| + |factorset| |output| |f02awf| |empty| |power!| |f02adf| |thetaCoord| + |uniform| |monomRDE| |readLine!| |enterInCache| |critB| |e04gcf| + |exprToUPS| |mindeg| |hclf| |removeRedundantFactorsInContents| + |heapSort| |OMreadFile| |distdfact| |padicFraction| |create| |solve| + |first| |psolve| |drawStyle| |exprHasLogarithmicWeights| + |setLabelValue| |e02dcf| |rightRegularRepresentation| |rightMult| + |generic?| |setOrder| |rest| |separateDegrees| |generalSqFr| + |outputFloating| |coHeight| |splitNodeOf!| |unknownEndian| |dmpToP| + |invmultisect| |numberOfNormalPoly| |substitute| |numberOfOperations| + |antisymmetric?| |ocf2ocdf| |vark| |OMgetAttr| |removeDuplicates| + |f02abf| |usingTable?| |ricDsolve| |oddInfiniteProduct| |c06ekf| + |rationalIfCan| |fractRagits| |listexp| |generalInfiniteProduct| + |graeffe| |simpleBounds?| |singleFactorBound| |leftFactor| + |littleEndian| |scanOneDimSubspaces| |next| |chiSquare1| |s17ahf| BY + |medialSet| |binaryTree| |in?| |numericIfCan| |unitsColorDefault| + |writeInt8!| |fixedPoints| |knownInfBasis| |leaves| |s18adf| + |rightLcm| |linearPolynomials| |push!| |qroot| |unexpand| + |extendedEuclidean| |factorSFBRlcUnit| |unaryFunction| |subtractIfCan| + |realRoots| |setScreenResolution3D| |resultantReduitEuclidean| + |monomRDEsys| |transcendent?| |applyQuote| |OMputBVar| + |leftRankPolynomial| |wordInStrongGenerators| |clearTheIFTable| + |stoseInternalLastSubResultant| |repSq| |reduction| |equality| + |expandTrigProducts| |computeCycleEntry| |exprToXXP| + |squareFreeFactors| |infieldIntegrate| |mainSquareFreePart| + |rischNormalize| |constantRight| |cup| |bivariateSLPEBR| |setLength!| + |csch2sinh| |pmintegrate| |rectangularMatrix| |variationOfParameters| + |charthRoot| |leftDivide| |measure| |constantLeft| |corrPoly| + |radicalEigenvector| |failed?| |ruleset| |symmetricSquare| |setValue!| + |moreAlgebraic?| |radicalSolve| |minPoints| |exactQuotient!| + |repeating?| NOT |elColumn2!| |semiDiscriminantEuclidean| + |exponential| |octon| |rationalApproximation| |represents| |bag| + |rightRankPolynomial| |lazyPrem| |coerceImages| |resize| OR |modulus| + |jordanAdmissible?| |constantKernel| |factorByRecursion| + |rewriteSetWithReduction| |style| |nlde| |primaryDecomp| + |partialFraction| AND |divide| |quasiMonic?| + |internalLastSubResultant| |suchThat| |scaleRoots| + |stoseInvertible?reg| |goto| |predicates| |powerAssociative?| + |complexEigenvectors| |signAround| |trigs2explogs| |prefix?| + |cycleSplit!| |arguments| |tanh2coth| |linearDependenceOverZ| + |inHallBasis?| |monomialIntPoly| |aromberg| |subMatrix| |e01bgf| + |f04faf| |conjugates| |convergents| |cyclicGroup| |incr| + |useEisensteinCriterion| |digamma| |satisfy?| |getProperties| |d03edf| + |setleaves!| |zeroDimPrimary?| + |generalizedContinuumHypothesisAssumed?| |sizePascalTriangle| + |atanhIfCan| |triangulate| |isList| |pdf2ef| |roughBasicSet| + |printingInfo?| |OMreceive| |semiResultantEuclidean1| |makeSketch| + |baseRDEsys| |supDimElseRittWu?| |hi| |exprHasWeightCosWXorSinWX| + |sncndn| |invertible?| |indices| |identityMatrix| |pointColorDefault| + |pascalTriangle| |cot2tan| |elliptic?| |singular?| |lieAlgebra?| + |notelem| |edf2efi| |char| |f02agf| |extendedint| |dimensions| + |cotIfCan| |currentScope| |antiAssociative?| |badNum| |regime| + |viewSizeDefault| |antisymmetricTensors| |flagFactor| |cos2sec| + |subQuasiComponent?| |taylorIfCan| |OMParseError?| |infix?| + |directory| |plusInfinity| |realEigenvectors| |newSubProgram| + |character?| |basicSet| |rk4qc| |gensym| |viewDefaults| |OMgetBVar| + |subscript| |mask| |radix| |minusInfinity| |cSinh| |collect| + |leftUnits| |lfextlimint| |complete| * |nonLinearPart| |vedf2vef| + |low| |delta| |patternVariable| |print| |magnitude| |tanintegrate| + |selectPolynomials| |condition| |setsubMatrix!| |iteratedInitials| + |poisson| |rem| |noncommutativeJordanAlgebra?| |fortranCarriageReturn| + |OMread| |solveLinearPolynomialEquation| |resolve| |addPointLast| + |morphism| |exponents| |d01alf| |e04mbf| |f07adf| |constant| |quo| + |principal?| |float| |varselect| |d01gaf| |inputOutputBinaryFile| + |scan| |noLinearFactor?| |leadingIndex| |readByte!| |iExquo| + |divideExponents| = |karatsubaOnce| |zeroOf| |OMclose| |stFuncN| + |changeWeightLevel| |OMgetEndBind| |numberOfChildren| |e04fdf| + |retractable?| |OMReadError?| |div| |OMputFloat| |evaluateInverse| + |ode1| |entry?| |OMsetEncoding| |type| |divergence| + |complexNumericIfCan| |s17aef| |triangSolve| + |stiffnessAndStabilityOfODEIF| |exquo| < |basisOfCentroid| + |factorsOfCyclicGroupSize| |overlabel| |s20acf| |oddintegers| + |hexDigit?| |pair?| |byteBuffer| |blankSeparate| LODO2FUN ~= > |trim| + |basisOfLeftNucloid| |node?| |setprevious!| |build| |rubiksGroup| + |removeCoshSq| |e02akf| |prepareSubResAlgo| ~ |check| |wreath| <= + |lambda| |LyndonWordsList| |consnewpol| |fortran| |leftQuotient| + |enqueue!| |eigenvectors| |resultantEuclideannaif| |localAbs| + |firstSubsetGray| |move| >= |euler| |frst| |KrullNumber| + |resultantnaif| |showAll?| |torsion?| |constant?| |primintegrate| + |OMputAttr| |jacobian| |rk4a| |anfactor| |f04maf| |mapUp!| + |pointSizeDefault| |key?| |linearDependence| |extractSplittingLeaf| + |f04qaf| |status| |/\\| |outputAsScript| |varList| + |createGenericMatrix| GE |commaSeparate| |sturmSequence| |addBadValue| + |possiblyInfinite?| |extractTop!| |d01ajf| |particularSolution| + |lambert| |ignore?| |\\/| + |aspFilename| GT |iiacos| + |showArrayValues| |finiteBound| |product| |useNagFunctions| + |alternative?| |repeatUntilLoop| |curry| |mapGen| - LE |coth2tanh| + |f04arf| |mainForm| |clipParametric| |createLowComplexityTable| + |LyndonBasis| |integral| |getSyntaxFormsFromFile| |lowerCase| + |toseInvertibleSet| / |inf| LT |ScanFloatIgnoreSpaces| + |stoseInvertibleSetreg| |intcompBasis| |head| |relerror| |cyclic?| + |outputArgs| |karatsuba| |overset?| |showTypeInOutput| |readUInt8!| + |inverseColeman| |multiEuclidean| |hex| |compile| |outputAsFortran| + |linSolve| |setPredicates| |e02agf| |listRepresentation| |phiCoord| + |rightMinimalPolynomial| |commutator| |redPo| |reducedSystem| + |retract| |zoom| |preprocess| |subResultantGcd| |myDegree| + |factorFraction| |selectPDERoutines| |setPosition| |totolex| + |expandPower| |contains?| |acschIfCan| |iiatanh| + |zeroSetSplitIntoTriangularSystems| |outputAsTex| |removeSinSq| + |rischDEsys| |unary?| |iiacoth| |FormatArabic| |aCubic| |palgRDE0| + |property| |normalDeriv| |doubleComplex?| |df2mf| |minRowIndex| + |imagJ| |simplify| |indiceSubResultantEuclidean| |seed| + |clipWithRanges| |coordinate| |pushup| |setTex!| + |cyclotomicDecomposition| |operator| |mdeg| |approxNthRoot| + |clipBoolean| |mergeFactors| |normalized?| |getOrder| |iisqrt3| F2FG + |prindINFO| |fprindINFO| |transform| |skewSFunction| |taylorRep| + |genericRightNorm| |merge!| |sort!| |units| |setAdaptive3D| + |infRittWu?| |identification| |upperCase!| |OMconnOutDevice| + |modifyPointData| |variable?| |OMgetEndAttr| |pol| |errorKind| + |updateStatus!| |createNormalPoly| |scripted?| |inrootof| + |leviCivitaSymbol| |ipow| |part?| |duplicates?| |wholeRadix| + |imaginary| |divisor| |diagonal?| |gcdprim| |basis| |Nul| |sorted?| + |gramschmidt| |resetAttributeButtons| |reverse| |plus| |clearCache| + |OMputEndObject| |endOfFile?| |makeVariable| |sts2stst| |df2ef| + |s13acf| |script| |rowEch| |strongGenerators| |univariateSolve| + |sortConstraints| |computeBasis| |numberOfImproperPartitions| + |alphanumeric| |subscriptedVariables| |setright!| |doubleFloatFormat| + |rename| |stoseInvertibleSetsqfreg| |iisinh| |code| |double?| |cCosh| + |sqfree| |qfactor| |patternMatch| |eq?| |c02agf| |quadraticForm| + |infiniteProduct| |orbits| |postfix| |e01saf| |viewWriteAvailable| + |c05adf| |sh| |callForm?| |s21baf| |vector| |bright| |tex| + |lexGroebner| |comp| |SturmHabichtSequence| |commutativeEquality| + |times| |bat| |derivative| |upperCase| |removeConstantTerm| + |quasiComponent| |initial| |differentiate| |indiceSubResultant| + |extractIndex| |s19abf| |integer?| |symbol?| |rootSimp| |denomRicDE| + |OMputAtp| |associatedSystem| |bipolar| |doubleRank| + |numberOfVariables| |leastPower| |is?| |acotIfCan| |primintfldpoly| + |function| |rangePascalTriangle| |bumptab1| + |tryFunctionalDecomposition?| |besselK| |basisOfCommutingElements| + |ksec| |partitions| |tan2cot| |showAllElements| |withPredicates| + |listConjugateBases| |modularGcdPrimitive| |infinityNorm| + |univariate?| |fglmIfCan| |failed| |rroot| |factorials| |f01rdf| + |maxrow| |dom| |genericLeftDiscriminant| |monom| |eval| |allRootsOf| + |quasiRegular| |irreducibleFactors| |rur| |numerator| |open?| + |limitedint| |removeSuperfluousCases| |elliptic| |escape| |rule| + |bandedJacobian| |semiIndiceSubResultantEuclidean| |solid?| + |seriesSolve| |coefficient| |qualifier| |pole?| |nextsubResultant2| + |mapUnivariate| |normalDenom| |rk4f| |semiResultantEuclideannaif| + |chebyshevT| |printHeader| |bfKeys| |prinpolINFO| + |univariatePolynomialsGcds| |slex| |var2StepsDefault| |common| + |getStream| |totalfract| |printCode| |getPickedPoints| |checkForZero| + |sechIfCan| |asimpson| |diagonal| |f2st| |subresultantSequence| + |partialDenominators| |split| |reify| |rationalPower| |modTree| + |extractClosed| |nextNormalPrimitivePoly| |mapdiv| |isEquiv| + |tryFunctionalDecomposition| |logGamma| |dflist| |f01mcf| |title| + |createRandomElement| |ScanRoman| |prologue| |makeop| |enterPointData| + |expr| |algebraicDecompose| |OMgetSymbol| |OMgetVariable| |Is| + |complex?| |members| |wordsForStrongGenerators| |stopTableInvSet!| + |numerators| |s18aef| |newLine| |round| |palgint| |coefficients| + |tubePlot| |lastSubResultantElseSplit| |compose| |flexible?| + |algebraicCoefficients?| |e| |readInt32!| |wordInGenerators| + |mapBivariate| |fortranLinkerArgs| |zCoord| |ran| |setref| |SFunction| + |scopes| |cAsech| |factorSquareFreePolynomial| + |drawComplexVectorField| |weight| |exQuo| |polar| |physicalLength!| + |lowerCase!| |variable| |true| |typeLists| |writeByte!| + |stopTableGcd!| |atrapezoidal| |read!| |characteristicSet| |iterators| + |invertibleSet| |ratDenom| |roughSubIdeal?| + |selectSumOfSquaresRoutines| |writable?| |perfectNthRoot| |nothing| + |basisOfLeftNucleus| |factorial| |d01bbf| |element?| FG2F |spherical| + |colorFunction| |isPower| |powers| |makeResult| |iilog| |nextItem| + |copyInto!| |primeFactor| |inverse| |characteristicPolynomial| |init| + |accuracyIF| |typeList| |bernoulliB| |isOp| |s18aff| |e02ddf| + |imports| |imagI| |SturmHabichtMultiple| |setCondition!| |meatAxe| + |sinh2csch| |extendedIntegrate| |s17adf| |setClosed| |numFunEvals3D| + |irreducible?| |d02gbf| |factorSquareFreeByRecursion| + |selectODEIVPRoutines| |upDateBranches| |factorPolynomial| + |chainSubResultants| |df2fi| |reindex| |explimitedint| |f02bjf| + |c06gcf| |setMinPoints3D| |properties| |quartic| |euclideanSize| + |meshPar2Var| |width| |remainder| |yCoord| |primitive?| |d02ejf| + |transcendentalDecompose| |translate| |applyRules| |cSec| |close!| + |mainCharacterization| |setleft!| |isImplies| |HenselLift| |addiag| + |curryLeft| |schwerpunkt| |d01amf| |integralAtInfinity?| |chiSquare| + |cPower| |defineProperty| |conical| |permutationGroup| + |nextNormalPoly| |internalIntegrate0| |maximumExponent| |getGoodPrime| + |torsionIfCan| |pdf2df| |normal01| |fullDisplay| |stFunc1| |diff| + |rank| |splitLinear| |every?| |swap!| |hostPlatform| |polyPart| + |mapUnivariateIfCan| |HermiteIntegrate| |rightTrace| |trueEqual| + |quadraticNorm| |rootDirectory| |weierstrass| |rotate!| |bothWays| + |factorGroebnerBasis| |anticoord| |safeCeiling| |extractPoint| + |removeRoughlyRedundantFactorsInPols| |hMonic| |kovacic| |oddlambert| + |discriminant| |minimize| |cAsin| |f02bbf| |compound?| |mapExponents| + |createIrreduciblePoly| |expint| |supRittWu?| |optional| |subst| + |cyclotomic| |returns| |setStatus!| |powmod| |child?| + |degreePartition| |mkPrim| |Ei| |scalarMatrix| |cyclicSubmodule| + |ScanFloatIgnoreSpacesIfCan| |shade| |maxrank| |cyclicCopy| + |interpret| |e01sef| |diagonals| |areEquivalent?| |stack| |green| + |collectQuasiMonic| |e02bdf| |completeEchelonBasis| |pushdterm| + |airyAi| |completeHensel| |complementaryBasis| |argscript| |ratPoly| + |binomThmExpt| |integralMatrixAtInfinity| |rightUnit| |isOr| |lists| + |degree| |internalInfRittWu?| |constantCoefficientRicDE| |light| + |mainDefiningPolynomial| |tower| |findBinding| |mapMatrixIfCan| + |permutations| |dequeue| |removeSquaresIfCan| |formula| |one?| + |external?| |B1solve| |setLegalFortranSourceExtensions| |viewpoint| + |fortranLogical| |positive?| |radPoly| |genericLeftTraceForm| |d01anf| + |iiacsc| |symmetricGroup| |internalIntegrate| |iicot| |totalLex| + |objects| |subResultantChain| |dim| |makeMulti| |s17aff| |back| + |lieAdmissible?| |mappingAst| |var1Steps| |maxIndex| |base| + |exteriorDifferential| |stoseSquareFreePart| |OMputString| + |startTableGcd!| SEGMENT |palglimint0| |createNormalElement| + |extendedResultant| |innerEigenvectors| |nil| |string?| |eulerPhi| + |sinhcosh| |nthFractionalTerm| |halfExtendedSubResultantGcd2| |nrows| + |getGraph| |minPoly| |OMgetFloat| |abs| |palgextint0| |e04dgf| + |complexNumeric| |firstNumer| |imagj| |lprop| |collectUnder| |ncols| + |OMputError| |OMserve| |nonSingularModel| |numericalIntegration| + |alternatingGroup| |lquo| |center| |getMultiplicationMatrix| |randnum| + |reseed| |pureLex| |pToDmp| |printTypes| |approximate| |kernels| + |goodnessOfFit| |bivariate?| |incrementKthElement| |fortranDouble| + |symmetricRemainder| |decimal| |squareTop| |OMwrite| + |brillhartIrreducible?| |complex| |log| |univariate| |prod| + |toseSquareFreePart| |multisect| |iCompose| |f02axf| |datalist| + |makeCrit| |OMsend| |monicRightDivide| |Lazard| |node| UTS2UP |biRank| + |diagonalMatrix| |maxint| |normFactors| |quasiRegular?| + |OMencodingSGML| |diagonalProduct| |totalDegree| + |regularRepresentation| |laguerreL| |erf| |headReduced?| + |fortranLiteralLine| |intersect| |inRadical?| + |removeRoughlyRedundantFactorsInPol| |complexForm| |wholePart| + |combineFeatureCompatibility| |printStats!| |initiallyReduced?| + |factor| |makeCos| |OMUnknownSymbol?| |power| |OMlistSymbols| + |evaluate| |subNode?| |concat| |rootPower| |compdegd| |quoted?| |sqrt| + |reducedForm| |backOldPos| |monomialIntegrate| |selectFiniteRoutines| + |componentUpperBound| |pointData| |f02ajf| |outputGeneral| |sequence| + |dilog| |minus!| |removeDuplicates!| |real| |lazyPremWithDefault| + |point| |OMgetError| |shuffle| |finiteBasis| |rowEchelonLocal| + |alphabetic| |previous| |exprex| |evenInfiniteProduct| |infinite?| + |sin| |imag| |algSplitSimple| |swapRows!| |mantissa| + |lazyPseudoDivide| |indicialEquationAtInfinity| |viewport2D| |plus!| + |directProduct| |top!| |e02aef| |cos| |shiftLeft| |doublyTransitive?| + |paren| |UnVectorise| |lepol| |submod| |inverseLaplace| + |basisOfMiddleNucleus| |solveid| |crushedSet| |rightDivide| |tan| + |blue| |series| |groebSolve| |numberOfComposites| |finite?| + |expressIdealMember| |removeRedundantFactors| |multMonom| + |derivationCoordinates| |brace| |Gamma| |cot| |eisensteinIrreducible?| + |e01bff| |point?| |addPoint2| |symmetricTensors| |column| + |kroneckerDelta| |unravel| |setnext!| |primitivePart!| |destruct| + |sec| |prevPrime| |distance| |laplace| |source| |getMeasure| |tab1| + |squareFree| |readInt8!| |rightPower| |showScalarValues| |maxPoints3D| + |csc| |iitan| |conjug| |nsqfree| |isTerm| |subNodeOf?| |refine| + |rightRank| |hypergeometric0F1| |nthCoef| |f04jgf| |selectfirst| + |asin| |linGenPos| |min| |category| |increment| |f2df| |revert| + |lagrange| |euclideanGroebner| |e01daf| |equation| |cycleRagits| + |acos| |cylindrical| |showTheFTable| |decrease| |domain| |d01gbf| + |middle| |reduced?| |numberOfMonomials| |OMUnknownCD?| |monomial| + |atan| |setEpilogue!| |associatorDependence| |imagk| + |conditionsForIdempotents| |entry| |package| |constantIfCan| |chvar| + |mainVariables| |readable?| |minPol| + |rewriteSetByReducingWithParticularGenerators| |show| |surface| + |multivariate| |acot| |readInt16!| |unparse| |exptMod| |infieldint| + |choosemon| |target| |dmp2rfi| |rightDiscriminant| |antiCommutative?| + |variables| |stoseInvertible?sqfreg| |asec| |generalTwoFactor| + |sayLength| |iiacosh| |integerIfCan| |parseString| |ReduceOrder| + |s21bcf| |antiCommutator| |hue| |trace| |imagE| |acsc| |c06frf| + |rdHack1| |mainVariable?| |fortranCompilerName| |llprop| |const| + |mapDown!| |inputBinaryFile| |sinh| |getCurve| |loopPoints| |parents| + |drawToScale| |simpson| |oneDimensionalArray| |powerSum| |remove!| + |expenseOfEvaluationIF| |cn| |realSolve| |iiabs| |cosh| |e02dff| + |f01qcf| |inspect| |pleskenSplit| |lazyPseudoRemainder| |ravel| + |freeOf?| |cTan| |monic?| |changeBase| |tanh| |iiexp| |leaf?| + |ip4Address| |iiacsch| |polygon| |reshape| |c05nbf| |findConstructor| + |composites| |schema| |coth| |taylor| |lowerPolynomial| |cschIfCan| + |geometric| |outputFixed| |insertMatch| |extendedSubResultantGcd| + |select!| |sdf2lst| |fortranComplex| |transpose| |sech| |laurent| + |OMgetBind| |setelt| |resultantReduit| |toroidal| |fractionPart| + |multinomial| |integralBasisAtInfinity| |leftCharacteristicPolynomial| + |integralLastSubResultant| |csch| |puiseux| |mat| |c05pbf| + |genericRightTrace| |denomLODE| |sub| |vertConcat| |cAcsch| + |horizConcat| |asinh| |nativeModuleExtension| |quoByVar| |copy| + |curve| |s21bdf| |OMgetType| |curveColorPalette| |listBranches| + |setImagSteps| |inv| |acosh| |showClipRegion| |any?| |hitherPlane| + |makeFR| |getRef| |lflimitedint| |OMputEndBind| + |firstUncouplingMatrix| |update| |concat!| |ground?| |e02gaf| + |replace| |atanh| |useSingleFactorBound?| |OMputBind| |parts| |f04atf| + |hcrf| |changeVar| |recoverAfterFail| |divisors| |changeMeasure| + |ground| |mainExpression| |solve1| |sinIfCan| |acoth| + |extensionDegree| |c06fuf| |autoCoerce| |sumSquares| |multiset| + |merge| |controlPanel| |size?| |edf2fi| |dAndcExp| |leadingMonomial| + |asech| |tanQ| |mix| RF2UTS |functionIsOscillatory| |palgLODE0| + |negative?| |s17dgf| |exp1| |OMgetApp| |leadingCoefficient| + |contractSolve| |basisOfRightNucloid| |leftFactorIfCan| |dimension| + |tubePoints| |rationalPoint?| |viewDeltaYDefault| |rootOf| + |polarCoordinates| |validExponential| |expextendedint| |multiple| + |primitiveMonomials| |setClipValue| |createPrimitiveElement| |arity| + |delete!| |fractionFreeGauss!| |e02ajf| |stopMusserTrials| |position| + |quadratic| |solveInField| |infLex?| |simpsono| |say| |ridHack1| + |difference| |stosePrepareSubResAlgo| |palgint0| |normDeriv2| + |intChoose| |s13adf| |ord| |factor1| |getOperands| |parabolic| + |tableForDiscreteLogarithm| |bitCoef| |match?| |distFact| + |basisOfCenter| |polynomialZeros| |laurentIfCan| |algebraicSort| + |bumprow| |htrigs| |iicosh| |elem?| |definingInequation| + |UpTriBddDenomInv| |f01qdf| |createPrimitiveNormalPoly| + |solveLinearlyOverQ| |harmonic| |hasHi| |isMult| |shrinkable| + |option?| |edf2ef| |decreasePrecision| |realEigenvalues| + |cRationalPower| |lighting| |processTemplate| |cCos| + |stripCommentsAndBlanks| |fortranReal| |denominators| + |showFortranOutputStack| |zag| |iterationVar| |mvar| |debug| + |possiblyNewVariety?| |keys| |hash| |addMatch| |iroot| + |createNormalPrimitivePoly| |OMmakeConn| |setProperties!| |bracket| + |problemPoints| |algint| |count| |invmod| D |stoseInvertibleSet| + |double| |solid| |qPot| |f01ref| |selectOrPolynomials| + |matrixDimensions| |hexDigit| |pointPlot| |decomposeFunc| + |movedPoints| |completeEval| |delay| |LyndonCoordinates| |returnType!| + |nthExponent| |belong?| |rightGcd| |operators| |dfRange| |arbitrary| + |var2Steps| |innerSolve1| |triangularSystems| |mapExpon| |composite| + |hconcat| |split!| |directSum| |e04jaf| |nand| |binaryFunction| + |OMgetEndBVar| |generalizedContinuumHypothesisAssumed| |lfextendedint| + |eigenvector| |selectIntegrationRoutines| |rarrow| + |semiSubResultantGcdEuclidean1| |idealSimplify| |radicalEigenvectors| + |Aleph| |rk4| |errorInfo| |symbolTable| |empty?| |mapCoef| + |useSingleFactorBound| |someBasis| |numFunEvals| |leftTrace| |hasoln| + |sample| |zeroDimPrime?| |indicialEquations| |fixedDivisor| + |clearTheSymbolTable| |beauzamyBound| |copies| |dequeue!| + |bubbleSort!| |integrate| |iibinom| |summation| |clearTheFTable| + |zero| |binarySearchTree| |chineseRemainder| |range| |simplifyPower| + |bytes| |reduceByQuasiMonic| |extend| |declare!| |critpOrder| + |leftRemainder| |laurentRep| |outputSpacing| |nthExpon| |bindings| + |contract| |cAcos| |gradient| |prime| |predicate| |leftZero| |omError| + |tube| |And| |quickSort| |complexSolve| |getMatch| |changeNameToObjf| + |primPartElseUnitCanonical!| |measure2Result| |swapColumns!| + |eigenvalues| |setMaxPoints| |uniform01| |Or| |palgintegrate| + |definingEquations| |OMcloseConn| |setButtonValue| |specialTrigs| + |duplicates| |mesh?| |graphState| |continuedFraction| |axes| |Not| + |zeroMatrix| |iFTable| |LagrangeInterpolation| |integral?| + |OMsupportsSymbol?| |semiLastSubResultantEuclidean| |solveRetract| + |ldf2vmf| |factors| |conjugate| |universe| |null?| |iipow| + |doubleResultant| |rightCharacteristicPolynomial| |pomopo!| + |enumerate| |leastAffineMultiple| |functionIsContinuousAtEndPoints| + |mathieu11| |linkToFortran| |epilogue| |graphImage| + |fillPascalTriangle| |genericPosition| |binding| |latex| |testModulus| + |headRemainder| |deepestInitial| |pack!| |nthFactor| |zerosOf| + |presuper| |userOrdered?| |content| |newTypeLists| |segment| |padecf| + |setMinPoints| |sincos| |algintegrate| + |removeIrreducibleRedundantFactors| |tanNa| |f01rcf| |clikeUniv| + |adaptive| |trivialIdeal?| |bipolarCylindrical| |homogeneous?| + |makeViewport2D| |listOfMonoms| |c06eaf| |iiasin| |generalizedInverse| + |shellSort| |symmetric?| |parameters| |innerSolve| |edf2df| |makeUnit| + |id| |birth| |s14abf| |mainContent| |prinb| |iiGamma| |lazyGintegrate| + |brillhartTrials| |OMconnectTCP| |equiv| |separateFactors| |iiacot| + |s14aaf| |prolateSpheroidal| |repeating| |hessian| |iisqrt2| + |degreeSubResultantEuclidean| |prime?| |cycleTail| |bezoutResultant| + |partialQuotients| |firstDenom| |OMgetEndError| |aLinear| |table| + |red| |linearlyDependentOverZ?| |leftRecip| |wholeRagits| |mulmod| + |cCsc| |nextPrimitivePoly| |viewZoomDefault| + |rewriteIdealWithQuasiMonicGenerators| |subset?| |new| + |makeYoungTableau| |s17dlf| |linearAssociatedExp| |complexEigenvalues| + |OMencodingBinary| |mathieu22| |makingStats?| |primeFrobenius| + |unitCanonical| |insert| |loadNativeModule| |viewDeltaXDefault| + |commonDenominator| |axesColorDefault| |inGroundField?| |stirling2| + |fortranDoubleComplex| |deleteRoutine!| |normalizeAtInfinity| + |indicialEquation| |integralDerivationMatrix| |isobaric?| + |getConstant| |nilFactor| |normalizedDivide| |principalAncestors| + |approximants| |bits| |elRow1!| |quotient| |pile| |heap| |index?| + |f07fdf| |options| |even?| |rightFactorCandidate| |linear| + |mainKernel| |rightTraceMatrix| |unitNormal| |mainMonomial| + |meshFun2Var| |monicModulo| |coerceListOfPairs| |pi| + |exportedOperators| |quasiAlgebraicSet| |normInvertible?| + |clearDenominator| |fortranLiteral| |drawComplex| |An| |d01asf| + |unitVector| |arrayStack| |df2st| |infinity| |minIndex| |integers| + |retractIfCan| |stoseIntegralLastSubResultant| |polynomial| |binomial| + |internal?| |transcendenceDegree| |subTriSet?| |largest| |prinshINFO| + |mathieu12| |string| |dot| |explogs2trigs| |romberg| |constDsolve| + |rst| |e02def| |localReal?| |initializeGroupForWordProblem| + |setVariableOrder| |OMputApp| |list?| |host| |s17dhf| |s17agf| |ptree| + |wrregime| |tanhIfCan| |sum| |tab| |divideIfCan| |kernel| |f01qef| + |iicsc| |direction| |inverseIntegralMatrix| |vspace| |ListOfTerms| + |rangeIsFinite| |groebnerIdeal| |s17def| |connect| |draw| |aQuartic| + |nextSubsetGray| |ParCond| |absolutelyIrreducible?| |nthRoot| + |simplifyExp| |OMgetEndAtp| |complexElementary| |startPolynomial| + |palgextint| |rightRecip| |e04ycf| |expIfCan| |createZechTable| |left| + |cyclotomicFactorization| |dioSolve| |iicsch| |gcdcofact| |groebgen| + |operation| |s19aaf| |rootOfIrreduciblePoly| |f04adf| + |representationType| |right| |approxSqrt| |isQuotient| |plot| + |deepCopy| |unvectorise| |characteristicSerie| |trapezoidalo| + |leftExactQuotient| |generators| |lp| |primPartElseUnitCanonical| + |sqfrFactor| |minimumExponent| |countRealRootsMultiple| |bfEntry| + |safetyMargin| |makeObject| |removeZeroes| |pointLists| |atoms| + |trigs| |map| |clipSurface| |normalise| |removeSinhSq| |redPol| + |normalizedAssociate| |s18dcf| |s19adf| |slash| |elt| |lllip| + |sparsityIF| |realElementary| |currentEnv| |primitivePart| |identity| + |pr2dmp| |Beta| |coef| |iiatan| |nthr| |Frobenius| + |ellipticCylindrical| |sumOfKthPowerDivisors| |rowEchelon| + |genericRightMinimalPolynomial| |copy!| |rotate| |screenResolution3D| + |semiResultantReduitEuclidean| |splitSquarefree| |nil| |infinite| + |arbitraryExponent| |approximate| |complex| |shallowMutable| + |canonical| |noetherian| |central| |partiallyOrderedSet| + |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| + |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| + |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| + |shallowlyMutable| |commutative|)
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T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2733 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2733 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2733 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2733 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-3860 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1297 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-4271 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3860 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1297 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4271 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) -((-4271 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1297 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-3860 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2733 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-858)) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1045)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -2733 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1045))) ((-637 |#1|) |has| |#1| (-1045)) ((-713 #0#) |has| |#1| (-556)) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) |has| |#1| (-556)) ((-722) -2733 (|has| |#1| (-1106)) (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-896 (-1170)) |has| |#1| (-1045)) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . 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(-1200 2895910 2896757 2897686 "TRMANIP" 2900407 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2895351 2895414 2895577 "TRIMAT" 2895842 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2893217 2893454 2893811 "TRIGMNIP" 2895100 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2892737 2892850 2892880 "TRIGCAT" 2893093 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2892406 2892485 2892626 "TRIGCAT-" 2892631 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2889251 2891264 2891545 "TREE" 2892160 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2888525 2889053 2889083 "TRANFUN" 2889118 T TRANFUN (NIL) -9 NIL 2889184 NIL) (-1193 2887804 2887995 2888275 "TRANFUN-" 2888280 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2887608 2887640 2887701 "TOPSP" 2887765 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2886956 2887071 2887225 "TOOLSIGN" 2887489 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2885590 2886133 2886372 "TEXTFILE" 2886739 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2883502 2884043 2884472 "TEX" 2885183 T TEX (NIL) -8 NIL NIL NIL) (-1188 2883283 2883314 2883386 "TEX1" 2883465 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2882931 2882994 2883084 "TEMUTL" 2883215 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2881085 2881365 2881690 "TBCMPPK" 2882654 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2872862 2879245 2879301 "TBAGG" 2879701 NIL TBAGG (NIL T T) -9 NIL 2879912 NIL) (-1184 2867932 2869420 2871174 "TBAGG-" 2871179 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2867316 2867423 2867568 "TANEXP" 2867821 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2860706 2867173 2867266 "TABLE" 2867271 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2860118 2860217 2860355 "TABLEAU" 2860603 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2854726 2855946 2857194 "TABLBUMP" 2858904 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2853948 2854095 2854276 "SYSTEM" 2854567 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2850407 2851106 2851889 "SYSSOLP" 2853199 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2849414 2849919 2850038 "SYSNNI" 2850224 NIL SYSNNI (NIL NIL) -8 NIL NIL 2850309) (-1176 2848684 2849143 2849222 "SYSINT" 2849282 NIL SYSINT (NIL NIL) -8 NIL NIL 2849327) (-1175 2845016 2845962 2846672 "SYNTAX" 2847996 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2842174 2842776 2843408 "SYMTAB" 2844406 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2837423 2838325 2839308 "SYMS" 2841213 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2834658 2836881 2837111 "SYMPOLY" 2837228 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2834175 2834250 2834373 "SYMFUNC" 2834570 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2830194 2831487 2832300 "SYMBOL" 2833384 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2823733 2825422 2827142 "SWITCH" 2828496 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2816967 2822554 2822857 "SUTS" 2823488 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2809033 2816214 2816487 "SUPXS" 2816752 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2800793 2808651 2808777 "SUP" 2808942 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2799952 2800079 2800296 "SUPFRACF" 2800661 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2799573 2799632 2799745 "SUP2" 2799887 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2798021 2798295 2798651 "SUMRF" 2799272 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2797356 2797422 2797614 "SUMFS" 2797942 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2781323 2796533 2796784 "SULS" 2797163 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2780925 2781145 2781215 "SUCHTAST" 2781275 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2780220 2780450 2780590 "SUCH" 2780833 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2774087 2775126 2776085 "SUBSPACE" 2779308 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2773517 2773607 2773771 "SUBRESP" 2773975 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2766882 2768182 2769493 "STTF" 2772253 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2761055 2762175 2763322 "STTFNC" 2765782 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2752366 2754237 2756031 "STTAYLOR" 2759296 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2745496 2752230 2752313 "STRTBL" 2752318 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2740860 2745451 2745482 "STRING" 2745487 T STRING (NIL) -8 NIL NIL NIL) (-1151 2735721 2740233 2740263 "STRICAT" 2740322 T STRICAT (NIL) -9 NIL 2740384 NIL) (-1150 2728476 2733340 2733951 "STREAM" 2735145 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2727986 2728063 2728207 "STREAM3" 2728393 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2726968 2727151 2727386 "STREAM2" 2727799 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2726656 2726708 2726801 "STREAM1" 2726910 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2725672 2725853 2726084 "STINPROD" 2726472 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2725224 2725434 2725464 "STEP" 2725544 T STEP (NIL) -9 NIL 2725622 NIL) (-1144 2718656 2725123 2725200 "STBL" 2725205 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2713782 2717877 2717920 "STAGG" 2718073 NIL STAGG (NIL T) -9 NIL 2718162 NIL) (-1142 2711484 2712086 2712958 "STAGG-" 2712963 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2709631 2711254 2711346 "STACK" 2711427 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2702327 2707772 2708228 "SREGSET" 2709261 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2694752 2696121 2697634 "SRDCMPK" 2700933 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2687669 2692192 2692222 "SRAGG" 2693525 T SRAGG (NIL) -9 NIL 2694133 NIL) (-1137 2686686 2686941 2687320 "SRAGG-" 2687325 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2681146 2685633 2686054 "SQMATRIX" 2686312 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2674832 2677864 2678591 "SPLTREE" 2680491 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2670795 2671488 2672134 "SPLNODE" 2674258 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2669842 2670075 2670105 "SPFCAT" 2670549 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2668579 2668789 2669053 "SPECOUT" 2669600 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2660205 2661975 2662005 "SPADXPT" 2666397 T SPADXPT (NIL) -9 NIL 2668431 NIL) (-1130 2659966 2660006 2660075 "SPADPRSR" 2660158 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2658121 2659921 2659952 "SPADAST" 2659957 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2650066 2651839 2651882 "SPACEC" 2656255 NIL SPACEC (NIL T) -9 NIL 2658071 NIL) (-1127 2648196 2649998 2650047 "SPACE3" 2650052 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2646948 2647119 2647410 "SORTPAK" 2648001 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2645040 2645343 2645755 "SOLVETRA" 2646612 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2644090 2644312 2644573 "SOLVESER" 2644813 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2639392 2640282 2641277 "SOLVERAD" 2643142 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2635207 2635816 2636545 "SOLVEFOR" 2638759 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2629477 2634556 2634653 "SNTSCAT" 2634658 NIL SNTSCAT (NIL T T T T) -9 NIL 2634728 NIL) (-1120 2623583 2627800 2628191 "SMTS" 2629167 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2618268 2623471 2623548 "SMP" 2623553 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2616427 2616728 2617126 "SMITH" 2617965 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2609287 2613478 2613581 "SMATCAT" 2614932 NIL SMATCAT (NIL NIL T T T) -9 NIL 2615482 NIL) (-1116 2606227 2607050 2608228 "SMATCAT-" 2608233 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2603893 2605463 2605506 "SKAGG" 2605767 NIL SKAGG (NIL T) -9 NIL 2605902 NIL) (-1114 2600201 2603309 2603504 "SINT" 2603691 T SINT (NIL) -8 NIL NIL 2603864) (-1113 2599973 2600011 2600077 "SIMPAN" 2600157 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2599252 2599508 2599648 "SIG" 2599855 T SIG (NIL) -8 NIL NIL NIL) (-1111 2598090 2598311 2598586 "SIGNRF" 2599011 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2596923 2597074 2597358 "SIGNEF" 2597919 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2596229 2596506 2596630 "SIGAST" 2596821 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2593919 2594373 2594879 "SHP" 2595770 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2587771 2593820 2593896 "SHDP" 2593901 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2587344 2587536 2587566 "SGROUP" 2587659 T SGROUP (NIL) -9 NIL 2587721 NIL) (-1105 2587202 2587228 2587301 "SGROUP-" 2587306 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2584037 2584735 2585458 "SGCF" 2586501 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2578405 2583484 2583581 "SFRTCAT" 2583586 NIL SFRTCAT (NIL T T T T) -9 NIL 2583625 NIL) (-1102 2571826 2572844 2573980 "SFRGCD" 2577388 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2564953 2566025 2567211 "SFQCMPK" 2570759 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2564573 2564662 2564773 "SFORT" 2564894 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2563691 2564413 2564534 "SEXOF" 2564539 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2562798 2563572 2563640 "SEX" 2563645 T SEX (NIL) -8 NIL NIL NIL) (-1097 2558311 2559026 2559121 "SEXCAT" 2562058 NIL SEXCAT (NIL T T T T T) -9 NIL 2562636 NIL) (-1096 2555464 2558245 2558293 "SET" 2558298 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2553688 2554177 2554482 "SETMN" 2555205 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2553184 2553336 2553366 "SETCAT" 2553542 T SETCAT (NIL) -9 NIL 2553652 NIL) (-1093 2552964 2553016 2553115 "SETCAT-" 2553120 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2549325 2551425 2551468 "SETAGG" 2552338 NIL SETAGG (NIL T) -9 NIL 2552678 NIL) (-1091 2548783 2548899 2549136 "SETAGG-" 2549141 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2548226 2548479 2548580 "SEQAST" 2548704 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2547425 2547719 2547780 "SEGXCAT" 2548066 NIL SEGXCAT (NIL T T) -9 NIL 2548186 NIL) (-1088 2546431 2547091 2547273 "SEG" 2547278 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2545410 2545624 2545667 "SEGCAT" 2546189 NIL SEGCAT (NIL T) -9 NIL 2546410 NIL) (-1086 2544411 2544789 2544989 "SEGBIND" 2545245 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2544032 2544091 2544204 "SEGBIND2" 2544346 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2543605 2543833 2543910 "SEGAST" 2543977 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2542824 2542950 2543154 "SEG2" 2543449 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2542234 2542759 2542806 "SDVAR" 2542811 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2534761 2542004 2542134 "SDPOL" 2542139 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2533354 2533620 2533939 "SCPKG" 2534476 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2532518 2532690 2532882 "SCOPE" 2533184 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2531738 2531872 2532051 "SCACHE" 2532373 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2531384 2531570 2531600 "SASTCAT" 2531605 T SASTCAT (NIL) -9 NIL 2531618 NIL) (-1076 2530871 2531219 2531295 "SAOS" 2531330 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2530436 2530471 2530644 "SAERFFC" 2530830 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2524375 2530333 2530413 "SAE" 2530418 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2523968 2524003 2524162 "SAEFACT" 2524334 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2522289 2522603 2523004 "RURPK" 2523634 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2520926 2521232 2521537 "RULESET" 2522123 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2518149 2518679 2519137 "RULE" 2520607 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2517761 2517943 2518026 "RULECOLD" 2518101 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2517551 2517579 2517650 "RTVALUE" 2517712 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2517022 2517268 2517362 "RSTRCAST" 2517479 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2511870 2512665 2513585 "RSETGCD" 2516221 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2501100 2506179 2506276 "RSETCAT" 2510395 NIL RSETCAT (NIL T T T T) -9 NIL 2511492 NIL) (-1064 2499027 2499566 2500390 "RSETCAT-" 2500395 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2491412 2492789 2494309 "RSDCMPK" 2497626 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489391 2489858 2489932 "RRCC" 2491018 NIL RRCC (NIL T T) -9 NIL 2491362 NIL) (-1061 2488742 2488916 2489195 "RRCC-" 2489200 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2488185 2488438 2488539 "RPTAST" 2488663 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2462456 2471805 2471872 "RPOLCAT" 2482536 NIL RPOLCAT (NIL T T T) -9 NIL 2485695 NIL) (-1058 2453954 2456294 2459416 "RPOLCAT-" 2459421 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2444885 2452165 2452647 "ROUTINE" 2453494 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2441683 2444511 2444651 "ROMAN" 2444767 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2439927 2440543 2440803 "ROIRC" 2441488 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2436285 2438563 2438593 "RNS" 2438897 T RNS (NIL) -9 NIL 2439170 NIL) (-1053 2434794 2435177 2435711 "RNS-" 2435786 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2434217 2434625 2434655 "RNG" 2434660 T RNG (NIL) -9 NIL 2434681 NIL) (-1051 2433583 2433971 2434014 "RMODULE" 2434076 NIL RMODULE (NIL T) -9 NIL 2434118 NIL) (-1050 2432419 2432513 2432849 "RMCAT2" 2433484 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2429269 2431765 2432062 "RMATRIX" 2432181 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2422185 2424445 2424560 "RMATCAT" 2427919 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2428901 NIL) (-1047 2421560 2421707 2422014 "RMATCAT-" 2422019 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2421127 2421202 2421330 "RINTERP" 2421479 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2420220 2420774 2420804 "RING" 2420860 T RING (NIL) -9 NIL 2420952 NIL) (-1044 2420012 2420056 2420153 "RING-" 2420158 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2418853 2419090 2419348 "RIDIST" 2419776 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2410142 2418321 2418527 "RGCHAIN" 2418701 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2409492 2409898 2409939 "RGBCSPC" 2409997 NIL RGBCSPC (NIL T) -9 NIL 2410049 NIL) (-1040 2408650 2409031 2409072 "RGBCMDL" 2409304 NIL RGBCMDL (NIL T) -9 NIL 2409418 NIL) (-1039 2405644 2406258 2406928 "RF" 2408014 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2405290 2405353 2405456 "RFFACTOR" 2405575 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2405015 2405050 2405147 "RFFACT" 2405249 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2403132 2403496 2403878 "RFDIST" 2404655 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2402585 2402677 2402840 "RETSOL" 2403034 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2402221 2402301 2402344 "RETRACT" 2402477 NIL RETRACT (NIL T) -9 NIL 2402564 NIL) (-1033 2402070 2402095 2402182 "RETRACT-" 2402187 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2401672 2401892 2401962 "RETAST" 2402022 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2394410 2401325 2401452 "RESULT" 2401567 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2393001 2393679 2393878 "RESRING" 2394313 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2392637 2392686 2392784 "RESLATC" 2392938 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2392342 2392377 2392484 "REPSQ" 2392596 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2389764 2390344 2390946 "REP" 2391762 T REP (NIL) -7 NIL NIL NIL) (-1026 2389461 2389496 2389607 "REPDB" 2389723 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2383361 2384750 2385973 "REP2" 2388273 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2379738 2380419 2381227 "REP1" 2382588 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2372434 2377879 2378335 "REGSET" 2379368 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2371199 2371582 2371832 "REF" 2372219 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2370576 2370679 2370846 "REDORDER" 2371083 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2366544 2369789 2370016 "RECLOS" 2370404 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2365596 2365777 2365992 "REALSOLV" 2366351 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2365442 2365483 2365513 "REAL" 2365518 T REAL (NIL) -9 NIL 2365553 NIL) (-1017 2361925 2362727 2363611 "REAL0Q" 2364607 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2357526 2358514 2359575 "REAL0" 2360906 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2356997 2357243 2357337 "RDUCEAST" 2357454 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2356402 2356474 2356681 "RDIV" 2356919 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2355470 2355644 2355857 "RDIST" 2356224 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2354067 2354354 2354726 "RDETRS" 2355178 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2351879 2352333 2352871 "RDETR" 2353609 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2350504 2350782 2351179 "RDEEFS" 2351595 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2349013 2349319 2349744 "RDEEF" 2350192 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2343239 2346149 2346179 "RCFIELD" 2347474 T RCFIELD (NIL) -9 NIL 2348204 NIL) (-1007 2341303 2341807 2342503 "RCFIELD-" 2342578 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2337572 2339404 2339447 "RCAGG" 2340531 NIL RCAGG (NIL T) -9 NIL 2340996 NIL) (-1005 2337200 2337294 2337457 "RCAGG-" 2337462 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2336535 2336647 2336812 "RATRET" 2337084 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2336088 2336155 2336276 "RATFACT" 2336463 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2335396 2335516 2335668 "RANDSRC" 2335958 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2335130 2335174 2335247 "RADUTIL" 2335345 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2328246 2333963 2334273 "RADIX" 2334854 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2319867 2328090 2328218 "RADFF" 2328223 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2319519 2319594 2319622 "RADCAT" 2319779 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2319304 2319352 2319449 "RADCAT-" 2319454 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2317407 2319079 2319168 "QUEUE" 2319248 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2313948 2317344 2317389 "QUAT" 2317394 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2313586 2313629 2313756 "QUATCT2" 2313899 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2307298 2310635 2310675 "QUATCAT" 2311455 NIL QUATCAT (NIL T) -9 NIL 2312221 NIL) (-992 2303442 2304479 2305866 "QUATCAT-" 2305960 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2300915 2302526 2302567 "QUAGG" 2302942 NIL QUAGG (NIL T) -9 NIL 2303117 NIL) (-990 2300520 2300740 2300808 "QQUTAST" 2300867 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2299418 2299918 2300090 "QFORM" 2300392 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2290596 2295835 2295875 "QFCAT" 2296533 NIL QFCAT (NIL T) -9 NIL 2297534 NIL) (-987 2286168 2287369 2288960 "QFCAT-" 2289054 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2285806 2285849 2285976 "QFCAT2" 2286119 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2285266 2285376 2285506 "QEQUAT" 2285696 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2278413 2279485 2280669 "QCMPACK" 2284199 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2275962 2276410 2276838 "QALGSET" 2278068 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2275207 2275381 2275613 "QALGSET2" 2275782 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2273897 2274121 2274438 "PWFFINTB" 2274980 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2272079 2272247 2272601 "PUSHVAR" 2273711 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2267997 2269051 2269092 "PTRANFN" 2270976 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2266399 2266690 2267012 "PTPACK" 2267708 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2266031 2266088 2266197 "PTFUNC2" 2266336 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2260510 2264903 2264944 "PTCAT" 2265240 NIL PTCAT (NIL T) -9 NIL 2265393 NIL) (-975 2260168 2260203 2260327 "PSQFR" 2260469 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2258763 2259061 2259395 "PSEUDLIN" 2259866 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2245526 2247897 2250221 "PSETPK" 2256523 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2238544 2241284 2241380 "PSETCAT" 2244401 NIL PSETCAT (NIL T T T T) -9 NIL 2245215 NIL) (-971 2236380 2237014 2237835 "PSETCAT-" 2237840 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2235729 2235894 2235922 "PSCURVE" 2236190 T PSCURVE (NIL) -9 NIL 2236357 NIL) (-969 2232051 2233567 2233632 "PSCAT" 2234476 NIL PSCAT (NIL T T T) -9 NIL 2234716 NIL) (-968 2231114 2231330 2231730 "PSCAT-" 2231735 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2229819 2230479 2230684 "PRTITION" 2230929 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2229294 2229540 2229632 "PRTDAST" 2229747 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2218384 2220598 2222786 "PRS" 2227156 NIL PRS (NIL T T) -7 NIL NIL 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(-952 2196536 2196592 2196703 "PREASSOC" 2196831 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2196011 2196144 2196172 "PPCURVE" 2196377 T PPCURVE (NIL) -9 NIL 2196513 NIL) (-950 2195606 2195806 2195889 "PORTNUM" 2195948 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2192965 2193364 2193956 "POLYROOT" 2195187 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2187147 2192569 2192729 "POLY" 2192838 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2186530 2186588 2186822 "POLYLIFT" 2187083 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2182805 2183254 2183883 "POLYCATQ" 2186075 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2169937 2175057 2175122 "POLYCAT" 2178636 NIL POLYCAT (NIL T T T) -9 NIL 2180514 NIL) (-944 2163386 2165248 2167632 "POLYCAT-" 2167637 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2162973 2163041 2163161 "POLY2UP" 2163312 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2162605 2162662 2162771 "POLY2" 2162910 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2161290 2161529 2161805 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2106603 2107151 2107238 "PI" 2107278 T PI (NIL) -8 NIL NIL 2107345) (-916 2104966 2105941 2105969 "PID" 2106151 T PID (NIL) -9 NIL 2106285 NIL) (-915 2104717 2104754 2104829 "PICOERCE" 2104923 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2104037 2104176 2104352 "PGROEB" 2104573 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2099624 2100438 2101343 "PGE" 2103152 T PGE (NIL) -7 NIL NIL NIL) (-912 2097747 2097994 2098360 "PGCD" 2099341 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2097085 2097188 2097349 "PFRPAC" 2097631 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2093726 2095633 2095986 "PFR" 2096764 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2092115 2092359 2092684 "PFOTOOLS" 2093473 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2090648 2090887 2091238 "PFOQ" 2091872 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2089149 2089361 2089717 "PFO" 2090432 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2085702 2089038 2089107 "PF" 2089112 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2083102 2084373 2084401 "PFECAT" 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"PDEPACK" 2059220 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2056212 2056402 2056653 "PDECOMP" 2057099 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2053791 2054634 2054662 "PDECAT" 2055449 T PDECAT (NIL) -9 NIL 2056162 NIL) (-890 2053542 2053575 2053665 "PCOMP" 2053752 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2051720 2052343 2052640 "PBWLB" 2053271 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2044193 2045793 2047131 "PATTERN" 2050403 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2043825 2043882 2043991 "PATTERN2" 2044130 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2041582 2041970 2042427 "PATTERN1" 2043414 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2038950 2039531 2040012 "PATRES" 2041147 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2038514 2038581 2038713 "PATRES2" 2038877 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2036397 2036802 2037209 "PATMATCH" 2038181 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2035907 2036116 2036157 "PATMAB" 2036264 NIL PATMAB (NIL T) -9 NIL 2036347 NIL) (-881 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(-869 2025683 2026295 2026655 "PAIR" 2026976 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2019553 2024942 2025136 "PADICRC" 2025538 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2012782 2018899 2019083 "PADICRAT" 2019401 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2011097 2012719 2012764 "PADIC" 2012769 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2008273 2009837 2009877 "PADICCT" 2010458 NIL PADICCT (NIL NIL) -9 NIL 2010740 NIL) (-864 2007230 2007430 2007698 "PADEPAC" 2008060 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2006442 2006575 2006781 "PADE" 2007092 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2004829 2005650 2005930 "OWP" 2006246 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2004322 2004535 2004632 "OVERSET" 2004752 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2003368 2003927 2004099 "OVAR" 2004190 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2002632 2002753 2002914 "OUT" 2003227 T OUT (NIL) -7 NIL NIL NIL) (-858 1991503 1993741 1995941 "OUTFORM" 2000452 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1990839 1991100 1991227 "OUTBFILE" 1991396 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1990146 1990311 1990339 "OUTBCON" 1990657 T OUTBCON (NIL) -9 NIL 1990823 NIL) (-855 1989747 1989859 1990016 "OUTBCON-" 1990021 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1989127 1989476 1989565 "OSI" 1989678 T OSI (NIL) -8 NIL NIL NIL) (-853 1988657 1988995 1989023 "OSGROUP" 1989028 T OSGROUP (NIL) -9 NIL 1989050 NIL) (-852 1987402 1987629 1987914 "ORTHPOL" 1988404 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1984953 1987237 1987358 "OREUP" 1987363 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1982356 1984644 1984771 "ORESUP" 1984895 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1979884 1980384 1980945 "OREPCTO" 1981845 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1973674 1975875 1975916 "OREPCAT" 1978264 NIL OREPCAT (NIL T) -9 NIL 1979368 NIL) (-847 1970821 1971603 1972661 "OREPCAT-" 1972666 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1969972 1970270 1970298 "ORDSET" 1970607 T ORDSET (NIL) -9 NIL 1970771 NIL) (-845 1969403 1969551 1969775 "ORDSET-" 1969780 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1968003 1968794 1968822 "ORDRING" 1969024 T ORDRING (NIL) -9 NIL 1969149 NIL) (-843 1967648 1967742 1967886 "ORDRING-" 1967891 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1967028 1967491 1967519 "ORDMON" 1967524 T ORDMON (NIL) -9 NIL 1967545 NIL) (-841 1966190 1966337 1966532 "ORDFUNS" 1966877 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1965528 1965947 1965975 "ORDFIN" 1966040 T ORDFIN (NIL) -9 NIL 1966114 NIL) (-839 1962087 1964114 1964523 "ORDCOMP" 1965152 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1961353 1961480 1961666 "ORDCOMP2" 1961947 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1957934 1958844 1959658 "OPTPROB" 1960559 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1954736 1955375 1956079 "OPTPACK" 1957250 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1952423 1953189 1953217 "OPTCAT" 1954036 T OPTCAT (NIL) -9 NIL 1954686 NIL) (-834 1951839 1952100 1952205 "OPSIG" 1952338 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1951607 1951646 1951712 "OPQUERY" 1951793 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1948738 1949918 1950422 "OP" 1951136 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1948247 1948444 1948485 "OPERCAT" 1948620 NIL OPERCAT (NIL T) -9 NIL 1948688 NIL) (-830 1948093 1948120 1948206 "OPERCAT-" 1948211 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1944905 1946890 1947259 "ONECOMP" 1947757 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1944210 1944325 1944499 "ONECOMP2" 1944777 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1943629 1943735 1943865 "OMSERVER" 1944100 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1940491 1943069 1943109 "OMSAGG" 1943170 NIL OMSAGG (NIL T) -9 NIL 1943234 NIL) (-825 1939114 1939377 1939659 "OMPKG" 1940229 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1938544 1938647 1938675 "OM" 1938974 T OM (NIL) -9 NIL NIL NIL) (-823 1937091 1938093 1938262 "OMLO" 1938425 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1936051 1936198 1936418 "OMEXPR" 1936917 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1935342 1935597 1935733 "OMERR" 1935935 T OMERR (NIL) -8 NIL NIL NIL) (-820 1934493 1934763 1934923 "OMERRK" 1935202 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1933944 1934170 1934278 "OMENC" 1934405 T OMENC (NIL) -8 NIL NIL NIL) (-818 1927839 1929024 1930195 "OMDEV" 1932793 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1926908 1927079 1927273 "OMCONN" 1927665 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1925495 1926471 1926499 "OINTDOM" 1926504 T OINTDOM (NIL) -9 NIL 1926525 NIL) (-815 1921274 1922485 1923201 "OFMONOID" 1924811 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1920685 1921211 1921256 "ODVAR" 1921261 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1918108 1920430 1920585 "ODR" 1920590 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1910689 1917884 1918010 "ODPOL" 1918015 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1904511 1910561 1910666 "ODP" 1910671 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1903277 1903492 1903767 "ODETOOLS" 1904285 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1900244 1900902 1901618 "ODESYS" 1902610 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1895126 1896034 1897059 "ODERTRIC" 1899319 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1894552 1894634 1894828 "ODERED" 1895038 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1891440 1891988 1892665 "ODERAT" 1893975 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1888397 1888864 1889461 "ODEPRRIC" 1890969 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1886340 1886936 1887422 "ODEPROB" 1887931 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1882860 1883345 1883992 "ODEPRIM" 1885819 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1882109 1882211 1882471 "ODEPAL" 1882752 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1878271 1879062 1879926 "ODEPACK" 1881265 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1877332 1877439 1877661 "ODEINT" 1878160 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1871433 1872858 1874305 "ODEIFTBL" 1875905 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1866831 1867617 1868569 "ODEEF" 1870592 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1866180 1866269 1866492 "ODECONST" 1866736 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1864305 1864966 1864994 "ODECAT" 1865599 T ODECAT (NIL) -9 NIL 1866130 NIL) (-795 1861177 1864017 1864136 "OCT" 1864218 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1860815 1860858 1860985 "OCTCT2" 1861128 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1855555 1857989 1858029 "OC" 1859126 NIL OC (NIL T) -9 NIL 1859984 NIL) (-792 1852782 1853530 1854520 "OC-" 1854614 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1852134 1852602 1852630 "OCAMON" 1852635 T OCAMON (NIL) -9 NIL 1852656 NIL) (-790 1851665 1852006 1852034 "OASGP" 1852039 T OASGP (NIL) -9 NIL 1852059 NIL) (-789 1850926 1851415 1851443 "OAMONS" 1851483 T OAMONS (NIL) -9 NIL 1851526 NIL) (-788 1850340 1850773 1850801 "OAMON" 1850806 T OAMON (NIL) -9 NIL 1850826 NIL) (-787 1849618 1850136 1850164 "OAGROUP" 1850169 T OAGROUP (NIL) -9 NIL 1850189 NIL) (-786 1849308 1849358 1849446 "NUMTUBE" 1849562 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1842881 1844399 1845935 "NUMQUAD" 1847792 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1838637 1839625 1840650 "NUMODE" 1841876 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1835992 1836872 1836900 "NUMINT" 1837823 T NUMINT (NIL) -9 NIL 1838587 NIL) (-782 1834940 1835137 1835355 "NUMFMT" 1835794 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1821299 1824244 1826776 "NUMERIC" 1832447 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1815669 1820748 1820843 "NTSCAT" 1820848 NIL NTSCAT (NIL T T T T) -9 NIL 1820887 NIL) (-779 1814863 1815028 1815221 "NTPOLFN" 1815508 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1802940 1811688 1812500 "NSUP" 1814084 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1802572 1802629 1802738 "NSUP2" 1802877 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1792800 1802346 1802479 "NSMP" 1802484 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1791232 1791533 1791890 "NREP" 1792488 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1789823 1790075 1790433 "NPCOEF" 1790975 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1788889 1789004 1789220 "NORMRETR" 1789704 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1786930 1787220 1787629 "NORMPK" 1788597 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1786615 1786643 1786767 "NORMMA" 1786896 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1786415 1786572 1786601 "NONE" 1786606 T NONE (NIL) -8 NIL NIL NIL) (-769 1786204 1786233 1786302 "NONE1" 1786379 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1785701 1785763 1785942 "NODE1" 1786136 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1783944 1784795 1785050 "NNI" 1785397 T NNI (NIL) -8 NIL NIL 1785632) (-766 1782364 1782677 1783041 "NLINSOL" 1783612 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1778605 1779600 1780499 "NIPROB" 1781485 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1777362 1777596 1777898 "NFINTBAS" 1778367 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1776536 1777012 1777053 "NETCLT" 1777225 NIL NETCLT (NIL T) -9 NIL 1777307 NIL) (-762 1775244 1775475 1775756 "NCODIV" 1776304 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1775006 1775043 1775118 "NCNTFRAC" 1775201 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1773186 1773550 1773970 "NCEP" 1774631 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1772057 1772830 1772858 "NASRING" 1772968 T NASRING (NIL) -9 NIL 1773048 NIL) (-758 1771852 1771896 1771990 "NASRING-" 1771995 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1770979 1771504 1771532 "NARNG" 1771649 T NARNG (NIL) -9 NIL 1771740 NIL) (-756 1770671 1770738 1770872 "NARNG-" 1770877 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1769550 1769757 1769992 "NAGSP" 1770456 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1760822 1762506 1764179 "NAGS" 1767897 T NAGS (NIL) -7 NIL NIL NIL) (-753 1759370 1759678 1760009 "NAGF07" 1760511 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1753908 1755199 1756506 "NAGF04" 1758083 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1746876 1748490 1750123 "NAGF02" 1752295 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1742100 1743200 1744317 "NAGF01" 1745779 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1735728 1737294 1738879 "NAGE04" 1740535 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1726897 1729018 1731148 "NAGE02" 1733618 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1722850 1723797 1724761 "NAGE01" 1725953 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1720645 1721179 1721737 "NAGD03" 1722312 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1712395 1714323 1716277 "NAGD02" 1718711 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1706206 1707631 1709071 "NAGD01" 1710975 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1702415 1703237 1704074 "NAGC06" 1705389 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1700880 1701212 1701568 "NAGC05" 1702079 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1700256 1700375 1700519 "NAGC02" 1700756 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1699290 1699873 1699913 "NAALG" 1699992 NIL NAALG (NIL T) -9 NIL 1700053 NIL) (-739 1699125 1699154 1699244 "NAALG-" 1699249 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1693075 1694183 1695370 "MULTSQFR" 1698021 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1692394 1692469 1692653 "MULTFACT" 1692987 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1685452 1689357 1689410 "MTSCAT" 1690480 NIL MTSCAT (NIL T T) -9 NIL 1690994 NIL) (-735 1685164 1685218 1685310 "MTHING" 1685392 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1684956 1684989 1685049 "MSYSCMD" 1685124 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1681038 1683711 1684031 "MSET" 1684669 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1678107 1680599 1680640 "MSETAGG" 1680645 NIL MSETAGG (NIL T) -9 NIL 1680679 NIL) (-731 1673948 1675486 1676231 "MRING" 1677407 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1673514 1673581 1673712 "MRF2" 1673875 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1673132 1673167 1673311 "MRATFAC" 1673473 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1670744 1671039 1671470 "MPRFF" 1672837 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1665041 1670598 1670695 "MPOLY" 1670700 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1664531 1664566 1664774 "MPCPF" 1665000 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1664045 1664088 1664272 "MPC3" 1664482 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1663240 1663321 1663542 "MPC2" 1663960 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1661541 1661878 1662268 "MONOTOOL" 1662900 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1660766 1661083 1661111 "MONOID" 1661330 T MONOID (NIL) -9 NIL 1661477 NIL) (-721 1660312 1660431 1660612 "MONOID-" 1660617 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1651136 1657079 1657138 "MONOGEN" 1657812 NIL MONOGEN (NIL T T) -9 NIL 1658268 NIL) (-719 1648354 1649089 1650089 "MONOGEN-" 1650208 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1647187 1647633 1647661 "MONADWU" 1648053 T MONADWU (NIL) -9 NIL 1648291 NIL) (-717 1646559 1646718 1646966 "MONADWU-" 1646971 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1645918 1646162 1646190 "MONAD" 1646397 T MONAD (NIL) -9 NIL 1646509 NIL) (-715 1645603 1645681 1645813 "MONAD-" 1645818 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1643892 1644516 1644795 "MOEBIUS" 1645356 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1643258 1643662 1643702 "MODULE" 1643707 NIL MODULE (NIL T) -9 NIL 1643733 NIL) (-712 1642826 1642922 1643112 "MODULE-" 1643117 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1640506 1641190 1641517 "MODRING" 1642650 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1637450 1638611 1639132 "MODOP" 1640035 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1636038 1636517 1636794 "MODMONOM" 1637313 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1626080 1634329 1634743 "MODMON" 1635675 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1623236 1624924 1625200 "MODFIELD" 1625955 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1622213 1622517 1622707 "MMLFORM" 1623066 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1621739 1621782 1621961 "MMAP" 1622164 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1619922 1620689 1620730 "MLO" 1621153 NIL MLO (NIL T) -9 NIL 1621395 NIL) (-703 1617288 1617804 1618406 "MLIFT" 1619403 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1616679 1616763 1616917 "MKUCFUNC" 1617199 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1616278 1616348 1616471 "MKRECORD" 1616602 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1615325 1615487 1615715 "MKFUNC" 1616089 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1614713 1614817 1614973 "MKFLCFN" 1615208 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1613990 1614092 1614277 "MKBCFUNC" 1614606 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1610697 1613544 1613680 "MINT" 1613874 T MINT (NIL) -8 NIL NIL NIL) (-696 1609509 1609752 1610029 "MHROWRED" 1610452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1604889 1608044 1608449 "MFLOAT" 1609124 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1604246 1604322 1604493 "MFINFACT" 1604801 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1600561 1601409 1602293 "MESH" 1603382 T MESH (NIL) -7 NIL NIL NIL) (-692 1598951 1599263 1599616 "MDDFACT" 1600248 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1595746 1598110 1598151 "MDAGG" 1598406 NIL MDAGG (NIL T) -9 NIL 1598549 NIL) (-690 1585489 1595039 1595246 "MCMPLX" 1595559 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1584630 1584776 1584976 "MCDEN" 1585338 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1582520 1582790 1583170 "MCALCFN" 1584360 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1581445 1581685 1581918 "MAYBE" 1582326 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1579057 1579580 1580142 "MATSTOR" 1580916 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1575014 1578429 1578677 "MATRIX" 1578842 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1570778 1571487 1572223 "MATLIN" 1574371 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1560884 1564070 1564147 "MATCAT" 1569027 NIL MATCAT (NIL T T T) -9 NIL 1570444 NIL) (-682 1557240 1558261 1559617 "MATCAT-" 1559622 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1555834 1555987 1556320 "MATCAT2" 1557075 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1553946 1554270 1554654 "MAPPKG3" 1555509 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1552927 1553100 1553322 "MAPPKG2" 1553770 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1551426 1551710 1552037 "MAPPKG1" 1552633 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1550505 1550832 1551009 "MAPPAST" 1551269 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1550116 1550174 1550297 "MAPHACK3" 1550441 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1549708 1549769 1549883 "MAPHACK2" 1550048 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1549145 1549249 1549391 "MAPHACK1" 1549599 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1547224 1547845 1548149 "MAGMA" 1548873 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1546703 1546948 1547039 "MACROAST" 1547153 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1543121 1544942 1545403 "M3D" 1546275 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1537227 1541490 1541531 "LZSTAGG" 1542313 NIL LZSTAGG (NIL T) -9 NIL 1542608 NIL) (-669 1533184 1534358 1535815 "LZSTAGG-" 1535820 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1530271 1531075 1531562 "LWORD" 1532729 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1529847 1530075 1530150 "LSTAST" 1530216 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1523013 1529618 1529752 "LSQM" 1529757 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1522237 1522376 1522604 "LSPP" 1522868 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1520049 1520350 1520806 "LSMP" 1521926 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1516828 1517502 1518232 "LSMP1" 1519351 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1510705 1515995 1516036 "LSAGG" 1516098 NIL LSAGG (NIL T) -9 NIL 1516176 NIL) (-661 1507400 1508324 1509537 "LSAGG-" 1509542 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1504999 1506544 1506793 "LPOLY" 1507195 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1504581 1504666 1504789 "LPEFRAC" 1504908 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1502902 1503675 1503928 "LO" 1504413 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1502554 1502666 1502694 "LOGIC" 1502805 T LOGIC (NIL) -9 NIL 1502886 NIL) (-656 1502416 1502439 1502510 "LOGIC-" 1502515 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1501609 1501749 1501942 "LODOOPS" 1502272 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1499032 1501525 1501591 "LODO" 1501596 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1497570 1497805 1498158 "LODOF" 1498779 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1493892 1496323 1496364 "LODOCAT" 1496802 NIL LODOCAT (NIL T) -9 NIL 1497013 NIL) (-651 1493625 1493683 1493810 "LODOCAT-" 1493815 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1490945 1493466 1493584 "LODO2" 1493589 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1488380 1490882 1490927 "LODO1" 1490932 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1487261 1487426 1487731 "LODEEF" 1488203 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1482500 1485391 1485432 "LNAGG" 1486379 NIL LNAGG (NIL T) -9 NIL 1486823 NIL) (-646 1481647 1481861 1482203 "LNAGG-" 1482208 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1477783 1478572 1479211 "LMOPS" 1481062 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1477152 1477540 1477581 "LMODULE" 1477642 NIL LMODULE (NIL T) -9 NIL 1477684 NIL) (-643 1474350 1476797 1476920 "LMDICT" 1477062 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1474049 1474258 1474318 "LITERAL" 1474323 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1467232 1472995 1473293 "LIST" 1473784 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1466757 1466831 1466970 "LIST3" 1467152 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1465764 1465942 1466170 "LIST2" 1466575 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1463898 1464210 1464609 "LIST2MAP" 1465411 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1462594 1463264 1463305 "LINEXP" 1463560 NIL LINEXP (NIL T) -9 NIL 1463709 NIL) (-636 1461241 1461501 1461798 "LINDEP" 1462346 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1458008 1458727 1459504 "LIMITRF" 1460496 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1456311 1456607 1457016 "LIMITPS" 1457703 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1450739 1455822 1456050 "LIE" 1456132 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1449762 1450231 1450271 "LIECAT" 1450411 NIL LIECAT (NIL T) -9 NIL 1450562 NIL) (-631 1449603 1449630 1449718 "LIECAT-" 1449723 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1442099 1449052 1449217 "LIB" 1449458 T LIB (NIL) -8 NIL NIL NIL) (-629 1437734 1438617 1439552 "LGROBP" 1441216 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1435743 1436017 1436366 "LF" 1437455 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1434583 1435275 1435303 "LFCAT" 1435510 T LFCAT (NIL) -9 NIL 1435649 NIL) (-626 1431485 1432115 1432803 "LEXTRIPK" 1433947 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1428229 1429055 1429558 "LEXP" 1431065 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1427705 1427950 1428042 "LETAST" 1428157 T LETAST (NIL) -8 NIL NIL NIL) (-623 1426103 1426416 1426817 "LEADCDET" 1427387 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1425293 1425367 1425596 "LAZM3PK" 1426024 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1420210 1423370 1423908 "LAUPOL" 1424805 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1419789 1419833 1419994 "LAPLACE" 1420160 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1417728 1418890 1419141 "LA" 1419622 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1416775 1417359 1417400 "LALG" 1417462 NIL LALG (NIL T) -9 NIL 1417521 NIL) (-617 1416489 1416548 1416684 "LALG-" 1416689 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1416324 1416348 1416389 "KVTFROM" 1416451 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1415097 1415541 1415770 "KTVLOGIC" 1416115 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1414932 1414956 1414997 "KRCFROM" 1415059 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1413836 1414023 1414322 "KOVACIC" 1414732 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1413671 1413695 1413736 "KONVERT" 1413798 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1413506 1413530 1413571 "KOERCE" 1413633 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1411188 1411976 1412377 "KERNEL" 1413138 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1410684 1410765 1410897 "KERNEL2" 1411102 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1404454 1409223 1409277 "KDAGG" 1409654 NIL KDAGG (NIL T T) -9 NIL 1409860 NIL) (-607 1403983 1404107 1404312 "KDAGG-" 1404317 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1397131 1403644 1403799 "KAFILE" 1403861 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1391559 1396642 1396870 "JORDAN" 1396952 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1390938 1391208 1391329 "JOINAST" 1391458 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1390784 1390843 1390898 "JAVACODE" 1390903 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1387036 1388989 1389043 "IXAGG" 1389972 NIL IXAGG (NIL T T) -9 NIL 1390431 NIL) (-601 1385955 1386261 1386680 "IXAGG-" 1386685 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1381487 1385877 1385936 "IVECTOR" 1385941 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1380253 1380490 1380756 "ITUPLE" 1381254 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1378767 1378944 1379237 "ITRIGMNP" 1380075 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1377512 1377716 1377999 "ITFUN3" 1378543 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1377144 1377201 1377310 "ITFUN2" 1377449 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1374946 1376006 1376305 "ITAYLOR" 1376878 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1363891 1369083 1370246 "ISUPS" 1373816 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1362995 1363135 1363371 "ISUMP" 1363738 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1358209 1362796 1362875 "ISTRING" 1362948 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1357685 1357930 1358022 "ISAST" 1358137 T ISAST (NIL) -8 NIL NIL NIL) (-590 1356895 1356976 1357192 "IRURPK" 1357599 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1355831 1356032 1356272 "IRSN" 1356675 T IRSN (NIL) -7 NIL NIL NIL) (-588 1353902 1354257 1354686 "IRRF2F" 1355469 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1353649 1353687 1353763 "IRREDFFX" 1353858 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1352264 1352523 1352822 "IROOT" 1353382 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1348868 1349948 1350640 "IR" 1351604 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1346481 1346976 1347542 "IR2" 1348346 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1345581 1345694 1345908 "IR2F" 1346364 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1345372 1345406 1345466 "IPRNTPK" 1345541 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1341952 1345261 1345330 "IPF" 1345335 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1340279 1341877 1341934 "IPADIC" 1341939 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1339591 1339839 1339969 "IP4ADDR" 1340169 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1339064 1339295 1339405 "IOMODE" 1339501 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1338137 1338661 1338788 "IOBFILE" 1338957 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1337625 1338041 1338069 "IOBCON" 1338074 T IOBCON (NIL) -9 NIL 1338095 NIL) (-575 1337136 1337194 1337377 "INVLAPLA" 1337561 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1326784 1329138 1331524 "INTTR" 1334800 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1323119 1323861 1324726 "INTTOOLS" 1325969 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1322705 1322796 1322913 "INTSLPE" 1323022 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1320659 1322628 1322687 "INTRVL" 1322692 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1318261 1318773 1319348 "INTRF" 1320144 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1317672 1317769 1317911 "INTRET" 1318159 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1315669 1316058 1316528 "INTRAT" 1317280 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1312932 1313515 1314134 "INTPM" 1315154 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1309676 1310276 1311014 "INTPAF" 1312318 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1304855 1305817 1306868 "INTPACK" 1308645 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1301732 1304584 1304711 "INT" 1304748 T INT (NIL) -8 NIL NIL NIL) (-563 1300984 1301136 1301344 "INTHERTR" 1301574 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1300423 1300503 1300691 "INTHERAL" 1300898 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1298269 1298712 1299169 "INTHEORY" 1299986 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1289675 1291296 1293068 "INTG0" 1296621 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1270248 1275038 1279848 "INTFTBL" 1284885 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1269497 1269635 1269808 "INTFACT" 1270107 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1266924 1267370 1267927 "INTEF" 1269051 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1265357 1266096 1266124 "INTDOM" 1266425 T INTDOM (NIL) -9 NIL 1266632 NIL) (-555 1264726 1264900 1265142 "INTDOM-" 1265147 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1261186 1263110 1263164 "INTCAT" 1263963 NIL INTCAT (NIL T) -9 NIL 1264283 NIL) (-553 1260658 1260761 1260889 "INTBIT" 1261078 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1259357 1259511 1259818 "INTALG" 1260503 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1258840 1258930 1259087 "INTAF" 1259261 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1252183 1258650 1258790 "INTABL" 1258795 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1251487 1251953 1252018 "INT8" 1252052 T INT8 (NIL) -8 NIL NIL 1252097) (-548 1250790 1251256 1251321 "INT64" 1251355 T INT64 (NIL) -8 NIL NIL 1251400) (-547 1250093 1250559 1250624 "INT32" 1250658 T INT32 (NIL) -8 NIL NIL 1250703) (-546 1249396 1249862 1249927 "INT16" 1249961 T INT16 (NIL) -8 NIL NIL 1250006) (-545 1244376 1247085 1247113 "INS" 1248047 T INS (NIL) -9 NIL 1248712 NIL) (-544 1241616 1242387 1243361 "INS-" 1243434 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1240391 1240618 1240916 "INPSIGN" 1241369 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1239509 1239626 1239823 "INPRODPF" 1240271 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1238403 1238520 1238757 "INPRODFF" 1239389 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1237403 1237555 1237815 "INNMFACT" 1238239 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1236600 1236697 1236885 "INMODGCD" 1237302 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1235108 1235353 1235677 "INFSP" 1236345 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1234292 1234409 1234592 "INFPROD0" 1234988 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1231147 1232357 1232872 "INFORM" 1233785 T INFORM (NIL) -8 NIL NIL NIL) (-535 1230757 1230817 1230915 "INFORM1" 1231082 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1230280 1230369 1230483 "INFINITY" 1230663 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1229456 1230000 1230101 "INETCLTS" 1230199 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1228072 1228322 1228643 "INEP" 1229204 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1227321 1227969 1228034 "INDE" 1228039 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1226885 1226953 1227070 "INCRMAPS" 1227248 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1225703 1226154 1226360 "INBFILE" 1226699 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1221003 1221939 1222883 "INBFF" 1224791 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1219911 1220180 1220208 "INBCON" 1220721 T INBCON (NIL) -9 NIL 1220987 NIL) (-526 1219163 1219386 1219662 "INBCON-" 1219667 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1218642 1218887 1218978 "INAST" 1219092 T INAST (NIL) -8 NIL NIL NIL) (-524 1218069 1218321 1218427 "IMPTAST" 1218556 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1214515 1217913 1218017 "IMATRIX" 1218022 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1213227 1213350 1213665 "IMATQF" 1214371 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1211447 1211674 1212011 "IMATLIN" 1212983 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1206025 1211371 1211429 "ILIST" 1211434 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1203930 1205885 1205998 "IIARRAY2" 1206003 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1199328 1203841 1203905 "IFF" 1203910 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1198675 1198945 1199061 "IFAST" 1199232 T IFAST (NIL) -8 NIL NIL NIL) (-516 1193670 1197967 1198155 "IFARRAY" 1198532 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1192850 1193574 1193647 "IFAMON" 1193652 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1192434 1192499 1192553 "IEVALAB" 1192760 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1192109 1192177 1192337 "IEVALAB-" 1192342 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1191740 1192023 1192086 "IDPO" 1192091 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1190990 1191629 1191704 "IDPOAMS" 1191709 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1190297 1190879 1190954 "IDPOAM" 1190959 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1189356 1189632 1189685 "IDPC" 1190098 NIL IDPC (NIL T T) -9 NIL 1190247 NIL) (-508 1188825 1189248 1189321 "IDPAM" 1189326 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1188201 1188717 1188790 "IDPAG" 1188795 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1187846 1188037 1188112 "IDENT" 1188146 T IDENT (NIL) -8 NIL NIL NIL) (-505 1184101 1184949 1185844 "IDECOMP" 1187003 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1176938 1178024 1179071 "IDEAL" 1183137 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1176102 1176214 1176413 "ICDEN" 1176822 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1175173 1175582 1175729 "ICARD" 1175975 T ICARD (NIL) -8 NIL NIL NIL) (-501 1173233 1173546 1173951 "IBPTOOLS" 1174850 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1168840 1172853 1172966 "IBITS" 1173152 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1165563 1166139 1166834 "IBATOOL" 1168257 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1163342 1163804 1164337 "IBACHIN" 1165098 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1161171 1163188 1163291 "IARRAY2" 1163296 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1157277 1161097 1161154 "IARRAY1" 1161159 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1151386 1155689 1156170 "IAN" 1156816 T IAN (NIL) -8 NIL NIL NIL) (-494 1150897 1150954 1151127 "IALGFACT" 1151323 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1150425 1150538 1150566 "HYPCAT" 1150773 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1149963 1150080 1150266 "HYPCAT-" 1150271 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1149558 1149758 1149841 "HOSTNAME" 1149900 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1149403 1149440 1149481 "HOMOTOP" 1149486 NIL HOMOTOP (NIL T) -9 NIL 1149519 NIL) (-489 1146035 1147413 1147454 "HOAGG" 1148435 NIL HOAGG (NIL T) -9 NIL 1149114 NIL) (-488 1144629 1145028 1145554 "HOAGG-" 1145559 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1138633 1144224 1144373 "HEXADEC" 1144500 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1137381 1137603 1137866 "HEUGCD" 1138410 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1136457 1137218 1137348 "HELLFDIV" 1137353 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1134636 1136234 1136322 "HEAP" 1136401 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133899 1134188 1134322 "HEADAST" 1134522 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127765 1133814 1133876 "HDP" 1133881 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1121753 1127400 1127552 "HDMP" 1127666 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1121077 1121217 1121381 "HB" 1121609 T HB (NIL) -7 NIL NIL NIL) (-479 1114463 1120923 1121027 "HASHTBL" 1121032 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113939 1114184 1114276 "HASAST" 1114391 T HASAST (NIL) -8 NIL NIL NIL) (-477 1111717 1113561 1113743 "HACKPI" 1113777 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1107385 1111570 1111683 "GTSET" 1111688 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100800 1107263 1107361 "GSTBL" 1107366 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1093078 1099831 1100096 "GSERIES" 1100591 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1092219 1092636 1092664 "GROUP" 1092867 T GROUP (NIL) -9 NIL 1093001 NIL) (-472 1091585 1091744 1091995 "GROUP-" 1092000 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089952 1090273 1090660 "GROEBSOL" 1091262 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088866 1089154 1089205 "GRMOD" 1089734 NIL GRMOD (NIL T T) -9 NIL 1089902 NIL) (-469 1088634 1088670 1088798 "GRMOD-" 1088803 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083924 1084988 1085988 "GRIMAGE" 1087654 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1082390 1082651 1082975 "GRDEF" 1083620 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081834 1081950 1082091 "GRAY" 1082269 T GRAY (NIL) -7 NIL NIL NIL) (-465 1081021 1081427 1081478 "GRALG" 1081631 NIL GRALG (NIL T T) -9 NIL 1081724 NIL) (-464 1080682 1080755 1080918 "GRALG-" 1080923 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1077459 1080267 1080445 "GPOLSET" 1080589 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076813 1076870 1077128 "GOSPER" 1077396 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072545 1073251 1073777 "GMODPOL" 1076512 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071550 1071734 1071972 "GHENSEL" 1072357 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065706 1066549 1067569 "GENUPS" 1070634 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1065403 1065454 1065543 "GENUFACT" 1065649 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064815 1064892 1065057 "GENPGCD" 1065321 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1064289 1064324 1064537 "GENMFACT" 1064774 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062855 1063112 1063419 "GENEEZ" 1064032 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1057001 1062466 1062628 "GDMP" 1062778 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1046343 1050772 1051878 "GCNAALG" 1055984 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1044736 1045598 1045626 "GCDDOM" 1045881 T GCDDOM (NIL) -9 NIL 1046038 NIL) (-451 1044206 1044333 1044548 "GCDDOM-" 1044553 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042878 1043063 1043367 "GB" 1043985 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1031494 1033824 1036216 "GBINTERN" 1040569 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1029331 1029623 1030044 "GBF" 1031169 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1028112 1028277 1028544 "GBEUCLID" 1029147 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1027461 1027586 1027735 "GAUSSFAC" 1027983 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025828 1026130 1026444 "GALUTIL" 1027180 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1024136 1024410 1024734 "GALPOLYU" 1025555 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1021501 1021791 1022198 "GALFACTU" 1023833 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1013307 1014806 1016414 "GALFACT" 1019933 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1010695 1011353 1011381 "FVFUN" 1012537 T FVFUN (NIL) -9 NIL 1013257 NIL) (-440 1009961 1010143 1010171 "FVC" 1010462 T FVC (NIL) -9 NIL 1010645 NIL) (-439 1009604 1009786 1009854 "FUNDESC" 1009913 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1009219 1009401 1009482 "FUNCTION" 1009556 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006963 1007541 1008007 "FT" 1008773 T FT (NIL) -8 NIL NIL NIL) (-436 1005754 1006264 1006467 "FTEM" 1006780 T FTEM (NIL) -8 NIL NIL NIL) (-435 1004045 1004334 1004731 "FSUPFACT" 1005445 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1002442 1002731 1003063 "FST" 1003733 T FST (NIL) -8 NIL NIL NIL) (-433 1001641 1001747 1001935 "FSRED" 1002324 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1000340 1000596 1000943 "FSPRMELT" 1001356 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 997646 998084 998570 "FSPECF" 999903 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 979801 988125 988166 "FS" 992050 NIL FS (NIL T) -9 NIL 994339 NIL) (-429 968444 971437 975494 "FS-" 975794 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 967972 968026 968196 "FSINT" 968385 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 966264 966965 967268 "FSERIES" 967751 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 965306 965422 965646 "FSCINT" 966144 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 961514 964250 964291 "FSAGG" 964661 NIL FSAGG (NIL T) -9 NIL 964920 NIL) (-424 959276 959877 960673 "FSAGG-" 960768 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 958318 958461 958688 "FSAGG2" 959129 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 956000 956280 956827 "FS2UPS" 958036 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 955634 955677 955806 "FS2" 955951 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 954512 954683 954985 "FS2EXPXP" 955459 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 953938 954053 954205 "FRUTIL" 954392 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 945352 949433 950791 "FR" 952612 NIL FR (NIL T) -8 NIL NIL NIL) (-417 940400 943070 943110 "FRNAALG" 944506 NIL FRNAALG (NIL T) -9 NIL 945113 NIL) (-416 936073 937149 938424 "FRNAALG-" 939174 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 935711 935754 935881 "FRNAAF2" 936024 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 934091 934565 934860 "FRMOD" 935523 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 931842 932474 932791 "FRIDEAL" 933882 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 931037 931124 931413 "FRIDEAL2" 931749 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 930170 930584 930625 "FRETRCT" 930630 NIL FRETRCT (NIL T) -9 NIL 930806 NIL) (-410 929282 929513 929864 "FRETRCT-" 929869 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 926460 927670 927729 "FRAMALG" 928611 NIL FRAMALG (NIL T T) -9 NIL 928903 NIL) (-408 924594 925049 925679 "FRAMALG-" 925902 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 918515 924069 924345 "FRAC" 924350 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 918151 918208 918315 "FRAC2" 918452 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 917787 917844 917951 "FR2" 918088 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 912425 915312 915340 "FPS" 916459 T FPS (NIL) -9 NIL 917016 NIL) (-403 911874 911983 912147 "FPS-" 912293 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 909294 910963 910991 "FPC" 911216 T FPC (NIL) -9 NIL 911358 NIL) (-401 909087 909127 909224 "FPC-" 909229 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 907877 908575 908616 "FPATMAB" 908621 NIL FPATMAB (NIL T) -9 NIL 908773 NIL) (-399 905550 906053 906479 "FPARFRAC" 907514 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900943 901442 902124 "FORTRAN" 904982 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 898659 899159 899698 "FORT" 900424 T FORT (NIL) -7 NIL NIL NIL) (-396 896335 896897 896925 "FORTFN" 897985 T FORTFN (NIL) -9 NIL 898609 NIL) (-395 896099 896149 896177 "FORTCAT" 896236 T FORTCAT (NIL) -9 NIL 896298 NIL) (-394 894205 894715 895105 "FORMULA" 895729 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893993 894023 894092 "FORMULA1" 894169 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 893516 893568 893741 "FORDER" 893935 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 892612 892776 892969 "FOP" 893343 T FOP (NIL) -7 NIL NIL NIL) (-390 891193 891892 892066 "FNLA" 892494 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889922 890337 890365 "FNCAT" 890825 T FNCAT (NIL) -9 NIL 891085 NIL) (-388 889461 889881 889909 "FNAME" 889914 T FNAME (NIL) -8 NIL NIL NIL) (-387 888090 889053 889081 "FMTC" 889086 T FMTC (NIL) -9 NIL 889122 NIL) (-386 884423 885613 886242 "FMONOID" 887494 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 883615 884165 884314 "FM" 884319 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 881039 881685 881713 "FMFUN" 882857 T FMFUN (NIL) -9 NIL 883565 NIL) (-383 880308 880489 880517 "FMC" 880807 T FMC (NIL) -9 NIL 880989 NIL) (-382 877476 878336 878390 "FMCAT" 879585 NIL FMCAT (NIL T T) -9 NIL 880080 NIL) (-381 876342 877242 877342 "FM1" 877421 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 874116 874532 875026 "FLOATRP" 875893 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867690 871845 872466 "FLOAT" 873515 T FLOAT (NIL) -8 NIL NIL NIL) (-378 865128 865628 866206 "FLOATCP" 867157 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863903 864741 864782 "FLINEXP" 864787 NIL FLINEXP (NIL T) -9 NIL 864880 NIL) (-376 863057 863292 863620 "FLINEXP-" 863625 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 862133 862277 862501 "FLASORT" 862909 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 859324 860192 860244 "FLALG" 861471 NIL FLALG (NIL T T) -9 NIL 861938 NIL) (-373 853060 856810 856851 "FLAGG" 858113 NIL FLAGG (NIL T) -9 NIL 858765 NIL) (-372 851786 852125 852615 "FLAGG-" 852620 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850828 850971 851198 "FLAGG2" 851639 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847769 848777 848836 "FINRALG" 849964 NIL FINRALG (NIL T T) -9 NIL 850472 NIL) (-369 846929 847158 847497 "FINRALG-" 847502 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 846309 846548 846576 "FINITE" 846772 T FINITE (NIL) -9 NIL 846879 NIL) (-367 838741 840928 840968 "FINAALG" 844635 NIL FINAALG (NIL T) -9 NIL 846088 NIL) (-366 834073 835123 836267 "FINAALG-" 837646 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833441 833828 833931 "FILE" 834003 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 832099 832437 832491 "FILECAT" 833175 NIL FILECAT (NIL T T) -9 NIL 833391 NIL) (-363 829933 831461 831489 "FIELD" 831529 T FIELD (NIL) -9 NIL 831609 NIL) (-362 828553 828938 829449 "FIELD-" 829454 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826403 827188 827535 "FGROUP" 828239 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825493 825657 825877 "FGLMICPK" 826235 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821325 825418 825475 "FFX" 825480 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820926 820987 821122 "FFSLPE" 821258 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816915 817698 818494 "FFPOLY" 820162 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816419 816455 816664 "FFPOLY2" 816873 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812262 816338 816401 "FFP" 816406 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807660 812173 812237 "FF" 812242 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802786 807003 807193 "FFNBX" 807514 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797715 801921 802179 "FFNBP" 802640 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792348 796999 797210 "FFNB" 797548 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791180 791378 791693 "FFINTBAS" 792145 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787373 789587 789615 "FFIELDC" 790235 T FFIELDC (NIL) -9 NIL 790611 NIL) (-348 786035 786406 786903 "FFIELDC-" 786908 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785604 785650 785774 "FFHOM" 785977 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783299 783786 784303 "FFF" 785119 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778917 783041 783142 "FFCGX" 783242 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774538 778649 778756 "FFCGP" 778860 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769721 774265 774373 "FFCG" 774474 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751519 760592 760678 "FFCAT" 765843 NIL FFCAT (NIL T T T) -9 NIL 767294 NIL) (-341 746717 747764 749078 "FFCAT-" 750308 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 746128 746171 746406 "FFCAT2" 746668 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735450 739100 740320 "FEXPR" 744980 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734450 734885 734926 "FEVALAB" 735010 NIL FEVALAB (NIL T) -9 NIL 735271 NIL) (-337 733609 733819 734157 "FEVALAB-" 734162 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732175 732992 733195 "FDIV" 733508 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729215 729956 730071 "FDIVCAT" 731639 NIL FDIVCAT (NIL T T T T) -9 NIL 732076 NIL) (-334 728977 729004 729174 "FDIVCAT-" 729179 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728197 728284 728561 "FDIV2" 728884 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726883 727142 727431 "FCPAK1" 727928 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725982 726383 726524 "FCOMP" 726774 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709684 713132 716670 "FC" 722464 T FC (NIL) -8 NIL NIL NIL) (-329 702228 706248 706288 "FAXF" 708090 NIL FAXF (NIL T) -9 NIL 708782 NIL) (-328 699504 700162 700987 "FAXF-" 701452 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694556 698880 699056 "FARRAY" 699361 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689775 691841 691894 "FAMR" 692917 NIL FAMR (NIL T T) -9 NIL 693377 NIL) (-325 688665 688967 689402 "FAMR-" 689407 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687834 688587 688640 "FAMONOID" 688645 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685620 686330 686383 "FAMONC" 687324 NIL FAMONC (NIL T T) -9 NIL 687710 NIL) (-322 684285 685374 685511 "FAGROUP" 685516 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 682080 682399 682802 "FACUTIL" 683966 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681179 681364 681586 "FACTFUNC" 681890 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673601 680482 680681 "EXPUPXS" 681035 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 671084 671624 672210 "EXPRTUBE" 673035 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667355 667947 668677 "EXPRODE" 670423 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652840 666004 666433 "EXPR" 666959 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647394 647981 648787 "EXPR2UPS" 652138 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 647026 647083 647192 "EXPR2" 647331 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638417 646179 646469 "EXPEXPAN" 646863 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638217 638374 638403 "EXIT" 638408 T EXIT (NIL) -8 NIL NIL NIL) (-311 637697 637941 638032 "EXITAST" 638146 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637324 637386 637499 "EVALCYC" 637629 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636865 636983 637024 "EVALAB" 637194 NIL EVALAB (NIL T) -9 NIL 637298 NIL) (-308 636346 636468 636689 "EVALAB-" 636694 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633780 635082 635110 "EUCDOM" 635665 T EUCDOM (NIL) -9 NIL 636015 NIL) (-306 632185 632627 633217 "EUCDOM-" 633222 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619723 622483 625233 "ESTOOLS" 629455 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619355 619412 619521 "ESTOOLS2" 619660 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 619106 619148 619228 "ESTOOLS1" 619307 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 613143 614751 614779 "ES" 617547 T ES (NIL) -9 NIL 618957 NIL) (-301 608090 609377 611194 "ES-" 611358 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604464 605225 606005 "ESCONT" 607330 T ESCONT (NIL) -7 NIL NIL NIL) (-299 604209 604241 604323 "ESCONT1" 604426 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603884 603934 604034 "ES2" 604153 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603514 603572 603681 "ES1" 603820 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602730 602859 603035 "ERROR" 603358 T ERROR (NIL) -7 NIL NIL NIL) (-295 596122 602589 602680 "EQTBL" 602685 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588625 591436 592885 "EQ" 594706 NIL -2077 (NIL T) -8 NIL NIL NIL) (-293 588257 588314 588423 "EQ2" 588562 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583546 584595 585688 "EP" 587196 NIL EP (NIL T) -7 NIL NIL NIL) (-291 582146 582437 582743 "ENV" 583260 T ENV (NIL) -8 NIL NIL NIL) (-290 581291 581845 581873 "ENTIRER" 581878 T ENTIRER (NIL) -9 NIL 581924 NIL) (-289 577758 579246 579616 "EMR" 581090 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576902 577087 577141 "ELTAGG" 577521 NIL ELTAGG (NIL T T) -9 NIL 577732 NIL) (-287 576621 576683 576824 "ELTAGG-" 576829 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576410 576439 576493 "ELTAB" 576577 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575536 575682 575881 "ELFUTS" 576261 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575278 575334 575362 "ELEMFUN" 575467 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 575148 575169 575237 "ELEMFUN-" 575242 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569992 573248 573289 "ELAGG" 574229 NIL ELAGG (NIL T) -9 NIL 574692 NIL) (-281 568277 568711 569374 "ELAGG-" 569379 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566942 567220 567513 "ELABEXPR" 568004 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559806 561609 562436 "EFUPXS" 566218 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553256 555057 555867 "EFULS" 559082 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550741 551099 551571 "EFSTRUC" 552888 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 540592 542158 543705 "EF" 549256 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 539666 540077 540226 "EAB" 540463 T EAB (NIL) -8 NIL NIL NIL) (-274 538848 539625 539653 "E04UCFA" 539658 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 538030 538807 538835 "E04NAFA" 538840 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 537212 537989 538017 "E04MBFA" 538022 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 536394 537171 537199 "E04JAFA" 537204 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 535578 536353 536381 "E04GCFA" 536386 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534762 535537 535565 "E04FDFA" 535570 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533944 534721 534749 "E04DGFA" 534754 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 528117 529469 530833 "E04AGNT" 532600 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526797 527303 527343 "DVARCAT" 527818 NIL DVARCAT (NIL T) -9 NIL 528017 NIL) (-265 526001 526213 526527 "DVARCAT-" 526532 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 519138 525800 525929 "DSMP" 525934 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513920 515083 516151 "DROPT" 518090 T DROPT (NIL) -8 NIL NIL NIL) (-262 513585 513644 513742 "DROPT1" 513855 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 508700 509826 510963 "DROPT0" 512468 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 507045 507370 507756 "DRAWPT" 508334 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 501632 502555 503634 "DRAW" 506019 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 501265 501318 501436 "DRAWHACK" 501573 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499996 500265 500556 "DRAWCX" 500994 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 499511 499580 499731 "DRAWCURV" 499922 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489979 491941 494056 "DRAWCFUN" 497416 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 486745 488674 488715 "DQAGG" 489344 NIL DQAGG (NIL T) -9 NIL 489617 NIL) (-253 475289 481750 481833 "DPOLCAT" 483685 NIL DPOLCAT (NIL T T T T) -9 NIL 484230 NIL) (-252 470125 471474 473432 "DPOLCAT-" 473437 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 463247 469986 470084 "DPMO" 470089 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 456272 463027 463194 "DPMM" 463199 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 455877 456191 456239 "DOMCTOR" 456244 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 455145 455399 455536 "DOMAIN" 455760 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 449133 454780 454932 "DMP" 455046 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 448733 448789 448933 "DLP" 449071 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 442555 448060 448250 "DLIST" 448575 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 439352 441408 441449 "DLAGG" 441999 NIL DLAGG (NIL T) -9 NIL 442229 NIL) (-243 438131 438795 438823 "DIVRING" 438915 T DIVRING (NIL) -9 NIL 438998 NIL) (-242 437368 437558 437858 "DIVRING-" 437863 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 435470 435827 436233 "DISPLAY" 436982 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 429358 435384 435447 "DIRPROD" 435452 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 428206 428409 428674 "DIRPROD2" 429151 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 417415 423421 423474 "DIRPCAT" 423884 NIL DIRPCAT (NIL NIL T) -9 NIL 424724 NIL) (-237 414741 415383 416264 "DIRPCAT-" 416601 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414028 414188 414374 "DIOSP" 414575 T DIOSP (NIL) -7 NIL NIL NIL) (-235 410683 412940 412981 "DIOPS" 413415 NIL DIOPS (NIL T) -9 NIL 413644 NIL) (-234 410232 410346 410537 "DIOPS-" 410542 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409090 409718 409746 "DIFRING" 409933 T DIFRING (NIL) -9 NIL 410043 NIL) (-232 408736 408813 408965 "DIFRING-" 408970 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 406507 407779 407820 "DIFEXT" 408183 NIL DIFEXT (NIL T) -9 NIL 408477 NIL) (-230 404792 405220 405886 "DIFEXT-" 405891 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402067 404324 404365 "DIAGG" 404370 NIL DIAGG (NIL T) -9 NIL 404390 NIL) (-228 401451 401608 401860 "DIAGG-" 401865 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396868 400410 400687 "DHMATRIX" 401220 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 392480 393389 394399 "DFSFUN" 395878 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 387558 391411 391723 "DFLOAT" 392188 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385821 386102 386491 "DFINTTLS" 387266 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382850 383842 384242 "DERHAM" 385487 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 380651 382625 382714 "DEQUEUE" 382794 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379905 380038 380221 "DEGRED" 380513 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376335 377080 377926 "DEFINTRF" 379133 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373890 374359 374951 "DEFINTEF" 375854 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373240 373510 373625 "DEFAST" 373795 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367244 372835 372984 "DECIMAL" 373111 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 364756 365214 365720 "DDFACT" 366788 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364352 364395 364546 "DBLRESP" 364707 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362224 362585 362945 "DBASE" 364119 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 361466 361704 361850 "DATAARY" 362123 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 360572 361425 361453 "D03FAFA" 361458 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359679 360531 360559 "D03EEFA" 360564 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 357629 358095 358584 "D03AGNT" 359210 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356918 357588 357616 "D02EJFA" 357621 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356207 356877 356905 "D02CJFA" 356910 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 355496 356166 356194 "D02BHFA" 356199 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354785 355455 355483 "D02BBFA" 355488 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347982 349571 351177 "D02AGNT" 353199 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345750 346273 346819 "D01WGTS" 347456 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344817 345709 345737 "D01TRNS" 345742 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343885 344776 344804 "D01GBFA" 344809 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342953 343844 343872 "D01FCFA" 343877 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342021 342912 342940 "D01ASFA" 342945 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341089 341980 342008 "D01AQFA" 342013 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340157 341048 341076 "D01APFA" 341081 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339225 340116 340144 "D01ANFA" 340149 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338293 339184 339212 "D01AMFA" 339217 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337361 338252 338280 "D01ALFA" 338285 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336429 337320 337348 "D01AKFA" 337353 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335497 336388 336416 "D01AJFA" 336421 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328792 330345 331906 "D01AGNT" 333956 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328129 328257 328409 "CYCLOTOM" 328660 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324864 325577 326304 "CYCLES" 327422 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324176 324310 324481 "CVMP" 324725 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322017 322275 322644 "CTRIGMNP" 323904 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321485 321811 321884 "CTOR" 321964 T CTOR (NIL) -8 NIL NIL NIL) (-186 320994 321216 321317 "CTORKIND" 321404 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320316 320601 320629 "CTORCAT" 320811 T CTORCAT (NIL) -9 NIL 320924 NIL) (-184 319914 320025 320184 "CTORCAT-" 320189 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319403 319617 319715 "CTORCALL" 319836 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318777 318876 319029 "CSTTOOLS" 319300 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314576 315233 315991 "CRFP" 318089 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314051 314297 314389 "CRCEAST" 314504 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313098 313283 313511 "CRAPACK" 313855 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312482 312583 312787 "CPMATCH" 312974 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312207 312235 312341 "CPIMA" 312448 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308571 309243 309961 "COORDSYS" 311542 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307983 308104 308246 "CONTOUR" 308449 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303874 305986 306478 "CONTFRAC" 307523 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303754 303775 303803 "CONDUIT" 303840 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302893 303447 303475 "COMRING" 303480 T COMRING (NIL) -9 NIL 303532 NIL) (-171 301947 302251 302435 "COMPPROP" 302729 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301608 301643 301771 "COMPLPAT" 301906 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291902 301417 301526 "COMPLEX" 301531 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291538 291595 291702 "COMPLEX2" 291839 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291256 291291 291389 "COMPFACT" 291497 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275732 285715 285755 "COMPCAT" 286759 NIL COMPCAT (NIL T) -9 NIL 288105 NIL) (-165 265243 268171 271798 "COMPCAT-" 272154 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264972 265000 265103 "COMMUPC" 265209 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264766 264800 264859 "COMMONOP" 264933 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264322 264517 264604 "COMM" 264699 T COMM (NIL) -8 NIL NIL NIL) (-161 263898 264126 264201 "COMMAAST" 264267 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263147 263341 263369 "COMBOPC" 263707 T COMBOPC (NIL) -9 NIL 263882 NIL) (-159 262043 262253 262495 "COMBINAT" 262937 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258500 259074 259701 "COMBF" 261465 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257258 257616 257851 "COLOR" 258285 T COLOR (NIL) -8 NIL NIL NIL) (-156 256734 256979 257071 "COLONAST" 257186 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256374 256421 256546 "CMPLXRT" 256681 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255822 256074 256173 "CLLCTAST" 256295 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251322 252352 253432 "CLIP" 254762 T CLIP (NIL) -7 NIL NIL NIL) (-152 249668 250428 250667 "CLIF" 251149 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245843 247814 247855 "CLAGG" 248784 NIL CLAGG (NIL T) -9 NIL 249320 NIL) (-150 244265 244722 245305 "CLAGG-" 245310 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243809 243894 244034 "CINTSLPE" 244174 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241310 241781 242329 "CHVAR" 243337 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240519 241073 241101 "CHARZ" 241106 T CHARZ (NIL) -9 NIL 241121 NIL) (-146 240273 240313 240391 "CHARPOL" 240473 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239366 239953 239981 "CHARNZ" 240028 T CHARNZ (NIL) -9 NIL 240084 NIL) (-144 237328 238056 238391 "CHAR" 239051 T CHAR (NIL) -8 NIL NIL NIL) (-143 237054 237115 237143 "CFCAT" 237254 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236299 236410 236592 "CDEN" 236938 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232264 235452 235732 "CCLASS" 236039 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231571 231714 231877 "CATEGORY" 232121 T -10 (NIL) -8 NIL NIL NIL) (-139 231176 231490 231538 "CATCTOR" 231543 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230627 230879 230977 "CATAST" 231098 T CATAST (NIL) -8 NIL NIL NIL) (-137 230103 230348 230440 "CASEAST" 230555 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225112 226132 226885 "CARTEN" 229406 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224220 224368 224589 "CARTEN2" 224959 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222535 223370 223627 "CARD" 223983 T CARD (NIL) -8 NIL NIL NIL) (-133 222111 222339 222414 "CAPSLAST" 222480 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221615 221823 221851 "CACHSET" 221983 T CACHSET (NIL) -9 NIL 222061 NIL) (-131 221085 221407 221435 "CABMON" 221485 T CABMON (NIL) -9 NIL 221541 NIL) (-130 220558 220789 220899 "BYTEORD" 220995 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219534 220092 220234 "BYTE" 220397 T BYTE (NIL) -8 NIL NIL 220519) (-128 214884 219039 219211 "BYTEBUF" 219382 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212393 214576 214683 "BTREE" 214810 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209842 212041 212163 "BTOURN" 212303 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207212 209312 209353 "BTCAT" 209421 NIL BTCAT (NIL T) -9 NIL 209498 NIL) (-124 206879 206959 207108 "BTCAT-" 207113 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202144 206022 206050 "BTAGG" 206272 T BTAGG (NIL) -9 NIL 206433 NIL) (-122 201634 201759 201965 "BTAGG-" 201970 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198629 200912 201127 "BSTREE" 201451 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197767 197893 198077 "BRILL" 198485 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194419 196493 196534 "BRAGG" 197183 NIL BRAGG (NIL T) -9 NIL 197441 NIL) (-118 192948 193354 193909 "BRAGG-" 193914 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186177 192294 192478 "BPADICRT" 192796 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184492 186114 186159 "BPADIC" 186164 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184190 184220 184334 "BOUNDZRO" 184456 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179282 180480 181423 "BOP" 183267 T BOP (NIL) -8 NIL NIL NIL) (-113 177063 177467 177942 "BOP1" 178840 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175738 176487 176680 "BOOLEAN" 176890 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175074 175478 175532 "BMODULE" 175537 NIL BMODULE (NIL T T) -9 NIL 175602 NIL) (-110 170875 174872 174945 "BITS" 175021 T BITS (NIL) -8 NIL NIL NIL) (-109 170296 170415 170555 "BINDING" 170755 T BINDING (NIL) -8 NIL NIL NIL) (-108 164303 169893 170041 "BINARY" 170168 T BINARY (NIL) -8 NIL NIL NIL) (-107 162083 163558 163599 "BGAGG" 163859 NIL BGAGG (NIL T) -9 NIL 163996 NIL) (-106 161914 161946 162037 "BGAGG-" 162042 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160985 161298 161503 "BFUNCT" 161729 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159675 159853 160141 "BEZOUT" 160809 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156144 158527 158857 "BBTREE" 159378 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155878 155931 155959 "BASTYPE" 156078 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155731 155759 155832 "BASTYPE-" 155837 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155165 155241 155393 "BALFACT" 155642 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154021 154580 154766 "AUTOMOR" 155010 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153747 153752 153778 "ATTREG" 153783 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151999 152444 152796 "ATTRBUT" 153413 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151607 151827 151893 "ATTRAST" 151951 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151143 151256 151282 "ATRIG" 151483 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150952 150993 151080 "ATRIG-" 151085 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150597 150783 150809 "ASTCAT" 150814 T ASTCAT (NIL) -9 NIL 150844 NIL) (-92 150324 150383 150502 "ASTCAT-" 150507 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148473 150100 150188 "ASTACK" 150267 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146978 147275 147640 "ASSOCEQ" 148155 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146010 146637 146761 "ASP9" 146885 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145773 145958 145997 "ASP8" 146002 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144641 145378 145520 "ASP80" 145662 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143539 144276 144408 "ASP7" 144540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142493 143216 143334 "ASP78" 143452 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141462 142173 142290 "ASP77" 142407 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140374 141100 141231 "ASP74" 141362 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139274 140009 140141 "ASP73" 140273 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138378 139100 139200 "ASP6" 139205 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137322 138055 138173 "ASP55" 138291 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136271 136996 137115 "ASP50" 137234 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135359 135972 136082 "ASP4" 136192 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134447 135060 135170 "ASP49" 135280 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133231 133986 134154 "ASP42" 134336 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132007 132764 132934 "ASP41" 133118 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130957 131684 131802 "ASP35" 131920 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130722 130905 130944 "ASP34" 130949 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130459 130526 130602 "ASP33" 130677 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129352 130094 130226 "ASP31" 130358 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129117 129300 129339 "ASP30" 129344 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128852 128921 128997 "ASP29" 129072 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128617 128800 128839 "ASP28" 128844 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128382 128565 128604 "ASP27" 128609 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127466 128080 128191 "ASP24" 128302 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126542 127268 127380 "ASP20" 127385 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125630 126243 126353 "ASP1" 126463 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124572 125304 125423 "ASP19" 125542 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124309 124376 124452 "ASP12" 124527 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123161 123908 124052 "ASP10" 124196 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121012 123005 123096 "ARRAY2" 123101 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116777 120660 120774 "ARRAY1" 120929 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115809 115982 116203 "ARRAY12" 116600 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110121 112039 112114 "ARR2CAT" 114744 NIL ARR2CAT (NIL T T T) -9 NIL 115502 NIL) (-56 107555 108299 109253 "ARR2CAT-" 109258 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106872 107182 107307 "ARITY" 107448 T ARITY (NIL) -8 NIL NIL NIL) (-54 105648 105800 106099 "APPRULE" 106708 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105299 105347 105466 "APPLYORE" 105594 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104246 104564 104759 "ANY" 105122 T ANY (NIL) -8 NIL NIL NIL) (-51 103524 103647 103804 "ANY1" 104120 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101054 101961 102288 "ANTISYM" 103248 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100546 100761 100857 "ANON" 100976 T ANON (NIL) -8 NIL NIL NIL) (-48 94795 99085 99539 "AN" 100110 T AN (NIL) -8 NIL NIL NIL) (-47 91017 92405 92456 "AMR" 93204 NIL AMR (NIL T T) -9 NIL 93804 NIL) (-46 90129 90350 90713 "AMR-" 90718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74568 90046 90107 "ALIST" 90112 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71370 74162 74331 "ALGSC" 74486 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 67925 68480 69087 "ALGPKG" 70810 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67202 67303 67487 "ALGMFACT" 67811 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63154 63760 64378 "ALGMANIP" 66762 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54524 62780 62930 "ALGFF" 63087 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53720 53851 54030 "ALGFACT" 54382 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52751 53351 53389 "ALGEBRA" 53394 NIL ALGEBRA (NIL T) -9 NIL 53435 NIL) (-37 52469 52528 52660 "ALGEBRA-" 52665 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34562 50471 50523 "ALAGG" 50659 NIL ALAGG (NIL T T) -9 NIL 50820 NIL) (-35 34098 34211 34237 "AHYP" 34438 T AHYP (NIL) -9 NIL NIL NIL) (-34 33029 33277 33303 "AGG" 33802 T AGG (NIL) -9 NIL 34081 NIL) (-33 32463 32625 32839 "AGG-" 32844 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30269 30692 31097 "AF" 32105 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29749 29994 30084 "ADDAST" 30197 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29017 29276 29432 "ACPLOT" 29611 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18557 26360 26398 "ACFS" 27005 NIL ACFS (NIL T) -9 NIL 27244 NIL) (-28 16584 17074 17836 "ACFS-" 17841 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12823 14751 14777 "ACF" 15656 T ACF (NIL) -9 NIL 16068 NIL) (-26 11527 11861 12354 "ACF-" 12359 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11099 11294 11320 "ABELSG" 11412 T ABELSG (NIL) -9 NIL 11477 NIL) (-24 10966 10991 11057 "ABELSG-" 11062 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10309 10596 10622 "ABELMON" 10792 T ABELMON (NIL) -9 NIL 10904 NIL) (-22 9973 10057 10195 "ABELMON-" 10200 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9804 T ABELGRP (NIL) -9 NIL 9886 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 3205518 3205523 3205528 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3205503 3205508 3205513 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3205488 3205493 3205498 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3205473 3205478 3205483 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3204615 3205348 3205425 "ZMOD" 3205430 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3203725 3203889 3204098 "ZLINDEP" 3204447 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3193025 3194793 3196765 "ZDSOLVE" 3201855 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3192271 3192412 3192601 "YSTREAM" 3192871 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3190045 3191572 3191776 "XRPOLY" 3192114 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3186598 3187916 3188491 "XPR" 3189517 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3184319 3185929 3186133 "XPOLY" 3186429 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3182076 3183444 3183499 "XPOLYC" 3183787 NIL XPOLYC (NIL T T) -9 NIL 3183900 NIL) (-1279 3178452 3180593 3180981 "XPBWPOLY" 3181734 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3174328 3176615 3176657 "XF" 3177278 NIL XF (NIL T) -9 NIL 3177678 NIL) (-1277 3173949 3174037 3174206 "XF-" 3174211 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3169249 3170538 3170593 "XFALG" 3172765 NIL XFALG (NIL T T) -9 NIL 3173554 NIL) (-1275 3168382 3168486 3168691 "XEXPPKG" 3169141 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3166491 3168232 3168328 "XDPOLY" 3168333 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3165402 3166002 3166045 "XALG" 3166050 NIL XALG (NIL T) -9 NIL 3166161 NIL) (-1272 3158844 3163379 3163873 "WUTSET" 3164994 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3157100 3157896 3158219 "WP" 3158655 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3156702 3156922 3156992 "WHILEAST" 3157052 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3156174 3156419 3156513 "WHEREAST" 3156630 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3155060 3155258 3155553 "WFFINTBS" 3155971 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3152964 3153391 3153853 "WEIER" 3154632 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3152085 3152535 3152577 "VSPACE" 3152713 NIL VSPACE (NIL T) -9 NIL 3152787 NIL) (-1265 3151923 3151950 3152041 "VSPACE-" 3152046 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3151731 3151774 3151842 "VOID" 3151877 T VOID (NIL) -8 NIL NIL NIL) (-1263 3149867 3150226 3150632 "VIEW" 3151347 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3146291 3146930 3147667 "VIEWDEF" 3149152 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3135595 3137839 3140012 "VIEW3D" 3144140 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3127846 3129506 3131085 "VIEW2D" 3134038 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3123200 3127616 3127708 "VECTOR" 3127789 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3121777 3122036 3122354 "VECTOR2" 3122930 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3115256 3119561 3119604 "VECTCAT" 3120597 NIL VECTCAT (NIL T) -9 NIL 3121183 NIL) (-1256 3114270 3114524 3114914 "VECTCAT-" 3114919 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3113724 3113921 3114041 "VARIABLE" 3114185 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3113657 3113662 3113692 "UTYPE" 3113697 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3112487 3112641 3112903 "UTSODETL" 3113483 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3109927 3110387 3110911 "UTSODE" 3112028 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3101764 3107553 3108042 "UTS" 3109496 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3092972 3098331 3098374 "UTSCAT" 3099486 NIL UTSCAT (NIL T) -9 NIL 3100243 NIL) (-1249 3090320 3091042 3092031 "UTSCAT-" 3092036 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3089947 3089990 3090123 "UTS2" 3090271 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3084173 3086785 3086828 "URAGG" 3088898 NIL URAGG (NIL T) -9 NIL 3089621 NIL) (-1246 3081112 3081975 3083098 "URAGG-" 3083103 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3076822 3079747 3080212 "UPXSSING" 3080776 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3068888 3076069 3076342 "UPXS" 3076607 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3061961 3068792 3068864 "UPXSCONS" 3068869 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3052171 3058956 3059018 "UPXSCCA" 3059592 NIL UPXSCCA (NIL T T) -9 NIL 3059825 NIL) (-1241 3051809 3051894 3052068 "UPXSCCA-" 3052073 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3041872 3048430 3048473 "UPXSCAT" 3049121 NIL UPXSCAT (NIL T) -9 NIL 3049729 NIL) (-1239 3041302 3041381 3041560 "UPXS2" 3041787 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3039956 3040209 3040560 "UPSQFREE" 3041045 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3033709 3036758 3036813 "UPSCAT" 3037974 NIL UPSCAT (NIL T T) -9 NIL 3038748 NIL) (-1236 3032913 3033120 3033447 "UPSCAT-" 3033452 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3019028 3026788 3026831 "UPOLYC" 3028932 NIL UPOLYC (NIL T) -9 NIL 3030153 NIL) (-1234 3010356 3012782 3015929 "UPOLYC-" 3015934 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3009983 3010026 3010159 "UPOLYC2" 3010307 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 3001794 3009666 3009795 "UP" 3009902 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 3001133 3001240 3001404 "UPMP" 3001683 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 3000686 3000767 3000906 "UPDIVP" 3001046 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2999254 2999503 2999819 "UPDECOMP" 3000435 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2998489 2998601 2998786 "UPCDEN" 2999138 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2998008 2998077 2998226 "UP2" 2998414 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2996475 2997212 2997489 "UNISEG" 2997766 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2995690 2995817 2996022 "UNISEG2" 2996318 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2994750 2994930 2995156 "UNIFACT" 2995506 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2978682 2993927 2994178 "ULS" 2994557 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2966681 2978586 2978658 "ULSCONS" 2978663 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2949262 2961239 2961301 "ULSCCAT" 2961939 NIL ULSCCAT (NIL T T) -9 NIL 2962227 NIL) (-1220 2948312 2948557 2948945 "ULSCCAT-" 2948950 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2938152 2944624 2944667 "ULSCAT" 2945530 NIL ULSCAT (NIL T) -9 NIL 2946260 NIL) (-1218 2937582 2937661 2937840 "ULS2" 2938067 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2936672 2937182 2937289 "UINT8" 2937400 T UINT8 (NIL) -8 NIL NIL 2937485) (-1216 2935761 2936271 2936378 "UINT64" 2936489 T UINT64 (NIL) -8 NIL NIL 2936574) (-1215 2934850 2935360 2935467 "UINT32" 2935578 T UINT32 (NIL) -8 NIL NIL 2935663) (-1214 2933939 2934449 2934556 "UINT16" 2934667 T UINT16 (NIL) -8 NIL NIL 2934752) (-1213 2932308 2933265 2933295 "UFD" 2933507 T UFD (NIL) -9 NIL 2933621 NIL) (-1212 2932102 2932148 2932243 "UFD-" 2932248 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2931184 2931367 2931583 "UDVO" 2931908 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2929000 2929409 2929880 "UDPO" 2930748 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2928933 2928938 2928968 "TYPE" 2928973 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2928693 2928888 2928919 "TYPEAST" 2928924 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2927664 2927866 2928106 "TWOFACT" 2928487 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2926687 2927073 2927308 "TUPLE" 2927464 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2924378 2924897 2925436 "TUBETOOL" 2926170 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2923227 2923432 2923673 "TUBE" 2924171 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2917956 2922199 2922482 "TS" 2922979 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2906596 2910715 2910812 "TSETCAT" 2916081 NIL TSETCAT (NIL T T T T) -9 NIL 2917612 NIL) (-1201 2901328 2902928 2904819 "TSETCAT-" 2904824 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2895967 2896814 2897743 "TRMANIP" 2900464 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2895408 2895471 2895634 "TRIMAT" 2895899 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2893274 2893511 2893868 "TRIGMNIP" 2895157 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2892794 2892907 2892937 "TRIGCAT" 2893150 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2892463 2892542 2892683 "TRIGCAT-" 2892688 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2889308 2891321 2891602 "TREE" 2892217 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2888582 2889110 2889140 "TRANFUN" 2889175 T TRANFUN (NIL) -9 NIL 2889241 NIL) (-1193 2887861 2888052 2888332 "TRANFUN-" 2888337 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2887665 2887697 2887758 "TOPSP" 2887822 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2887013 2887128 2887282 "TOOLSIGN" 2887546 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2885647 2886190 2886429 "TEXTFILE" 2886796 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2883559 2884100 2884529 "TEX" 2885240 T TEX (NIL) -8 NIL NIL NIL) (-1188 2883340 2883371 2883443 "TEX1" 2883522 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2882988 2883051 2883141 "TEMUTL" 2883272 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2881142 2881422 2881747 "TBCMPPK" 2882711 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2872919 2879302 2879358 "TBAGG" 2879758 NIL TBAGG (NIL T T) -9 NIL 2879969 NIL) (-1184 2867989 2869477 2871231 "TBAGG-" 2871236 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2867373 2867480 2867625 "TANEXP" 2867878 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2860763 2867230 2867323 "TABLE" 2867328 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2860175 2860274 2860412 "TABLEAU" 2860660 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2854783 2856003 2857251 "TABLBUMP" 2858961 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2854005 2854152 2854333 "SYSTEM" 2854624 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2850464 2851163 2851946 "SYSSOLP" 2853256 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2849471 2849976 2850095 "SYSNNI" 2850281 NIL SYSNNI (NIL NIL) -8 NIL NIL 2850366) (-1176 2848741 2849200 2849279 "SYSINT" 2849339 NIL SYSINT (NIL NIL) -8 NIL NIL 2849384) (-1175 2845073 2846019 2846729 "SYNTAX" 2848053 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2842231 2842833 2843465 "SYMTAB" 2844463 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2837480 2838382 2839365 "SYMS" 2841270 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2834715 2836938 2837168 "SYMPOLY" 2837285 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2834232 2834307 2834430 "SYMFUNC" 2834627 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2830251 2831544 2832357 "SYMBOL" 2833441 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2823790 2825479 2827199 "SWITCH" 2828553 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2817024 2822611 2822914 "SUTS" 2823545 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2809090 2816271 2816544 "SUPXS" 2816809 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2800850 2808708 2808834 "SUP" 2808999 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2800009 2800136 2800353 "SUPFRACF" 2800718 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2799630 2799689 2799802 "SUP2" 2799944 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2798078 2798352 2798708 "SUMRF" 2799329 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2797413 2797479 2797671 "SUMFS" 2797999 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2781380 2796590 2796841 "SULS" 2797220 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2780982 2781202 2781272 "SUCHTAST" 2781332 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2780277 2780507 2780647 "SUCH" 2780890 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2774144 2775183 2776142 "SUBSPACE" 2779365 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2773574 2773664 2773828 "SUBRESP" 2774032 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2766939 2768239 2769550 "STTF" 2772310 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2761112 2762232 2763379 "STTFNC" 2765839 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2752423 2754294 2756088 "STTAYLOR" 2759353 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2745553 2752287 2752370 "STRTBL" 2752375 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2740917 2745508 2745539 "STRING" 2745544 T STRING (NIL) -8 NIL NIL NIL) (-1151 2735778 2740290 2740320 "STRICAT" 2740379 T STRICAT (NIL) -9 NIL 2740441 NIL) (-1150 2728533 2733397 2734008 "STREAM" 2735202 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2728043 2728120 2728264 "STREAM3" 2728450 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2727025 2727208 2727443 "STREAM2" 2727856 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2726713 2726765 2726858 "STREAM1" 2726967 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2725729 2725910 2726141 "STINPROD" 2726529 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2725281 2725491 2725521 "STEP" 2725601 T STEP (NIL) -9 NIL 2725679 NIL) (-1144 2718713 2725180 2725257 "STBL" 2725262 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2713839 2717934 2717977 "STAGG" 2718130 NIL STAGG (NIL T) -9 NIL 2718219 NIL) (-1142 2711541 2712143 2713015 "STAGG-" 2713020 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2709688 2711311 2711403 "STACK" 2711484 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2702384 2707829 2708285 "SREGSET" 2709318 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2694809 2696178 2697691 "SRDCMPK" 2700990 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2687726 2692249 2692279 "SRAGG" 2693582 T SRAGG (NIL) -9 NIL 2694190 NIL) (-1137 2686743 2686998 2687377 "SRAGG-" 2687382 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2681203 2685690 2686111 "SQMATRIX" 2686369 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2674889 2677921 2678648 "SPLTREE" 2680548 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2670852 2671545 2672191 "SPLNODE" 2674315 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2669899 2670132 2670162 "SPFCAT" 2670606 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2668636 2668846 2669110 "SPECOUT" 2669657 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2660262 2662032 2662062 "SPADXPT" 2666454 T SPADXPT (NIL) -9 NIL 2668488 NIL) (-1130 2660023 2660063 2660132 "SPADPRSR" 2660215 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2658178 2659978 2660009 "SPADAST" 2660014 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2650123 2651896 2651939 "SPACEC" 2656312 NIL SPACEC (NIL T) -9 NIL 2658128 NIL) (-1127 2648253 2650055 2650104 "SPACE3" 2650109 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2647005 2647176 2647467 "SORTPAK" 2648058 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2645097 2645400 2645812 "SOLVETRA" 2646669 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2644147 2644369 2644630 "SOLVESER" 2644870 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2639449 2640339 2641334 "SOLVERAD" 2643199 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2635264 2635873 2636602 "SOLVEFOR" 2638816 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2629534 2634613 2634710 "SNTSCAT" 2634715 NIL SNTSCAT (NIL T T T T) -9 NIL 2634785 NIL) (-1120 2623640 2627857 2628248 "SMTS" 2629224 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2618325 2623528 2623605 "SMP" 2623610 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2616484 2616785 2617183 "SMITH" 2618022 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2609344 2613535 2613638 "SMATCAT" 2614989 NIL SMATCAT (NIL NIL T T T) -9 NIL 2615539 NIL) (-1116 2606284 2607107 2608285 "SMATCAT-" 2608290 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2603950 2605520 2605563 "SKAGG" 2605824 NIL SKAGG (NIL T) -9 NIL 2605959 NIL) (-1114 2600258 2603366 2603561 "SINT" 2603748 T SINT (NIL) -8 NIL NIL 2603921) (-1113 2600030 2600068 2600134 "SIMPAN" 2600214 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2599309 2599565 2599705 "SIG" 2599912 T SIG (NIL) -8 NIL NIL NIL) (-1111 2598147 2598368 2598643 "SIGNRF" 2599068 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2596980 2597131 2597415 "SIGNEF" 2597976 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2596286 2596563 2596687 "SIGAST" 2596878 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2593976 2594430 2594936 "SHP" 2595827 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2587828 2593877 2593953 "SHDP" 2593958 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2587401 2587593 2587623 "SGROUP" 2587716 T SGROUP (NIL) -9 NIL 2587778 NIL) (-1105 2587259 2587285 2587358 "SGROUP-" 2587363 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2584094 2584792 2585515 "SGCF" 2586558 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2578462 2583541 2583638 "SFRTCAT" 2583643 NIL SFRTCAT (NIL T T T T) -9 NIL 2583682 NIL) (-1102 2571883 2572901 2574037 "SFRGCD" 2577445 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2565010 2566082 2567268 "SFQCMPK" 2570816 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2564630 2564719 2564830 "SFORT" 2564951 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2563748 2564470 2564591 "SEXOF" 2564596 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2562855 2563629 2563697 "SEX" 2563702 T SEX (NIL) -8 NIL NIL NIL) (-1097 2558368 2559083 2559178 "SEXCAT" 2562115 NIL SEXCAT (NIL T T T T T) -9 NIL 2562693 NIL) (-1096 2555521 2558302 2558350 "SET" 2558355 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2553745 2554234 2554539 "SETMN" 2555262 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2553241 2553393 2553423 "SETCAT" 2553599 T SETCAT (NIL) -9 NIL 2553709 NIL) (-1093 2553021 2553073 2553172 "SETCAT-" 2553177 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2549382 2551482 2551525 "SETAGG" 2552395 NIL SETAGG (NIL T) -9 NIL 2552735 NIL) (-1091 2548840 2548956 2549193 "SETAGG-" 2549198 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2548283 2548536 2548637 "SEQAST" 2548761 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2547482 2547776 2547837 "SEGXCAT" 2548123 NIL SEGXCAT (NIL T T) -9 NIL 2548243 NIL) (-1088 2546488 2547148 2547330 "SEG" 2547335 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2545467 2545681 2545724 "SEGCAT" 2546246 NIL SEGCAT (NIL T) -9 NIL 2546467 NIL) (-1086 2544468 2544846 2545046 "SEGBIND" 2545302 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2544089 2544148 2544261 "SEGBIND2" 2544403 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2543662 2543890 2543967 "SEGAST" 2544034 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2542881 2543007 2543211 "SEG2" 2543506 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2542291 2542816 2542863 "SDVAR" 2542868 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2534818 2542061 2542191 "SDPOL" 2542196 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2533411 2533677 2533996 "SCPKG" 2534533 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2532575 2532747 2532939 "SCOPE" 2533241 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2531795 2531929 2532108 "SCACHE" 2532430 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2531441 2531627 2531657 "SASTCAT" 2531662 T SASTCAT (NIL) -9 NIL 2531675 NIL) (-1076 2530928 2531276 2531352 "SAOS" 2531387 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2530493 2530528 2530701 "SAERFFC" 2530887 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2524432 2530390 2530470 "SAE" 2530475 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2524025 2524060 2524219 "SAEFACT" 2524391 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2522346 2522660 2523061 "RURPK" 2523691 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2520983 2521289 2521594 "RULESET" 2522180 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2518206 2518736 2519194 "RULE" 2520664 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2517818 2518000 2518083 "RULECOLD" 2518158 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2517608 2517636 2517707 "RTVALUE" 2517769 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2517079 2517325 2517419 "RSTRCAST" 2517536 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2511927 2512722 2513642 "RSETGCD" 2516278 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2501157 2506236 2506333 "RSETCAT" 2510452 NIL RSETCAT (NIL T T T T) -9 NIL 2511549 NIL) (-1064 2499084 2499623 2500447 "RSETCAT-" 2500452 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2491469 2492846 2494366 "RSDCMPK" 2497683 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489448 2489915 2489989 "RRCC" 2491075 NIL RRCC (NIL T T) -9 NIL 2491419 NIL) (-1061 2488799 2488973 2489252 "RRCC-" 2489257 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2488242 2488495 2488596 "RPTAST" 2488720 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2462513 2471862 2471929 "RPOLCAT" 2482593 NIL RPOLCAT (NIL T T T) -9 NIL 2485752 NIL) (-1058 2454011 2456351 2459473 "RPOLCAT-" 2459478 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2444942 2452222 2452704 "ROUTINE" 2453551 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2441740 2444568 2444708 "ROMAN" 2444824 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2439984 2440600 2440860 "ROIRC" 2441545 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2436342 2438620 2438650 "RNS" 2438954 T RNS (NIL) -9 NIL 2439227 NIL) (-1053 2434851 2435234 2435768 "RNS-" 2435843 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2434274 2434682 2434712 "RNG" 2434717 T RNG (NIL) -9 NIL 2434738 NIL) (-1051 2433640 2434028 2434071 "RMODULE" 2434133 NIL RMODULE (NIL T) -9 NIL 2434175 NIL) (-1050 2432476 2432570 2432906 "RMCAT2" 2433541 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2429326 2431822 2432119 "RMATRIX" 2432238 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2422242 2424502 2424617 "RMATCAT" 2427976 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2428958 NIL) (-1047 2421617 2421764 2422071 "RMATCAT-" 2422076 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2421184 2421259 2421387 "RINTERP" 2421536 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2420277 2420831 2420861 "RING" 2420917 T RING (NIL) -9 NIL 2421009 NIL) (-1044 2420069 2420113 2420210 "RING-" 2420215 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2418910 2419147 2419405 "RIDIST" 2419833 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2410199 2418378 2418584 "RGCHAIN" 2418758 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2409549 2409955 2409996 "RGBCSPC" 2410054 NIL RGBCSPC (NIL T) -9 NIL 2410106 NIL) (-1040 2408707 2409088 2409129 "RGBCMDL" 2409361 NIL RGBCMDL (NIL T) -9 NIL 2409475 NIL) (-1039 2405701 2406315 2406985 "RF" 2408071 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2405347 2405410 2405513 "RFFACTOR" 2405632 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2405072 2405107 2405204 "RFFACT" 2405306 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2403189 2403553 2403935 "RFDIST" 2404712 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2402642 2402734 2402897 "RETSOL" 2403091 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2402278 2402358 2402401 "RETRACT" 2402534 NIL RETRACT (NIL T) -9 NIL 2402621 NIL) (-1033 2402127 2402152 2402239 "RETRACT-" 2402244 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2401729 2401949 2402019 "RETAST" 2402079 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2394467 2401382 2401509 "RESULT" 2401624 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2393058 2393736 2393935 "RESRING" 2394370 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2392694 2392743 2392841 "RESLATC" 2392995 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2392399 2392434 2392541 "REPSQ" 2392653 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2389821 2390401 2391003 "REP" 2391819 T REP (NIL) -7 NIL NIL NIL) (-1026 2389518 2389553 2389664 "REPDB" 2389780 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2383418 2384807 2386030 "REP2" 2388330 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2379795 2380476 2381284 "REP1" 2382645 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2372491 2377936 2378392 "REGSET" 2379425 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2371256 2371639 2371889 "REF" 2372276 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2370633 2370736 2370903 "REDORDER" 2371140 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2366601 2369846 2370073 "RECLOS" 2370461 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2365653 2365834 2366049 "REALSOLV" 2366408 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2365499 2365540 2365570 "REAL" 2365575 T REAL (NIL) -9 NIL 2365610 NIL) (-1017 2361982 2362784 2363668 "REAL0Q" 2364664 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2357583 2358571 2359632 "REAL0" 2360963 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2357054 2357300 2357394 "RDUCEAST" 2357511 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2356459 2356531 2356738 "RDIV" 2356976 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2355527 2355701 2355914 "RDIST" 2356281 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2354124 2354411 2354783 "RDETRS" 2355235 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2351936 2352390 2352928 "RDETR" 2353666 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2350561 2350839 2351236 "RDEEFS" 2351652 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2349070 2349376 2349801 "RDEEF" 2350249 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2343296 2346206 2346236 "RCFIELD" 2347531 T RCFIELD (NIL) -9 NIL 2348261 NIL) (-1007 2341360 2341864 2342560 "RCFIELD-" 2342635 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2337629 2339461 2339504 "RCAGG" 2340588 NIL RCAGG (NIL T) -9 NIL 2341053 NIL) (-1005 2337257 2337351 2337514 "RCAGG-" 2337519 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2336592 2336704 2336869 "RATRET" 2337141 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2336145 2336212 2336333 "RATFACT" 2336520 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2335453 2335573 2335725 "RANDSRC" 2336015 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2335187 2335231 2335304 "RADUTIL" 2335402 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2328303 2334020 2334330 "RADIX" 2334911 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2319924 2328147 2328275 "RADFF" 2328280 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2319576 2319651 2319679 "RADCAT" 2319836 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2319361 2319409 2319506 "RADCAT-" 2319511 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 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(-984 2278470 2279542 2280726 "QCMPACK" 2284256 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2276019 2276467 2276895 "QALGSET" 2278125 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2275264 2275438 2275670 "QALGSET2" 2275839 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2273954 2274178 2274495 "PWFFINTB" 2275037 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2272136 2272304 2272658 "PUSHVAR" 2273768 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2268054 2269108 2269149 "PTRANFN" 2271033 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2266456 2266747 2267069 "PTPACK" 2267765 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2266088 2266145 2266254 "PTFUNC2" 2266393 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2260567 2264960 2265001 "PTCAT" 2265297 NIL PTCAT (NIL T) -9 NIL 2265450 NIL) (-975 2260225 2260260 2260384 "PSQFR" 2260526 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2258820 2259118 2259452 "PSEUDLIN" 2259923 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2245583 2247954 2250278 "PSETPK" 2256580 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2238601 2241341 2241437 "PSETCAT" 2244458 NIL PSETCAT (NIL T T T T) -9 NIL 2245272 NIL) (-971 2236437 2237071 2237892 "PSETCAT-" 2237897 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2235786 2235951 2235979 "PSCURVE" 2236247 T PSCURVE (NIL) -9 NIL 2236414 NIL) (-969 2232108 2233624 2233689 "PSCAT" 2234533 NIL PSCAT (NIL T T T) -9 NIL 2234773 NIL) (-968 2231171 2231387 2231787 "PSCAT-" 2231792 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2229876 2230536 2230741 "PRTITION" 2230986 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2229351 2229597 2229689 "PRTDAST" 2229804 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2218441 2220655 2222843 "PRS" 2227213 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2216252 2217791 2217831 "PRQAGG" 2218014 NIL PRQAGG (NIL T) -9 NIL 2218116 NIL) (-963 2215456 2215761 2215789 "PROPLOG" 2216036 T PROPLOG (NIL) -9 NIL 2216202 NIL) (-962 2213886 2214407 2214664 "PROPFRML" 2215232 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2213355 2213462 2213590 "PROPERTY" 2213778 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2207413 2211521 2212341 "PRODUCT" 2212581 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2204691 2206871 2207105 "PR" 2207224 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2204487 2204519 2204578 "PRINT" 2204652 T PRINT (NIL) -7 NIL NIL NIL) (-957 2203827 2203944 2204096 "PRIMES" 2204367 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2201892 2202293 2202759 "PRIMELT" 2203406 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2201621 2201670 2201698 "PRIMCAT" 2201822 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2197736 2201559 2201604 "PRIMARR" 2201609 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2196743 2196921 2197149 "PRIMARR2" 2197554 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2196386 2196442 2196553 "PREASSOC" 2196681 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2195861 2195994 2196022 "PPCURVE" 2196227 T PPCURVE (NIL) -9 NIL 2196363 NIL) (-950 2195456 2195656 2195739 "PORTNUM" 2195798 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 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"PNTHEORY" 2154607 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2151607 2151904 2152303 "PMTOOLS" 2152847 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2151200 2151278 2151395 "PMSYM" 2151523 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2150710 2150779 2150953 "PMQFCAT" 2151125 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2150065 2150175 2150331 "PMPRED" 2150587 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2149458 2149544 2149706 "PMPREDFS" 2149966 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2148122 2148330 2148708 "PMPLCAT" 2149220 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2147654 2147733 2147885 "PMLSAGG" 2148037 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2147127 2147203 2147385 "PMKERNEL" 2147572 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2146744 2146819 2146932 "PMINS" 2147046 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2146186 2146255 2146464 "PMFS" 2146669 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2145414 2145532 2145737 "PMDOWN" 2146063 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) 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2030986 2031088 "PARSURF" 2031233 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2030555 2030612 2030721 "PARSU2" 2030860 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2030319 2030359 2030426 "PARSER" 2030508 T PARSER (NIL) -7 NIL NIL NIL) (-875 2029940 2030003 2030105 "PARSCURV" 2030250 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2029572 2029629 2029738 "PARSC2" 2029877 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2029211 2029269 2029366 "PARPCURV" 2029508 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2028843 2028900 2029009 "PARPC2" 2029148 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2028363 2028449 2028568 "PAN2EXPR" 2028744 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2027140 2027484 2027712 "PALETTE" 2028155 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2025533 2026145 2026505 "PAIR" 2026826 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2019403 2024792 2024986 "PADICRC" 2025388 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2012632 2018749 2018933 "PADICRAT" 2019251 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2010947 2012569 2012614 "PADIC" 2012619 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2008123 2009687 2009727 "PADICCT" 2010308 NIL PADICCT (NIL NIL) -9 NIL 2010590 NIL) (-864 2007080 2007280 2007548 "PADEPAC" 2007910 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2006292 2006425 2006631 "PADE" 2006942 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2004679 2005500 2005780 "OWP" 2006096 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2004172 2004385 2004482 "OVERSET" 2004602 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2003218 2003777 2003949 "OVAR" 2004040 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2002482 2002603 2002764 "OUT" 2003077 T OUT (NIL) -7 NIL NIL NIL) (-858 1991353 1993591 1995791 "OUTFORM" 2000302 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1990689 1990950 1991077 "OUTBFILE" 1991246 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1989996 1990161 1990189 "OUTBCON" 1990507 T OUTBCON (NIL) -9 NIL 1990673 NIL) (-855 1989597 1989709 1989866 "OUTBCON-" 1989871 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1988977 1989326 1989415 "OSI" 1989528 T OSI (NIL) -8 NIL NIL NIL) (-853 1988507 1988845 1988873 "OSGROUP" 1988878 T OSGROUP (NIL) -9 NIL 1988900 NIL) (-852 1987252 1987479 1987764 "ORTHPOL" 1988254 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1984803 1987087 1987208 "OREUP" 1987213 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1982206 1984494 1984621 "ORESUP" 1984745 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1979734 1980234 1980795 "OREPCTO" 1981695 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1973524 1975725 1975766 "OREPCAT" 1978114 NIL OREPCAT (NIL T) -9 NIL 1979218 NIL) (-847 1970671 1971453 1972511 "OREPCAT-" 1972516 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1969822 1970120 1970148 "ORDSET" 1970457 T ORDSET (NIL) -9 NIL 1970621 NIL) (-845 1969253 1969401 1969625 "ORDSET-" 1969630 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1967853 1968644 1968672 "ORDRING" 1968874 T ORDRING (NIL) -9 NIL 1968999 NIL) (-843 1967498 1967592 1967736 "ORDRING-" 1967741 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1966878 1967341 1967369 "ORDMON" 1967374 T ORDMON (NIL) -9 NIL 1967395 NIL) (-841 1966040 1966187 1966382 "ORDFUNS" 1966727 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1965378 1965797 1965825 "ORDFIN" 1965890 T ORDFIN (NIL) -9 NIL 1965964 NIL) (-839 1961937 1963964 1964373 "ORDCOMP" 1965002 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1961203 1961330 1961516 "ORDCOMP2" 1961797 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1957784 1958694 1959508 "OPTPROB" 1960409 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1954586 1955225 1955929 "OPTPACK" 1957100 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1952273 1953039 1953067 "OPTCAT" 1953886 T OPTCAT (NIL) -9 NIL 1954536 NIL) (-834 1951689 1951950 1952055 "OPSIG" 1952188 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1951457 1951496 1951562 "OPQUERY" 1951643 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1948588 1949768 1950272 "OP" 1950986 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1948097 1948294 1948335 "OPERCAT" 1948470 NIL OPERCAT (NIL T) -9 NIL 1948538 NIL) (-830 1947943 1947970 1948056 "OPERCAT-" 1948061 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1944755 1946740 1947109 "ONECOMP" 1947607 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1944060 1944175 1944349 "ONECOMP2" 1944627 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1943479 1943585 1943715 "OMSERVER" 1943950 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1940341 1942919 1942959 "OMSAGG" 1943020 NIL OMSAGG (NIL T) -9 NIL 1943084 NIL) (-825 1938964 1939227 1939509 "OMPKG" 1940079 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1938394 1938497 1938525 "OM" 1938824 T OM (NIL) -9 NIL NIL NIL) (-823 1936941 1937943 1938112 "OMLO" 1938275 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1935901 1936048 1936268 "OMEXPR" 1936767 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1935192 1935447 1935583 "OMERR" 1935785 T OMERR (NIL) -8 NIL NIL NIL) (-820 1934343 1934613 1934773 "OMERRK" 1935052 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1933794 1934020 1934128 "OMENC" 1934255 T OMENC (NIL) -8 NIL NIL NIL) (-818 1927689 1928874 1930045 "OMDEV" 1932643 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1926758 1926929 1927123 "OMCONN" 1927515 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1925345 1926321 1926349 "OINTDOM" 1926354 T OINTDOM (NIL) -9 NIL 1926375 NIL) (-815 1921124 1922335 1923051 "OFMONOID" 1924661 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1920535 1921061 1921106 "ODVAR" 1921111 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1917958 1920280 1920435 "ODR" 1920440 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1910539 1917734 1917860 "ODPOL" 1917865 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1904361 1910411 1910516 "ODP" 1910521 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1903127 1903342 1903617 "ODETOOLS" 1904135 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1900094 1900752 1901468 "ODESYS" 1902460 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1894976 1895884 1896909 "ODERTRIC" 1899169 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1894402 1894484 1894678 "ODERED" 1894888 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1891290 1891838 1892515 "ODERAT" 1893825 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1888247 1888714 1889311 "ODEPRRIC" 1890819 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1886190 1886786 1887272 "ODEPROB" 1887781 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1882710 1883195 1883842 "ODEPRIM" 1885669 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1881959 1882061 1882321 "ODEPAL" 1882602 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1878121 1878912 1879776 "ODEPACK" 1881115 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1877182 1877289 1877511 "ODEINT" 1878010 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1871283 1872708 1874155 "ODEIFTBL" 1875755 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1866681 1867467 1868419 "ODEEF" 1870442 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1866030 1866119 1866342 "ODECONST" 1866586 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1864155 1864816 1864844 "ODECAT" 1865449 T ODECAT (NIL) -9 NIL 1865980 NIL) (-795 1861027 1863867 1863986 "OCT" 1864068 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1860665 1860708 1860835 "OCTCT2" 1860978 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1855405 1857839 1857879 "OC" 1858976 NIL OC (NIL T) -9 NIL 1859834 NIL) (-792 1852632 1853380 1854370 "OC-" 1854464 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1851984 1852452 1852480 "OCAMON" 1852485 T OCAMON (NIL) -9 NIL 1852506 NIL) (-790 1851515 1851856 1851884 "OASGP" 1851889 T OASGP (NIL) -9 NIL 1851909 NIL) (-789 1850776 1851265 1851293 "OAMONS" 1851333 T OAMONS (NIL) -9 NIL 1851376 NIL) (-788 1850190 1850623 1850651 "OAMON" 1850656 T OAMON (NIL) -9 NIL 1850676 NIL) (-787 1849468 1849986 1850014 "OAGROUP" 1850019 T OAGROUP (NIL) -9 NIL 1850039 NIL) (-786 1849158 1849208 1849296 "NUMTUBE" 1849412 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1842731 1844249 1845785 "NUMQUAD" 1847642 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1838487 1839475 1840500 "NUMODE" 1841726 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1835842 1836722 1836750 "NUMINT" 1837673 T NUMINT (NIL) -9 NIL 1838437 NIL) (-782 1834790 1834987 1835205 "NUMFMT" 1835644 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1821149 1824094 1826626 "NUMERIC" 1832297 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1815519 1820598 1820693 "NTSCAT" 1820698 NIL NTSCAT (NIL T T T T) -9 NIL 1820737 NIL) (-779 1814713 1814878 1815071 "NTPOLFN" 1815358 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1802790 1811538 1812350 "NSUP" 1813934 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1802422 1802479 1802588 "NSUP2" 1802727 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1792650 1802196 1802329 "NSMP" 1802334 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1791082 1791383 1791740 "NREP" 1792338 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1789673 1789925 1790283 "NPCOEF" 1790825 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1788739 1788854 1789070 "NORMRETR" 1789554 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1786780 1787070 1787479 "NORMPK" 1788447 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1786465 1786493 1786617 "NORMMA" 1786746 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1786265 1786422 1786451 "NONE" 1786456 T NONE (NIL) -8 NIL NIL NIL) (-769 1786054 1786083 1786152 "NONE1" 1786229 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1785551 1785613 1785792 "NODE1" 1785986 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1783794 1784645 1784900 "NNI" 1785247 T NNI (NIL) -8 NIL NIL 1785482) (-766 1782214 1782527 1782891 "NLINSOL" 1783462 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1778455 1779450 1780349 "NIPROB" 1781335 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1777212 1777446 1777748 "NFINTBAS" 1778217 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1776386 1776862 1776903 "NETCLT" 1777075 NIL NETCLT (NIL T) -9 NIL 1777157 NIL) (-762 1775094 1775325 1775606 "NCODIV" 1776154 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1774856 1774893 1774968 "NCNTFRAC" 1775051 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1773036 1773400 1773820 "NCEP" 1774481 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1771907 1772680 1772708 "NASRING" 1772818 T NASRING (NIL) -9 NIL 1772898 NIL) (-758 1771702 1771746 1771840 "NASRING-" 1771845 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1770829 1771354 1771382 "NARNG" 1771499 T NARNG (NIL) -9 NIL 1771590 NIL) (-756 1770521 1770588 1770722 "NARNG-" 1770727 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1769400 1769607 1769842 "NAGSP" 1770306 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1760672 1762356 1764029 "NAGS" 1767747 T NAGS (NIL) -7 NIL NIL NIL) (-753 1759220 1759528 1759859 "NAGF07" 1760361 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1753758 1755049 1756356 "NAGF04" 1757933 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1746726 1748340 1749973 "NAGF02" 1752145 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1741950 1743050 1744167 "NAGF01" 1745629 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1735578 1737144 1738729 "NAGE04" 1740385 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1726747 1728868 1730998 "NAGE02" 1733468 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1722700 1723647 1724611 "NAGE01" 1725803 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1720495 1721029 1721587 "NAGD03" 1722162 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1712245 1714173 1716127 "NAGD02" 1718561 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1706056 1707481 1708921 "NAGD01" 1710825 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1702265 1703087 1703924 "NAGC06" 1705239 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1700730 1701062 1701418 "NAGC05" 1701929 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1700106 1700225 1700369 "NAGC02" 1700606 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1699140 1699723 1699763 "NAALG" 1699842 NIL NAALG (NIL T) -9 NIL 1699903 NIL) (-739 1698975 1699004 1699094 "NAALG-" 1699099 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1692925 1694033 1695220 "MULTSQFR" 1697871 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1692244 1692319 1692503 "MULTFACT" 1692837 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1685302 1689207 1689260 "MTSCAT" 1690330 NIL MTSCAT (NIL T T) -9 NIL 1690844 NIL) (-735 1685014 1685068 1685160 "MTHING" 1685242 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1684806 1684839 1684899 "MSYSCMD" 1684974 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1680888 1683561 1683881 "MSET" 1684519 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1677957 1680449 1680490 "MSETAGG" 1680495 NIL MSETAGG (NIL T) -9 NIL 1680529 NIL) (-731 1673798 1675336 1676081 "MRING" 1677257 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1673364 1673431 1673562 "MRF2" 1673725 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1672982 1673017 1673161 "MRATFAC" 1673323 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1670594 1670889 1671320 "MPRFF" 1672687 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1664891 1670448 1670545 "MPOLY" 1670550 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1664381 1664416 1664624 "MPCPF" 1664850 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1663895 1663938 1664122 "MPC3" 1664332 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1663090 1663171 1663392 "MPC2" 1663810 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1661391 1661728 1662118 "MONOTOOL" 1662750 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1660616 1660933 1660961 "MONOID" 1661180 T MONOID (NIL) -9 NIL 1661327 NIL) (-721 1660162 1660281 1660462 "MONOID-" 1660467 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1650986 1656929 1656988 "MONOGEN" 1657662 NIL MONOGEN (NIL T T) -9 NIL 1658118 NIL) (-719 1648204 1648939 1649939 "MONOGEN-" 1650058 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1647037 1647483 1647511 "MONADWU" 1647903 T MONADWU (NIL) -9 NIL 1648141 NIL) (-717 1646409 1646568 1646816 "MONADWU-" 1646821 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1645768 1646012 1646040 "MONAD" 1646247 T MONAD (NIL) -9 NIL 1646359 NIL) (-715 1645453 1645531 1645663 "MONAD-" 1645668 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1643742 1644366 1644645 "MOEBIUS" 1645206 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1643108 1643512 1643552 "MODULE" 1643557 NIL MODULE (NIL T) -9 NIL 1643583 NIL) (-712 1642676 1642772 1642962 "MODULE-" 1642967 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1640356 1641040 1641367 "MODRING" 1642500 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1637300 1638461 1638982 "MODOP" 1639885 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1635888 1636367 1636644 "MODMONOM" 1637163 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1625930 1634179 1634593 "MODMON" 1635525 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1623086 1624774 1625050 "MODFIELD" 1625805 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1622063 1622367 1622557 "MMLFORM" 1622916 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1621589 1621632 1621811 "MMAP" 1622014 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1619772 1620539 1620580 "MLO" 1621003 NIL MLO (NIL T) -9 NIL 1621245 NIL) (-703 1617138 1617654 1618256 "MLIFT" 1619253 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1616529 1616613 1616767 "MKUCFUNC" 1617049 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1616128 1616198 1616321 "MKRECORD" 1616452 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1615175 1615337 1615565 "MKFUNC" 1615939 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1614563 1614667 1614823 "MKFLCFN" 1615058 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1613840 1613942 1614127 "MKBCFUNC" 1614456 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1610547 1613394 1613530 "MINT" 1613724 T MINT (NIL) -8 NIL NIL NIL) (-696 1609359 1609602 1609879 "MHROWRED" 1610302 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1604739 1607894 1608299 "MFLOAT" 1608974 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1604096 1604172 1604343 "MFINFACT" 1604651 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1600411 1601259 1602143 "MESH" 1603232 T MESH (NIL) -7 NIL NIL NIL) (-692 1598801 1599113 1599466 "MDDFACT" 1600098 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1595596 1597960 1598001 "MDAGG" 1598256 NIL MDAGG (NIL T) -9 NIL 1598399 NIL) (-690 1585339 1594889 1595096 "MCMPLX" 1595409 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1584480 1584626 1584826 "MCDEN" 1585188 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1582370 1582640 1583020 "MCALCFN" 1584210 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1581295 1581535 1581768 "MAYBE" 1582176 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1578907 1579430 1579992 "MATSTOR" 1580766 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1574864 1578279 1578527 "MATRIX" 1578692 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1570628 1571337 1572073 "MATLIN" 1574221 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1560734 1563920 1563997 "MATCAT" 1568877 NIL MATCAT (NIL T T T) -9 NIL 1570294 NIL) (-682 1557090 1558111 1559467 "MATCAT-" 1559472 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1555684 1555837 1556170 "MATCAT2" 1556925 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1553796 1554120 1554504 "MAPPKG3" 1555359 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1552777 1552950 1553172 "MAPPKG2" 1553620 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1551276 1551560 1551887 "MAPPKG1" 1552483 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1550355 1550682 1550859 "MAPPAST" 1551119 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1549966 1550024 1550147 "MAPHACK3" 1550291 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1549558 1549619 1549733 "MAPHACK2" 1549898 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1548995 1549099 1549241 "MAPHACK1" 1549449 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1547074 1547695 1547999 "MAGMA" 1548723 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1546553 1546798 1546889 "MACROAST" 1547003 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1542971 1544792 1545253 "M3D" 1546125 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1537077 1541340 1541381 "LZSTAGG" 1542163 NIL LZSTAGG (NIL T) -9 NIL 1542458 NIL) (-669 1533034 1534208 1535665 "LZSTAGG-" 1535670 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1530121 1530925 1531412 "LWORD" 1532579 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1529697 1529925 1530000 "LSTAST" 1530066 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1522863 1529468 1529602 "LSQM" 1529607 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1522087 1522226 1522454 "LSPP" 1522718 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1519899 1520200 1520656 "LSMP" 1521776 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1516678 1517352 1518082 "LSMP1" 1519201 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1510555 1515845 1515886 "LSAGG" 1515948 NIL LSAGG (NIL T) -9 NIL 1516026 NIL) (-661 1507250 1508174 1509387 "LSAGG-" 1509392 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1504849 1506394 1506643 "LPOLY" 1507045 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1504431 1504516 1504639 "LPEFRAC" 1504758 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1502752 1503525 1503778 "LO" 1504263 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1502404 1502516 1502544 "LOGIC" 1502655 T LOGIC (NIL) -9 NIL 1502736 NIL) (-656 1502266 1502289 1502360 "LOGIC-" 1502365 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1501459 1501599 1501792 "LODOOPS" 1502122 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1498882 1501375 1501441 "LODO" 1501446 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1497420 1497655 1498008 "LODOF" 1498629 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1493742 1496173 1496214 "LODOCAT" 1496652 NIL LODOCAT (NIL T) -9 NIL 1496863 NIL) (-651 1493475 1493533 1493660 "LODOCAT-" 1493665 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1490795 1493316 1493434 "LODO2" 1493439 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1488230 1490732 1490777 "LODO1" 1490782 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1487111 1487276 1487581 "LODEEF" 1488053 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1482350 1485241 1485282 "LNAGG" 1486229 NIL LNAGG (NIL T) -9 NIL 1486673 NIL) (-646 1481497 1481711 1482053 "LNAGG-" 1482058 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1477633 1478422 1479061 "LMOPS" 1480912 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1477002 1477390 1477431 "LMODULE" 1477492 NIL LMODULE (NIL T) -9 NIL 1477534 NIL) (-643 1474200 1476647 1476770 "LMDICT" 1476912 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1473899 1474108 1474168 "LITERAL" 1474173 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1467082 1472845 1473143 "LIST" 1473634 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1466607 1466681 1466820 "LIST3" 1467002 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1465614 1465792 1466020 "LIST2" 1466425 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1463748 1464060 1464459 "LIST2MAP" 1465261 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1462444 1463114 1463155 "LINEXP" 1463410 NIL LINEXP (NIL T) -9 NIL 1463559 NIL) (-636 1461091 1461351 1461648 "LINDEP" 1462196 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1457858 1458577 1459354 "LIMITRF" 1460346 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1456161 1456457 1456866 "LIMITPS" 1457553 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1450589 1455672 1455900 "LIE" 1455982 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1449612 1450081 1450121 "LIECAT" 1450261 NIL LIECAT (NIL T) -9 NIL 1450412 NIL) (-631 1449453 1449480 1449568 "LIECAT-" 1449573 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1441949 1448902 1449067 "LIB" 1449308 T LIB (NIL) -8 NIL NIL NIL) (-629 1437584 1438467 1439402 "LGROBP" 1441066 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1435593 1435867 1436216 "LF" 1437305 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1434433 1435125 1435153 "LFCAT" 1435360 T LFCAT (NIL) -9 NIL 1435499 NIL) (-626 1431335 1431965 1432653 "LEXTRIPK" 1433797 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1428079 1428905 1429408 "LEXP" 1430915 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1427555 1427800 1427892 "LETAST" 1428007 T LETAST (NIL) -8 NIL NIL NIL) (-623 1425953 1426266 1426667 "LEADCDET" 1427237 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1425143 1425217 1425446 "LAZM3PK" 1425874 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1420060 1423220 1423758 "LAUPOL" 1424655 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1419639 1419683 1419844 "LAPLACE" 1420010 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1417578 1418740 1418991 "LA" 1419472 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1416625 1417209 1417250 "LALG" 1417312 NIL LALG (NIL T) -9 NIL 1417371 NIL) (-617 1416339 1416398 1416534 "LALG-" 1416539 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1416174 1416198 1416239 "KVTFROM" 1416301 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1414947 1415391 1415620 "KTVLOGIC" 1415965 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1414782 1414806 1414847 "KRCFROM" 1414909 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1413686 1413873 1414172 "KOVACIC" 1414582 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1413521 1413545 1413586 "KONVERT" 1413648 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1413356 1413380 1413421 "KOERCE" 1413483 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1411038 1411826 1412227 "KERNEL" 1412988 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1410534 1410615 1410747 "KERNEL2" 1410952 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1404304 1409073 1409127 "KDAGG" 1409504 NIL KDAGG (NIL T T) -9 NIL 1409710 NIL) (-607 1403833 1403957 1404162 "KDAGG-" 1404167 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1396981 1403494 1403649 "KAFILE" 1403711 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1391409 1396492 1396720 "JORDAN" 1396802 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1390788 1391058 1391179 "JOINAST" 1391308 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1390634 1390693 1390748 "JAVACODE" 1390753 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1386886 1388839 1388893 "IXAGG" 1389822 NIL IXAGG (NIL T T) -9 NIL 1390281 NIL) (-601 1385805 1386111 1386530 "IXAGG-" 1386535 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1381337 1385727 1385786 "IVECTOR" 1385791 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1380103 1380340 1380606 "ITUPLE" 1381104 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1378617 1378794 1379087 "ITRIGMNP" 1379925 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1377362 1377566 1377849 "ITFUN3" 1378393 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1376994 1377051 1377160 "ITFUN2" 1377299 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1374796 1375856 1376155 "ITAYLOR" 1376728 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1363741 1368933 1370096 "ISUPS" 1373666 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1362845 1362985 1363221 "ISUMP" 1363588 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1358059 1362646 1362725 "ISTRING" 1362798 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1357535 1357780 1357872 "ISAST" 1357987 T ISAST (NIL) -8 NIL NIL NIL) (-590 1356745 1356826 1357042 "IRURPK" 1357449 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1355681 1355882 1356122 "IRSN" 1356525 T IRSN (NIL) -7 NIL NIL NIL) (-588 1353752 1354107 1354536 "IRRF2F" 1355319 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1353499 1353537 1353613 "IRREDFFX" 1353708 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1352114 1352373 1352672 "IROOT" 1353232 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1348718 1349798 1350490 "IR" 1351454 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1346331 1346826 1347392 "IR2" 1348196 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1345431 1345544 1345758 "IR2F" 1346214 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1345222 1345256 1345316 "IPRNTPK" 1345391 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1341802 1345111 1345180 "IPF" 1345185 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1340129 1341727 1341784 "IPADIC" 1341789 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1339441 1339689 1339819 "IP4ADDR" 1340019 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1338914 1339145 1339255 "IOMODE" 1339351 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1337987 1338511 1338638 "IOBFILE" 1338807 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1337475 1337891 1337919 "IOBCON" 1337924 T IOBCON (NIL) -9 NIL 1337945 NIL) (-575 1336986 1337044 1337227 "INVLAPLA" 1337411 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1326634 1328988 1331374 "INTTR" 1334650 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1322969 1323711 1324576 "INTTOOLS" 1325819 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1322555 1322646 1322763 "INTSLPE" 1322872 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1320509 1322478 1322537 "INTRVL" 1322542 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1318111 1318623 1319198 "INTRF" 1319994 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1317522 1317619 1317761 "INTRET" 1318009 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1315519 1315908 1316378 "INTRAT" 1317130 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1312782 1313365 1313984 "INTPM" 1315004 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1309526 1310126 1310864 "INTPAF" 1312168 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1304705 1305667 1306718 "INTPACK" 1308495 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1301582 1304434 1304561 "INT" 1304598 T INT (NIL) -8 NIL NIL NIL) (-563 1300834 1300986 1301194 "INTHERTR" 1301424 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1300273 1300353 1300541 "INTHERAL" 1300748 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1298119 1298562 1299019 "INTHEORY" 1299836 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1289525 1291146 1292918 "INTG0" 1296471 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1270098 1274888 1279698 "INTFTBL" 1284735 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1269347 1269485 1269658 "INTFACT" 1269957 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1266774 1267220 1267777 "INTEF" 1268901 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1265207 1265946 1265974 "INTDOM" 1266275 T INTDOM (NIL) -9 NIL 1266482 NIL) (-555 1264576 1264750 1264992 "INTDOM-" 1264997 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1261036 1262960 1263014 "INTCAT" 1263813 NIL INTCAT (NIL T) -9 NIL 1264133 NIL) (-553 1260508 1260611 1260739 "INTBIT" 1260928 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1259207 1259361 1259668 "INTALG" 1260353 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1258690 1258780 1258937 "INTAF" 1259111 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1252033 1258500 1258640 "INTABL" 1258645 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1251337 1251803 1251868 "INT8" 1251902 T INT8 (NIL) -8 NIL NIL 1251947) (-548 1250640 1251106 1251171 "INT64" 1251205 T INT64 (NIL) -8 NIL NIL 1251250) (-547 1249943 1250409 1250474 "INT32" 1250508 T INT32 (NIL) -8 NIL NIL 1250553) (-546 1249246 1249712 1249777 "INT16" 1249811 T INT16 (NIL) -8 NIL NIL 1249856) (-545 1244226 1246935 1246963 "INS" 1247897 T INS (NIL) -9 NIL 1248562 NIL) (-544 1241466 1242237 1243211 "INS-" 1243284 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1240241 1240468 1240766 "INPSIGN" 1241219 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1239359 1239476 1239673 "INPRODPF" 1240121 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1238253 1238370 1238607 "INPRODFF" 1239239 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1237253 1237405 1237665 "INNMFACT" 1238089 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1236450 1236547 1236735 "INMODGCD" 1237152 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1234958 1235203 1235527 "INFSP" 1236195 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1234142 1234259 1234442 "INFPROD0" 1234838 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1230997 1232207 1232722 "INFORM" 1233635 T INFORM (NIL) -8 NIL NIL NIL) (-535 1230607 1230667 1230765 "INFORM1" 1230932 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1230130 1230219 1230333 "INFINITY" 1230513 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1229306 1229850 1229951 "INETCLTS" 1230049 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1227922 1228172 1228493 "INEP" 1229054 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1227171 1227819 1227884 "INDE" 1227889 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1226735 1226803 1226920 "INCRMAPS" 1227098 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1225553 1226004 1226210 "INBFILE" 1226549 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1220853 1221789 1222733 "INBFF" 1224641 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1219761 1220030 1220058 "INBCON" 1220571 T INBCON (NIL) -9 NIL 1220837 NIL) (-526 1219013 1219236 1219512 "INBCON-" 1219517 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1218492 1218737 1218828 "INAST" 1218942 T INAST (NIL) -8 NIL NIL NIL) (-524 1217919 1218171 1218277 "IMPTAST" 1218406 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1214365 1217763 1217867 "IMATRIX" 1217872 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1213077 1213200 1213515 "IMATQF" 1214221 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1211297 1211524 1211861 "IMATLIN" 1212833 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1205875 1211221 1211279 "ILIST" 1211284 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1203780 1205735 1205848 "IIARRAY2" 1205853 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1199178 1203691 1203755 "IFF" 1203760 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1198525 1198795 1198911 "IFAST" 1199082 T IFAST (NIL) -8 NIL NIL NIL) (-516 1193520 1197817 1198005 "IFARRAY" 1198382 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1192700 1193424 1193497 "IFAMON" 1193502 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1192284 1192349 1192403 "IEVALAB" 1192610 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1191959 1192027 1192187 "IEVALAB-" 1192192 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1191590 1191873 1191936 "IDPO" 1191941 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1190840 1191479 1191554 "IDPOAMS" 1191559 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1190147 1190729 1190804 "IDPOAM" 1190809 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1189206 1189482 1189535 "IDPC" 1189948 NIL IDPC (NIL T T) -9 NIL 1190097 NIL) (-508 1188675 1189098 1189171 "IDPAM" 1189176 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1188051 1188567 1188640 "IDPAG" 1188645 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1187696 1187887 1187962 "IDENT" 1187996 T IDENT (NIL) -8 NIL NIL NIL) (-505 1183951 1184799 1185694 "IDECOMP" 1186853 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1176788 1177874 1178921 "IDEAL" 1182987 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1175952 1176064 1176263 "ICDEN" 1176672 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1175023 1175432 1175579 "ICARD" 1175825 T ICARD (NIL) -8 NIL NIL NIL) (-501 1173083 1173396 1173801 "IBPTOOLS" 1174700 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1168690 1172703 1172816 "IBITS" 1173002 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1165413 1165989 1166684 "IBATOOL" 1168107 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1163192 1163654 1164187 "IBACHIN" 1164948 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1161021 1163038 1163141 "IARRAY2" 1163146 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1157127 1160947 1161004 "IARRAY1" 1161009 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1151236 1155539 1156020 "IAN" 1156666 T IAN (NIL) -8 NIL NIL NIL) (-494 1150747 1150804 1150977 "IALGFACT" 1151173 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1150275 1150388 1150416 "HYPCAT" 1150623 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1149813 1149930 1150116 "HYPCAT-" 1150121 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1149408 1149608 1149691 "HOSTNAME" 1149750 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1149253 1149290 1149331 "HOMOTOP" 1149336 NIL HOMOTOP (NIL T) -9 NIL 1149369 NIL) (-489 1145885 1147263 1147304 "HOAGG" 1148285 NIL HOAGG (NIL T) -9 NIL 1148964 NIL) (-488 1144479 1144878 1145404 "HOAGG-" 1145409 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1138483 1144074 1144223 "HEXADEC" 1144350 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1137231 1137453 1137716 "HEUGCD" 1138260 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1136307 1137068 1137198 "HELLFDIV" 1137203 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1134486 1136084 1136172 "HEAP" 1136251 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133749 1134038 1134172 "HEADAST" 1134372 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127615 1133664 1133726 "HDP" 1133731 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1121603 1127250 1127402 "HDMP" 1127516 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1120927 1121067 1121231 "HB" 1121459 T HB (NIL) -7 NIL NIL NIL) (-479 1114313 1120773 1120877 "HASHTBL" 1120882 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113789 1114034 1114126 "HASAST" 1114241 T HASAST (NIL) -8 NIL NIL NIL) (-477 1111567 1113411 1113593 "HACKPI" 1113627 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1107235 1111420 1111533 "GTSET" 1111538 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100650 1107113 1107211 "GSTBL" 1107216 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092928 1099681 1099946 "GSERIES" 1100441 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1092069 1092486 1092514 "GROUP" 1092717 T GROUP (NIL) -9 NIL 1092851 NIL) (-472 1091435 1091594 1091845 "GROUP-" 1091850 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089802 1090123 1090510 "GROEBSOL" 1091112 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088716 1089004 1089055 "GRMOD" 1089584 NIL GRMOD (NIL T T) -9 NIL 1089752 NIL) (-469 1088484 1088520 1088648 "GRMOD-" 1088653 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083774 1084838 1085838 "GRIMAGE" 1087504 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1082240 1082501 1082825 "GRDEF" 1083470 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081684 1081800 1081941 "GRAY" 1082119 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080871 1081277 1081328 "GRALG" 1081481 NIL GRALG (NIL T T) -9 NIL 1081574 NIL) (-464 1080532 1080605 1080768 "GRALG-" 1080773 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1077309 1080117 1080295 "GPOLSET" 1080439 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076663 1076720 1076978 "GOSPER" 1077246 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072395 1073101 1073627 "GMODPOL" 1076362 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071400 1071584 1071822 "GHENSEL" 1072207 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065556 1066399 1067419 "GENUPS" 1070484 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1065253 1065304 1065393 "GENUFACT" 1065499 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064665 1064742 1064907 "GENPGCD" 1065171 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1064139 1064174 1064387 "GENMFACT" 1064624 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062705 1062962 1063269 "GENEEZ" 1063882 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056851 1062316 1062478 "GDMP" 1062628 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1046193 1050622 1051728 "GCNAALG" 1055834 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1044586 1045448 1045476 "GCDDOM" 1045731 T GCDDOM (NIL) -9 NIL 1045888 NIL) (-451 1044056 1044183 1044398 "GCDDOM-" 1044403 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042728 1042913 1043217 "GB" 1043835 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1031344 1033674 1036066 "GBINTERN" 1040419 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1029181 1029473 1029894 "GBF" 1031019 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027962 1028127 1028394 "GBEUCLID" 1028997 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1027311 1027436 1027585 "GAUSSFAC" 1027833 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025678 1025980 1026294 "GALUTIL" 1027030 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023986 1024260 1024584 "GALPOLYU" 1025405 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1021351 1021641 1022048 "GALFACTU" 1023683 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1013157 1014656 1016264 "GALFACT" 1019783 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1010545 1011203 1011231 "FVFUN" 1012387 T FVFUN (NIL) -9 NIL 1013107 NIL) (-440 1009811 1009993 1010021 "FVC" 1010312 T FVC (NIL) -9 NIL 1010495 NIL) (-439 1009454 1009636 1009704 "FUNDESC" 1009763 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1009069 1009251 1009332 "FUNCTION" 1009406 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006813 1007391 1007857 "FT" 1008623 T FT (NIL) -8 NIL NIL NIL) (-436 1005604 1006114 1006317 "FTEM" 1006630 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003895 1004184 1004581 "FSUPFACT" 1005295 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1002292 1002581 1002913 "FST" 1003583 T FST (NIL) -8 NIL NIL NIL) (-433 1001491 1001597 1001785 "FSRED" 1002174 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1000190 1000446 1000793 "FSPRMELT" 1001206 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 997496 997934 998420 "FSPECF" 999753 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 979651 987975 988016 "FS" 991900 NIL FS (NIL T) -9 NIL 994189 NIL) (-429 968294 971287 975344 "FS-" 975644 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 967822 967876 968046 "FSINT" 968235 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 966114 966815 967118 "FSERIES" 967601 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 965156 965272 965496 "FSCINT" 965994 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 961364 964100 964141 "FSAGG" 964511 NIL FSAGG (NIL T) -9 NIL 964770 NIL) (-424 959126 959727 960523 "FSAGG-" 960618 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 958168 958311 958538 "FSAGG2" 958979 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 955850 956130 956677 "FS2UPS" 957886 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 955484 955527 955656 "FS2" 955801 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 954362 954533 954835 "FS2EXPXP" 955309 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 953788 953903 954055 "FRUTIL" 954242 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 945202 949283 950641 "FR" 952462 NIL FR (NIL T) -8 NIL NIL NIL) (-417 940250 942920 942960 "FRNAALG" 944356 NIL FRNAALG (NIL T) -9 NIL 944963 NIL) (-416 935923 936999 938274 "FRNAALG-" 939024 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 935561 935604 935731 "FRNAAF2" 935874 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 933941 934415 934710 "FRMOD" 935373 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 931692 932324 932641 "FRIDEAL" 933732 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 930887 930974 931263 "FRIDEAL2" 931599 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 930020 930434 930475 "FRETRCT" 930480 NIL FRETRCT (NIL T) -9 NIL 930656 NIL) (-410 929132 929363 929714 "FRETRCT-" 929719 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 926310 927520 927579 "FRAMALG" 928461 NIL FRAMALG (NIL T T) -9 NIL 928753 NIL) (-408 924444 924899 925529 "FRAMALG-" 925752 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 918365 923919 924195 "FRAC" 924200 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 918001 918058 918165 "FRAC2" 918302 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 917637 917694 917801 "FR2" 917938 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 912275 915162 915190 "FPS" 916309 T FPS (NIL) -9 NIL 916866 NIL) (-403 911724 911833 911997 "FPS-" 912143 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 909144 910813 910841 "FPC" 911066 T FPC (NIL) -9 NIL 911208 NIL) (-401 908937 908977 909074 "FPC-" 909079 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 907727 908425 908466 "FPATMAB" 908471 NIL FPATMAB (NIL T) -9 NIL 908623 NIL) (-399 905400 905903 906329 "FPARFRAC" 907364 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900793 901292 901974 "FORTRAN" 904832 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 898509 899009 899548 "FORT" 900274 T FORT (NIL) -7 NIL NIL NIL) (-396 896185 896747 896775 "FORTFN" 897835 T FORTFN (NIL) -9 NIL 898459 NIL) (-395 895949 895999 896027 "FORTCAT" 896086 T FORTCAT (NIL) -9 NIL 896148 NIL) (-394 894055 894565 894955 "FORMULA" 895579 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893843 893873 893942 "FORMULA1" 894019 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 893366 893418 893591 "FORDER" 893785 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 892462 892626 892819 "FOP" 893193 T FOP (NIL) -7 NIL NIL NIL) (-390 891043 891742 891916 "FNLA" 892344 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889772 890187 890215 "FNCAT" 890675 T FNCAT (NIL) -9 NIL 890935 NIL) (-388 889311 889731 889759 "FNAME" 889764 T FNAME (NIL) -8 NIL NIL NIL) (-387 887940 888903 888931 "FMTC" 888936 T FMTC (NIL) -9 NIL 888972 NIL) (-386 884273 885463 886092 "FMONOID" 887344 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 883465 884015 884164 "FM" 884169 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880889 881535 881563 "FMFUN" 882707 T FMFUN (NIL) -9 NIL 883415 NIL) (-383 880158 880339 880367 "FMC" 880657 T FMC (NIL) -9 NIL 880839 NIL) (-382 877326 878186 878240 "FMCAT" 879435 NIL FMCAT (NIL T T) -9 NIL 879930 NIL) (-381 876192 877092 877192 "FM1" 877271 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873966 874382 874876 "FLOATRP" 875743 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867540 871695 872316 "FLOAT" 873365 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864978 865478 866056 "FLOATCP" 867007 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863753 864591 864632 "FLINEXP" 864637 NIL FLINEXP (NIL T) -9 NIL 864730 NIL) (-376 862907 863142 863470 "FLINEXP-" 863475 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861983 862127 862351 "FLASORT" 862759 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 859174 860042 860094 "FLALG" 861321 NIL FLALG (NIL T T) -9 NIL 861788 NIL) (-373 852910 856660 856701 "FLAGG" 857963 NIL FLAGG (NIL T) -9 NIL 858615 NIL) (-372 851636 851975 852465 "FLAGG-" 852470 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850678 850821 851048 "FLAGG2" 851489 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847619 848627 848686 "FINRALG" 849814 NIL FINRALG (NIL T T) -9 NIL 850322 NIL) (-369 846779 847008 847347 "FINRALG-" 847352 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 846159 846398 846426 "FINITE" 846622 T FINITE (NIL) -9 NIL 846729 NIL) (-367 838591 840778 840818 "FINAALG" 844485 NIL FINAALG (NIL T) -9 NIL 845938 NIL) (-366 833923 834973 836117 "FINAALG-" 837496 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833291 833678 833781 "FILE" 833853 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831949 832287 832341 "FILECAT" 833025 NIL FILECAT (NIL T T) -9 NIL 833241 NIL) (-363 829783 831311 831339 "FIELD" 831379 T FIELD (NIL) -9 NIL 831459 NIL) (-362 828403 828788 829299 "FIELD-" 829304 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826253 827038 827385 "FGROUP" 828089 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825343 825507 825727 "FGLMICPK" 826085 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821175 825268 825325 "FFX" 825330 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820776 820837 820972 "FFSLPE" 821108 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816765 817548 818344 "FFPOLY" 820012 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816269 816305 816514 "FFPOLY2" 816723 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812112 816188 816251 "FFP" 816256 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807510 812023 812087 "FF" 812092 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802636 806853 807043 "FFNBX" 807364 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797565 801771 802029 "FFNBP" 802490 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792198 796849 797060 "FFNB" 797398 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791030 791228 791543 "FFINTBAS" 791995 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787223 789437 789465 "FFIELDC" 790085 T FFIELDC (NIL) -9 NIL 790461 NIL) (-348 785885 786256 786753 "FFIELDC-" 786758 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785454 785500 785624 "FFHOM" 785827 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783149 783636 784153 "FFF" 784969 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778767 782891 782992 "FFCGX" 783092 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774388 778499 778606 "FFCGP" 778710 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769571 774115 774223 "FFCG" 774324 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751369 760442 760528 "FFCAT" 765693 NIL FFCAT (NIL T T T) -9 NIL 767144 NIL) (-341 746567 747614 748928 "FFCAT-" 750158 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745978 746021 746256 "FFCAT2" 746518 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735300 738950 740170 "FEXPR" 744830 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734300 734735 734776 "FEVALAB" 734860 NIL FEVALAB (NIL T) -9 NIL 735121 NIL) (-337 733459 733669 734007 "FEVALAB-" 734012 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732025 732842 733045 "FDIV" 733358 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729065 729806 729921 "FDIVCAT" 731489 NIL FDIVCAT (NIL T T T T) -9 NIL 731926 NIL) (-334 728827 728854 729024 "FDIVCAT-" 729029 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728047 728134 728411 "FDIV2" 728734 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726733 726992 727281 "FCPAK1" 727778 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725832 726233 726374 "FCOMP" 726624 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709534 712982 716520 "FC" 722314 T FC (NIL) -8 NIL NIL NIL) (-329 702078 706098 706138 "FAXF" 707940 NIL FAXF (NIL T) -9 NIL 708632 NIL) (-328 699354 700012 700837 "FAXF-" 701302 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694406 698730 698906 "FARRAY" 699211 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689625 691691 691744 "FAMR" 692767 NIL FAMR (NIL T T) -9 NIL 693227 NIL) (-325 688515 688817 689252 "FAMR-" 689257 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687684 688437 688490 "FAMONOID" 688495 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685470 686180 686233 "FAMONC" 687174 NIL FAMONC (NIL T T) -9 NIL 687560 NIL) (-322 684135 685224 685361 "FAGROUP" 685366 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681930 682249 682652 "FACUTIL" 683816 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681029 681214 681436 "FACTFUNC" 681740 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673451 680332 680531 "EXPUPXS" 680885 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670934 671474 672060 "EXPRTUBE" 672885 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667205 667797 668527 "EXPRODE" 670273 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652690 665854 666283 "EXPR" 666809 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647244 647831 648637 "EXPR2UPS" 651988 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646876 646933 647042 "EXPR2" 647181 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638267 646029 646319 "EXPEXPAN" 646713 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638067 638224 638253 "EXIT" 638258 T EXIT (NIL) -8 NIL NIL NIL) (-311 637547 637791 637882 "EXITAST" 637996 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637174 637236 637349 "EVALCYC" 637479 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636715 636833 636874 "EVALAB" 637044 NIL EVALAB (NIL T) -9 NIL 637148 NIL) (-308 636196 636318 636539 "EVALAB-" 636544 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633630 634932 634960 "EUCDOM" 635515 T EUCDOM (NIL) -9 NIL 635865 NIL) (-306 632035 632477 633067 "EUCDOM-" 633072 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619573 622333 625083 "ESTOOLS" 629305 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619205 619262 619371 "ESTOOLS2" 619510 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618956 618998 619078 "ESTOOLS1" 619157 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612993 614601 614629 "ES" 617397 T ES (NIL) -9 NIL 618807 NIL) (-301 607940 609227 611044 "ES-" 611208 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604314 605075 605855 "ESCONT" 607180 T ESCONT (NIL) -7 NIL NIL NIL) (-299 604059 604091 604173 "ESCONT1" 604276 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603734 603784 603884 "ES2" 604003 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603364 603422 603531 "ES1" 603670 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602580 602709 602885 "ERROR" 603208 T ERROR (NIL) -7 NIL NIL NIL) (-295 595972 602439 602530 "EQTBL" 602535 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588475 591286 592735 "EQ" 594556 NIL -2032 (NIL T) -8 NIL NIL NIL) (-293 588107 588164 588273 "EQ2" 588412 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583396 584445 585538 "EP" 587046 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581996 582287 582593 "ENV" 583110 T ENV (NIL) -8 NIL NIL NIL) (-290 581141 581695 581723 "ENTIRER" 581728 T ENTIRER (NIL) -9 NIL 581774 NIL) (-289 577608 579096 579466 "EMR" 580940 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576752 576937 576991 "ELTAGG" 577371 NIL ELTAGG (NIL T T) -9 NIL 577582 NIL) (-287 576471 576533 576674 "ELTAGG-" 576679 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576260 576289 576343 "ELTAB" 576427 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575386 575532 575731 "ELFUTS" 576111 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575128 575184 575212 "ELEMFUN" 575317 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574998 575019 575087 "ELEMFUN-" 575092 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569842 573098 573139 "ELAGG" 574079 NIL ELAGG (NIL T) -9 NIL 574542 NIL) (-281 568127 568561 569224 "ELAGG-" 569229 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566792 567070 567363 "ELABEXPR" 567854 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559656 561459 562286 "EFUPXS" 566068 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553106 554907 555717 "EFULS" 558932 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550591 550949 551421 "EFSTRUC" 552738 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 540442 542008 543555 "EF" 549106 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 539516 539927 540076 "EAB" 540313 T EAB (NIL) -8 NIL NIL NIL) (-274 538698 539475 539503 "E04UCFA" 539508 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537880 538657 538685 "E04NAFA" 538690 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 537062 537839 537867 "E04MBFA" 537872 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 536244 537021 537049 "E04JAFA" 537054 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 535428 536203 536231 "E04GCFA" 536236 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534612 535387 535415 "E04FDFA" 535420 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533794 534571 534599 "E04DGFA" 534604 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527967 529319 530683 "E04AGNT" 532450 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526647 527153 527193 "DVARCAT" 527668 NIL DVARCAT (NIL T) -9 NIL 527867 NIL) (-265 525851 526063 526377 "DVARCAT-" 526382 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518988 525650 525779 "DSMP" 525784 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513770 514933 516001 "DROPT" 517940 T DROPT (NIL) -8 NIL NIL NIL) (-262 513435 513494 513592 "DROPT1" 513705 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 508550 509676 510813 "DROPT0" 512318 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506895 507220 507606 "DRAWPT" 508184 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 501482 502405 503484 "DRAW" 505869 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 501115 501168 501286 "DRAWHACK" 501423 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499846 500115 500406 "DRAWCX" 500844 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 499361 499430 499581 "DRAWCURV" 499772 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489829 491791 493906 "DRAWCFUN" 497266 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 486595 488524 488565 "DQAGG" 489194 NIL DQAGG (NIL T) -9 NIL 489467 NIL) (-253 475139 481600 481683 "DPOLCAT" 483535 NIL DPOLCAT (NIL T T T T) -9 NIL 484080 NIL) (-252 469975 471324 473282 "DPOLCAT-" 473287 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 463097 469836 469934 "DPMO" 469939 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 456122 462877 463044 "DPMM" 463049 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 455727 456041 456089 "DOMCTOR" 456094 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454995 455249 455386 "DOMAIN" 455610 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 448983 454630 454782 "DMP" 454896 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 448583 448639 448783 "DLP" 448921 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 442405 447910 448100 "DLIST" 448425 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 439202 441258 441299 "DLAGG" 441849 NIL DLAGG (NIL T) -9 NIL 442079 NIL) (-243 437981 438645 438673 "DIVRING" 438765 T DIVRING (NIL) -9 NIL 438848 NIL) (-242 437218 437408 437708 "DIVRING-" 437713 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 435320 435677 436083 "DISPLAY" 436832 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 429208 435234 435297 "DIRPROD" 435302 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 428056 428259 428524 "DIRPROD2" 429001 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 417265 423271 423324 "DIRPCAT" 423734 NIL DIRPCAT (NIL NIL T) -9 NIL 424574 NIL) (-237 414591 415233 416114 "DIRPCAT-" 416451 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 413878 414038 414224 "DIOSP" 414425 T DIOSP (NIL) -7 NIL NIL NIL) (-235 410533 412790 412831 "DIOPS" 413265 NIL DIOPS (NIL T) -9 NIL 413494 NIL) (-234 410082 410196 410387 "DIOPS-" 410392 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408940 409568 409596 "DIFRING" 409783 T DIFRING (NIL) -9 NIL 409893 NIL) (-232 408586 408663 408815 "DIFRING-" 408820 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 406357 407629 407670 "DIFEXT" 408033 NIL DIFEXT (NIL T) -9 NIL 408327 NIL) (-230 404642 405070 405736 "DIFEXT-" 405741 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401917 404174 404215 "DIAGG" 404220 NIL DIAGG (NIL T) -9 NIL 404240 NIL) (-228 401301 401458 401710 "DIAGG-" 401715 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396718 400260 400537 "DHMATRIX" 401070 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 392330 393239 394249 "DFSFUN" 395728 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 387408 391261 391573 "DFLOAT" 392038 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385671 385952 386341 "DFINTTLS" 387116 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382700 383692 384092 "DERHAM" 385337 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 380501 382475 382564 "DEQUEUE" 382644 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379755 379888 380071 "DEGRED" 380363 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376185 376930 377776 "DEFINTRF" 378983 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373740 374209 374801 "DEFINTEF" 375704 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373090 373360 373475 "DEFAST" 373645 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367094 372685 372834 "DECIMAL" 372961 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 364606 365064 365570 "DDFACT" 366638 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364202 364245 364396 "DBLRESP" 364557 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362074 362435 362795 "DBASE" 363969 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 361316 361554 361700 "DATAARY" 361973 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 360422 361275 361303 "D03FAFA" 361308 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359529 360381 360409 "D03EEFA" 360414 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 357479 357945 358434 "D03AGNT" 359060 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356768 357438 357466 "D02EJFA" 357471 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356057 356727 356755 "D02CJFA" 356760 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 355346 356016 356044 "D02BHFA" 356049 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354635 355305 355333 "D02BBFA" 355338 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347832 349421 351027 "D02AGNT" 353049 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345600 346123 346669 "D01WGTS" 347306 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344667 345559 345587 "D01TRNS" 345592 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343735 344626 344654 "D01GBFA" 344659 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342803 343694 343722 "D01FCFA" 343727 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341871 342762 342790 "D01ASFA" 342795 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340939 341830 341858 "D01AQFA" 341863 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340007 340898 340926 "D01APFA" 340931 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339075 339966 339994 "D01ANFA" 339999 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338143 339034 339062 "D01AMFA" 339067 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337211 338102 338130 "D01ALFA" 338135 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336279 337170 337198 "D01AKFA" 337203 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335347 336238 336266 "D01AJFA" 336271 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328642 330195 331756 "D01AGNT" 333806 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327979 328107 328259 "CYCLOTOM" 328510 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324714 325427 326154 "CYCLES" 327272 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324026 324160 324331 "CVMP" 324575 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321867 322125 322494 "CTRIGMNP" 323754 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321335 321661 321734 "CTOR" 321814 T CTOR (NIL) -8 NIL NIL NIL) (-186 320844 321066 321167 "CTORKIND" 321254 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320166 320451 320479 "CTORCAT" 320661 T CTORCAT (NIL) -9 NIL 320774 NIL) (-184 319764 319875 320034 "CTORCAT-" 320039 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319253 319467 319565 "CTORCALL" 319686 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318627 318726 318879 "CSTTOOLS" 319150 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314426 315083 315841 "CRFP" 317939 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313901 314147 314239 "CRCEAST" 314354 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312948 313133 313361 "CRAPACK" 313705 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312332 312433 312637 "CPMATCH" 312824 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312057 312085 312191 "CPIMA" 312298 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308421 309093 309811 "COORDSYS" 311392 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307833 307954 308096 "CONTOUR" 308299 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303724 305836 306328 "CONTFRAC" 307373 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303604 303625 303653 "CONDUIT" 303690 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302743 303297 303325 "COMRING" 303330 T COMRING (NIL) -9 NIL 303382 NIL) (-171 301797 302101 302285 "COMPPROP" 302579 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301458 301493 301621 "COMPLPAT" 301756 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291752 301267 301376 "COMPLEX" 301381 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291388 291445 291552 "COMPLEX2" 291689 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291106 291141 291239 "COMPFACT" 291347 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275582 285565 285605 "COMPCAT" 286609 NIL COMPCAT (NIL T) -9 NIL 287955 NIL) (-165 265093 268021 271648 "COMPCAT-" 272004 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264822 264850 264953 "COMMUPC" 265059 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264616 264650 264709 "COMMONOP" 264783 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264172 264367 264454 "COMM" 264549 T COMM (NIL) -8 NIL NIL NIL) (-161 263748 263976 264051 "COMMAAST" 264117 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262997 263191 263219 "COMBOPC" 263557 T COMBOPC (NIL) -9 NIL 263732 NIL) (-159 261893 262103 262345 "COMBINAT" 262787 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258350 258924 259551 "COMBF" 261315 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257108 257466 257701 "COLOR" 258135 T COLOR (NIL) -8 NIL NIL NIL) (-156 256584 256829 256921 "COLONAST" 257036 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256224 256271 256396 "CMPLXRT" 256531 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255672 255924 256023 "CLLCTAST" 256145 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251172 252202 253282 "CLIP" 254612 T CLIP (NIL) -7 NIL NIL NIL) (-152 249518 250278 250517 "CLIF" 250999 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245693 247664 247705 "CLAGG" 248634 NIL CLAGG (NIL T) -9 NIL 249170 NIL) (-150 244115 244572 245155 "CLAGG-" 245160 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243659 243744 243884 "CINTSLPE" 244024 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241160 241631 242179 "CHVAR" 243187 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240369 240923 240951 "CHARZ" 240956 T CHARZ (NIL) -9 NIL 240971 NIL) (-146 240123 240163 240241 "CHARPOL" 240323 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239216 239803 239831 "CHARNZ" 239878 T CHARNZ (NIL) -9 NIL 239934 NIL) (-144 237178 237906 238241 "CHAR" 238901 T CHAR (NIL) -8 NIL NIL NIL) (-143 236904 236965 236993 "CFCAT" 237104 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236149 236260 236442 "CDEN" 236788 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232114 235302 235582 "CCLASS" 235889 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231421 231564 231727 "CATEGORY" 231971 T -10 (NIL) -8 NIL NIL NIL) (-139 231026 231340 231388 "CATCTOR" 231393 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230477 230729 230827 "CATAST" 230948 T CATAST (NIL) -8 NIL NIL NIL) (-137 229953 230198 230290 "CASEAST" 230405 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224962 225982 226735 "CARTEN" 229256 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224070 224218 224439 "CARTEN2" 224809 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222385 223220 223477 "CARD" 223833 T CARD (NIL) -8 NIL NIL NIL) (-133 221961 222189 222264 "CAPSLAST" 222330 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221465 221673 221701 "CACHSET" 221833 T CACHSET (NIL) -9 NIL 221911 NIL) (-131 220935 221257 221285 "CABMON" 221335 T CABMON (NIL) -9 NIL 221391 NIL) (-130 220408 220639 220749 "BYTEORD" 220845 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219384 219942 220084 "BYTE" 220247 T BYTE (NIL) -8 NIL NIL 220369) (-128 214734 218889 219061 "BYTEBUF" 219232 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212243 214426 214533 "BTREE" 214660 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209692 211891 212013 "BTOURN" 212153 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207062 209162 209203 "BTCAT" 209271 NIL BTCAT (NIL T) -9 NIL 209348 NIL) (-124 206729 206809 206958 "BTCAT-" 206963 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201994 205872 205900 "BTAGG" 206122 T BTAGG (NIL) -9 NIL 206283 NIL) (-122 201484 201609 201815 "BTAGG-" 201820 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198479 200762 200977 "BSTREE" 201301 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197617 197743 197927 "BRILL" 198335 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194269 196343 196384 "BRAGG" 197033 NIL BRAGG (NIL T) -9 NIL 197291 NIL) (-118 192798 193204 193759 "BRAGG-" 193764 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186027 192144 192328 "BPADICRT" 192646 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184342 185964 186009 "BPADIC" 186014 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184040 184070 184184 "BOUNDZRO" 184306 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179132 180330 181273 "BOP" 183117 T BOP (NIL) -8 NIL NIL NIL) (-113 176913 177317 177792 "BOP1" 178690 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175738 176487 176636 "BOOLEAN" 176784 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175074 175478 175532 "BMODULE" 175537 NIL BMODULE (NIL T T) -9 NIL 175602 NIL) (-110 170875 174872 174945 "BITS" 175021 T BITS (NIL) -8 NIL NIL NIL) (-109 170296 170415 170555 "BINDING" 170755 T BINDING (NIL) -8 NIL NIL NIL) (-108 164303 169893 170041 "BINARY" 170168 T BINARY (NIL) -8 NIL NIL NIL) (-107 162083 163558 163599 "BGAGG" 163859 NIL BGAGG (NIL T) -9 NIL 163996 NIL) (-106 161914 161946 162037 "BGAGG-" 162042 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160985 161298 161503 "BFUNCT" 161729 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159675 159853 160141 "BEZOUT" 160809 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156144 158527 158857 "BBTREE" 159378 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155878 155931 155959 "BASTYPE" 156078 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155731 155759 155832 "BASTYPE-" 155837 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155165 155241 155393 "BALFACT" 155642 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154021 154580 154766 "AUTOMOR" 155010 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153747 153752 153778 "ATTREG" 153783 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151999 152444 152796 "ATTRBUT" 153413 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151607 151827 151893 "ATTRAST" 151951 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151143 151256 151282 "ATRIG" 151483 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150952 150993 151080 "ATRIG-" 151085 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150597 150783 150809 "ASTCAT" 150814 T ASTCAT (NIL) -9 NIL 150844 NIL) (-92 150324 150383 150502 "ASTCAT-" 150507 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148473 150100 150188 "ASTACK" 150267 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146978 147275 147640 "ASSOCEQ" 148155 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146010 146637 146761 "ASP9" 146885 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145773 145958 145997 "ASP8" 146002 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144641 145378 145520 "ASP80" 145662 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143539 144276 144408 "ASP7" 144540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142493 143216 143334 "ASP78" 143452 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141462 142173 142290 "ASP77" 142407 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140374 141100 141231 "ASP74" 141362 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139274 140009 140141 "ASP73" 140273 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138378 139100 139200 "ASP6" 139205 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137322 138055 138173 "ASP55" 138291 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136271 136996 137115 "ASP50" 137234 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135359 135972 136082 "ASP4" 136192 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134447 135060 135170 "ASP49" 135280 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133231 133986 134154 "ASP42" 134336 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132007 132764 132934 "ASP41" 133118 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130957 131684 131802 "ASP35" 131920 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130722 130905 130944 "ASP34" 130949 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130459 130526 130602 "ASP33" 130677 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129352 130094 130226 "ASP31" 130358 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129117 129300 129339 "ASP30" 129344 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128852 128921 128997 "ASP29" 129072 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128617 128800 128839 "ASP28" 128844 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128382 128565 128604 "ASP27" 128609 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127466 128080 128191 "ASP24" 128302 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126542 127268 127380 "ASP20" 127385 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125630 126243 126353 "ASP1" 126463 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124572 125304 125423 "ASP19" 125542 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124309 124376 124452 "ASP12" 124527 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123161 123908 124052 "ASP10" 124196 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121012 123005 123096 "ARRAY2" 123101 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116777 120660 120774 "ARRAY1" 120929 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115809 115982 116203 "ARRAY12" 116600 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110121 112039 112114 "ARR2CAT" 114744 NIL ARR2CAT (NIL T T T) -9 NIL 115502 NIL) (-56 107555 108299 109253 "ARR2CAT-" 109258 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106872 107182 107307 "ARITY" 107448 T ARITY (NIL) -8 NIL NIL NIL) (-54 105648 105800 106099 "APPRULE" 106708 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105299 105347 105466 "APPLYORE" 105594 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104246 104564 104759 "ANY" 105122 T ANY (NIL) -8 NIL NIL NIL) (-51 103524 103647 103804 "ANY1" 104120 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101054 101961 102288 "ANTISYM" 103248 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100546 100761 100857 "ANON" 100976 T ANON (NIL) -8 NIL NIL NIL) (-48 94795 99085 99539 "AN" 100110 T AN (NIL) -8 NIL NIL NIL) (-47 91017 92405 92456 "AMR" 93204 NIL AMR (NIL T T) -9 NIL 93804 NIL) (-46 90129 90350 90713 "AMR-" 90718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74568 90046 90107 "ALIST" 90112 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71370 74162 74331 "ALGSC" 74486 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 67925 68480 69087 "ALGPKG" 70810 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67202 67303 67487 "ALGMFACT" 67811 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63154 63760 64378 "ALGMANIP" 66762 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54524 62780 62930 "ALGFF" 63087 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53720 53851 54030 "ALGFACT" 54382 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52751 53351 53389 "ALGEBRA" 53394 NIL ALGEBRA (NIL T) -9 NIL 53435 NIL) (-37 52469 52528 52660 "ALGEBRA-" 52665 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34562 50471 50523 "ALAGG" 50659 NIL ALAGG (NIL T T) -9 NIL 50820 NIL) (-35 34098 34211 34237 "AHYP" 34438 T AHYP (NIL) -9 NIL NIL NIL) (-34 33029 33277 33303 "AGG" 33802 T AGG (NIL) -9 NIL 34081 NIL) (-33 32463 32625 32839 "AGG-" 32844 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30269 30692 31097 "AF" 32105 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29749 29994 30084 "ADDAST" 30197 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29017 29276 29432 "ACPLOT" 29611 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18557 26360 26398 "ACFS" 27005 NIL ACFS (NIL T) -9 NIL 27244 NIL) (-28 16584 17074 17836 "ACFS-" 17841 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12823 14751 14777 "ACF" 15656 T ACF (NIL) -9 NIL 16068 NIL) (-26 11527 11861 12354 "ACF-" 12359 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11099 11294 11320 "ABELSG" 11412 T ABELSG (NIL) -9 NIL 11477 NIL) (-24 10966 10991 11057 "ABELSG-" 11062 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10309 10596 10622 "ABELMON" 10792 T ABELMON (NIL) -9 NIL 10904 NIL) (-22 9973 10057 10195 "ABELMON-" 10200 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9804 T ABELGRP (NIL) -9 NIL 9886 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 b1888eb4..93c87604 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,156 +1,118 @@ -(731757 . 3452261760) -(((*1 *2 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1209)) (-4 *4 (-373 *3)) - (-4 *5 (-373 *3)) (-5 *2 (-767)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1048 *3 *4 *5 *6 *7)) (-4 *5 (-1045)) - (-4 *6 (-238 *4 *5)) (-4 *7 (-238 *3 *5)) (-5 *2 (-767))))) -(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-1002))))) -(((*1 *2 *1) (-12 (-4 *1 (-670 *2)) (-4 *2 (-1209))))) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-1221 *3 *2)) (-4 *3 (-1045)) - (-4 *2 (-1250 *3))))) -(((*1 *2 *1) - (-12 (-4 *4 (-1094)) (-5 *2 (-112)) (-5 *1 (-881 *3 *4 *5)) - (-4 *3 (-1094)) (-4 *5 (-662 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-885 *3 *4)) (-4 *3 (-1094)) - (-4 *4 (-1094))))) -(((*1 *2 *1) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-1166 *3))))) -(((*1 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(-1094) (-34))) - (-4 *4 (-13 (-1094) (-34)))))) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1235 *5)) (-4 *5 (-363)) + (-5 *2 (-2 (|:| -1909 (-418 *3)) (|:| |special| (-418 *3)))) + (-5 *1 (-723 *5 *3))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-452)) (-4 *4 (-556)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| -3831 *4))) (-5 *1 (-965 *4 *3)) + (-4 *3 (-1235 *4))))) +(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-922))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-564)) (-5 *2 (-1264)) (-5 *1 (-1261)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-379)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-686 *3))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1166 (-407 (-948 *3)))) (-5 *1 (-453 *3 *4 *5 *6)) + (-4 *3 (-556)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) (((*1 *2 *2) - (-12 (-5 *2 (-939 *3)) (-4 *3 (-13 (-363) (-1194) (-998))) - (-5 *1 (-176 *3))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-1 (-1120 *4 *3 *5))) (-4 *4 (-38 (-407 (-564)))) - (-4 *4 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(-870)) (-5 *1 (-1262)))) - ((*1 *2 *2) (-12 (-5 *2 (-870)) (-5 *1 (-1262))))) + (-12 (-5 *2 (-1 (-939 *3) (-939 *3))) (-5 *1 (-176 *3)) + (-4 *3 (-13 (-363) (-1194) (-998)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-349)) (-4 *4 (-329 *3)) (-4 *5 (-1235 *4)) + (-5 *1 (-773 *3 *4 *5 *2 *6)) (-4 *2 (-1235 *5)) (-14 *6 (-917)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-767)) (-4 *1 (-1278 *3)) (-4 *3 (-363)) (-4 *3 (-368)))) + ((*1 *1 *1) (-12 (-4 *1 (-1278 *2)) (-4 *2 (-363)) (-4 *2 (-368))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-452) (-1034 (-564)) (-637 (-564)))) + (-12 (-4 *5 (-789)) (-4 *6 (-846)) (-4 *7 (-556)) + (-4 *3 (-945 *7 *5 *6)) (-5 *2 - (-3 (|:| |%expansion| (-313 *5 *3 *6 *7)) - (|:| |%problem| (-2 (|:| |func| (-1152)) (|:| |prob| (-1152)))))) - (-5 *1 (-420 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1194) (-430 *5))) - (-14 *6 (-1170)) (-14 *7 *3)))) -(((*1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-1179))))) -(((*1 *1 *1) (-4 *1 (-95))) - ((*1 *2 *2) + (-2 (|:| -2005 (-767)) (|:| -4375 *3) 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(-437)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3020 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3134 (-641 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1259 (-695))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3020 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3134 (-641 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-441)))) @@ -12025,7 +11868,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-641 (-2 (|:| -4290 *3) (|:| -3124 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -4375 *3) (|:| -3206 *4)))) (-4 *3 (-1045)) (-4 *4 (-722)) (-5 *1 (-731 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-759)))) ((*1 *1 *2) @@ 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|fn| (-316 (-225))) (|:| -3958 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3338 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -3958 (-641 (-225))))))) + (|:| -3338 (-641 (-225))))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3958 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3338 (-641 (-225))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -3958 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3338 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (-5 *1 (-837)))) @@ -12187,141 +12030,134 @@ ((*1 *1 *2) (-12 (-5 *2 (-660 *3 *4)) (-4 *3 (-846)) (-4 *4 (-172)) (-5 *1 (-1279 *3 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1094)) (-4 *4 (-1094)) - (-4 *6 (-1094)) (-5 *2 (-1 *6 *5)) (-5 *1 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*7))))) + (-12 (-4 *4 (-1045)) (-4 *2 (-683 *4 *5 *6)) + (-5 *1 (-104 *4 *3 *2 *5 *6)) (-4 *3 (-1235 *4)) (-4 *5 (-373 *4)) + (-4 *6 (-373 *4))))) +(((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-678 *3)) (-4 *3 (-1094))))) +(((*1 *2 *3) + (-12 (-4 *4 (-556)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *7 (-1059 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-641 *7)) (|:| |badPols| (-641 *7)))) + (-5 *1 (-973 *4 *5 *6 *7)) (-5 *3 (-641 *7))))) (((*1 *2 *3 *2) (|partial| -12 (-5 *3 (-917)) (-5 *1 (-442 *2)) (-4 *2 (-1235 (-564))))) @@ -14300,153 +14295,202 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-917)) (-5 *4 (-418 *2)) (-4 *2 (-1235 *5)) (-5 *1 (-444 *5 *2)) (-4 *5 (-1045))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-972 *3 *4 *2 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *2 (-846)) (-4 *5 (-1059 *3 *4 *2))))) -(((*1 *1) (-5 *1 (-112))) ((*1 *1) (-5 *1 (-615)))) -(((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) - (|partial| -12 (-5 *2 (-641 (-1166 *13))) (-5 *3 (-1166 *13)) - (-5 *4 (-641 *12)) (-5 *5 (-641 *10)) (-5 *6 (-641 *13)) 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