diff options
| author | dos-reis <gdr@axiomatics.org> | 2009-01-03 10:26:16 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2009-01-03 10:26:16 +0000 |
| commit | ad0d6445de436a1c7c04cfe14316d620cb9202b3 (patch) | |
| tree | 2165a9a2446cc52a27bd6545359607e7dc376599 /src/share | |
| parent | 844be40b5b876fffd816f285f87711cca6ef3121 (diff) | |
| download | open-axiom-ad0d6445de436a1c7c04cfe14316d620cb9202b3.tar.gz | |
2009-01-03 Gabriel Dos Reis <gdr@cs.tamu.edu>
* Makefile.pamphlet (AXIOM_SRC_TARGETS): Add all-databases.
src/ChangeLog
2009-01-03 Gabriel Dos Reis <gdr@cs.tamu.edu>
* lisp/core.lisp.in (|%algebraSystemIsComplete|): New.
(|%basicSystemIsComplete|): Use it.
* interp/wi1.boot (setqSingle): Use maximalSuperType.
(coerceSubset): Simplify.
(compCoerce1): Tidy.
* interp/i-resolv.boot (resolveTCat): Use superType.
* interp/lisplib.boot (findConstructorSlotNumber): Use isSubset.
(sigsMatch): Likewise.
(findDomainSlotNumber): Likewise.
* interp/define.boot (compSubDomain1): Reject for complex subdomain
predicate. Support paramterized subdomains.
* interp/daase.lisp (interpOpen): Read superdomain slot.
(getdatabase): Remove adhoc hardcoded superdomain info.
Return superdomain info stored in database.
(localnrlib): Read superdomain info.
(write-interpdb): Write superdomain info.
(database): Add superdomain slot.
* interp/g-util.boot (superType): New.
(maximalSuperType): Rework. Support parameterized subdomains.
(noteSubDomainInfo): New.
(isSubDomain): Rework.
* interp/c-util.boot (isSubset): Rework.
* interp/g-opt.boot (optEQ): Remove.
* interp/g-cndata.boot (getImmediateSuperDomain): Remove.
(maximalSuperType): Move to g-util.boot.
* interp/types.boot (%Constructor): New type specifier.
(%Instantiation): Likewise.
* interp/compiler.boot (primitiveType): Don't return $NegativeInteger.
(maxSuperType): Remove.
(hasType): Use maximalSuperType.
(satisfies): New.
(coerceSubset): Use it. Simplify.
* interp/wi2.boot (smallIntegerStep): Use maximalSuperType.
* interp/sys-constants.boot ($AtVariables): New.
($NegativeInteger): Remove.
($NonPositiveInteger): Likewise.
($CategoryNames): Category is not a category.
* interp/property.lisp: Remove Subsets property settings.
* interp/i-coerce.boot (coerceSubDomain): Simplify.
(coerceImmediateSubDomain): Remove.
(getSubDomainPredicate): Simplify.
* interp/category.boot (SourceLevelSubset): Use isSubDomain.
(MachineLevelSubset): Likewise.
* interp/modemap.boot (mergeModemap): Likewise.
(isSuperDomain): Remove.
(augModemapsFromDomain): Support parameterized subdomains.
* interp/i-util.boot (isSubDomain): Move to g-util.boot.
* Makefile.pamphlet (all-databases): New target.
* interp/Makefile.pamphlet ($(AXIOMSYS)): Push
:open-axiom-algebra-system onto *FEATURES*.
* etc/Makefile.in (all-databases): New target.
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 634 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1212 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1311 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8783 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31236 |
5 files changed, 21590 insertions, 21586 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 3f2a3e54..06dabb7d 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2276553 . 3439392485) +(2276553 . 3439752255) (-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 -3215) +(-32 R -3160) ((|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 -1028) (QUOTE (-558))))) @@ -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 -3215 UP UPUP -1415) +(-40 -3160 UP UPUP -4169) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3998 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3998 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3998 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3998 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-41 R -3215) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3986 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3986 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3986 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3986 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +(-41 R -3160) ((|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 (-450))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|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."))) ((-4382 . T) (-4383 . T)) -((-3998 (-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|))))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|))))))) +((-3986 (-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|))))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3215) +(-54 |Base| R -3160) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-60 R) ((|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}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-61 -1324) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +(-61 -3072) ((|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 -1324) +(-62 -3072) ((|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 -1324) +(-63 -3072) ((|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 -1324) +(-64 -3072) ((|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 -1324) +(-65 -3072) ((|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 -1324) +(-66 -3072) ((|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 -1324) +(-67 -3072) ((|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 -1324) +(-68 -3072) ((|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 -1324) +(-69 -3072) ((|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 -1324) +(-70 -3072) ((|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 -1324) +(-71 -3072) ((|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 -1324) +(-72 -3072) ((|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 -1324) +(-73 -3072) ((|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 -1324) +(-74 -3072) ((|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 -1324) +(-77 -3072) ((|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 -1324) +(-78 -3072) ((|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 -1324) +(-79 -3072) ((|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 -1324) +(-80 -3072) ((|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 -1324) +(-81 -3072) ((|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 -1324) +(-82 -3072) ((|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 -1324) +(-83 -3072) ((|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 -1324) +(-84 -3072) ((|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 -1324) +(-85 -3072) ((|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 -1324) +(-86 -3072) ((|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 -1324) +(-87 -3072) ((|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 -1324) +(-88 -3072) ((|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 -1324) +(-89 -3072) ((|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 @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3998 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|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| (((|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!| (($ $ (|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| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} 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.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|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}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3215 UP) +(-115 -3160 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 @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3998 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) +((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3986 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3998 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) +((-3986 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3986 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -464,11 +464,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4384 "*") . T)) NIL -(-134 |minix| -3084 S T$) +(-134 |minix| -4269 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -3084 R) +(-135 |minix| -4269 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -491,7 +491,7 @@ NIL (-140) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4382 . T) (-4372 . T) (-4383 . T)) -((-3998 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-3986 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-141 R Q A) ((|constructor| (NIL "CommonDenominator 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|)) |#3|) "\\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| |#3|) "\\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| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -516,7 +516,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4379 . T)) NIL -(-147 -3215 UP UPUP) +(-147 -3160 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 @@ -556,7 +556,7 @@ 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 -(-157 R -3215) +(-157 R -3160) ((|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 @@ -590,7 +590,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-992))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4378)) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-841)))) (-165 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| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4375 -3998 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4378 |has| |#1| (-6 -4378)) (-4381 |has| |#1| (-6 -4381)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 -3986 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4378 |has| |#1| (-6 -4378)) (-4381 |has| |#1| (-6 -4381)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-166 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."))) @@ -602,8 +602,8 @@ NIL NIL (-168 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}."))) -((-4375 -3998 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4378 |has| |#1| (-6 -4378)) (-4381 |has| |#1| (-6 -4381)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . 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T) (-4376 . T) (-4377 . T) (-4379 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-819)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-841)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1012)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1185)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -606) 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(|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-899)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-899))))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (QUOTE (-1048))) (-12 (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasAttribute| |#1| (QUOTE -4378)) (|HasAttribute| |#1| (QUOTE -4381)) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-348))))) (-169 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"))) NIL @@ -676,7 +676,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors."))) NIL NIL -(-187 R -3215) +(-187 R -3160) ((|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 @@ -784,23 +784,23 @@ 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 -(-214 -3215 UP UPUP R) +(-214 -3160 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 -(-215 -3215 FP) +(-215 -3160 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 (-216) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3998 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-217) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-218 R -3215) +(-218 R -3160) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -815,18 +815,18 @@ NIL (-221 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-222 |CoefRing| |listIndVar|) ((|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}."))) ((-4379 . T)) NIL -(-223 R -3215) +(-223 R -3160) ((|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 (-224) ((|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}."))) -((-1352 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-225) ((|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)}.}"))) @@ -835,7 +835,7 @@ NIL (-226 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-227 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -872,22 +872,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-236 S -3084 R) +(-236 S -4269 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 (-362))) (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (QUOTE (-839))) (|HasAttribute| |#3| (QUOTE -4379)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (QUOTE (-1087)))) -(-237 -3084 R) +(-237 -4269 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"))) ((-4376 |has| |#2| (-1039)) (-4377 |has| |#2| (-1039)) (-4379 |has| |#2| (-6 -4379)) ((-4384 "*") |has| |#2| (-171)) (-4382 . T)) NIL -(-238 -3084 A B) +(-238 -4269 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 -(-239 -3084 R) +(-239 -4269 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."))) ((-4376 |has| |#2| (-1039)) (-4377 |has| |#2| (-1039)) (-4379 |has| |#2| (-6 -4379)) ((-4384 "*") |has| |#2| (-171)) (-4382 . 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -907,7 +907,7 @@ NIL (-244 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-245 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -915,7 +915,7 @@ NIL (-246 |vl| R) ((|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 lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (-3986 (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (|HasCategory| |#3| (QUOTE (-717))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163)))))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-3986 (|HasCategory| |#3| (QUOTE (-1039))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1087)))) (-3986 (|HasAttribute| |#3| (QUOTE -4379)) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-251 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -983,7 +983,7 @@ NIL (-263 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-264 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1028,11 +1028,11 @@ 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 -(-275 R -3215) +(-275 R -3160) ((|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 -(-276 R -3215) +(-276 R -3160) ((|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 @@ -1080,7 +1080,7 @@ 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 -(-288 S R |Mod| -4050 -1949 |exactQuo|) +(-288 S R |Mod| -4218 -2596 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL @@ -1102,21 +1102,21 @@ NIL NIL (-293 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-295) ((|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 -(-296 -3215 S) +(-296 -3160 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 -(-297 E -3215) +(-297 E -3160) ((|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 @@ -1164,7 +1164,7 @@ 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 -(-309 -3215) +(-309 -3160) ((|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 @@ -1179,7 +1179,7 @@ NIL (-312 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1012))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (-3998 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1138))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-543))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))) (-3998 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))))) +((|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1012))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (-3986 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1138))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-543))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))) (-3986 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))))) (-313 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1190,9 +1190,9 @@ NIL NIL (-315 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."))) -((-4379 -3998 (-2084 (|has| |#1| (-1039)) (|has| |#1| (-631 (-558)))) (-12 (|has| |#1| (-550)) (-3998 (-2084 (|has| |#1| (-1039)) (|has| |#1| (-631 (-558)))) (|has| |#1| (-1039)) (|has| |#1| (-471)))) (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) ((-4384 "*") |has| |#1| (-550)) (-4375 |has| |#1| (-550)) (-4380 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(-25))) (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))))) (-3986 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-1039)))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) +(-316 R -3160) ((|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 @@ -1203,7 +1203,7 @@ NIL (-318 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."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-319 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 @@ -1235,12 +1235,12 @@ NIL (-326 S) ((|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."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-327 S -3215) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-327 S -3160) ((|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 (-367)))) -(-328 -3215) +(-328 -3160) ((|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."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL @@ -1260,15 +1260,15 @@ 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 -(-333 S -3215 UP UPUP R) +(-333 S -3160 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 -(-334 -3215 UP UPUP R) +(-334 -3160 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 -(-335 -3215 UP UPUP R) +(-335 -3160 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 @@ -1288,26 +1288,26 @@ 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 -(-340 S -3215 UP UPUP) +(-340 S -3160 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 (-367))) (|HasCategory| |#2| (QUOTE (-362)))) -(-341 -3215 UP UPUP) +(-341 -3160 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."))) ((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-342 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-3986 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) (-343 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-344 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-345 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1324,31 +1324,31 @@ 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."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL -(-349 R UP -3215) +(-349 R UP -3160) ((|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 (-350 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-3986 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) (-351 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-352 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-353 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-3986 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) (-354 GF |defpol|) ((|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."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) -(-355 -3215 GF) +((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +(-355 -3160 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 @@ -1356,14 +1356,14 @@ 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 -(-357 -3215 FP FPP) +(-357 -3160 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 (-358 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-359 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1442,7 +1442,7 @@ NIL NIL (-378) ((|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}."))) -((-4365 . T) (-4373 . T) (-1352 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4365 . T) (-4373 . T) (-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-379 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1492,7 +1492,7 @@ NIL ((|constructor| (NIL "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 -(-391 -3215 UP UPUP R) +(-391 -3160 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 @@ -1516,11 +1516,11 @@ 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 -(-397 -1324 |returnType| -1431 |symbols|) +(-397 -3072 |returnType| -3987 |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 -(-398 -3215 UP) +(-398 -3160 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1542,7 +1542,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4365)) (|HasAttribute| |#1| (QUOTE -4373))) (-403) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-1352 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-404 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."))) @@ -1555,7 +1555,7 @@ NIL (-406 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4369 -12 (|has| |#1| (-6 -4380)) (|has| |#1| (-450)) (|has| |#1| (-6 -4369))) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3998 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4380)) (|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3986 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4380)) (|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-407 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-412 R -3215 UP A) +(-412 R -3160 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4379 . T)) NIL -(-413 R -3215 UP A |ibasis|) +(-413 R -3160 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 -1028) (|devaluate| |#2|)))) @@ -1599,7 +1599,7 @@ NIL (-417 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) +((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) (-418 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1628,7 +1628,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4382 . T) (-4372 . T) (-4383 . T)) NIL -(-425 R -3215) +(-425 R -3160) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4369 -12 (|has| |#1| (-6 -4369)) (|has| |#2| (-6 -4369))) (-4376 . T) (-4377 . T) (-4379 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4369)) (|HasAttribute| |#2| (QUOTE -4369)))) -(-427 R -3215) +(-427 R -3160) ((|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 @@ -1646,17 +1646,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (-429 R) ((|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}."))) -((-4379 -3998 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) ((-4384 "*") |has| |#1| (-550)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-550)) (-4374 |has| |#1| (-550))) +((-4379 -3986 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) ((-4384 "*") |has| |#1| (-550)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-550)) (-4374 |has| |#1| (-550))) NIL -(-430 R -3215) +(-430 R -3160) ((|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 -(-431 R -3215) +(-431 R -3160) ((|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)))) -(-432 R -3215) +(-432 R -3160) ((|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 @@ -1664,7 +1664,7 @@ 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 -(-434 R -3215 UP) +(-434 R -3160 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 -1028) (QUOTE (-48))))) @@ -1692,7 +1692,7 @@ 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 -(-441 R UP -3215) +(-441 R UP -3160) ((|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 @@ -1739,7 +1739,7 @@ NIL (-452 |vl| R E) ((|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 specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3998 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3998 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((|HasCategory| |#2| (QUOTE (-899))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-453 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1804,7 +1804,7 @@ 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 -(-469 |lv| -3215 R) +(-469 |lv| -3160 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 @@ -1819,11 +1819,11 @@ NIL (-472 |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."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-473 |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."))) ((-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087)))) +((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087)))) (-474 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)}"))) ((-4383 . T) (-4382 . T)) @@ -1839,7 +1839,7 @@ NIL (-477 |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."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-478) ((|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 @@ -1847,11 +1847,11 @@ NIL (-479 |vl| R) ((|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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(QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-839))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-841))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3986 (|HasCategory| |#2| (QUOTE (-1039))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasAttribute| |#2| (QUOTE -4379)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-481) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1859,8 +1859,8 @@ NIL (-482 S) ((|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}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-483 -3215 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +(-483 -3160 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 @@ -1871,7 +1871,7 @@ NIL (-485) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3998 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-486 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1896,7 +1896,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-492 -3215 UP |AlExt| |AlPol|) +(-492 -3160 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 @@ -1907,16 +1907,16 @@ NIL (-494 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-495 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-496 K R UP) ((|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 -(-497 R UP -3215) +(-497 R UP -3160) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1936,7 +1936,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-502 -3215 |Expon| |VarSet| |DPoly|) +(-502 -3160 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-1163))))) @@ -1987,7 +1987,7 @@ NIL (-514 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-515) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -1995,15 +1995,15 @@ NIL (-516 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#1|) (QUOTE (-144)))) +((-3986 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#1|) (QUOTE (-144)))) (-517 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-518 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-519 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2015,7 +2015,7 @@ NIL (-521 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-522) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2048,7 +2048,7 @@ 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 -(-530 K -3215 |Par|) +(-530 K -3160 |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 @@ -2072,7 +2072,7 @@ 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 -(-536 K -3215 |Par|) +(-536 K -3160 |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 @@ -2107,12 +2107,12 @@ NIL (-544 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-545 R -3215) +((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +(-545 R -3160) ((|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 -(-546 R0 -3215 UP UPUP R) +(-546 R0 -3160 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 @@ -2122,7 +2122,7 @@ NIL NIL (-548 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."))) -((-1352 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1399 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-549 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."))) @@ -2132,7 +2132,7 @@ 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."))) ((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL -(-551 R -3215) +(-551 R -3160) ((|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 @@ -2144,7 +2144,7 @@ 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 -(-554 R -3215 L) +(-554 R -3160 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 -646) (|devaluate| |#2|)))) @@ -2152,11 +2152,11 @@ 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 -(-556 -3215 UP UPUP R) +(-556 -3160 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 -(-557 -3215 UP) +(-557 -3160 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 @@ -2168,15 +2168,15 @@ 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 -(-560 R -3215 L) +(-560 R -3160 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 -646) (|devaluate| |#2|)))) -(-561 R -3215) +(-561 R -3160) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1126)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-621))))) -(-562 -3215 UP) +(-562 -3160 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 @@ -2184,27 +2184,27 @@ 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 -(-564 -3215) +(-564 -3160) ((|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 (-565 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."))) -((-1352 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1399 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-566) ((|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 -(-567 R -3215) +(-567 R -3160) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-621))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-550)))) -(-568 -3215 UP) +(-568 -3160 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 -(-569 R -3215) +(-569 R -3160) ((|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 @@ -2236,15 +2236,15 @@ 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 -(-577 R -3215) +(-577 R -3160) ((|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 -(-578 E -3215) +(-578 E -3160) ((|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 -(-579 -3215) +(-579 -3160) ((|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}."))) ((-4377 . T) (-4376 . T)) ((|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163))))) @@ -2275,7 +2275,7 @@ NIL (-586 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3998 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-3986 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3986 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-587 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2283,7 +2283,7 @@ NIL (-588 |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}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) (-589 |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.}"))) ((-4377 |has| |#1| (-550)) (-4376 |has| |#1| (-550)) ((-4384 "*") |has| |#1| (-550)) (-4375 |has| |#1| (-550)) (-4379 . T)) @@ -2296,7 +2296,7 @@ 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 -(-592 R -3215 FG) +(-592 R -3160 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 @@ -2307,7 +2307,7 @@ NIL (-594 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-595 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2326,12 +2326,12 @@ NIL NIL (-599 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4379 -3998 (-2084 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4377 . T) (-4376 . T)) -((-3998 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4379 -3986 (-2146 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4377 . T) (-4376 . T)) +((-3986 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-600 |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."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-601 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 @@ -2356,7 +2356,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-607 -3215 UP) +(-607 -3160 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2384,7 +2384,7 @@ 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}."))) ((-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| |#1| (QUOTE (-839)))) -(-614 R -3215) +(-614 R -3160) ((|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 @@ -2416,18 +2416,18 @@ 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 -(-622 R -3215) +(-622 R -3160) ((|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 -(-623 |lv| -3215) +(-623 |lv| -3160) ((|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 (-624) ((|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."))) ((-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2981) (QUOTE (-52))))))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (QUOTE (-1087)))) +((-12 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2957) (QUOTE (-52))))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087)))) (-625 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2438,8 +2438,8 @@ NIL NIL (-627 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4379 -3998 (-2084 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4377 . T) (-4376 . T)) -((-3998 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4379 -3986 (-2146 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4377 . T) (-4376 . T)) +((-3986 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-628 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))}."))) NIL @@ -2451,7 +2451,7 @@ NIL (-630 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 -((-3304 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) +((-2137 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) (-631 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4379 . T)) @@ -2471,7 +2471,7 @@ NIL (-635 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-636 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2479,7 +2479,7 @@ NIL (-637 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-638 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2496,7 +2496,7 @@ 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 -(-642 R -3215 L) +(-642 R -3160 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 @@ -2516,11 +2516,11 @@ 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}."))) ((-4376 . T) (-4377 . T) (-4379 . T)) NIL -(-647 -3215 UP) +(-647 -3160 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)))) -(-648 A -1975) +(-648 A -3058) ((|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}}"))) ((-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) @@ -2556,11 +2556,11 @@ 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}."))) ((-4383 . T) (-4382 . T)) NIL -(-657 -3215) +(-657 -3160) ((|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 -(-658 -3215 |Row| |Col| M) +(-658 -3160 |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 @@ -2571,7 +2571,7 @@ NIL (-660 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4379 . T) (-4382 . T) (-4376 . T) (-4377 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3998 (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3986 (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-661) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2591,7 +2591,7 @@ NIL (-665 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-666) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2647,7 +2647,7 @@ NIL (-679 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4382 . T) (-4383 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-680 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2656,7 +2656,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} 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}."))) NIL NIL -(-682 S -3215 FLAF FLAS) +(-682 S -3160 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 @@ -2667,7 +2667,7 @@ NIL (-684) ((|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"))) ((-4375 . T) (-4380 |has| (-689) (-362)) (-4374 |has| (-689) (-362)) (-4381 |has| (-689) (-6 -4381)) (-4378 |has| (-689) (-6 -4378)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-689) (QUOTE (-146))) (|HasCategory| (-689) (QUOTE (-144))) (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-367))) (|HasCategory| (-689) (QUOTE (-362))) (-3998 (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-232))) (-3998 (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-348)))) (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (LIST (QUOTE -285) (QUOTE (-689)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -308) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-689) (LIST (QUOTE -606) 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(|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-899)))) (-12 (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (QUOTE (-899))))) (|HasCategory| (-689) (QUOTE (-543))) (-12 (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-1185)))) (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899))) (-3986 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-362)))) (-3986 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-550)))) (-12 (|HasCategory| (-689) (QUOTE (-232))) (|HasCategory| (-689) (QUOTE (-362)))) (-12 (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-841))) (|HasCategory| (-689) (QUOTE (-550))) (|HasAttribute| (-689) (QUOTE -4381)) (|HasAttribute| (-689) (QUOTE -4378)) (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-144)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-348))))) (-685 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}."))) ((-4383 . T)) @@ -2680,13 +2680,13 @@ 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 -(-688 OV E -3215 PG) +(-688 OV E -3160 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 (-689) ((|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}"))) -((-1352 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-690 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."))) @@ -2716,7 +2716,7 @@ 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 -(-697 S -1866 I) +(-697 S -2897 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 @@ -2736,14 +2736,14 @@ 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 -(-702 R |Mod| -4050 -1949 |exactQuo|) +(-702 R |Mod| -4218 -2596 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-703 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4378 |has| |#1| (-362)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-704 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2752,7 +2752,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-706 R |Mod| -4050 -1949 |exactQuo|) +(-706 R |Mod| -4218 -2596 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4379 . T)) NIL @@ -2764,7 +2764,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4377 . T) (-4376 . T)) NIL -(-709 -3215) +(-709 -3160) ((|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]]}."))) ((-4379 . T)) NIL @@ -2800,7 +2800,7 @@ 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 -(-718 -3215 UP) +(-718 -3160 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 @@ -2819,7 +2819,7 @@ NIL (-722 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3998 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3998 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((|HasCategory| |#2| (QUOTE (-899))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-723 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2952,11 +2952,11 @@ 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 -(-756 -3215) +(-756 -3160) ((|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 -(-757 P -3215) +(-757 P -3160) ((|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 @@ -2964,7 +2964,7 @@ NIL NIL NIL NIL -(-759 UP -3215) +(-759 UP -3160) ((|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 @@ -2980,7 +2980,7 @@ 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."))) (((-4384 "*") . T)) NIL -(-763 R -3215) +(-763 R -3160) ((|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 @@ -3000,7 +3000,7 @@ 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 -(-768 -3215 |ExtF| |SUEx| |ExtP| |n|) +(-768 -3160 |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 @@ -3015,7 +3015,7 @@ NIL (-771 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."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) 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|#1| (QUOTE (-543)))) (-2137 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2137 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-558))))) (-2137 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2137 (|HasCategory| |#1| (LIST (QUOTE -982) (QUOTE (-558))))))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-772 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 @@ -3023,7 +3023,7 @@ NIL (-773 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4378 |has| |#1| (-362)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-774 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3084,23 +3084,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4376 . T) (-4377 . T) (-4379 . T)) NIL -(-789 -3998 R OS S) +(-789 -3986 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-790 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3998 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3986 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (-791) ((|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 -(-792 R -3215 L) +(-792 R -3160 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 -(-793 R -3215) +(-793 R -3160) ((|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 @@ -3108,7 +3108,7 @@ 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 -(-795 R -3215) +(-795 R -3160) ((|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 @@ -3116,11 +3116,11 @@ 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 -(-797 -3215 UP UPUP R) +(-797 -3160 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 -(-798 -3215 UP L LQ) +(-798 -3160 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 @@ -3128,38 +3128,38 @@ 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 -(-800 -3215 UP L LQ) +(-800 -3160 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 -(-801 -3215 UP) +(-801 -3160 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 -(-802 -3215 L UP A LO) +(-802 -3160 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 -(-803 -3215 UP) +(-803 -3160 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)))) -(-804 -3215 LO) +(-804 -3160 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 -(-805 -3215 LODO) +(-805 -3160 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)]}."))) 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|#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasAttribute| |#2| (QUOTE -4379)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-807 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-808 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4384 "*") |has| |#2| (-362)) (-4375 |has| |#2| (-362)) (-4380 |has| |#2| (-362)) (-4374 |has| |#2| (-362)) (-4379 . T) (-4377 . T) (-4376 . T)) @@ -3227,7 +3227,7 @@ NIL (-824 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4379 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3998 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3998 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-839))) (-3986 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-825 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3267,12 +3267,12 @@ NIL (-834 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4379 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3998 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3998 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-839))) (-3986 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-835) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-836 -3084 S) +(-836 -4269 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 @@ -3308,11 +3308,11 @@ 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 (-362))) (|HasCategory| |#1| (QUOTE (-550)))) -(-845 R |sigma| -2465) +(-845 R |sigma| -1310) ((|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."))) ((-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-846 |x| R |sigma| -2465) +(-846 |x| R |sigma| -1310) ((|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}."))) ((-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-362)))) @@ -3375,15 +3375,15 @@ NIL (-861 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3998 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) +((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3986 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) (-862 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3998 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3986 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-863 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-864) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3439,7 +3439,7 @@ NIL (-877 |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 (-3304 (|HasCategory| |#2| (QUOTE (-1039)))) (-3304 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-3304 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) +((-12 (-2137 (|HasCategory| |#2| (QUOTE (-1039)))) (-2137 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-2137 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-878 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 @@ -3448,7 +3448,7 @@ 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 -(-880 R -1866) +(-880 R -2897) ((|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 @@ -3472,7 +3472,7 @@ 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 -(-886 UP -3215) +(-886 UP -3160) ((|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 @@ -3495,7 +3495,7 @@ NIL (-891 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-892 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3511,7 +3511,7 @@ NIL (-895 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4379 . T)) -((-3998 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) +((-3986 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (-896 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3532,7 +3532,7 @@ 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."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-901 R0 -3215 UP UPUP R) +(-901 R0 -3160 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 @@ -3560,7 +3560,7 @@ 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 -(-908 -3215) +(-908 -3160) ((|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 @@ -3576,11 +3576,11 @@ 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}."))) (((-4384 "*") . T)) NIL -(-912 -3215 P) +(-912 -3160 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-913 |xx| -3215) +(-913 |xx| -3160) ((|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 @@ -3604,7 +3604,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-919 R -3215) +(-919 R -3160) ((|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| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3616,7 +3616,7 @@ 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 -(-922 S R -3215) +(-922 S R -3160) ((|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 @@ -3636,11 +3636,11 @@ 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 -876) (|devaluate| |#1|)))) -(-927 R -3215 -1866) +(-927 R -3160 -2897) ((|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 -(-928 -1866) +(-928 -2897) ((|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 @@ -3663,7 +3663,7 @@ NIL (-933 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-934 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3688,7 +3688,7 @@ 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}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) NIL -(-940 E V R P -3215) +(-940 E V R P -3160) ((|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 @@ -3699,8 +3699,8 @@ NIL (-942 R) ((|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}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-943 E V R P -3215) +((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-943 E V R P -3160) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-450)))) @@ -3723,12 +3723,12 @@ NIL (-948 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-949) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-950 -3215) +(-950 -3160) ((|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 @@ -3743,11 +3743,11 @@ NIL (-953 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4380))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4380))) (-954 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4379 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-955) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3828,7 +3828,7 @@ 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 -(-975 K R UP -3215) +(-975 K R UP -3160) ((|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 @@ -3887,11 +3887,11 @@ NIL (-989 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4375 |has| |#1| (-289)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) (-990 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-991 S) ((|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3900,14 +3900,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-993 -3215 UP UPUP |radicnd| |n|) +(-993 -3160 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3998 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3998 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3998 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3998 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3986 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3986 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3986 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3986 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) (-994 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3998 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-995) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3940,19 +3940,19 @@ 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}}"))) ((-4375 . T) (-4380 . T) (-4374 . T) (-4377 . T) (-4376 . T) ((-4384 "*") . T) (-4379 . T)) NIL -(-1003 R -3215) +(-1003 R -3160) ((|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 -(-1004 R -3215) +(-1004 R -3160) ((|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 -(-1005 -3215 UP) +(-1005 -3160 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 -(-1006 -3215 UP) +(-1006 -3160 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 @@ -3987,8 +3987,8 @@ NIL (-1014 |TheField|) ((|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"))) ((-4375 . T) (-4380 . T) (-4374 . T) (-4377 . T) (-4376 . T) ((-4384 "*") . T) (-4379 . T)) -((-3998 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) -(-1015 -3215 L) +((-3986 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) +(-1015 -3160 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 @@ -4024,14 +4024,14 @@ 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 -(-1024 -3215 |Expon| |VarSet| |FPol| |LFPol|) +(-1024 -3160 |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"))) (((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-1025) ((|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.}"))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -2981) (QUOTE (-52))))))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -2957) (QUOTE (-52))))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) (-1026) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4088,7 +4088,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4379 . T)) NIL -(-1040 |xx| -3215) +(-1040 |xx| -3160) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4103,7 +4103,7 @@ NIL (-1043 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4382 . T) (-4377 . T) (-4376 . T)) -((-3998 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) +((-3986 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) (-1044 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4135,7 +4135,7 @@ NIL (-1051) ((|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}"))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -2981) (QUOTE (-52))))))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -2957) (QUOTE (-52))))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) (-1052 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 @@ -4180,11 +4180,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1063 |Base| R -3215) +(-1063 |Base| R -3160) ((|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 -(-1064 |Base| R -3215) +(-1064 |Base| R -3160) ((|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 @@ -4199,7 +4199,7 @@ NIL (-1067 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4375 |has| |#1| (-362)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) (-1068 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4227,7 +4227,7 @@ NIL (-1074 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1075 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4287,7 +4287,7 @@ NIL (-1089 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) ((-4382 . T) (-4372 . T) (-4383 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1090 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4331,7 +4331,7 @@ NIL (-1100 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 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(QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-839))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-841))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3986 (|HasCategory| |#3| (QUOTE (-1039))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1087)))) (|HasAttribute| |#3| (QUOTE -4379)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-1101 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4340,7 +4340,7 @@ 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 -(-1103 R -3215) +(-1103 R -3160) ((|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 @@ -4379,16 +4379,16 @@ NIL (-1112 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3998 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1113 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) (-1114 R E V P) ((|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}"))) ((-4383 . T) (-4382 . T)) NIL -(-1115 UP -3215) +(-1115 UP -3160) ((|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 @@ -4443,11 +4443,11 @@ NIL (-1128 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3998 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3986 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) (-1129 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4379 . T) (-4371 |has| |#2| (-6 (-4384 "*"))) (-4382 . T) (-4376 . T) (-4377 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3998 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3998 (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3986 (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-1130 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4467,7 +4467,7 @@ NIL (-1134 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1135 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4479,7 +4479,7 @@ NIL (-1137 |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."))) ((-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087)))) +((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087)))) (-1138) ((|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 @@ -4503,7 +4503,7 @@ NIL (-1143 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1144) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4383 . T) (-4382 . T)) @@ -4511,11 +4511,11 @@ NIL (-1145) NIL ((-4383 . T) (-4382 . 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(|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 @@ -4546,9 +4546,9 @@ NIL NIL (-1154 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4384 "*") -3998 (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-811))) (|has| |#1| (-171)) (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-899)))) (-4375 -3998 (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-811))) (|has| |#1| (-550)) (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . 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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}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-961) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasAttribute| |#1| (QUOTE -4380))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-961) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasAttribute| |#1| (QUOTE -4380))) (-1166) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4623,7 +4623,7 @@ NIL (-1173 |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}"))) ((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2700) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2981) (|devaluate| |#2|)))))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3998 (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-1174 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 @@ -4675,7 +4675,7 @@ NIL (-1186 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4383 . T) (-4382 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1187 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4684,7 +4684,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1189 R -3215) +(-1189 R -3160) ((|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 @@ -4692,7 +4692,7 @@ 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 -(-1191 R -3215) +(-1191 R -3160) ((|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 -606) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -876) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -876) (|devaluate| |#1|))))) @@ -4707,7 +4707,7 @@ NIL (-1194 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) (-1195 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4720,7 +4720,7 @@ 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 (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1198 -3215) +(-1198 -3160) ((|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}.")) 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(LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| (-1238 |#1| |#2| |#3|) (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1238 |#1| |#2| |#3|) (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-171)))) (-12 (|HasCategory| (-1238 |#1| |#2| |#3|) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-1238 |#1| |#2| |#3|) (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-362)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-1238 |#1| |#2| |#3|) (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1238 |#1| |#2| |#3|) (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1211 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4807,7 +4807,7 @@ NIL (-1219 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4378 |has| |#2| (-362)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4823,7 +4823,7 @@ NIL (-1223 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 -890) (QUOTE (-1163)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3220) (LIST (|devaluate| |#2|) (QUOTE (-1163)))))) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2540) (LIST (|devaluate| |#2|) (QUOTE (-1163)))))) (-1224 |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."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) @@ -4851,15 +4851,15 @@ NIL (-1230 |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)}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) +((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-1231 |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}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1232 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))}."))) (((-4384 "*") |has| (-1231 |#2| |#3| |#4|) (-171)) (-4375 |has| (-1231 |#2| |#3| |#4|) (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3998 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) +((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3986 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) (-1233 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4237) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2296) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) (-1237 |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."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) @@ -4883,12 +4883,12 @@ NIL (-1238 |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}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1239 |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 -(-1240 -3215 UP L UTS) +(-1240 -3160 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 (-550)))) @@ -4915,7 +4915,7 @@ NIL (-1246 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4383 . T) (-4382 . T)) -((-3998 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3998 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3998 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1247) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4948,7 +4948,7 @@ 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 -(-1255 K R UP -3215) +(-1255 K R UP -3160) ((|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 @@ -4984,11 +4984,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4375 |has| |#2| (-6 -4375)) (-4377 . T) (-4376 . T) (-4379 . T)) NIL -(-1264 S -3215) +(-1264 S -3160) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1265 -3215) +(-1265 -3160) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 7aa2ba39..5ee57dc2 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(161873 . 3439392491) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) #0#) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) -((((-558)) . T) (($) -3998 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-1028 (-406 (-558))))) ((|#1|) . T)) +(161873 . 3439752261) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) +((((-558)) . T) (($) -3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-1028 (-406 (-558))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-558)) . T)) -((($ $) -3998 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) ((|#2| |#2|) . T) ((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558))))) +((($ $) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) ((|#2| |#2|) . T) ((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#2|) . T)) -((($) -3998 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) ((|#2|) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558))))) +((($) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) ((|#2|) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558))))) (|has| |#1| (-899)) ((((-853)) . T)) ((((-853)) . T)) @@ -24,19 +24,19 @@ ((((-224)) . T) (((-853)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1|) . T)) -(-3998 (|has| |#1| (-21)) (|has| |#1| (-839))) -((($ $) . T) ((#0=(-406 (-558)) #0#) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) -(-3998 (|has| |#1| (-811)) (|has| |#1| (-841))) +(-3986 (|has| |#1| (-21)) (|has| |#1| (-839))) +((($ $) . T) ((#0=(-406 (-558)) #0#) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) +(-3986 (|has| |#1| (-811)) (|has| |#1| (-841))) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-839)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1| |#2| |#3|) . T)) ((((-1168)) . T)) ((((-558)) . T) (((-860 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) -((($) . T) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) . T) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-853)) . T)) ((((-1168)) . T)) (((|#4|) . T)) @@ -46,13 +46,13 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1168)) . T)) (((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(((|#2| (-480 (-2755 |#1|) (-762))) . T)) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(((|#2| (-480 (-1427 |#1|) (-762))) . T)) (((|#1| (-529 (-1163))) . T)) (((#0=(-860 |#1|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((((-1145)) . T) (((-853)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (|has| |#4| (-367)) (|has| |#3| (-367)) (((|#1|) . T)) @@ -63,13 +63,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-550)) -((((-558)) . T) (((-406 (-558))) -3998 (|has| |#2| (-38 (-406 (-558)))) (|has| |#2| (-1028 (-406 (-558))))) ((|#2|) . T) (($) -3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((-855 |#1|)) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -((((-2 (|:| -2851 |#1|) (|:| -2825 |#2|))) . T)) +((((-558)) . 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T)) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((((-534)) |has| |#1| (-606 (-534)))) ((((-1163)) . T)) ((((-558)) . T) (($) . T)) @@ -80,66 +80,66 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-406 (-558))) . T) (($) . T)) -((((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) +((((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) ((((-853)) . T)) (((|#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) -(((|#1|) . T) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) . T)) +(((|#1|) . T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) . T)) (((|#1| |#2|) . T)) ((((-853)) . T)) (((|#1|) . T)) -(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3998 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3986 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) (((|#1|) . T)) (((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) (($) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) -((($) -3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T) (((-558)) . T)) -(((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558)))) ((|#1| |#1|) . T) (($ $) -3998 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) +(((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558)))) ((|#1| |#1|) . T) (($ $) -3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) (((|#2|) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T) (($) -3998 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T) (($) -3986 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) ((($ $) . T)) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) -((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) . 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T)) -(-3998 (|has| |#4| (-784)) (|has| |#4| (-839))) -(-3998 (|has| |#4| (-784)) (|has| |#4| (-839))) -(-3998 (|has| |#3| (-784)) (|has| |#3| (-839))) -(-3998 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3986 (|has| |#4| (-784)) (|has| |#4| (-839))) +(-3986 (|has| |#4| (-784)) (|has| |#4| (-839))) +(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1087)) @@ -153,33 +153,33 @@ ((((-558)) . T)) ((((-558)) . T)) (((|#1|) . T)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#1| (-762)) . T)) (|has| |#2| (-784)) -(-3998 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) (|has| |#2| (-839)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1145) |#1|) . T)) ((((-558) (-129)) . T)) (((|#1|) . 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T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) (|has| |#1| (-38 (-406 (-558)))) -((((-387) (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-387) (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#2| (-1138)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) ((((-853)) . T) (((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) @@ -781,7 +781,7 @@ ((((-387) (-1145)) . T)) (|has| |#1| (-550)) ((((-558) |#1|) . T)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) (((|#2|) . T)) @@ -797,7 +797,7 @@ ((((-635 |#1|)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#2|) |has| |#2| (-308 |#2|))) (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -807,7 +807,7 @@ (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((($) . T) (((-558)) . T) (((-406 (-558))) . T)) (|has| |#2| (-367)) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) @@ -821,8 +821,8 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((($) . T) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-112)) . T)) @@ -846,26 +846,26 @@ ((((-853)) . T)) ((((-1168)) . T)) (|has| |#1| (-811)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#1| (-841)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) (|has| |#1| (-550)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (((-558)) . T)) (|has| |#1| (-899)) (((|#1|) . T)) (|has| |#1| (-1087)) ((((-853)) . 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T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#) ((|#2|) . T) (((-558)) . T)) (((|#1| |#2| |#3|) . T)) -(-3998 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +(-3986 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) (|has| $ (-146)) (|has| $ (-146)) ((((-1168)) . T)) @@ -938,14 +938,14 @@ ((((-853)) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) ((($ $) |has| |#1| (-285 $ $)) ((|#1| $) |has| |#1| (-285 |#1| |#1|))) (((|#1| (-406 (-558))) . T)) (((|#1|) . T)) ((((-1163)) . T)) (|has| |#1| (-550)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-550)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) @@ -956,7 +956,7 @@ (|has| |#1| (-146)) (|has| |#1| (-144)) (|has| |#4| (-839)) -(((|#2| (-239 (-2755 |#1|) (-762)) (-855 |#1|)) . T)) +(((|#2| (-239 (-1427 |#1|) (-762)) (-855 |#1|)) . T)) (|has| |#3| (-839)) (((|#1| (-529 |#3|) |#3|) . T)) (|has| |#1| (-146)) @@ -970,20 +970,20 @@ (|has| |#1| (-144)) ((((-406 (-558))) |has| |#2| (-362)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3998 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#1| (-348)) (|has| |#1| (-367))) ((((-1129 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-171)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-232)) (|has| |#2| (-1039))) -(((|#2|) . T) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -(-3998 (|has| |#3| (-784)) (|has| |#3| (-839))) -(-3998 (|has| |#3| (-784)) (|has| |#3| (-839))) +(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) ((((-853)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-689)) . T)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (|has| |#1| (-550)) (((|#1|) . T)) (((|#1|) . T)) @@ -1007,11 +1007,11 @@ (((|#1| (-406 (-558))) . T)) (((|#3|) . T) (((-604 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -((((-558)) -3998 (|has| |#2| (-171)) (|has| |#2| (-839)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039))) ((|#2|) -3998 (|has| |#2| (-171)) (|has| |#2| (-1087))) (((-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-558)) -3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039))) ((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-1087))) (((-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1019,8 +1019,8 @@ ((((-853)) . T)) ((((-853)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) |has| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (-308 (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))))) ((((-853)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1031,10 +1031,10 @@ ((($ $) . T) ((#0=(-855 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-308 |#1|))) @@ -1122,11 +1122,11 @@ (|has| |#1| (-367)) ((((-1163) $) |has| |#1| (-512 (-1163) $)) (($ $) |has| |#1| (-308 $)) ((|#1| |#1|) |has| |#1| (-308 |#1|)) (((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|))) ((((-1163)) |has| |#1| (-890 (-1163)))) -(-3998 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) +(-3986 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-387) |#1|) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-1087)) (((|#2|) . T) (((-853)) . T)) ((((-853)) . T)) @@ -1134,8 +1134,8 @@ ((((-900 |#1|)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-1168)) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) -((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1144,16 +1144,16 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) (((|#1| |#1|) . T)) (((#0=(-860 |#1|)) |has| #0# (-308 #0#))) -((((-558)) . T) (($) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-1028 (-406 (-558))))) ((|#1|) . T)) +((((-558)) . T) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-1028 (-406 (-558))))) ((|#1|) . T)) (((|#1| |#2|) . T)) -(-3998 (|has| |#2| (-784)) (|has| |#2| (-839))) -(-3998 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) (-12 (|has| |#1| (-784)) (|has| |#2| (-784))) (((|#1|) . T)) (-12 (|has| |#1| (-784)) (|has| |#2| (-784))) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (|has| |#1| (-1185)) (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((((-406 (-558))) . T) (($) . T)) @@ -1164,8 +1164,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-406 (-558)) #0#) . T)) (|has| |#1| (-362)) ((((-558)) . T) (((-406 (-558))) . T) (($) . T)) -((($ $) . T) ((#0=(-406 (-558)) #0#) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((($ $) . T) ((#0=(-406 (-558)) #0#) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -1180,14 +1180,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-839)) (|has| |#1| (-839)) -((($) . T) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-550))) +((($) . T) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) ((($) . T)) -(((#0=(-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) #0#) |has| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (-308 (-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))))) +(((#0=(-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) #0#) |has| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))))) (|has| |#2| (-841)) ((($) . T)) (((|#2|) |has| |#2| (-1087))) -((((-853)) -3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) +((((-853)) -3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) (|has| |#1| (-841)) (|has| |#1| (-841)) ((((-1145) (-52)) . T)) @@ -1196,10 +1196,10 @@ ((((-558)) |has| #0=(-406 |#2|) (-631 (-558))) ((#0#) . T)) ((($) . T) (((-558)) . T)) ((((-558) (-143)) . T)) -((((-558) (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T) ((|#1| |#2|) . T)) +((((-558) (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T) ((|#1| |#2|) . T)) ((((-406 (-558))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-853)) . T)) ((((-900 |#1|)) . T)) (|has| |#1| (-362)) @@ -1226,21 +1226,21 @@ ((((-853)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-558) (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T) ((|#1| |#2|) . T)) +((((-558) (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-171))) -((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-558)) . T) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-558)) . T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (((|#1|) . T)) ((((-534)) |has| |#1| (-606 (-534))) (((-882 (-378))) |has| |#1| (-606 (-882 (-378)))) (((-882 (-558))) |has| |#1| (-606 (-882 (-558))))) ((((-853)) . T)) -(((|#2|) . T) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-504)) . T)) (|has| |#2| (-839)) ((((-504)) . T)) @@ -1248,39 +1248,39 @@ (|has| |#1| (-550)) ((((-1145) |#1|) . T)) (|has| |#1| (-1138)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-948 |#1|)) . T)) -(((#0=(-406 (-558)) #0#) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($ $) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) ((|#1| |#1|) . T)) +(((#0=(-406 (-558)) #0#) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($ $) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) ((|#1| |#1|) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-558))) (((-558)) |has| |#1| (-1028 (-558))) (((-1163)) |has| |#1| (-1028 (-1163))) ((|#1|) . T)) ((((-558) |#2|) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . 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T)) ((((-1163)) |has| (-406 |#2|) (-890 (-1163)))) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) #0#) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-853)) -3998 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-605 (-853))) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) (((-1246 |#3|)) . T)) +((((-853)) -3986 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-605 (-853))) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) (((-1246 |#3|)) . T)) ((((-558) |#2|) . T)) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) -(((|#2| |#2|) -3998 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($ $) |has| |#2| (-171))) +(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(((|#2| |#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($ $) |has| |#2| (-171))) (((|#2|) . T) (((-558)) . T)) ((((-853)) . T)) ((((-853)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T) ((|#2|) . T)) ((((-853)) . T)) ((((-853)) . T)) ((((-1145) (-1163) (-558) (-224) (-853)) . T)) @@ -1315,8 +1315,8 @@ (|has| |#1| (-38 (-406 (-558)))) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -(((|#2|) -3998 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($) |has| |#2| (-171))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +(((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($) |has| |#2| (-171))) (|has| $ (-146)) ((((-406 |#2|)) . T)) ((((-883 |#1|)) . T) ((|#2|) . T) (((-558)) . T) (((-810 |#1|)) . T)) @@ -1328,11 +1328,11 @@ (((|#3|) |has| |#3| (-171))) (|has| |#1| (-146)) (|has| |#1| (-144)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) (((|#1|) . T)) (|has| |#2| (-232)) @@ -1369,7 +1369,7 @@ ((((-989 |#1|)) . T) ((|#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-406 (-558))) . T) (((-406 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1159 |#1|)) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1377,9 +1377,9 @@ (|has| |#1| (-841)) (((|#2|) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) ((((-558) |#2|) . T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#2|) . T)) ((((-558) |#3|) . T)) (((|#2|) . T)) @@ -1394,7 +1394,7 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) #0#) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) (((|#2| |#2|) . T)) (((|#1|) . T)) (|has| |#2| (-362)) @@ -1427,19 +1427,19 @@ (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1| |#2|) . T)) ((((-558) (-143)) . T)) -(((#0=(-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) #0#) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) -((($) -3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +(((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) +((($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (|has| |#1| (-841)) (((|#2| (-762) (-1069)) . T)) (((|#1| |#2|) . T)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) (|has| |#1| (-782)) (((|#1|) |has| |#1| (-171))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3998 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) -(-3998 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) +(-3986 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) +(-3986 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) (((|#4|) . T)) (|has| |#1| (-144)) ((((-1145) |#1|) . T)) @@ -1453,10 +1453,10 @@ (((|#3|) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-853)) . T)) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#1|) . T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087))) (((-948 |#1|)) . T)) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087))) (((-948 |#1|)) . T)) (|has| |#1| (-839)) (|has| |#1| (-839)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) @@ -1470,8 +1470,8 @@ ((($) . T)) ((((-387) (-1145)) . T)) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((((-853)) -3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2700 (-1145)) (|:| -2981 #0#))) . T)) +((((-853)) -3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2045 (-1145)) (|:| -2957 #0#))) . T)) (((|#1|) . T)) ((((-853)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) @@ -1479,7 +1479,7 @@ (|has| |#2| (-144)) (|has| |#2| (-146)) (|has| |#1| (-471)) -(-3998 (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +(-3986 (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) (|has| |#1| (-362)) ((((-853)) . T)) (|has| |#1| (-38 (-406 (-558)))) @@ -1490,8 +1490,8 @@ (|has| |#1| (-839)) ((((-853)) . T)) (((|#2|) . T)) -((((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3998 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) -(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3998 (|has| |#1| (-362)) (|has| |#1| (-550)))) +((((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) +(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550)))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#2|) . T) (((-558)) . T) (((-810 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1500,7 +1500,7 @@ ((((-853)) . T)) ((((-853)) . T)) (|has| |#1| (-1087)) -(((|#2| (-480 (-2755 |#1|) (-762)) (-855 |#1|)) . T)) +(((|#2| (-480 (-1427 |#1|) (-762)) (-855 |#1|)) . T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1| (-529 (-1163)) (-1163)) . T)) (((|#1|) . T)) @@ -1520,16 +1520,16 @@ (|has| |#1| (-146)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -((((-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-1163) (-52)) . T)) ((($ $) . T)) (((|#1| (-558)) . T)) ((((-900 |#1|)) . T)) -(((|#1|) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039))) (($) -3998 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) +(((|#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039))) (($) -3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) (((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) (|has| |#1| (-841)) (|has| |#1| (-841)) @@ -1547,11 +1547,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) (|has| |#2| (-841)) (|has| |#1| (-841)) -(((|#3|) -3998 (|has| |#3| (-171)) (|has| |#3| (-362)))) -(-3998 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-899))) +(((|#3|) -3986 (|has| |#3| (-171)) (|has| |#3| (-362)))) +(-3986 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-899))) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) ((((-558) |#2|) . T)) -(((|#2|) -3998 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)))) (|has| |#1| (-348)) (((|#3| |#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1087)))) (((|#2|) . T) (((-558)) . T)) @@ -1560,7 +1560,7 @@ (|has| |#1| (-811)) (|has| |#1| (-811)) (((|#1|) . T)) -(-3998 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-839)) (|has| |#1| (-839)) (|has| |#1| (-839)) @@ -1569,13 +1569,13 @@ ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-558)))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-1163)) |has| |#1| (-890 (-1163))) (((-1069)) . T)) (((|#1|) . T)) (|has| |#1| (-839)) -(((#0=(-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) #0#) |has| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (-308 (-2 (|:| -2700 (-1145)) (|:| -2981 (-52)))))) +(((#0=(-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) #0#) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (|has| |#1| (-1087)) ((((-853)) . T) (((-1168)) . T)) @@ -1594,11 +1594,11 @@ (((|#1| (-762) (-1069)) . T)) (((|#3|) . T)) ((((-143)) . T)) -((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3998 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) +((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3986 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) (((|#1|) . T)) ((((-143)) . T)) (((|#2|) |has| |#2| (-171))) -(-3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((|#1|) . T)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -1621,32 +1621,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) ((((-662 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1655,7 +1655,7 @@ ((((-853)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) ((((-1168)) . T)) ((((-406 (-558))) . T) (($) . T) (((-406 |#1|)) . T) ((|#1|) . T) (((-558)) . T)) (((|#3|) . T) (((-558)) . T) (((-604 $)) . T)) @@ -1663,12 +1663,12 @@ ((((-853)) . T)) ((((-853)) . T)) (((|#2|) . 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T)) (|has| |#1| (-1185)) (|has| |#1| (-1185)) -(-3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (|has| |#1| (-1185)) (|has| |#1| (-1185)) (((|#3| |#3|) . T)) @@ -1681,16 +1681,16 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((((-1145) (-52)) . T)) (|has| |#1| (-1087)) -(-3998 (|has| |#2| (-811)) (|has| |#2| (-841))) +(-3986 (|has| |#2| (-811)) (|has| |#2| (-841))) (((|#1|) . T)) (((|#1|) |has| |#1| (-171)) (($) . T)) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((($) . T)) ((((-1161 |#1| |#2| |#3|)) -12 (|has| (-1161 |#1| |#2| |#3|) (-308 (-1161 |#1| |#2| |#3|))) (|has| |#1| (-362)))) ((((-853)) . T)) ((((-558)) . T) (($) . T)) ((((-762)) . T)) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) ((($) . T) (((-558)) . T)) @@ -1698,29 +1698,29 @@ (|has| |#2| (-899)) (|has| |#1| (-362)) (((|#2|) |has| |#2| (-1087))) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-534)) . T) (((-406 (-1159 (-558)))) . T) (((-224)) . T) (((-378)) . T)) ((((-378)) . T) (((-224)) . T) (((-853)) . T)) (|has| |#1| (-899)) (|has| |#1| (-899)) (|has| |#1| (-899)) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-899))) ((($) . T) ((|#2|) . T)) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) ((($ $) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((($ $) . T)) ((((-558) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-558)) . T)) ((((-112)) . T)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-38 (-406 (-558)))) (((|#1| (-558)) . T)) ((($) . T)) @@ -1742,7 +1742,7 @@ (((|#1| (-1210 |#1| |#2| |#3|)) . T)) (((|#1| (-762)) . T)) (((|#1|) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-853)) . T)) (|has| |#1| (-1087)) ((((-1145) |#1|) . T)) @@ -1762,18 +1762,18 @@ (((|#1|) . T)) ((((-558)) . T)) ((((-853)) . T)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-853)) . T)) (((|#3|) . T)) -(-3998 (|has| |#3| (-171)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3986 (|has| |#3| (-171)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-853)) . T)) ((((-1231 |#2| |#3| |#4|)) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T)) ((((-853)) . T)) -((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-604 $)) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) -3998 (-12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) +((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-604 $)) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) -3986 (-12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-762)) . T)) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (((|#1|) |has| |#1| (-308 |#1|))) ((((-1232 |#1| |#2| |#3| |#4|)) . T)) ((((-558)) |has| |#1| (-876 (-558))) (((-378)) |has| |#1| (-876 (-378)))) @@ -1781,7 +1781,7 @@ (|has| |#1| (-550)) (((|#1|) . T)) ((((-853)) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) @@ -1789,7 +1789,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1087))) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) -(((|#2|) -3998 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)))) ((((-1231 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-811)) @@ -1799,8 +1799,8 @@ (|has| |#1| (-839)) (|has| |#1| (-839)) (((|#1| (-558) (-1069)) . T)) -(-3998 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +(-3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#1| (-406 (-558)) (-1069)) . T)) (((|#1| (-762) (-1069)) . T)) (|has| |#1| (-841)) @@ -1813,33 +1813,33 @@ (|has| |#1| (-1087)) ((((-900 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-1087)) -((((-558)) -3998 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) +((((-558)) -3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) (((|#1|) . T)) (|has| |#1| (-1087)) ((((-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-631 (-558)))) ((|#2|) |has| |#1| (-362))) -(-3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) -((((-679 (-338 (-3233) (-3233 (QUOTE X) (QUOTE HESS)) (-689)))) . T)) +(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +((((-679 (-338 (-2551) (-2551 (QUOTE X) (QUOTE HESS)) (-689)))) . T)) (((|#2|) |has| |#2| (-171))) (((|#1|) |has| |#1| (-171))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) ((((-853)) . T)) (|has| |#3| (-839)) ((((-853)) . T)) ((((-1231 |#2| |#3| |#4|) (-318 |#2| |#3| |#4|)) . T)) ((((-853)) . T)) -(((|#1| |#1|) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) +(((|#1| |#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) (((|#1|) . T)) ((((-558)) . T)) ((((-558)) . T)) -(((|#1|) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) +(((|#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) (((|#2|) |has| |#2| (-362))) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-362))) (|has| |#1| (-841)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))) |has| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (-308 (-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))))) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-899))) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) |has| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-899))) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) ((((-853)) . T)) ((((-853)) . T)) @@ -1870,25 +1870,25 @@ (|has| |#1| (-144)) ((((-558)) . T) ((|#1|) . T) (($) . T) (((-406 (-558))) . T) (((-1163)) |has| |#1| (-1028 (-1163)))) (((|#1| |#2|) . T)) -((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3998 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) +((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3986 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) ((((-143)) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (((|#1|) . T)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-558)) . T)) ((((-853)) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| (-406 |#2|) (-232)) ((((-635 |#1|)) . T)) (|has| |#1| (-899)) (((|#2|) |has| |#2| (-1039))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) (|has| |#1| (-362)) (((|#1|) |has| |#1| (-171))) (((|#1| |#1|) . T)) @@ -1915,7 +1915,7 @@ (((|#1| (-406 (-558)) (-1069)) . T)) (((|#1| (-762) (-1069)) . T)) (((#0=(-406 |#2|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-558)) -3998 (|has| (-406 (-558)) (-1028 (-558))) (|has| |#1| (-1028 (-558)))) (((-406 (-558))) . T)) +(((|#1|) . T) (((-558)) -3986 (|has| (-406 (-558)) (-1028 (-558))) (|has| |#1| (-1028 (-558)))) (((-406 (-558))) . T)) (((|#1| (-594 |#1| |#3|) (-594 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -1936,25 +1936,25 @@ (((|#2|) |has| |#2| (-171))) (|has| |#2| (-839)) ((((-558)) . T) ((|#2|) . T) (((-406 (-558))) |has| |#2| (-1028 (-406 (-558))))) -((((-112)) |has| |#1| (-1087)) (((-853)) -3998 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087)))) +((((-112)) |has| |#1| (-1087)) (((-853)) -3986 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 (-52)))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) . T)) ((((-853)) . T)) ((((-558) |#1|) . T)) ((((-853)) . T)) ((((-689)) . T) (((-406 (-558))) . T) (((-558)) . T)) (((|#1| |#1|) |has| |#1| (-171))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) ((((-378)) . T)) ((((-689)) . T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1|) |has| |#1| (-171))) ((((-406 (-942 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#2|) . T)) (|has| |#2| (-841)) (|has| |#2| (-899)) @@ -1964,14 +1964,14 @@ (((|#3|) |has| |#3| (-1039))) ((((-1163)) |has| |#2| (-890 (-1163)))) ((((-853)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-406 (-558))) . T) (($) . T)) (|has| |#1| (-471)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-362)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) (|has| |#1| (-38 (-406 (-558)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1992,11 +1992,11 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-841)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) |has| (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)) (-308 (-2 (|:| -2700 |#1|) (|:| -2981 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2014,11 +2014,11 @@ ((((-534)) |has| |#1| (-606 (-534))) (((-882 (-558))) |has| |#1| (-606 (-882 (-558)))) (((-882 (-378))) |has| |#1| (-606 (-882 (-378)))) (((-378)) . #0=(|has| |#1| (-1012))) (((-224)) . #0#)) (((|#1|) |has| |#1| (-362))) ((((-853)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((($ $) . T) (((-604 $) $) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) ((($) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T) (((-406 (-558))) . T)) -((($) -3998 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-550))) +((($) -3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| |#1| (-362)) @@ -2029,11 +2029,11 @@ ((((-378)) . T)) (((|#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1087)))) ((((-853)) . T)) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-899))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-899))) (((|#1|) . T)) (|has| |#1| (-841)) (|has| |#1| (-841)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-534)) |has| |#1| (-606 (-534)))) (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) ((((-762)) . T)) @@ -2044,13 +2044,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((((-558)) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((#0=(-1231 |#2| |#3| |#4|)) . T) (((-406 (-558))) |has| #0# (-38 (-406 (-558)))) (($) . T)) ((((-558)) . T)) (|has| |#1| (-362)) -(-3998 (-12 (|has| (-1238 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) -(-3998 (-12 (|has| (-1238 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) +(-3986 (-12 (|has| (-1238 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) +(-3986 (-12 (|has| (-1238 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) (|has| |#1| (-362)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -2065,23 +2065,23 @@ (((|#2|) . T)) (|has| |#1| (-1087)) (((|#1| |#2|) . T)) -((((-558)) . T) ((|#1|) . 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T) (($ $) -3998 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-558)) #0#) |has| |#1| (-362))) -((((-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -3986 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-558)) #0#) |has| |#1| (-362))) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) ((((-942 |#1|)) . T)) ((($) . T)) ((((-558) |#1|) . T)) ((((-1163)) |has| (-406 |#2|) (-890 (-1163)))) -(((|#1|) . T) (($) -3998 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-558))) |has| |#1| (-362))) +(((|#1|) . T) (($) -3986 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-558))) |has| |#1| (-362))) ((((-534)) |has| |#2| (-606 (-534)))) ((((-679 |#2|)) . T) (((-853)) . T)) (((|#1|) . T)) @@ -2089,8 +2089,8 @@ (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) ((((-860 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3998 (|has| |#4| (-784)) (|has| |#4| (-839))) -(-3998 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3986 (|has| |#4| (-784)) (|has| |#4| (-839))) +(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) ((((-853)) . T)) ((((-853)) . T)) (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) @@ -2106,17 +2106,17 @@ ((((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T)) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-1204))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-1204))) ((($) . T)) ((((-406 (-558))) |has| #0=(-406 |#2|) (-1028 (-406 (-558)))) (((-558)) |has| #0# (-1028 (-558))) ((#0#) . T)) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) (((|#1| (-762)) . T)) (|has| |#1| (-841)) (((|#1|) . T) (((-558)) |has| |#1| (-631 (-558)))) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3998 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-558)) . T)) (|has| |#1| (-38 (-406 (-558)))) -((((-2 (|:| -2700 (-1145)) (|:| -2981 (-52)))) |has| (-2 (|:| -2700 (-1145)) (|:| -2981 (-52))) (-308 (-2 (|:| -2700 (-1145)) (|:| -2981 (-52)))))) +((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (|has| |#1| (-839)) (|has| |#1| (-38 (-406 (-558)))) @@ -2139,29 +2139,29 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) ((((-1145)) . T) (((-1163)) . T) (((-224)) . T) (((-558)) . T)) -(((|#2|) . T) (((-558)) . T) (($) -3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -((($) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((((-534)) |has| |#4| (-606 (-534)))) ((((-853)) . T) (((-635 |#4|)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-839)) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) |has| (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|)) (-308 (-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))))) (|has| |#1| (-1087)) (|has| |#1| (-362)) (|has| |#1| (-841)) @@ -2170,16 +2170,16 @@ (((|#1|) . T)) ((((-662 |#1|)) . T)) ((($) . T) (((-406 (-558))) . T)) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (|has| |#1| (-144)) (|has| |#1| (-146)) -(-3998 (-12 (|has| (-1161 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) -(-3998 (-12 (|has| (-1161 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) +(-3986 (-12 (|has| (-1161 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) +(-3986 (-12 (|has| (-1161 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) (|has| |#1| (-839)) (((|#1| |#2|) . T)) @@ -2203,9 +2203,9 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -(((|#1|) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)))) +(((|#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)))) ((((-315 |#1|)) . T)) (((|#2|) |has| |#2| (-362))) (((|#2|) . T)) @@ -2227,13 +2227,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((($ $) . T)) -(-3998 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) +(-3986 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) (|has| |#1| (-550)) (((|#2|) . T)) ((((-558)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#1|) . T)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((((-575 |#1|)) . T)) ((($) . T)) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) @@ -2249,7 +2249,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1231 |#2| |#3| |#4|)) . T) (((-558)) . 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T)) ((((-406 (-558))) |has| |#2| (-1028 (-406 (-558)))) (((-558)) |has| |#2| (-1028 (-558))) ((|#2|) . T) (((-855 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-406 (-558))) . T)) ((((-1112 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) @@ -2262,12 +2262,12 @@ (((|#1| |#2|) . T)) ((((-1163) |#1|) . T)) (((|#4|) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1163) (-52)) . T)) ((((-1231 |#2| |#3| |#4|) (-318 |#2| |#3| |#4|)) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . T)) ((((-853)) . T)) -(-3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((#0=(-1232 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-171)) ((#0=(-406 (-558)) #0#) |has| |#1| (-550)) (($ $) |has| |#1| (-550))) (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) @@ -2287,14 +2287,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((|#2| |#3|) . T)) -(-3998 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1| (-529 |#2|)) . T)) (((|#1| (-762)) . T)) (((|#1| (-529 (-1075 (-1163)))) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (|has| |#2| (-899)) -(-3998 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) ((((-853)) . T)) ((($ $) . T) ((#0=(-1231 |#2| |#3| |#4|) #0#) . T) ((#1=(-406 (-558)) #1#) |has| #0# (-38 (-406 (-558))))) ((((-900 |#1|)) . T)) @@ -2303,14 +2303,14 @@ ((((-853)) . T)) ((($) . T)) ((($) . T)) -(-3998 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-362)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1231 |#2| |#3| |#4|)) . T) (((-406 (-558))) |has| #0# (-38 (-406 (-558))))) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -(-3998 (-12 (|has| |#1| (-306)) (|has| |#1| (-899))) (|has| |#1| (-362)) (|has| |#1| (-348))) -(-3998 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +(-3986 (-12 (|has| |#1| (-306)) (|has| |#1| (-899))) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) ((((-558)) |has| |#1| (-631 (-558))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-853)) . T)) @@ -2343,27 +2343,27 @@ (((|#1|) |has| |#1| (-171))) ((((-853)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) -(((|#2|) -3998 (|has| |#2| (-6 (-4384 "*"))) (|has| |#2| (-171)))) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(((|#2|) -3986 (|has| |#2| (-6 (-4384 "*"))) (|has| |#2| (-171)))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#2| (-841)) (|has| |#2| (-899)) (|has| |#1| (-899)) (((|#2|) |has| |#2| (-171))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-853)) . T)) ((((-853)) . T)) ((((-534)) . T) (((-558)) . T) (((-882 (-558))) . T) (((-378)) . T) (((-224)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 (-52)))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) . T)) (((|#1|) . T)) ((((-853)) . T)) (((|#1| |#2|) . T)) (((|#1| (-406 (-558))) . T)) (((|#1|) . T)) -(-3998 (|has| |#1| (-289)) (|has| |#1| (-362))) +(-3986 (|has| |#1| (-289)) (|has| |#1| (-362))) ((((-143)) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) (|has| |#1| (-839)) @@ -2379,7 +2379,7 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-186)) . T) (((-853)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -2392,7 +2392,7 @@ ((((-853)) . T)) ((((-1145)) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) (|has| |#1| (-841)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) @@ -2404,16 +2404,16 @@ (((|#2|) . T)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T)) ((($) . T) (((-558)) . T) (((-406 (-558))) . T) (((-604 $)) . T)) -(-3998 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) -(-3998 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3986 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) +(-3986 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-1163) (-52)) . T)) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (|has| |#1| (-899)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) (|has| |#1| (-899)) @@ -2430,12 +2430,12 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#1| (-811)) (((#0=(-900 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-558)) #1#) . T)) ((((-406 |#2|)) . T)) (|has| |#1| (-839)) -((((-1186 |#1|)) . T) (((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-1186 |#1|)) . T) (((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) . T) ((#1=(-558) #1#) . T) (($ $) . T)) ((((-900 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) (((|#2|) |has| |#2| (-1039)) (((-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039)))) @@ -2446,25 +2446,25 @@ (((|#2|) . T)) ((((-853)) . T)) ((((-406 (-558))) . T) (((-689)) . T) (($) . T) (((-558)) . T)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) -((((-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2700 (-1163)) (|:| -2981 #0#))) . T)) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2045 (-1163)) (|:| -2957 #0#))) . T)) (|has| |#1| (-348)) ((((-558)) . T)) ((((-853)) . T)) (((#0=(-1232 |#1| |#2| |#3| |#4|) $) |has| #0# (-285 #0# #0#))) (|has| |#1| (-362)) (((#0=(-1069) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (((#0=(-406 (-558)) #0#) . T) ((#1=(-689) #1#) . T) (($ $) . T)) ((((-315 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) |has| |#1| (-362))) (|has| |#1| (-1087)) (((|#1|) . T)) -(((|#1|) -3998 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) -(((|#1|) -3998 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -3986 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -3986 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) (((|#2|) . T)) ((((-406 (-558))) . T) (((-689)) . T) (($) . T)) ((((-573)) . T)) @@ -2487,7 +2487,7 @@ (((|#1|) . T)) ((((-558)) . T)) (((|#2|) . T) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (($) . T) (((-558)) . T)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2525,7 +2525,7 @@ (|has| |#2| (-1012)) ((($) . T)) (|has| |#1| (-899)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2533,9 +2533,9 @@ ((($) . T)) (|has| |#1| (-362)) ((((-900 |#1|)) . T)) -((($) -3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) -(-3998 (|has| |#1| (-367)) (|has| |#1| (-841))) +(-3986 (|has| |#1| (-367)) (|has| |#1| (-841))) (((|#1|) . T)) ((((-762)) . T)) ((((-853)) . T)) @@ -2546,16 +2546,16 @@ ((((-558)) . T) (($) . T)) ((((-558)) . T) (($) . T)) ((((-762) |#1|) . T)) -(((|#2| (-239 (-2755 |#1|) (-762))) . T)) +(((|#2| (-239 (-1427 |#1|) (-762))) . T)) (((|#1| (-529 |#3|)) . T)) ((((-406 (-558))) . T)) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-1145)) . T) (((-853)) . T)) -(((#0=(-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) #0#) |has| (-2 (|:| -2700 (-1163)) (|:| -2981 (-52))) (-308 (-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))))) +(((#0=(-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) #0#) |has| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))))) ((((-1145)) . T)) (|has| |#1| (-899)) (|has| |#2| (-362)) -(-3998 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-853)) . T)) (((|#1|) . T)) @@ -2572,11 +2572,11 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3998 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-558)))) (-12 (|has| |#1| (-543)) (|has| |#1| (-819))) ((((-853)) . T)) -((((-1163)) -3998 (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-890 (-1163)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-890 (-1163)))))) +((((-1163)) -3986 (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-890 (-1163)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-890 (-1163)))))) (|has| |#1| (-362)) ((((-1163)) -12 (|has| |#1| (-15 * (|#1| (-406 (-558)) |#1|))) (|has| |#1| (-890 (-1163))))) (|has| |#1| (-362)) @@ -2587,7 +2587,7 @@ (((|#2|) |has| |#1| (-362))) (((|#2|) |has| |#1| (-362))) ((((-558)) . T) (($) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -2612,9 +2612,9 @@ ((((-378)) -12 (|has| |#1| (-362)) (|has| |#2| (-876 (-378)))) (((-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-876 (-558))))) (|has| |#1| (-362)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-362)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-550)) (((|#1|) . T)) @@ -2623,22 +2623,22 @@ ((((-1145)) . T) (((-1163)) . T) (((-224)) . T) (((-558)) . T)) (((|#1|) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) -(-3998 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#2|) . T)) (((|#2|) . T)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (|has| |#1| (-38 (-406 (-558)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-406 (-558)))) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-1145) |#1|) . T)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-575 |#1|)) . T)) ((($) . T)) @@ -2646,7 +2646,7 @@ (|has| |#1| (-550)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3998 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-853)) . T)) ((($) . T)) @@ -2673,7 +2673,7 @@ ((((-853)) . T)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2695,7 +2695,7 @@ ((((-558)) . T)) ((((-853)) . T)) ((((-558)) . T)) -(-3998 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -2707,9 +2707,9 @@ (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -(-3998 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +(-3986 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) (|has| |#1| (-1138)) ((((-558) |#1|) . T)) (((|#1|) . T)) @@ -2728,8 +2728,8 @@ (((|#1|) . T)) (|has| |#1| (-550)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) ((((-378)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2738,7 +2738,7 @@ (|has| |#1| (-550)) (|has| |#1| (-1087)) ((((-771 |#1| (-855 |#2|))) |has| (-771 |#1| (-855 |#2|)) (-308 (-771 |#1| (-855 |#2|))))) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2750,13 +2750,13 @@ (|has| |#2| (-362)) ((((-575 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) ((((-558)) . T) (((-406 (-558))) . T) (($) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 (-52)))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-558)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) ((((-853)) . 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T)) +((((-1159 |#1|)) . T) (((-558)) . T) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558)))))) +(-3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +((((-1112 |#1| (-1163))) . T) (((-558)) . T) (((-1075 (-1163))) . T) (($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-1163)) . T)) (((#0=(-575 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-558)) #1#) . T)) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) (((|#1|) |has| |#1| (-171))) @@ -2786,7 +2786,7 @@ (((|#1|) . T)) ((((-853)) . T)) ((((-293 |#3|)) . T)) -(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3998 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3986 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T)) @@ -2794,21 +2794,21 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) -((($ $) -3998 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) -((($ $) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . 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T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) +((($ $) -3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) ((((-853)) . T)) -((($) -3998 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((($) -3998 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (|has| |#2| (-899)) (|has| |#1| (-899)) -((($) -3998 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((((-853)) . T)) (((|#1|) . T)) -((((-2 (|:| -2700 (-1145)) (|:| -2981 |#1|))) . T)) +((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2823,10 +2823,10 @@ (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((#0=(-406 (-558)) #0#) . T)) ((((-406 (-558))) . T)) -(-3998 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#1|) . T)) (((|#1|) . T)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-406 (-558))) . T) (((-558)) . T) (($) . T)) ((((-534)) . T)) ((((-853)) . T)) @@ -2843,12 +2843,12 @@ ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) ((((-1163)) |has| |#1| (-890 (-1163)))) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T)) -((($) . T) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) . T)) -(((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558)))) ((|#1| |#1|) . T) (($ $) -3998 (|has| |#1| (-171)) (|has| |#1| (-550)))) +((($) . T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) . T)) +(((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558)))) ((|#1| |#1|) . T) (($ $) -3986 (|has| |#1| (-171)) (|has| |#1| (-550)))) ((($) . T) (((-406 (-558))) . T)) (((|#1|) . T) (((-406 (-558))) . T) (((-558)) . T) (($) . T)) (((|#2|) |has| |#2| (-1039)) (((-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039)))) -((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) . T) (($) -3998 (|has| |#1| (-171)) (|has| |#1| (-550)))) +((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) . T) (($) -3986 (|has| |#1| (-171)) (|has| |#1| (-550)))) (|has| |#1| (-550)) (((|#1|) |has| |#1| (-362))) ((((-558)) . T)) @@ -2867,8 +2867,8 @@ ((((-853)) . T)) (|has| |#2| (-811)) (|has| |#2| (-811)) -((((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#2|) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-406 (-558))) -3998 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) . T)) +((((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#2|) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) ((((-558)) |has| |#1| (-876 (-558))) (((-378)) |has| |#1| (-876 (-378)))) @@ -2894,12 +2894,12 @@ (((|#2| (-762)) . T)) ((((-1163)) . T)) ((((-860 |#1|)) . 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T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-1168)) . T)) (((|#1|) |has| |#1| (-171))) ((((-1168)) . T)) @@ -3275,13 +3275,13 @@ ((((-1168)) . T)) ((((-1168)) . T)) ((((-1168)) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-348))) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1168)) . T)) ((((-1168)) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -(-3998 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) (((|#1| (-558)) . T)) (((|#1| (-406 (-558))) . T)) (((|#1| (-762)) . T)) @@ -3296,16 +3296,16 @@ ((((-882 (-378))) . T) (((-882 (-558))) . T) (((-1163)) . T) (((-534)) . T)) (((|#1|) . T)) ((((-853)) . 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T)) -(-3998 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3986 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) -(-3998 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-717)) (|has| |#2| (-717)))) +(-3986 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-717)) (|has| |#2| (-717)))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-362)) @@ -3331,7 +3331,7 @@ (((|#1| |#2|) . T)) ((((-558)) . T) ((|#2|) |has| |#2| (-171))) ((((-114)) . T) ((|#1|) . T) (((-558)) . T)) -(-3998 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-3986 (|has| |#1| (-348)) (|has| |#1| (-367))) (((|#1| |#2|) . T)) ((((-224)) . T)) ((((-406 (-558))) . T) (($) . T) (((-558)) . T)) @@ -3343,7 +3343,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((($) . T) (((-406 (-558))) . T)) (|has| |#1| (-899)) (|has| |#1| (-899)) @@ -3354,14 +3354,14 @@ (((|#1| |#1|) |has| |#1| (-171))) (((|#1|) . T) (((-558)) . T)) ((((-1168)) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3998 (|has| |#1| (-21)) (|has| |#1| (-839))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3986 (|has| |#1| (-21)) (|has| |#1| (-839))) (((|#2|) . T)) -(-3998 (|has| |#1| (-21)) (|has| |#1| (-839))) +(-3986 (|has| |#1| (-21)) (|has| |#1| (-839))) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (((|#1|) . 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T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -(((|#2|) . T) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) -((((-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1012)) -(((|#2|) . T) (((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) ((((-853)) . T)) ((((-534)) |has| |#2| (-606 (-534))) (((-882 (-558))) |has| |#2| (-606 (-882 (-558)))) (((-882 (-378))) |has| |#2| (-606 (-882 (-378)))) (((-378)) . #0=(|has| |#2| (-1012))) (((-224)) . #0#)) ((((-293 |#3|)) . T)) @@ -3419,15 +3419,15 @@ ((((-1161 |#1| |#2| |#3|)) . T)) ((((-1161 |#1| |#2| |#3|)) . T) (((-1154 |#1| |#2| |#3|)) . T)) ((((-853)) . T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-558) |#1|) . 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T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-129)) . T) (((-853)) . T)) ((((-558) |#1|) . T)) ((((-129)) . T)) @@ -3451,13 +3451,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-362)) (|has| |#2| (-285 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3998 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) -(-3998 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) ((((-853)) . T)) ((((-853)) . T)) ((((-853)) . T)) (((|#1| (-529 |#2|)) . T)) -((((-2 (|:| -2700 (-1163)) (|:| -2981 (-52)))) . T)) +((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) ((((-558) (-129)) . T)) (((|#1| (-558)) . T)) (((|#1| (-406 (-558))) . T)) @@ -3471,8 +3471,8 @@ ((((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) -(-3998 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3998 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((($) . T)) (((|#2| (-529 (-855 |#1|))) . T)) ((((-1168)) . T)) @@ -3487,13 +3487,13 @@ ((((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-1168)) . T)) -((((-853)) -3998 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1|) . T)) (((|#2| (-762)) . T)) (((|#1| |#2|) . T)) ((((-1145) |#1|) . T)) ((((-406 |#2|)) . T)) -((((-2 (|:| -2700 |#1|) (|:| -2981 |#2|))) . T)) +((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) (|has| |#1| (-550)) (|has| |#1| (-550)) ((($) . T) ((|#2|) . T)) @@ -3502,14 +3502,14 @@ ((((-558)) . T) (($) . 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. -605) 155542) ((-50 . -1046) T) ((-250 . -717) 155452) ((-249 . -717) 155362) ((-1194 . -1087) T) ((-660 . -23) T) ((-575 . -1046) T) ((-516 . -1046) T) ((-378 . -1045) 155327) ((-321 . -111) 155302) ((-73 . -382) T) ((-73 . -394) T) ((-1014 . -38) 155239) ((-684 . -399) 155221) ((-99 . -102) T) ((-702 . -1087) T) ((-993 . -144) 155193) ((-993 . -146) 155165) ((-378 . -111) 155121) ((-318 . -1204) 155100) ((-472 . -992) 155066) ((-353 . -38) 155031) ((-40 . -369) 155003) ((-863 . -605) 154875) ((-127 . -125) 154859) ((-121 . -125) 154843) ((-827 . -1045) 154813) ((-824 . -21) 154765) ((-818 . -1045) 154749) ((-824 . -25) 154701) ((-318 . -550) 154652) ((-515 . -608) 154633) ((-558 . -819) T) ((-239 . -1200) T) ((-1024 . -608) 154602) ((-827 . -111) 154567) ((-818 . -111) 154546) ((-1230 . -605) 154528) ((-1209 . -605) 154510) ((-1209 . -606) 154181) ((-1159 . -899) 154160) ((-1112 . -899) 154139) ((-48 . -38) 154104) ((-1268 . -1099) T) ((-594 . -605) 154016) ((-594 . -606) 153977) 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137112) ((-1143 . -150) 137096) ((-250 . -890) 137028) ((-249 . -890) 136960) ((-1069 . -841) T) ((-413 . -1099) T) ((-1043 . -23) T) ((-900 . -1039) T) ((-321 . -638) 136942) ((-1014 . -839) T) ((-1194 . -992) 136908) ((-1160 . -910) 136887) ((-1154 . -910) 136866) ((-1154 . -811) NIL) ((-900 . -242) T) ((-808 . -362) 136845) ((-384 . -23) T) ((-127 . -1087) 136823) ((-121 . -1087) 136801) ((-900 . -232) T) ((-128 . -34) T) ((-378 . -638) 136766) ((-860 . -708) 136753) ((-1036 . -150) 136718) ((-40 . -171) T) ((-684 . -410) 136700) ((-703 . -308) 136687) ((-827 . -638) 136647) ((-818 . -638) 136621) ((-318 . -25) T) ((-318 . -21) T) ((-648 . -285) 136600) ((-574 . -1087) T) ((-558 . -1087) T) ((-493 . -1087) T) ((-244 . -287) 136577) ((-312 . -230) 136538) ((-1159 . -876) NIL) ((-55 . -1087) T) ((-1112 . -876) 136397) ((-129 . -841) T) ((-1159 . -1028) 136277) ((-1112 . -1028) 136160) ((-182 . -605) 136142) ((-845 . -1028) 136038) ((-773 . -285) 135965) ((-808 . -1099) T) ((-1024 . -717) T) ((-594 . -641) 135949) ((-1036 . -966) 135878) ((-989 . -102) T) ((-808 . -23) T) ((-703 . -1138) 135856) ((-684 . -1046) T) ((-594 . -372) 135840) ((-350 . -450) T) ((-342 . -289) T) ((-1247 . -1087) T) ((-247 . -1087) T) ((-398 . -102) T) ((-288 . -21) T) ((-288 . -25) T) ((-360 . -717) T) ((-701 . -1087) T) ((-689 . -1087) T) ((-360 . -471) T) ((-1194 . -605) 135822) ((-1159 . -376) 135806) ((-1112 . -376) 135790) ((-1014 . -410) 135752) ((-140 . -228) 135734) ((-378 . -785) T) ((-378 . -782) T) ((-860 . -171) T) ((-378 . -717) T) ((-702 . -605) 135716) ((-703 . -38) 135545) ((-1246 . -1244) 135529) ((-350 . -401) T) ((-1246 . -1087) 135479) ((-574 . -708) 135466) ((-558 . -708) 135453) ((-493 . -708) 135418) ((-315 . -621) 135397) ((-827 . -717) T) ((-818 . -717) T) ((-635 . -1200) T) ((-1067 . -631) 135345) ((-1159 . -890) 135288) ((-1112 . -890) 135272) ((-652 . -1045) 135256) ((-108 . -631) 135238) ((-480 . -130) 135108) ((-1165 . -1099) T) ((-942 . -47) 135077) ((-615 . -1087) T) ((-652 . -111) 135056) ((-489 . -605) 135022) ((-326 . -287) 134999) ((-479 . -47) 134956) ((-1165 . -23) T) ((-117 . -1087) T) ((-103 . -102) 134934) ((-1258 . -1099) T) ((-1043 . -130) T) ((-1014 . -1046) T) ((-810 . -1028) 134918) ((-993 . -715) 134890) ((-1258 . -23) T) ((-689 . -708) 134855) ((-579 . -605) 134837) ((-385 . -1028) 134821) ((-353 . -1046) T) ((-384 . -130) T) ((-323 . -1028) 134805) ((-224 . -876) 134787) ((-994 . -910) T) ((-91 . -34) T) ((-994 . -811) T) ((-904 . -910) T) ((-1180 . -605) 134769) ((-1107 . -819) T) ((-485 . -1204) T) ((-1092 . -1087) T) ((-1067 . -21) T) ((-1067 . -25) T) ((-216 . -1204) T) ((-989 . -308) 134734) ((-224 . -1028) 134694) ((-40 . -289) T) ((-705 . -638) 134654) ((-671 . -608) 134635) ((-666 . -608) 134616) ((-485 . -550) T) ((-476 . -608) 134597) ((-358 . -25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -550) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -608) 134574) ((-137 . -608) 134555) ((-136 . -608) 134536) ((-132 . -608) 134517) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1046) T) ((-574 . -171) T) ((-558 . -171) T) ((-493 . -171) T) ((-648 . -605) 134499) ((-728 . -727) 134483) ((-335 . -605) 134465) ((-68 . -382) T) ((-68 . -394) T) ((-1089 . -107) 134449) ((-1050 . -876) 134431) ((-942 . -876) 134356) ((-643 . -1099) T) ((-615 . -708) 134343) ((-479 . -876) NIL) ((-1133 . -102) T) ((-1081 . -610) 134327) ((-1050 . -1028) 134309) ((-97 . -605) 134291) ((-475 . -146) T) ((-942 . -1028) 134171) ((-117 . -708) 134116) ((-643 . -23) T) ((-479 . -1028) 133992) ((-1074 . -606) NIL) ((-1074 . -605) 133974) ((-773 . -606) NIL) ((-773 . -605) 133935) ((-771 . -606) 133569) ((-771 . -605) 133483) ((-1100 . -631) 133389) ((-459 . -605) 133371) ((-452 . -605) 133353) ((-452 . -606) 133214) ((-1025 . -228) 133160) ((-862 . -899) 133139) ((-126 . -34) T) ((-808 . -130) T) ((-639 . -605) 133121) ((-572 . -102) T) ((-354 . -1265) 133105) ((-351 . -1265) 133089) ((-343 . -1265) 133073) 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. -394) T) ((-216 . -23) T) ((-1270 . -1263) 130923) ((-574 . -289) T) ((-558 . -289) T) ((-667 . -1028) 130907) ((-493 . -289) T) ((-135 . -468) 130862) ((-48 . -1087) T) ((-703 . -230) 130846) ((-861 . -890) NIL) ((-1219 . -876) NIL) ((-879 . -102) T) ((-875 . -102) T) ((-387 . -1087) T) ((-168 . -376) 130830) ((-168 . -337) 130814) ((-1219 . -1028) 130694) ((-846 . -1028) 130590) ((-1129 . -102) T) ((-643 . -130) T) ((-117 . -512) 130498) ((-652 . -783) 130477) ((-652 . -786) 130456) ((-565 . -1028) 130438) ((-293 . -1253) 130408) ((-856 . -102) T) ((-953 . -550) 130387) ((-1194 . -1045) 130270) ((-480 . -631) 130176) ((-894 . -1087) T) ((-1014 . -708) 130113) ((-702 . -1045) 130078) ((-609 . -102) T) ((-594 . -34) T) ((-1134 . -1200) T) ((-1194 . -111) 129947) ((-472 . -638) 129844) ((-353 . -708) 129789) ((-168 . -890) 129748) ((-689 . -289) T) ((-684 . -171) T) ((-702 . -111) 129704) ((-1274 . -1046) T) ((-1219 . -376) 129688) ((-417 . -1204) 129666) ((-1105 . -605) 129648) 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. -1046) T) ((-684 . -992) NIL) ((-3 . |UnionCategory|) T) ((-1230 . -47) 121181) ((-1209 . -47) 121158) ((-1128 . -1000) 121129) ((-224 . -910) T) ((-40 . -111) 121058) ((-862 . -1028) 120922) ((-1107 . -708) 120909) ((-1092 . -605) 120891) ((-1067 . -146) 120870) ((-1067 . -144) 120821) ((-994 . -362) T) ((-318 . -1188) 120787) ((-378 . -306) T) ((-318 . -1185) 120753) ((-315 . -171) 120732) ((-312 . -171) T) ((-993 . -230) 120709) ((-904 . -362) T) ((-575 . -1265) 120696) ((-516 . -1265) 120673) ((-358 . -146) 120652) ((-358 . -144) 120603) ((-352 . -146) 120582) ((-352 . -144) 120533) ((-600 . -1176) 120509) ((-344 . -146) 120488) ((-344 . -144) 120439) ((-318 . -35) 120405) ((-473 . -1176) 120384) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120350) ((-378 . -1012) T) ((-108 . -146) T) ((-108 . -144) NIL) ((-45 . -234) 120300) ((-644 . -1087) T) ((-600 . -107) 120247) ((-483 . -130) T) ((-473 . -107) 120197) ((-239 . -1099) 120107) ((-862 . -376) 120091) ((-862 . -337) 120075) 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93395) ((-116 . -289) T) ((-1232 . -717) T) ((-1230 . -362) 93374) ((-1209 . -362) 93353) ((-1259 . -34) T) ((-117 . -1200) T) ((-108 . -230) 93335) ((-1165 . -102) T) ((-475 . -1087) T) ((-521 . -487) 93319) ((-728 . -34) T) ((-480 . -38) 93289) ((-140 . -34) T) ((-117 . -874) 93266) ((-117 . -876) NIL) ((-615 . -1028) 93149) ((-635 . -841) 93128) ((-1258 . -102) T) ((-294 . -102) T) ((-703 . -367) 93107) ((-117 . -1028) 93084) ((-389 . -708) 93068) ((-613 . -708) 93052) ((-45 . -308) 92856) ((-807 . -144) 92835) ((-807 . -146) 92814) ((-1269 . -381) 92793) ((-810 . -841) T) ((-1248 . -1087) T) ((-1146 . -228) 92740) ((-385 . -841) 92719) ((-1238 . -1188) 92685) ((-1238 . -1185) 92651) ((-1231 . -1185) 92617) ((-513 . -130) T) ((-1231 . -1188) 92583) ((-1210 . -1185) 92549) ((-1210 . -1188) 92515) ((-1238 . -35) 92481) ((-1238 . -95) 92447) ((-627 . -605) 92416) ((-599 . -605) 92385) ((-224 . -841) T) ((-1231 . -95) 92351) ((-1231 . -35) 92317) ((-1230 . -1099) T) ((-1107 . -638) 92304) ((-1210 . -95) 92270) ((-1209 . -1099) T) ((-586 . -150) 92252) ((-1067 . -348) 92231) ((-173 . -289) T) ((-117 . -376) 92208) ((-117 . -337) 92185) ((-1210 . -35) 92151) ((-860 . -306) T) ((-312 . -785) NIL) ((-312 . -782) NIL) ((-315 . -717) 92000) ((-312 . -717) T) ((-472 . -362) 91979) ((-358 . -348) 91958) ((-352 . -348) 91937) ((-344 . -348) 91916) ((-315 . -471) 91895) ((-1230 . -23) T) ((-1209 . -23) T) ((-709 . -1099) T) ((-705 . -130) T) ((-643 . -102) T) ((-475 . -708) 91860) ((-45 . -281) 91810) ((-105 . -1087) T) ((-68 . -605) 91792) ((-960 . -102) T) ((-855 . -102) T) ((-615 . -890) 91751) ((-1270 . -1087) T) ((-380 . -1087) T) ((-1199 . -1087) T) ((-1100 . -230) 91720) ((-82 . -1200) T) ((-1050 . -841) T) ((-942 . -841) 91699) ((-117 . -890) NIL) ((-773 . -910) 91678) ((-704 . -841) T) ((-529 . -1087) T) ((-498 . -1087) T) ((-354 . -1204) T) ((-351 . -1204) T) ((-343 . -1204) T) ((-263 . -1204) 91657) ((-246 . -1204) 91636) ((-531 . -851) T) ((-479 . -841) 91615) 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-605) 83480) ((-1100 . -1046) 83410) ((-574 . -910) T) ((-558 . -811) T) ((-558 . -910) T) ((-493 . -910) T) ((-135 . -1028) 83394) ((-224 . -95) T) ((-75 . -439) T) ((-75 . -394) T) ((0 . -605) 83376) ((-168 . -146) 83355) ((-168 . -144) 83306) ((-224 . -35) T) ((-49 . -605) 83288) ((-475 . -1046) T) ((-485 . -230) 83270) ((-482 . -958) 83254) ((-480 . -839) 83233) ((-216 . -230) 83215) ((-81 . -439) T) ((-81 . -394) T) ((-1133 . -34) T) ((-806 . -171) 83194) ((-722 . -102) T) ((-1016 . -605) 83161) ((-498 . -285) 83136) ((-315 . -376) 83105) ((-312 . -376) 83066) ((-312 . -337) 83027) ((-1072 . -605) 83009) ((-807 . -939) 82956) ((-652 . -130) T) ((-1219 . -144) 82935) ((-1219 . -146) 82914) ((-1161 . -102) T) ((-1160 . -102) T) ((-1154 . -102) T) ((-1146 . -1087) T) ((-1113 . -102) T) ((-221 . -34) T) ((-288 . -708) 82901) ((-1146 . -602) 82877) ((-586 . -308) NIL) ((-482 . -1087) 82855) ((-389 . -605) 82837) ((-508 . -841) T) ((-1137 . -228) 82787) ((-1238 . -1237) 82771) ((-1238 . -1224) 82748) ((-1231 . -1229) 82709) ((-1231 . -1224) 82679) ((-1231 . -1227) 82663) ((-1210 . -1208) 82624) ((-1210 . -1224) 82601) ((-613 . -605) 82583) ((-1210 . -1206) 82567) ((-689 . -910) T) ((-1161 . -283) 82533) ((-1160 . -283) 82499) ((-1154 . -283) 82465) ((-1067 . -1087) T) ((-1049 . -1087) T) ((-48 . -301) T) ((-315 . -890) 82431) ((-312 . -890) NIL) ((-1049 . -1056) 82410) ((-1107 . -876) 82392) ((-790 . -38) 82376) ((-263 . -631) 82324) ((-246 . -631) 82272) ((-691 . -1045) 82259) ((-588 . -1224) 82236) ((-1113 . -283) 82202) ((-318 . -171) 82133) ((-358 . -1087) T) ((-352 . -1087) T) ((-344 . -1087) T) ((-498 . -19) 82115) ((-1107 . -1028) 82097) ((-1089 . -150) 82081) ((-108 . -1087) T) ((-116 . -1045) 82068) ((-702 . -362) T) ((-498 . -596) 82043) ((-691 . -111) 82028) ((-435 . -102) T) ((-45 . -1136) 81978) ((-116 . -111) 81963) ((-627 . -711) T) ((-599 . -711) T) ((-806 . -512) 81896) ((-1025 . -1200) T) ((-933 . -150) 81880) ((-1159 . -450) 81811) ((-1153 . -1087) T) ((-1145 . -1087) T) ((-523 . -102) T) ((-518 . -102) 81761) ((-1129 . -638) 81735) ((-1112 . -450) 81686) ((-1074 . -1204) 81665) ((-773 . -1204) 81644) ((-771 . -1204) 81623) ((-62 . -1200) T) ((-475 . -605) 81575) ((-475 . -606) 81497) ((-1074 . -550) 81428) ((-984 . -1087) T) ((-773 . -550) 81339) ((-771 . -550) 81270) ((-480 . -410) 81239) ((-615 . -910) 81218) ((-452 . -1204) 81197) ((-722 . -308) 81184) ((-691 . -608) 81156) ((-397 . -605) 81138) ((-665 . -512) 81071) ((-654 . -25) T) ((-654 . -21) T) ((-452 . -550) 81002) ((-354 . -25) T) ((-354 . -21) T) ((-117 . -910) T) ((-117 . -811) NIL) ((-351 . -25) T) ((-351 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-263 . -25) T) ((-263 . -21) T) ((-246 . -25) T) ((-246 . -21) T) ((-83 . -383) T) ((-83 . -394) T) ((-133 . -608) 80984) ((-116 . -608) 80956) ((-1248 . -605) 80938) ((-1194 . -1099) T) ((-1194 . -23) T) ((-1154 . -308) 80823) ((-1113 . -308) 80810) ((-1067 . -708) 80678) ((-856 . -638) 80638) ((-933 . -970) 80622) 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. -372) 23136) ((-342 . -1253) 23113) ((-1017 . -1200) T) ((-861 . -289) T) ((-1219 . -512) 23060) ((-474 . -1200) T) ((-461 . -1200) T) ((-579 . -102) T) ((-1159 . -285) 22987) ((-615 . -450) 22966) ((-990 . -985) 22950) ((-1261 . -381) 22922) ((-515 . -1087) T) ((-117 . -450) T) ((-1180 . -102) T) ((-1079 . -1087) 22900) ((-1024 . -1087) T) ((-1102 . -93) T) ((-883 . -841) T) ((-350 . -1204) T) ((-1238 . -1045) 22783) ((-1100 . -376) 22752) ((-1231 . -1045) 22587) ((-1210 . -1045) 22377) ((-1238 . -111) 22246) ((-1231 . -111) 22067) ((-1210 . -111) 21836) ((-1194 . -308) 21823) ((-350 . -550) T) ((-364 . -605) 21805) ((-288 . -306) T) ((-589 . -1045) 21778) ((-588 . -1045) 21661) ((-360 . -1087) T) ((-321 . -1087) T) ((-250 . -605) 21622) ((-249 . -605) 21583) ((-993 . -130) T) ((-627 . -23) T) ((-684 . -408) 21550) ((-599 . -23) T) ((-648 . -102) T) ((-589 . -111) 21521) ((-588 . -111) 21390) ((-378 . -1087) T) ((-335 . -102) T) ((-168 . -289) 21301) ((-1209 . -839) 21254) ((-705 . 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 8f7ca44b..1b7e849c 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3439392482) +(30 . 3439752253) (4385 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -474,657 +474,658 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |deleteProperty!| |simpson| |representationType| - |quickSort| |c02aff| |monomRDEsys| |epilogue| |leftRankPolynomial| - |any?| |OMgetEndApp| |deepestTail| |symmetricRemainder| - |maximumExponent| |rst| |factorList| |eigenMatrix| |unitVector| - |pushFortranOutputStack| |simplifyExp| |cycleRagits| |cfirst| - 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|entry?| |rightFactorIfCan| LODO2FUN |digit| |cTanh| |ddFact| |comp| - |divideExponents| |extractTop!| |socf2socdf| |janko2| |setelt| - |prologue| |constantRight| |f02ajf| |hexDigit| |partitions| |remove| - |viewport3D| |groebnerFactorize| |addmod| |semicolonSeparate| - |goodnessOfFit| |nand| |character?| |tryFunctionalDecomposition?| - |coordinate| |continue| |pdf2df| |computePowers| |normFactors| - |hitherPlane| |copy| |createMultiplicationTable| |hypergeometric0F1| - |commonDenominator| |stirling1| |gcdcofact| |alternative?| |last| - |edf2efi| |firstSubsetGray| |ScanRoman| |expr| |integralBasis| - |setprevious!| |OMputEndApp| |assoc| |fortranCharacter| - |rootOfIrreduciblePoly| |low| |radicalSolve| |myDegree| |approxSqrt| - |lazyPrem| |raisePolynomial| |PollardSmallFactor| |match?| |rootsOf| - |infieldint| |branchIfCan| |shade| |autoCoerce| |s14aaf| |every?| - |e02bdf| |bandedHessian| |removeSinSq| |minPoly| - |createLowComplexityNormalBasis| |integralLastSubResultant| - |rationalFunction| |showTheSymbolTable| |nonLinearPart| |eulerE| - |algebraicCoefficients?| |localUnquote| |edf2ef| |bat| |f01brf| - |iipow| |variable| |leadingExponent| |deref| |mapUnivariate| - |partition| |rotate| |multMonom| |supDimElseRittWu?| |LiePoly| - |decompose| |romberg| |show| |weights| |iterators| |node?| - |listOfLists| |hMonic| |generalPosition| |sylvesterSequence| |fTable| - |cyclicGroup| |reindex| |parametric?| |fortranReal| |isOpen?| - |insertBottom!| |sortConstraints| |iiGamma| |mindeg| |optAttributes| - |operator| |nativeModuleExtension| |iiasinh| |trace| |htrigs| - |alternating| |d01amf| |cCsc| |partialNumerators| |makeResult| - |LyndonWordsList| |relationsIdeal| |secIfCan| |buildSyntax| - |rightFactorCandidate| |zoom| |squareTop| |smith| |viewPosDefault| - |semiResultantEuclidean1| |currentEnv| |makeTerm| |maxPoints| - |wholeRadix| |totalDifferential| |totolex| |processTemplate| - |inputOutputBinaryFile| |iCompose| |numberOfVariables| - |toseInvertible?| |points| |crest| |permanent| |selectAndPolynomials| - |next| |d01ajf| |changeMeasure| |resetNew| |shift| |bsolve| |mesh| - |morphism| |vconcat| |eulerPhi| |symmetricDifference| |setColumn!| - |binding| |outputFixed| |say| |showRegion| |OMsupportsSymbol?| = |nor| - |psolve| |stoseInvertibleSetsqfreg| |weakBiRank| |monicDecomposeIfCan| - |generalizedEigenvector| |createIrreduciblePoly| |reducedQPowers| - |readBytes!| |factorial| |nthFlag| |lfextendedint| |qinterval| - |evenInfiniteProduct| |fprindINFO| |gcdprim| |ellipticCylindrical| - |complexRoots| |factor1| |c06fuf| |complexEigenvectors| < |reset| - |subresultantSequence| |substring?| |rightRank| |fortranLiteral| - |lowerCase?| |rightExactQuotient| |OMputObject| |equiv?| - |basisOfCenter| |f02xef| |complement| |mapMatrixIfCan| > |addiag| - |relativeApprox| |eof?| |shufflein| |symmetric?| |push!| |laurentRep| - |getMultiplicationMatrix| |d01aqf| <= |expressIdealMember| |pastel| - |write| |cyclotomic| |suffix?| |coHeight| |perfectSqrt| |member?| - |subresultantVector| |cycleLength| |unary?| |multinomial| |save| - |lfintegrate| |s19acf| |qelt| |isMult| >= |shellSort| - |rightDiscriminant| |evaluate| |tubePoints| |OMgetError| |qsetelt| - |mapExponents| |definingEquations| |nextNormalPoly| - |monicRightFactorIfCan| |notelem| |prefix?| |plot| - |functionIsOscillatory| |hex| |physicalLength!| |realZeros| - |singleFactorBound| |compBound| |ceiling| |enqueue!| |xRange| - |denomRicDE| |powers| |isAbsolutelyIrreducible?| |convergents| - |s18def| |computeCycleEntry| |e02akf| |redPo| |d02bbf| |split!| - |yCoord| |magnitude| |yRange| |exponential1| + |iroot| |f07fef| - |headRemainder| |prime| |lquo| |clearCache| |inspect| |polyPart| - |basis| |intersect| |init| |zRange| |palglimint| - |iiacoth| |open?| - |diagonals| |eisensteinIrreducible?| |imagk| |numberOfHues| - |factorGroebnerBasis| |separateFactors| |map!| |zeroMatrix| |s13acf| / - |divide| |f2st| |semiDiscriminantEuclidean| |badNum| |setAdaptive| - |qsetelt!| |numberOfComputedEntries| |monomials| |split| |clip| - |createThreeSpace| |d01gaf| |rightMinimalPolynomial| |atanhIfCan| - |numberOfFactors| |compound?| |expt| |plenaryPower| |high| - |musserTrials| |infix?| |basisOfCentroid| |logical?| |plusInfinity| - |oddlambert| |lowerPolynomial| |cos2sec| |f07adf| |e01sef| |prime?| - |nextSubsetGray| |mask| |OMputSymbol| |rules| |minusInfinity| |fmecg| - |degree| |copyInto!| |pascalTriangle| |quadratic| |startPolynomial| - |nsqfree| |normInvertible?| |debug| |withPredicates| |mergeDifference| - |trigs| |bitLength| |column| |insert| |nextsousResultant2| |retract| - |iisec| |airyBi| D |minPoints3D| |flatten| |algSplitSimple| - |sumOfKthPowerDivisors| |setMaxPoints| |surface| |pToDmp| |numer| - |extractBottom!| |monicLeftDivide| |maxIndex| |acsch| |f04faf| - |scalarTypeOf| |showTheIFTable| |besselI| - |stoseInternalLastSubResultant| |lex| |denom| |stFunc2| - |blankSeparate| |mathieu24| |hue| |splitConstant| |represents| - |rewriteSetWithReduction| |heap| |d03faf| |product| - |curveColorPalette| |frobenius| |OMopenFile| |iifact| |finiteBound| - |lprop| |rightRegularRepresentation| |OMputError| |pi| |mainContent| - |mr| |numberOfOperations| |FormatRoman| |leftPower| |conditionP| - |type| |hclf| |cCoth| |variationOfParameters| |f01rdf| |s18acf| - |infinity| |hasPredicate?| |permutationGroup| |nullSpace| - |euclideanSize| |integral| |dictionary| |formula| |logGamma| - |curryLeft| |makeSeries| |sinhcosh| |componentUpperBound| |toroidal| - |mirror| |fortranDouble| |reducedDiscriminant| |reciprocalPolynomial| - |csch2sinh| |exp1| |hessian| |stopMusserTrials| |byteBuffer| - |toseSquareFreePart| |prepareDecompose| |submod| |integer?| |scopes| - |c06ekf| |d02gaf| |semiLastSubResultantEuclidean| |kernel| |merge| - |bubbleSort!| |getZechTable| |inHallBasis?| |dimensionsOf| |e02aef| - |basisOfRightNucleus| |s18dcf| |exteriorDifferential| |ldf2vmf| |draw| - |brillhartTrials| |palgLODE0| |internalLastSubResultant| |print| - |KrullNumber| |outerProduct| |bumptab1| |nrows| |rationalPoint?| - |purelyAlgebraicLeadingMonomial?| |subResultantsChain| - |listRepresentation| |increment| |OMcloseConn| |mantissa| |diff| - |resolve| |rdregime| |discriminant| |ncols| |conditionsForIdempotents| - |collect| |alphabetic| |ranges| |copies| |error| |radix| - |algebraicVariables| |aQuartic| |Si| |extractClosed| |superscript| - |currentCategoryFrame| |removeZeroes| |algint| |cot2tan| |assert| - |mainMonomials| |OMsupportsCD?| |d01bbf| |sumSquares| |inf| - |numFunEvals| |subTriSet?| |makeObject| |getProperties| |checkRur| - |e02def| |clearTheSymbolTable| |certainlySubVariety?| |imports| - |acoshIfCan| |pushuconst| |empty| |objectOf| |delay| |cycleSplit!| - |e04ycf| |external?| |primlimitedint| |antisymmetric?| |setleft!| - |digamma| |coef| |node| |shiftRight| |iiacsch| |sn| |atrapezoidal| - |argumentListOf| |setleaves!| |groebSolve| |conjugate| |pop!| - |changeWeightLevel| |recolor| |figureUnits| |d01apf| |pol| |leftMult| - |contours| |meshPar2Var| |selectFiniteRoutines| |iiacsc| |reverse!| - |regime| |iicsch| |back| |leftExactQuotient| |printCode| - |OMputEndError| |shrinkable| |polyRicDE| |identitySquareMatrix| - |rewriteIdealWithRemainder| |weierstrass| |nextPrimitivePoly| - |showSummary| |showTheRoutinesTable| |unexpand| |nthCoef| |besselY| - |cAcosh| |e02ajf| |rightZero| |lepol| |erf| |super| - |semiResultantEuclidean2| |stopTableGcd!| |putGraph| |dimension| - |multiEuclideanTree| |possiblyInfinite?| |returnType!| |selectfirst| - |closeComponent| |s13aaf| |skewSFunction| |linkToFortran| - |showAttributes| |numberOfFractionalTerms| |makeSin| |factorset| |and| - |critM| |degreeSubResultant| |resize| |nodeOf?| - |numberOfIrreduciblePoly| |fintegrate| |wordInStrongGenerators| - |discriminantEuclidean| |completeEval| |Hausdorff| |or| |eq?| |repSq| - |noncommutativeJordanAlgebra?| |dilog| |direction| |doubleFloatFormat| - |lazyIrreducibleFactors| |checkForZero| |content| |zerosOf| |sort!| - |xor| |extend| |tanintegrate| |asecIfCan| |stoseSquareFreePart| |sin| - |primeFactor| |rightGcd| |bright| |removeRedundantFactorsInContents| - |ramifiedAtInfinity?| |nextsubResultant2| |hspace| |case| |option?| - |pmintegrate| |removeConstantTerm| |cos| |unrankImproperPartitions1| - |squareMatrix| |rootBound| |s17ahf| |component| - |lastSubResultantElseSplit| |Zero| |expenseOfEvaluationIF| - |dimensionOfIrreducibleRepresentation| |hasoln| |tan| |compose| - |iiatanh| |completeEchelonBasis| |inGroundField?| |bracket| |dmpToP| - |One| |exprHasLogarithmicWeights| |idealiser| |s17def| |cot| - |property| |setOfMinN| |Ci| |functionIsContinuousAtEndPoints| - |triangularSystems| |stosePrepareSubResAlgo| |drawCurves| |OMputAttr| - |standardBasisOfCyclicSubmodule| |sec| |ocf2ocdf| |sPol| |reducedForm| - |branchPointAtInfinity?| |close!| |c05nbf| |capacity| - |repeatUntilLoop| |label| |trapezoidalo| |csc| |palgextint| |string?| - |swap!| |removeDuplicates!| |OMconnOutDevice| |root?| |totalGroebner| - |equation| |torsion?| |asin| |reduced?| |indicialEquation| |units| - |OMsetEncoding| |exprex| |f02aff| |getRef| |cothIfCan| |Lazard2| - |linearMatrix| |ratDsolve| |acos| |explicitEntries?| |prevPrime| - |list| |validExponential| |laplacian| |elt| |unknown| |leftQuotient| - |irreducible?| |outputMeasure| |atan| |lllp| |float?| |car| - |findBinding| |check| |applyRules| |s17adf| |stFunc1| |subMatrix| - |ListOfTerms| |acot| |summation| |basisOfRightNucloid| |cdr| |opeval| - |randomR| |df2mf| |perfectNthPower?| |setProperties!| |s14baf| - |interReduce| |asec| |edf2fi| |leftRecip| |declare| |setDifference| - |nthr| |invertibleElseSplit?| |reducedSystem| |extendedResultant| - |setClipValue| |extendedEuclidean| |code| |setIntersection| |laguerre| - |getProperty| |besselJ| |B1solve| |var1StepsDefault| |parts| - |ScanArabic| |predicates| |pr2dmp| |float| |antiCommutative?| - |palgLODE| |setUnion| |basisOfLeftNucleus| |virtualDegree| |solid| - |constructor| |enterInCache| |factorFraction| |delete!| |interpolate| - |quasiRegular?| |weighted| |apply| |normalizedAssociate| |andOperands| - |endSubProgram| |removeZero| |iiasec| |toseInvertibleSet| - |removeSuperfluousCases| |useNagFunctions| |trapezoidal| - |setMaxPoints3D| |semiSubResultantGcdEuclidean1| |f04qaf| - |sizeMultiplication| |redmat| |option| |linSolve| |univariateSolve| - |size| |finiteBasis| |rightExtendedGcd| |innerint| |intPatternMatch| - |OMmakeConn| |makeUnit| |triangular?| |addPoint| |newTypeLists| - |minRowIndex| |closed?| |bfEntry| |semiDegreeSubResultantEuclidean| - |rightTrim| |newLine| |inputBinaryFile| |expint| |binomial| - |factorPolynomial| |s17agf| |wronskianMatrix| |pushucoef| - |coercePreimagesImages| |leftTrim| |tanh2coth| |wholeRagits| - |extendIfCan| |RemainderList| |first| |e04mbf| |extensionDegree| - |alphanumeric| |Beta| |expintegrate| |changeVar| |RittWuCompare| - |llprop| |e02adf| |rest| |rk4f| |complexNormalize| |bindings| - |appendPoint| |modularGcd| |irreducibleRepresentation| - |stoseInvertibleSet| GE |rootKerSimp| |oneDimensionalArray| - |substitute| |lyndonIfCan| |branchPoint?| |expextendedint| |s17dhf| - |symmetricGroup| |shiftLeft| |showAllElements| GT |setfirst!| - |sqfrFactor| |removeDuplicates| |listexp| |poisson| |mapUp!| - |tubeRadiusDefault| |internal?| |fortranTypeOf| |iiasech| - |mainExpression| |vark| LE |unrankImproperPartitions0| - |continuedFraction| |fortranCompilerName| |constDsolve| |someBasis| - |cAtan| |distribute| |dequeue| |key?| |s14abf| LT |gderiv| - |removeRedundantFactors| |padicallyExpand| |upperCase| |signatureAst| - |quoByVar| |ip4Address| |unvectorise| |consnewpol| |s17dcf| - |eigenvalues| |zero| |factorAndSplit| |leftDiscriminant| - |solveInField| |reduceLODE| |crushedSet| |sort| |printHeader| - |OMputAtp| |cyclicSubmodule| |indicialEquations| |computeInt| |f01maf| - |inRadical?| |fglmIfCan| |insertRoot!| |leadingSupport| |tower| - |ef2edf| |critT| |minGbasis| |presub| |fortran| |And| - |restorePrecision| |puiseux| |double| |nlde| |argscript| |coth2trigh| - |ramified?| |e02ahf| |dAndcExp| |selectsecond| |defineProperty| - |explicitlyEmpty?| |Or| |startTableGcd!| |callForm?| - |numberOfImproperPartitions| |makeCos| |lastSubResultant| |divisor| - |rewriteIdealWithQuasiMonicGenerators| |numberOfChildren| |dimensions| - |pattern| |Not| |inv| |exponential| |minset| |mapmult| |testModulus| - |redpps| |random| |term| |tracePowMod| |gethi| |aCubic| |ground?| - |basisOfRightAnnihilator| |transcendentalDecompose| - |removeRoughlyRedundantFactorsInContents| |loadNativeModule| - |minimize| |f02bjf| |systemSizeIF| |jordanAlgebra?| |acotIfCan| - |useSingleFactorBound?| |ground| |subHeight| |rangeIsFinite| - |bombieriNorm| |constantOpIfCan| |abs| |leastPower| - |pmComplexintegrate| |removeRoughlyRedundantFactorsInPol| |condition| - |multiEuclidean| |leadingMonomial| |complexNumeric| |getVariableOrder| - |createNormalPrimitivePoly| |mapExpon| |exponentialOrder| - |OMgetString| |zeroSquareMatrix| |complexIntegrate| |polygon?| - |rightRecip| |message| |leadingCoefficient| |primeFrobenius| |delta| - |f02aef| |splitNodeOf!| |problemPoints| |divergence| |rational?| - |topPredicate| |create3Space| |kernels| |associative?| - |leftCharacteristicPolynomial| |primitiveMonomials| |eq| |declare!| - |f04asf| |extractProperty| |solveLinear| |birth| |datalist| - |increasePrecision| |prepareSubResAlgo| |externalList| |explimitedint| - |monomialIntegrate| |iter| |reductum| |monomRDE| |univariate| |depth| - |sample| |hdmpToP| |viewWriteAvailable| |subst| - |solveLinearPolynomialEquationByRecursion| |goto| |simpsono| - |addPoint2| |SturmHabichtCoefficients| |rootSplit| |setFormula!| - |youngGroup| |stopTableInvSet!| |rroot| |gcdPolynomial| - |stronglyReduced?| |hasSolution?| |drawComplexVectorField| |mat| - |generalLambert| |c05adf| |csubst| |cons| |OMgetType| - |associatedEquations| |simpleBounds?| |uniform| |ratDenom| |factor| - |leftAlternative?| |extendedIntegrate| |shallowExpand| |s15aef| - |rootPower| |zeroDimPrimary?| |cAcsc| |function| |iisech| |script| - |addBadValue| |sqrt| |OMencodingXML| |composites| - |integralBasisAtInfinity| |iomode| |groebnerIdeal| |box| - |setsubMatrix!| |retractable?| |lexTriangular| |bipolar| |lambda| - |real| |beauzamyBound| |e01bhf| |pushdterm| |tanhIfCan| |size?| - |adaptive3D?| |OMgetInteger| |eval| |d02kef| |imag| |generalTwoFactor| - |segment| |numberOfDivisors| |root| |getStream| |printStats!| - |parents| |objects| |LyndonCoordinates| |precision| - |possiblyNewVariety?| |acosIfCan| |mdeg| |tex| |directProduct| |pow| - |exp| |tensorProduct| |aLinear| |mkAnswer| |selectNonFiniteRoutines| - |matrixDimensions| |base| |over| |complementaryBasis| |composite| - |cSin| |simplifyPower| |getCode| |lifting1| |setAttributeButtonStep| - |subtractIfCan| |isOp| |source| |Vectorise| |log| - |regularRepresentation| |clikeUniv| |invertIfCan| |leftScalarTimes!| - |brace| |cTan| |diagonal| |dflist| |orthonormalBasis| |e04fdf| - |genericLeftTraceForm| |realSolve| |removeRedundantFactorsInPols| - |changeBase| |destruct| |topFortranOutputStack| |elColumn2!| - |linearAssociatedExp| |halfExtendedResultant1| |compile| |rk4| - |laplace| |f01qcf| |relerror| |innerSolve| |safeFloor| |extractIfCan| - |f04mbf| |create| |usingTable?| |associates?| |mapdiv| |uniform01| - |close| |nextPrimitiveNormalPoly| |thenBranch| |subQuasiComponent?| - |makeFloatFunction| |closedCurve| |finite?| |writable?| |acschIfCan| - |dominantTerm| |order| |inverseIntegralMatrix| |solve| - |linearDependence| |recur| |ravel| |s21bbf| |dmpToHdmp| - |rectangularMatrix| |rspace| |display| |leviCivitaSymbol| |monomial| - |linearPolynomials| |separate| |measure| |augment| |reshape| - |fixPredicate| |initTable!| |squareFreePart| |polyRDE| |drawToScale| - |multivariate| |iitanh| |e01bgf| |radPoly| |imagJ| |hyperelliptic| - |mainForm| |lcm| |arity| |stopTable!| |optpair| |variables| - |leastMonomial| |less?| |center| |expIfCan| |scan| |infRittWu?| |cup| - |messagePrint| |viewThetaDefault| |cPower| |trivialIdeal?| |pquo| - |iiatan| |extension| |exprHasAlgebraicWeight| |monic?| |leftZero| - |append| |numerator| |getExplanations| |highCommonTerms| - |radicalSimplify| |cAcoth| |insertMatch| |previous| |complexLimit| - |nextColeman| |compactFraction| |gcd| |key| |roman| |OMUnknownCD?| - |duplicates| |refine| |index?| |internalZeroSetSplit| |any| |false| - |integers| |splitSquarefree| |distance| |omError| |and?| - |clipParametric| |lifting| |binaryTree| |contractSolve| |goodPoint| - |leftNorm| |resultantReduit| |filename| |ptFunc| |localAbs| |taylor| - |insertTop!| |movedPoints| |rischNormalize| |row| |expandPower| - |rightLcm| |countRealRoots| |elliptic?| |not?| |se2rfi| |laurent| - |cyclic| |sturmVariationsOf| |polarCoordinates| |monicModulo| - |OMgetAttr| |rowEchelonLocal| |univariatePolynomial| |parse| |inR?| - |intcompBasis| |squareFreePrim| |gramschmidt| |rationalPower| |escape| - |initial| |rationalPoints| |shiftRoots| |setCondition!| |sum| |#| - |moduloP| |algebraicDecompose| |parabolicCylindrical| |OMgetEndBind| - |UP2ifCan| |viewWriteDefault| |cosSinInfo| |cylindrical| - |realEigenvalues| |UpTriBddDenomInv| |tube| |clipPointsDefault| - |constantIfCan| |internalSubQuasiComponent?| |OMreceive| |pile| |lp| - |genericLeftTrace| |trueEqual| |Ei| |solveLinearlyOverQ| |palgRDE| - |makeRecord| |OMputEndBind| |axes| |fibonacci| |binaryFunction| - |OMputFloat| |twoFactor| |iiexp| |ratpart| |rightDivide| |karatsuba| - |read!| |monicCompleteDecompose| |leftOne| |f02awf| - |radicalEigenvalues| |laguerreL| |setLength!| |explogs2trigs| |ode1| - |resetAttributeButtons| |coshIfCan| |modularGcdPrimitive| |positive?| - |graphState| |numeric| |ode| |rightPower| |fortranLogical| - |selectIntegrationRoutines| |integralRepresents| |rangePascalTriangle| - |groebner?| |seriesSolve| |nthExpon| |radical| |interpretString| - |rightCharacteristicPolynomial| |limitedint| |cycleEntry| |vector| - |setAdaptive3D| |rotatey| |times!| - |generalizedContinuumHypothesisAssumed?| |setLabelValue| |normalForm| - |exponent| |conditions| |iiacos| |c06gqf| |differentiate| - |identification| |exactQuotient| |sin2csc| |subResultantChain| |fi2df| - |readIfCan!| |diagonalProduct| |match| |addMatchRestricted| - |cyclicEqual?| |basicSet| |double?| |numberOfCycles| |zeroDim?| - |atom?| |rightAlternative?| |showFortranOutputStack| |dualSignature| - |innerEigenvectors| |bytes| |rule| |index| |makeSUP| - |leadingCoefficientRicDE| |elseBranch| |makingStats?| - |roughUnitIdeal?| |reduceByQuasiMonic| |e04dgf| |splitLinear| - |legendre| |optimize| |largest| |nextNormalPrimitivePoly| - |initializeGroupForWordProblem| |equiv| |f01ref| |lazyResidueClass| - |quasiMonic?| |cSinh| |transform| |mainKernel| |satisfy?| |anticoord| - |null?| |fixedPoint| |imagj| |twist| |recip| |OMgetEndError| |length| - |clearTheFTable| |pair| |dmp2rfi| |createPrimitiveElement| - |OMgetEndAttr| |nilFactor| |anfactor| |tanNa| |scripts| |reflect| - |unprotectedRemoveRedundantFactors| |btwFact| |frst| |iExquo| - |bumptab| |predicate| |inverseLaplace| |outputList| |cap| |pack!| - |removeSinhSq| |sizeLess?| |f04arf| |roughBase?| - |selectMultiDimensionalRoutines| |diophantineSystem| |variable?| - |f01mcf| |asinIfCan| |binarySearchTree| |rootOf| |void| |getOrder| - |karatsubaOnce| |exists?| |symbolTableOf| |s21baf| |powern| |sts2stst| - |minus!| |ran| |cCot| |dfRange| |setFieldInfo| |value| |calcRanges| - |result| |genericLeftDiscriminant| |exactQuotient!| - |createGenericMatrix| |middle| |OMUnknownSymbol?| |bandedJacobian| - |iteratedInitials| |halfExtendedResultant2| |leftGcd| |properties| - |genericLeftNorm| |characteristicPolynomial| |traverse| |insert!| - |var2StepsDefault| |deepCopy| |elRow2!| |corrPoly| |mkIntegral| - |integralDerivationMatrix| |unit?| |mainDefiningPolynomial| |terms| - |translate| |meshPar1Var| |octon| |matrixConcat3D| |find| |e02bcf| - |rur| |cyclicParents| |mapDown!| |one?| |asechIfCan| |central?| - |polyred| |truncate| |totalLex| |boundOfCauchy| |primitive?| - |normalise| |bezoutResultant| |radicalEigenvector| |square?| - |decrease| |quoted?| |s13adf| |hash| |setref| - |linearlyDependentOverZ?| |listConjugateBases| |zero?| |parameters| - |entry| |c06gsf| |hexDigit?| |rightNorm| |cycle| |child?| |count| - |superHeight| |symmetricPower| |tableau| |linearAssociatedOrder| - |imagK| |reify| |rCoord| |adjoint| |SturmHabicht| |userOrdered?| - |multisect| |cRationalPower| |elementary| |green| |solveid| |dot| - |exprHasWeightCosWXorSinWX| |makeYoungTableau| |scaleRoots| - |expandTrigProducts| |inverseIntegralMatrixAtInfinity| |elem?| - |axesColorDefault| |parabolic| |e01bff| |maxint| |isTimes| |host| - |xCoord| |showClipRegion| |errorInfo| |iisqrt3| - |univariatePolynomials| |deleteRoutine!| |OMputEndAttr| |quartic| - |cAsech| |tan2trig| |setRow!| |infinite?| |returns| |d02bhf| - |hermiteH| |cyclicCopy| |setEpilogue!| F2FG |OMread| |qfactor| - |preprocess| |abelianGroup| |firstDenom| |internalDecompose| |jacobi| - |ode2| |derivative| |selectOptimizationRoutines| |viewDeltaXDefault| - |mkcomm| |localReal?| |Aleph| |reduce| |checkPrecision| |OMgetAtp| - |light| |schema| |clipWithRanges| |getMatch| |quadraticNorm| - |quasiAlgebraicSet| |lazyPquo| |groebgen| |coefChoose| |coerceImages| - |setStatus!| |rightQuotient| |generalSqFr| |f02abf| |LazardQuotient| - |bernoulliB| |geometric| |mightHaveRoots| |retractIfCan| |Is| - |debug3D| |top| |intensity| |atoms| |lagrange| |quotient| |pointData| - |mesh?| |fortranComplex| |stoseInvertible?sqfreg| |indices| - |viewDefaults| |search| |dim| |pdf2ef| |complex?| |definingPolynomial| - |clearFortranOutputStack| |unmakeSUP| |loopPoints| |alphanumeric?| - |showScalarValues| |solve1| |rubiksGroup| |powerAssociative?| - |number?| |complexForm| |paraboloidal| |leadingBasisTerm| |iiperm| - 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|OMgetEndBVar| |computeBasis| |phiCoord| |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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|interReduce| |saturate| + |internalLastSubResultant| |normalElement| |dioSolve| |physicalLength| + |degreeSubResultant| |clikeUniv| |inc| |denomLODE| |append| |red| + |generalizedContinuumHypothesisAssumed| |findBinding| |df2ef| + |rootProduct| |unitNormalize| |degreePartition| |computePowers| + |redPol| |nil| |gcd| |expressIdealMember| |repeatUntilLoop| |expint| + |iidsum| |left| |presuper| |initiallyReduce| |getGraph| |eigenvectors| + |s17ahf| |false| |resultant| |lastSubResultantEuclidean| + |leftFactorIfCan| |fixedDivisor| |completeEchelonBasis| |isobaric?| + |formula| |lambda| |createGenericMatrix| |symmetric?| |right| + |subResultantsChain| |buildSyntax| |mantissa| |genericRightTrace| + |f01brf| |besselY| |represents| |largest| |approximate| + |rightQuotient| |totalDegree| |readLineIfCan!| |setPredicates| |bat1| + |mdeg| |UnVectorise| |halfExtendedResultant2| |s21bdf| |complex| + |laplacian| |tanAn| |mainVariable| |squareFree| |depth| |addPoint2| + |sayLength| |precision| |rewriteSetWithReduction| |quasiRegular?| + |cubic| |BumInSepFFE| |mkIntegral| |stoseLastSubResultant| + |addPointLast| |drawCurves| |curve| |#| |e01bff| |figureUnits| + |ScanRoman| |pointSizeDefault| |nrows| |conjugates| + |exprHasAlgebraicWeight| |internalIntegrate| |s17akf| |generators| + |OMencodingXML| |measure2Result| |close| |antiCommutator| + |solveLinearlyOverQ| |packageCall| |ncols| |contractSolve| + |approximants| |OMputVariable| |getSyntaxFormsFromFile| |surface| |mr| + |associatedSystem| |digit| |integralMatrix| |primitiveElement| + |showSummary| |script| |host| |constantIfCan| |showClipRegion| + |topFortranOutputStack| |expintfldpoly| |remove| |display| + |OMgetFloat| |safetyMargin| |roughUnitIdeal?| |cSec| BY |exponent| + |critMTonD1| |ratDsolve| |enqueue!| |possiblyInfinite?| |f07adf| + |chvar| |power!| |npcoef| |showAttributes| |headReduced?| + |reciprocalPolynomial| |musserTrials| |monomialIntegrate| + |pseudoRemainder| |last| |listConjugateBases| |pointPlot| + |defineProperty| |product| |tex| |xn| |minPoly| |oddlambert| + |leftPower| |sylvesterSequence| |assoc| |gcdPrimitive| + |computeCycleLength| |trailingCoefficient| |ellipticCylindrical| + |mkAnswer| |critpOrder| |quoted?| |e02aef| |initials| + |viewThetaDefault| |singRicDE| |subresultantSequence| |empty?| + |mapMatrixIfCan| |sech2cosh| |getMatch| |symbol| |representationType| + |rationalApproximation| |expPot| |input| |eigenvector| + |branchPointAtInfinity?| |iicot| |expenseOfEvaluationIF| + |FormatArabic| |notOperand| |expression| |medialSet| |complement| + |selectSumOfSquaresRoutines| |digit?| |library| |internalInfRittWu?| + |printInfo| |conditionsForIdempotents| |preprocess| |iisinh| + |pointColorPalette| |doubleComplex?| |cCosh| |mainCoefficients| + |integer| |solid| |e02zaf| |cAcot| |hasoln| |quasiMonic?| |romberg| + |sin?| |binding| |leftRankPolynomial| |relerror| |taylorIfCan| + |printInfo!| |mainKernel| |extractSplittingLeaf| |or?| |substring?| + |ReduceOrder| |factorSFBRlcUnit| |univariate?| |lifting| + |splitDenominator| |label| |any| |laurentRep| |iiasinh| |isPlus| + |setStatus| |minPoints| |logGamma| |bumprow| |close!| |removeZeroes| + |set| |bubbleSort!| |OMputObject| |wordInGenerators| |getProperties| + |genericLeftDiscriminant| |d02cjf| |node?| |rule| |blankSeparate| + |normalForm| |comp| |debug3D| |leftRank| |associator| + |algebraicDecompose| |iteratedInitials| |children| |unmakeSUP| + |divideIfCan!| |lazyPseudoQuotient| |iiexp| |changeThreshhold| + |extensionDegree| |nextSubsetGray| |numericalIntegration| + |realElementary| |groebSolve| |rightRegularRepresentation| + |changeBase| |f02bbf| |headAst| |nodes| |singularitiesOf| |expIfCan| + |ip4Address| |minPoints3D| |cyclePartition| |relativeApprox| |coth| + |extractTop!| |euclideanSize| |internal?| |palgRDE0| |basisOfCenter| + |euclideanGroebner| |bit?| |noKaratsuba| |meshPar1Var| |list| |sech| + |froot| |morphism| |commutativeEquality| |numberOfDivisors| |say| + |constructor| |ideal| |plenaryPower| |polyred| |mathieu11| + |graphCurves| |car| |csch| |pushup| |primextintfrac| + |numberOfFractionalTerms| |getDatabase| |unary?| |e04naf| |move| + |genericRightMinimalPolynomial| |cdr| |asinh| |subscriptedVariables| + |s14baf| |void| |makeViewport3D| |numeric| |addiag| |imports| + |setDifference| |showAll?| |ptFunc| |listYoungTableaus| |acosh| + |option| |ffactor| |df2fi| |notelem| |radical| |monicRightDivide| + |nullary?| |setIntersection| |pair?| |const| |lazyPrem| |atanh| + |identitySquareMatrix| |palglimint| |hash| |findCycle| + |nextNormalPrimitivePoly| |vedf2vef| |beauzamyBound| |setUnion| + |OMUnknownSymbol?| |algebraicVariables| |acoth| |count| |show| + |e02bef| |compound?| |tanintegrate| |getMultiplicationTable| |s21baf| + |clearTheIFTable| |OMUnknownCD?| |apply| |asech| |factorList| = + |inrootof| |callForm?| |rdregime| |OMgetEndApp| + |semiIndiceSubResultantEuclidean| |unravel| |explicitlyFinite?| + |partialFraction| |trace| |transpose| |cross| |commutative?| + |readable?| |size| |subSet| |stopTableGcd!| |lineColorDefault| + |multiple| < |head| |reducedContinuedFraction| |s17dhf| + |symmetricPower| |imaginary| |mergeDifference| |applyQuote| |repSq| > + |shallowExpand| |cExp| |triangular?| |rootRadius| |frobenius| + |rightTrim| |LazardQuotient| |toseSquareFreePart| <= |cyclicCopy| + |write!| |permutationRepresentation| |trivialIdeal?| |completeEval| + |removeZero| |modTree| |leftTrim| |symmetricGroup| |first| >= + |pushdown| |length| |changeNameToObjf| |irreducibleFactors| + |LowTriBddDenomInv| |e01daf| |schema| |iflist2Result| + |subResultantChain| |rest| |ruleset| |initTable!| |scripts| + |choosemon| |antisymmetric?| |deriv| |lepol| |substitute| + |setAdaptive3D| |laurentIfCan| |virtualDegree| |mappingAst| + |composites| |stoseIntegralLastSubResultant| |readIfCan!| + |removeDuplicates| |iisin| |diagonals| |pleskenSplit| + + |removeRedundantFactorsInPols| |mainMonomial| |coth2tanh| |generate| + |quasiMonicPolynomials| |expandLog| |reopen!| |f02fjf| |suchThat| - + |unvectorise| |s14abf| |FormatRoman| |matrixConcat3D| + |mapUnivariateIfCan| |nativeModuleExtension| |pattern| |zero| / + |plotPolar| |e02bdf| |updateStatus!| |squareFreeFactors| |incrementBy| + |finiteBasis| |characteristicSet| |OMputEndAtp| |dequeue!| |f02axf| + |iicsch| |tanQ| |s13aaf| |expand| |convergents| |divideIfCan| + |bezoutMatrix| |OMputSymbol| |And| |viewPhiDefault| |squareMatrix| + |empty| |showScalarValues| |filterWhile| |prinb| |positiveRemainder| + |algDsolve| |cyclicParents| |e01bef| |Or| |distance| |changeMeasure| + |filterUntil| |testDim| |mainMonomials| |cPower| |squareFreePart| + |message| |Not| |qroot| |traverse| |birth| |GospersMethod| + |getGoodPrime| |select| |antiAssociative?| |getRef| |universe| + |primintfldpoly| |leftExtendedGcd| |sqfree| |tensorProduct| |s21bcf| + |controlPanel| |nthFactor| |removeSuperfluousQuasiComponents| + |internalAugment| |nil?| |intermediateResultsIF| |extendedEuclidean| + |padicallyExpand| |digits| |palglimint0| |OMwrite| |edf2ef| |makeFR| + |compiledFunction| |badValues| |varList| |iitanh| |double?| |omError| + |subspace| |f02xef| |infiniteProduct| |getMultiplicationMatrix| + |evenlambert| |getOperator| |loopPoints| |zeroSquareMatrix| |elem?| + |nullity| |negative?| |style| |atrapezoidal| |rangePascalTriangle| + |cons| |OMgetObject| |outputBinaryFile| |bumptab1| |graphImage| + |polygon?| |delay| |prevPrime| |cAcoth| |removeSuperfluousCases| + |retract| |rischNormalize| |fglmIfCan| |selectNonFiniteRoutines| + |lazyPquo| |s19adf| |socf2socdf| |stoseInvertibleSetsqfreg| + |expintegrate| |compdegd| |coerceP| |setMinPoints3D| |jacobiIdentity?| + |modifyPoint| |matrix| |iisqrt3| |basisOfRightAnnihilator| + |numberOfIrreduciblePoly| |definingEquations| |rur| + |genericLeftMinimalPolynomial| |doubleDisc| |useEisensteinCriterion| + |rotate!| |sort| |completeSmith| |palgextint| |limitedIntegrate| + |matrixDimensions| |parent| |indiceSubResultantEuclidean| |resize| + |iomode| |shiftRoots| |rk4a| |outputFixed| |extension| |sumOfSquares| + |wrregime| |cAsinh| |imagI| |createLowComplexityNormalBasis| + |removeIrreducibleRedundantFactors| |internalSubPolSet?| |magnitude| + |graphState| |f01rcf| |setScreenResolution3D| |linSolve| |status| + |source| |scripted?| |createLowComplexityTable| |normDeriv2| |subst| + |sinh2csch| |s17dgf| |optpair| |leftUnit| |listBranches| + |checkForZero| |box| |slex| |bindings| |terms| |backOldPos| |random| + |quadratic?| |cLog| |quadratic| |endOfFile?| |d02bhf| |monomRDE| + |log2| |lazyPremWithDefault| |c06fuf| |increase| |f02aef| |dequeue| + |numberOfComposites| |gcdcofact| |permanent| |localAbs| |extendIfCan| + |LyndonCoordinates| |ptree| |noncommutativeJordanAlgebra?| + |interpretString| |coshIfCan| |compose| |linearMatrix| |limitedint| + |scan| |outlineRender| |subNode?| |hyperelliptic| |color| |escape| + |monicLeftDivide| |plus| |f02aaf| |OMputInteger| |e02adf| |isOpen?| + |obj| |iiasin| |f2st| |generateIrredPoly| + |rewriteIdealWithQuasiMonicGenerators| |purelyTranscendental?| + |associatorDependence| |constantCoefficientRicDE| |basisOfNucleus| + |recur| |cache| |objects| |setLabelValue| |showTheFTable| |module| + |lyndonIfCan| |keys| |poisson| |dihedralGroup| |rCoord| |OMReadError?| + |toseInvertibleSet| |parents| |base| |extractBottom!| |mainVariables| + |linear?| |symmetricRemainder| |s01eaf| |fracPart| |iiGamma| + |basisOfMiddleNucleus| |testModulus| |oddintegers| |summation| + |partialNumerators| |interval| |setValue!| |polarCoordinates| |paren| + |sechIfCan| |times| |drawStyle| |deleteProperty!| |iiacsc| + |separateFactors| |binaryFunction| |isQuotient| |signatureAst| |node| + |generalizedInverse| |normal01| |rootSplit| |myDegree| |bernoulli| + |key| |outputAsTex| |karatsuba| |processTemplate| |OMputApp| |root| + |list?| |minGbasis| |meshFun2Var| |high| |lflimitedint| + |quadraticForm| |antiCommutative?| |curryRight| |e02akf| |adaptive?| + |maxColIndex| |coHeight| |filename| |mainForm| |nand| |diagonal| + |reduceBasisAtInfinity| |binary| |unitCanonical| |symbolTable| |row| + |selectAndPolynomials| |setEpilogue!| |monom| |char| |inspect| |not?| + |subMatrix| |concat!| |finite?| |cot2tan| |minordet| |hostPlatform| + |upperCase?| |setTex!| |setButtonValue| |entry?| |parse| |Ei| + |OMlistSymbols| |height| |cfirst| |constantLeft| |showTheIFTable| + |matrixGcd| |numberOfCycles| |pdct| |cCoth| |cscIfCan| |OMgetType| + |characteristicSerie| |common| |OMreadFile| |shallowCopy| |members| + |multiset| |flexible?| |dec| |pushucoef| |OMgetEndAttr| + |indiceSubResultant| |llprop| |coerceS| |reverseLex| |weight| + |toseInvertible?| |approxNthRoot| |vspace| |exponential| |zerosOf| + |region| |extractIfCan| |showTypeInOutput| |null| |collectQuasiMonic| + |innerEigenvectors| |youngGroup| |previous| |float| |intcompBasis| + |compBound| |increment| |exponentialOrder| |zag| |nonSingularModel| + |c05pbf| |not| |lazyVariations| |makeVariable| |LazardQuotient2| + |groebnerFactorize| |mainContent| |lazyResidueClass| + |chainSubResultants| |typeLists| |and| |less?| |realSolve| |updatD| + |gcdPolynomial| |tail| |yellow| |alternating| |integralAtInfinity?| + |copy!| |d02bbf| |setleft!| |s18adf| |or| |mapDown!| |mapUp!| + |normalizedAssociate| |highCommonTerms| |legendreP| |orOperands| + |minRowIndex| |raisePolynomial| |pushFortranOutputStack| |xor| + |stoseInternalLastSubResultant| |binaryTree| |fortranCarriageReturn| + |messagePrint| |ratPoly| |Lazard| |critM| |expandPower| + |sizeMultiplication| |popFortranOutputStack| |case| + |resultantReduitEuclidean| |numFunEvals3D| |startTableGcd!| |dihedral| + |createZechTable| |fortranDouble| |characteristic| |changeName| + |usingTable?| |equation| |Zero| |OMgetError| |diagonal?| |lowerCase?| + |iiasech| |prefixRagits| |OMbindTCP| |operator| |nonQsign| + |localReal?| |split!| |One| |extractClosed| |readLine!| |invertible?| + |invertibleElseSplit?| |index| |randnum| |isOp| |acoshIfCan| + |numerators| |divisor| |prinpolINFO| |cosh2sech| |bitTruth| |equiv?| + |elRow1!| |applyRules| |lastSubResultant| |doubleRank| + |leadingCoefficientRicDE| |RittWuCompare| |currentCategoryFrame| + |f04mbf| |viewport2D| |union| |cosIfCan| |tableau| |unitVector| + |getStream| |symmetricProduct| |leftZero| |weierstrass| |contains?| + |squareFreePolynomial| |deref| |pair| |option?| |mathieu24| |factors| + |getCurve| |li| |numericIfCan| |polygamma| |scalarTypeOf| |f01qcf| + |wordsForStrongGenerators| |selectfirst| |perspective| |arity| + |string?| GF2FG |hasSolution?| |elt| |d01fcf| |cycleEntry| |upperCase| + |hex| |linearlyDependent?| |recoverAfterFail| |generalLambert| + |overlap| |lex| |s20adf| |invmultisect| |explogs2trigs| + |expandTrigProducts| |pascalTriangle| |factorByRecursion| |printCode| + |stopMusserTrials| |curveColor| |numberOfOperations| |bounds| + |decimal| |lexico| |comparison| |mapUnivariate| |leadingTerm| + |lambert| |iiacoth| |pmComplexintegrate| |doubleFloatFormat| |suffix?| + |useSingleFactorBound?| |d01apf| |fortranCharacter| |extendedint| + |radPoly| |value| |mix| |tubePointsDefault| |tubeRadiusDefault| + |bfKeys| |pastel| |integrate| |genericLeftTrace| |lexTriangular| + |imagk| |semiSubResultantGcdEuclidean1| |iicsc| |prefix?| |rightGcd| + |extend| |showArrayValues| |deepCopy| + |setLegalFortranSourceExtensions| |elColumn2!| |totalDifferential| + |countRealRoots| |PollardSmallFactor| |exprToXXP| |newReduc| + |leftTraceMatrix| |imagJ| |cAcosh| |pile| |derivative| |d01bbf| |init| + |e01baf| |viewWriteAvailable| |localIntegralBasis| |nilFactor| + |subscript| |insertRoot!| |iibinom| |predicate| |float?| |setEmpty!| + |integers| |computeInt| |UpTriBddDenomInv| |thenBranch| |outputArgs| + |cyclotomicFactorization| |rangeIsFinite| |test| |permutationGroup| + |domainOf| |ddFact| |mpsode| |univariateSolve| |e02ajf| |pade| + |splitConstant| |checkRur| |numberOfHues| |selectsecond| |maxrow| + |e04gcf| |listRepresentation| |s18acf| |OMputEndObject| |powmod| + |possiblyNewVariety?| |connectTo| |infix?| |leftUnits| |limit| + |distdfact| |maxPoints3D| |nthFlag| |OMgetBVar| |mask| + |mainDefiningPolynomial| |laguerreL| |primPartElseUnitCanonical| + |d01ajf| |selectOrPolynomials| |prefix| |realRoots| |e01bhf| + |numberOfMonomials| |rotate| |getZechTable| |lintgcd| |primaryDecomp| + |setright!| |polyRDE| |constDsolve| |assign| |swap!| |coefChoose| + |maxIndex| |ran| |d01anf| |loadNativeModule| |optional?| |cyclicGroup| + |coerceL| |refine| |solve1| |OMcloseConn| |semiResultantEuclideannaif| + |light| |divide| |cothIfCan| |reduceByQuasiMonic| |meshPar2Var| + |d03edf| |parameters| |alternative?| |sequences| |rectangularMatrix| + |has?| |jacobian| |rootKerSimp| |lowerCase| |numFunEvals| |quoByVar| + |subPolSet?| |isList| |sign| |semiResultantEuclidean1| |clearTable!| + |sturmVariationsOf| |rquo| |normalizeAtInfinity| |coefficient| + |e02def| |bringDown| |tube| |tubePlot| |principal?| |transform| + |getOrder| |balancedFactorisation| |e01sff| |upperCase!| |asinhIfCan| + |viewWriteDefault| |problemPoints| |semiDiscriminantEuclidean| + |setAdaptive| |stosePrepareSubResAlgo| |binaryTournament| + |OMgetEndBVar| |e04mbf| |sh| |simpsono| |mathieu23| |key?| + |maxRowIndex| |subQuasiComponent?| |rootDirectory| |groebgen| + |factorFraction| |integralCoordinates| |generalSqFr| + |mainPrimitivePart| |integralBasis| |newTypeLists| |triangSolve| + |tubeRadius| |tab| |ode1| |search| |e01sef| |makingStats?| |weighted| + |unparse| |reverse!| |eigenMatrix| |eyeDistance| |output| + |simplifyLog| |rowEch| |totalLex| |f04maf| |invertibleSet| + |rationalPoints| |any?| |OMconnectTCP| |screenResolution| + |removeSinhSq| |moduleSum| |invertIfCan| |byteBuffer| + |extractProperty| |dictionary| |toseLastSubResultant| |biRank| |radix| + F2FG |hdmpToDmp| |critT| |infieldint| |nextIrreduciblePoly| + |fprindINFO| |equivOperands| |algebraicSort| |btwFact| |vector| + |differentialVariables| |hclf| |enumerate| |doubleResultant| + |denomRicDE| |parabolic| |supRittWu?| |pack!| |nextsubResultant2| + |exportedOperators| |squareTop| |modularFactor| |resetVariableOrder| + |anfactor| |selectPDERoutines| |rightZero| |digamma| |branchIfCan| + |Beta| |innerSolve| |true| |delete!| |commonDenominator| + |univariatePolynomial| |iExquo| |groebner| |lowerPolynomial| |eulerE| + |arbitrary| |sPol| UTS2UP ~= |stoseSquareFreePart| |rightExtendedGcd| + |vectorise| |irreducibleFactor| |variationOfParameters| + |resultantReduit| |radicalEigenvectors| |external?| |tanSum| + |fortranComplex| |wreath| |createNormalPoly| |sparsityIF| |coerce| + |noLinearFactor?| |factor1| |setprevious!| |df2mf| |bitCoef| + |cycleLength| |numberOfImproperPartitions| |polar| |isMult| |c06ebf| + |construct| |rational?| |revert| |insertTop!| + |factorsOfCyclicGroupSize| |midpoints| |radicalRoots| |minPol| + |standardBasisOfCyclicSubmodule| |setClipValue| |var2Steps| + |factorsOfDegree| |implies?| |makeCos| |cos2sec| |f01mcf| |odd?| + |setrest!| |erf| |super| |f04axf| |mapdiv| |setMaxPoints3D| |roman| + |sncndn| |getCode| |leaves| |alphanumeric?| + |semiSubResultantGcdEuclidean2| |belong?| |inRadical?| + |currentSubProgram| |s18aff| |is?| |selectPolynomials| |stack| + |explicitlyEmpty?| |extendedSubResultantGcd| |binarySearchTree| + |var2StepsDefault| |integerBound| |perfectNthRoot| |redPo| + |fractRadix| |solveLinearPolynomialEquationByRecursion| |merge| + |leadingIndex| |badNum| |pol| |imagE| |PDESolve| |dilog| |ceiling| + |realEigenvectors| |argumentListOf| |c06gsf| |connect| + |ramifiedAtInfinity?| |viewpoint| |expenseOfEvaluation| + |makeViewport2D| |traceMatrix| |systemCommand| |sin| |eq?| |rotatey| + |quasiRegular| |rootSimp| |baseRDE| |bits| |inputOutputBinaryFile| + |makeSeries| |bfEntry| |systemSizeIF| |f04asf| |cos| |vark| + |bipolarCylindrical| |d02gbf| |derivationCoordinates| |imagK| + |getExplanations| |nthExpon| |evenInfiniteProduct| |character?| + |factorPolynomial| |and?| |lift| |tan| |frst| |rootBound| |coth2trigh| + |expt| |superscript| |stoseInvertibleSetreg| |lookup| |cAtanh| + |exteriorDifferential| |forLoop| |trace2PowMod| |reduce| |normal| + |cot| |completeHensel| |relationsIdeal| |eulerPhi| |ignore?| |over| + |basisOfCentroid| |evaluate| |d01asf| |subResultantGcdEuclidean| |mat| + |sec| |setTopPredicate| |consnewpol| |pushNewContour| |e02ahf| + |adjoint| |sizePascalTriangle| |c05adf| |cyclotomicDecomposition| + |triangulate| |d01alf| |resetBadValues| |csc| |flagFactor| + |setPosition| |palgintegrate| |OMputEndError| |ode| |rootPower| + |basisOfCommutingElements| |intPatternMatch| |prepareDecompose| + |SturmHabicht| |cn| |mainCharacterization| |asin| |reduced?| + |modularGcd| |aCubic| |e04fdf| |OMgetBind| |symbolIfCan| |uniform| + |iiatanh| |ratpart| |baseRDEsys| |acos| |besselJ| |sinIfCan| + |rightFactorIfCan| |point| |denominators| |euler| |splitLinear| + |f07fdf| |colorFunction| |ScanFloatIgnoreSpacesIfCan| |position!| + |atan| |stFunc2| |discreteLog| |conditionP| |complexRoots| + |difference| |reducedSystem| |f01rdf| |irreducibleRepresentation| + |sincos| |normalDenom| |acot| |outputMeasure| |eigenvalues| |overbar| + |linkToFortran| |quotientByP| |rightMinimalPolynomial| |conjugate| + |dualSignature| |groebnerIdeal| |fortranLinkerArgs| |asec| + |readBytes!| |OMgetInteger| |upDateBranches| |series| |reflect| + |commaSeparate| |yCoord| |resetNew| |c06fpf| |f01maf| |acsc| |green| + |adaptive| |startTable!| |leftOne| |hasPredicate?| |port| |tanhIfCan| + |shrinkable| |polCase| |sinh| |totalGroebner| |safeFloor| |measure| + |elseBranch| |allRootsOf| |create| |trigs| |ricDsolve| + |replaceKthElement| |cosh| |subResultantGcd| |goodPoint| + |headRemainder| |coercePreimagesImages| |infRittWu?| |e02baf| + |sts2stst| |edf2df| |number?| |tanh| |genericRightNorm| |plot| + |prepareSubResAlgo| |min| |triangularSystems| |complexForm| + |LagrangeInterpolation| |rationalIfCan| |jacobi| |outputForm| + |moebius| |goto| |leftNorm| |nextColeman| |tab1| + |antisymmetricTensors| |clipSurface| |palgLODE| |isExpt| 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|commutator| |tableForDiscreteLogarithm| |basis| |toScale| + |check| |dimensionOfIrreducibleRepresentation| |OMunhandledSymbol| + |bitior| |weights| |OMputError| |transcendenceDegree| |pdf2df| + |internalIntegrate0| |addMatch| |points| |roughSubIdeal?| |repeating| + |write| |floor| |laplace| |times!| |abelianGroup| |numberOfVariables| + |retractable?| |removeRedundantFactors| |save| |cAcsc| + |showIntensityFunctions| |reduceLODE| |halfExtendedSubResultantGcd1| + |mindegTerm| |partitions| D |discriminant| |OMputEndAttr| |implies| + |removeRoughlyRedundantFactorsInPols| |operators| |reorder| |double| + |paraboloidal| |prindINFO| |member?| |Aleph| |simplifyPower| |untab| + |blue| |mapExpon| |unrankImproperPartitions1| |idealiser| |prem| + |continuedFraction| |mvar| |generalizedEigenvectors| + |clearFortranOutputStack| |integralMatrixAtInfinity| |kroneckerDelta| + |s18def| |bernoulliB| |setMinPoints| |setnext!| |genericPosition| + |extendedResultant| |lexGroebner| |startPolynomial| + |singularAtInfinity?| |iitan| |sumOfKthPowerDivisors| |xCoord| + |setPoly| |internalSubQuasiComponent?| |divergence| |superHeight| + |unit| |primeFrobenius| |charthRoot| |basisOfRightNucloid| |e01sbf| + |initiallyReduced?| |knownInfBasis| |corrPoly| |atanIfCan| + |perfectNthPower?| |reducedQPowers| |overlabel| |dflist| |integral| + |linears| |roughBasicSet| |alphanumeric| |iterationVar| |composite| + |entry| |primlimitedint| |cCsc| |c02agf| |rombergo| |whitePoint| + |c06ekf| |gramschmidt| |makeEq| |stronglyReduced?| + |rightFactorCandidate| |null?| |declare!| |setProperties!| |ODESolve| + |sec2cos| |radicalSimplify| |principalIdeal| |normalizeIfCan| |f01bsf| + |realZeros| |e02bcf| |OMputBVar| |nextNormalPoly| |lighting| + |factorSquareFree| |taylorRep| |f02bjf| |print| |hdmpToP| + |semiLastSubResultantEuclidean| |stFunc1| |fullDisplay| + |purelyAlgebraic?| |getVariableOrder| |resolve| |pointColorDefault| + |Vectorise| |constant?| |setRow!| |rightScalarTimes!| |Frobenius| + |rootOf| |solve| |genericRightTraceForm| |insertBottom!| |conical| + |autoReduced?| |returns| |acschIfCan| |flatten| |variable?| |bat| + |basicSet| |s19aaf| |qPot| |distribute| |edf2fi| |retractIfCan| + |OMgetEndObject| |inHallBasis?| |degreeSubResultantEuclidean| |solid?| + |shanksDiscLogAlgorithm| |deepestInitial| |att2Result| LODO2FUN + |palgRDE| |isTimes| |complexSolve| |anticoord| |mapGen| |overset?| + |conjug| |numer| |mainSquareFreePart| |uncouplingMatrices| |sdf2lst| + |bag| |roughEqualIdeals?| |viewPosDefault| |setFormula!| |pow| + |e04ucf| |f04mcf| |segment| |top| |denom| |makeYoungTableau| |powern| + |OMgetVariable| |pomopo!| |groebner?| |splitNodeOf!| + |genericLeftTraceForm| |zeroMatrix| |headReduce| |nextPrimitivePoly| + |semicolonSeparate| |euclideanNormalForm| |f07aef| |diff| |contours| + |numericalOptimization| |trueEqual| |flexibleArray| |minimumDegree| + |removeRedundantFactorsInContents| |pi| |lquo| |complexEigenvectors| + |solveLinear| |polyRicDE| |addMatchRestricted| |nextPrime| |name| + |parabolicCylindrical| |exQuo| |dimensionsOf| + |linearlyDependentOverZ?| |infinity| |companionBlocks| + |structuralConstants| |iilog| |rename| |SturmHabichtSequence| + |quasiAlgebraicSet| |body| |newLine| |alphabetic| + |initializeGroupForWordProblem| |lfunc| |coerceListOfPairs| + |divisorCascade| |csubst| |generalizedEigenvector| + |genericRightDiscriminant| |laguerre| |rootNormalize| |logIfCan| + |exquo| |operation| |fortranTypeOf| |createPrimitiveElement| + |leastPower| |bipolar| |leftRegularRepresentation| |perfectSqrt| + |halfExtendedResultant1| |monic?| |cardinality| |LiePolyIfCan| + |iFTable| |t| |div| |tanNa| |tRange| |outerProduct| |kernel| + |pseudoDivide| |besselK| |nthr| |putColorInfo| |logpart| |stirling1| + |prolateSpheroidal| |draw| |map| |rightLcm| |quo| |kovacic| + |getMeasure| |rightRankPolynomial| |axesColorDefault| Y |firstNumer| + |cAtan| |complexIntegrate| |ScanFloatIgnoreSpaces| |iisec| |s17ajf| + |multiplyExponents| |shift| |indicialEquationAtInfinity| |normal?| + |minimumExponent| |viewDeltaYDefault| |startStats!| |sumSquares| + |OMputEndApp| |polynomialZeros| |freeOf?| |rem| |setref| |lifting1| + |regime| |linear| |real?| |subtractIfCan| |rationalPower| |find| + |unprotectedRemoveRedundantFactors| |sumOfDivisors| F |decomposeFunc| + |symmetricTensors| |unrankImproperPartitions0| |pdf2ef| + |zeroSetSplitIntoTriangularSystems| |center| |setImagSteps| + |insertionSort!| |gradient| |complexEigenvalues| |simpson| + |makeObject| |categoryFrame| |parametric?| |makeCrit| + |OMencodingUnknown| |polynomial| |OMParseError?| |orbits| |property| + |orthonormalBasis| |hspace| |closeComponent| |simplify| |convert| + |compactFraction| |nullSpace| |leastMonomial| |explicitEntries?| + |sturmSequence| |clipParametric| |iiatan| |root?| + |monicDecomposeIfCan| |setProperty!| |basisOfLeftNucloid| + |deepestTail| |ScanArabic| |nodeOf?| |leadingExponent| |coef| + |fixPredicate| |fTable| |sizeLess?| |nthFractionalTerm| |s17acf| + |dAndcExp| |basisOfLeftAnnihilator| |stoseInvertible?sqfreg| |redmat| + |startTableInvSet!| |pointLists| |rk4f| |units| |primlimintfrac| + |viewport3D| |leftDivide| |OMsend| |iisech| |primitive?| |c02aff| + |adaptive3D?| |drawToScale| |cotIfCan| |shade| |internalZeroSetSplit| + |transcendentalDecompose| |accuracyIF| |infieldIntegrate| + |extractPoint| |leviCivitaSymbol| |alternatingGroup| + |absolutelyIrreducible?| |reducedDiscriminant| |ParCondList| + |repeating?| |firstSubsetGray| |sum| |sin2csc| |child?| RF2UTS |iicos| + |halfExtendedSubResultantGcd2| |Nul| |central?| + |wordInStrongGenerators| |acosIfCan| |directSum| ** |complex?| + |s17def| |child| |copyInto!| |prinshINFO| |f02ajf| |lp| |qfactor| + |differentiate| |OMputString| |calcRanges| |palgLODE0| |zeroVector| + |multiEuclidean| |failed?| |firstUncouplingMatrix| |pquo| |rightNorm| + |code| |lSpaceBasis| |getOperands| |inGroundField?| |collectUpper| + |shuffle| |decrease| |padicFraction| |cAsin| |lazyPseudoRemainder| EQ + |modularGcdPrimitive| |insertMatch| |rightRank| |deepExpand| + |heapSort| |s19acf| |insert!| |modifyPointData| |primintegrate| + |epilogue| |e02dcf| |balancedBinaryTree| + |selectMultiDimensionalRoutines| |cosSinInfo| |lazyIntegrate| |f02awf| + |ocf2ocdf| |iprint| |dfRange| |binomial| |outputAsFortran| |split| + |partition| |rank| |computeCycleEntry| |optAttributes| + |nextPrimitiveNormalPoly| |viewZoomDefault| |minimize| + |showAllElements| |squareFreePrim| |s17dcf| |transcendent?| + |evaluateInverse| |cRationalPower| |f02agf| |primextendedint| |rroot| + |setProperties| |palgint| |psolve| |quotedOperators| |s17aef| + |mapmult| |read!| |lieAdmissible?| |radicalEigenvector| + |cyclicEntries| |makeSketch| |LyndonWordsList1| |s21bbf| |octon| + |se2rfi| |dom| |quotient| |OMsupportsSymbol?| |lazyIrreducibleFactors| + |removeCosSq| |kind| |setProperty| |stirling2| |univariatePolynomials| + |palgextint0| |intensity| |rightMult| |c06gcf| |getIdentifier| + |s15adf| |category| |curve?| |op| |leadingIdeal| |exists?| + |outputAsScript| |f02wef| |torsionIfCan| |lfextlimint| + |zeroDimensional?| |addBadValue| |trim| |domain| |bsolve| |options| + |declare| |identification| |cSin| |graphStates| |e01saf| |axes| + |hermite| |monicCompleteDecompose| |push| |createMultiplicationMatrix| + |package| |solveRetract| |signature| |multinomial| |c06frf| + |fortranLiteralLine| |karatsubaOnce| |unknown| |asimpson| + |stoseInvertible?| |index?| |lists| |unaryFunction| |bumptab| |infix| + |hasHi| |nonLinearPart| |cycleSplit!| |definingInequation| |nextItem| + |getConstant| |title| |OMopenString| |droot| |lfintegrate| + |rewriteIdealWithRemainder| |string| |airyBi| |Si| |f02adf| + |arrayStack| |cAsech| |createIrreduciblePoly| |leftAlternative?| + |scalarMatrix| |dot| |rightCharacteristicPolynomial| |iisqrt2| + |jordanAlgebra?| |approxSqrt| |hexDigit?| |OMgetSymbol| |maxrank| + |heap| |complexElementary| |swapRows!| |outputList| |duplicates| + |smith| |pushdterm| |phiCoord| |f07fef| |algebraicCoefficients?| + |s14aaf| |e| |ldf2vmf| |front| |createThreeSpace| |setLength!| + |tryFunctionalDecomposition?| |df2st| |mainVariable?| |clipBoolean| + |create3Space| |chebyshevU| |fixedPoint| |numberOfComponents| + |critBonD| |rk4| |outputGeneral| |OMgetEndAtp| |permutations| + |pointData| |parametersOf| |subset?| |scaleRoots| |errorKind| + |setelt!| |factorGroebnerBasis| |inputBinaryFile| |chiSquare1| + |sortConstraints| |setCondition!| |setRealSteps| |nothing| + |rischDEsys| |numberOfNormalPoly| |closedCurve?| |atoms| + |patternMatchTimes| |partialDenominators| |integral?| |f01qef| |pole?| + |currentEnv| |gcdprim| |varselect| |order| |univariatePolynomialsGcds| + |maxint| |numerator| |rightUnit| |mapSolve| |someBasis| + |basisOfRightNucleus| |solveid| |s13acf| |c06fqf| |elementary| + |irreducible?| |d01gbf| |subCase?| |seed| |exprToGenUPS| + |lazyPseudoDivide| |generic?| |distFact| |fortranInteger| + |lfextendedint| |sinhIfCan| |gderiv| |showTheSymbolTable| |mkcomm| + |nthCoef| |OMputAttr| |cond| |henselFact| |width| |rdHack1| + |diagonalProduct| |leftQuotient| |crest| |exp1| |nextsousResultant2| + |closed?| |s19abf| |setsubMatrix!| |secIfCan| + |rewriteSetByReducingWithParticularGenerators| |changeWeightLevel| + |s20acf| |useEisensteinCriterion?| |s17dlf| |minus!| |firstDenom| + |OMlistCDs| |rspace| |createNormalElement| |limitPlus| + |clearTheFTable| |writeByteIfCan!| |fractionPart| + |selectIntegrationRoutines| |viewDeltaXDefault| |cSech| |augment| + |addmod| |lprop| |diophantineSystem| |even?| |legendre| |column| + |iroot| |OMreceive| |qinterval| |clearDenominator| |perfectSquare?| + |lyndon?| |setPrologue!| |setVariableOrder| |OMencodingSGML| |isPower| + |content| |graphs| |nary?| |countRealRootsMultiple| |rk4qc| + |integralDerivationMatrix| |checkPrecision| |bivariate?| |randomR| + |orbit| |powerSum| |positiveSolve| |iiasec| |diag| |reverse| |lo| + |leftGcd| |tower| |infinityNorm| |rubiksGroup| |ridHack1| + |patternMatch| |linearPart| |leftFactor| |optional| |OMsetEncoding| + |symbol?| |generalPosition| |plusInfinity| |condition| |lllip| + |coordinates| |iicoth| |lieAlgebra?| |top!| |infinite?| |c06gbf| + |f02aff| |inv| |polygon| |minusInfinity| |divideExponents| |graeffe| + |randomLC| |f02abf| |functionIsOscillatory| |associative?| + |jordanAdmissible?| |LyndonBasis| |ground?| |complexExpand| + |leftDiscriminant| |mainValue| |changeVar| |thetaCoord| |eq| + |specialTrigs| |tanh2coth| |basisOfLeftNucleus| |iiacos| |ground| + |hue| |typeList| |exponents| |multiEuclideanTree| |extractIndex| + |iter| |/\\| |leadingMonomial| |infLex?| |removeSquaresIfCan| + |stoseInvertible?reg| |complexNumeric| |drawComplexVectorField| + |airyAi| |neglist| |cCsch| |imagj| |prologue| |\\/| |factorials| + |powers| |numberOfPrimitivePoly| |leadingCoefficient| |rules| + |deleteRoutine!| |f02akf| |swap| |LyndonWordsList| |edf2efi| + |getPickedPoints| |outputFloating| |tanIfCan| |extendedIntegrate| + |primitiveMonomials| |kernels| |resetAttributeButtons| |interpolate| + |complexNumericIfCan| |recip| |level| |inverse| |alphabetic?| |cAcos| + |tablePow| |int| |inconsistent?| |reductum| |univariate| |type| + |mesh?| |cyclicEqual?| |partialQuotients| |aspFilename| + |associatedEquations| |purelyAlgebraicLeadingMonomial?| + |makeFloatFunction| |tan2trig| SEGMENT |back| |OMputAtp| |e02ddf| + |HermiteIntegrate| |normalizedDivide| |imagi| |crushedSet| |nullary| + |chebyshevT| |qelt| |getBadValues| |postfix| |clipWithRanges| + |gcdcofactprim| |totalfract| |setStatus!| |colorDef| |qsetelt| |low| + |lfinfieldint| |errorInfo| |quickSort| |factor| |ratDenom| + |isConnected?| |printStatement| |unitNormal| |palgint0| |exp| + |elliptic| |createMultiplicationTable| |xRange| |diagonalMatrix| + |plus!| |sqrt| |makeGraphImage| |twist| |numberOfChildren| |torsion?| + |particularSolution| |swapColumns!| |rischDE| |yRange| |asinIfCan| + |ref| |real| |complementaryBasis| |subHeight| |concat| |determinant| + |pointColor| |fortranLiteral| |exprToUPS| |indices| |zRange| + |OMsupportsCD?| |inverseIntegralMatrix| |imag| |genus| |cCos| + |OMreadStr| |component| |curry| |error| |ldf2lst| |OMopenFile| |map!| + |pushuconst| |directProduct| |critB| |compile| |BasicMethod| |iiabs| + |bytes| |cAcsch| |subresultantVector| |assert| |qsetelt!| + |rightAlternative?| |charpol| |lyndon| |OMencodingBinary| + |completeHermite| |cschIfCan| |generalInfiniteProduct| |appendPoint| + |dimension| |opeval| |exptMod| |linearPolynomials| |geometric| |brace| + |bezoutResultant| |s15aef| |subNodeOf?| |idealSimplify| + |mainExpression| |credPol| |janko2| |abs| |lllp| |destruct| + |eisensteinIrreducible?| |collectUnder| |exponential1| |clip| + |OMgetString| |iifact| |writeBytes!| |monicModulo| |multiple?| + |replace| |rightUnits| |zero?| |primitivePart| |dominantTerm| + |normalize| |mapCoef| |rowEchelon| |externalList| |stoseInvertibleSet| + |writable?| |primPartElseUnitCanonical!| |equality| |finiteBound| + |padecf| |acsch| |stripCommentsAndBlanks| |separate| |listLoops| + |algebraic?| |normalDeriv| |constantKernel| |iiacot| |f01qdf| ~ + |tracePowMod| |shufflein| |linGenPos| |Lazard2| |bandedJacobian| + |monomial| |minrank| |complexLimit| |s18aef| |d01gaf| |complete| + |makeTerm| |satisfy?| |round| |showTheRoutinesTable| |multivariate| + |generalTwoFactor| |semiResultantReduitEuclidean| |denominator| + |linearAssociatedOrder| |minColIndex| |open| |d01amf| |reseed| + |intChoose| |direction| |setAttributeButtonStep| |variables| + |makeUnit| |ef2edf| |square?| |mulmod| |acscIfCan| |algebraicOf| + |clearTheSymbolTable| |cTanh| |lastSubResultantElseSplit| + |outputSpacing| |printingInfo?| |minIndex| |target| |hconcat| + |writeLine!| |functionIsContinuousAtEndPoints| |B1solve| |elRow2!| + |OMgetEndBind| |makeprod| |factorSquareFreeByRecursion| |primes| + |resultantEuclideannaif| |objectOf| |viewDefaults| |elliptic?| + |iiacsch| |complexNormalize| |chiSquare| |primitivePart!| + |useNagFunctions| |rightRemainder| |bright| |powerAssociative?| + |rowEchelonLocal| |leftLcm| |linearAssociatedExp| |leftRemainder| + |strongGenerators| |bezoutDiscriminant| |f04jgf| |zeroDimPrimary?| + |monicDivide| |initial| |returnType!| |d03faf| |c06eaf| |setchildren!| + |submod| |redpps| |lowerCase!| |fintegrate| |zoom| |weakBiRank| + |taylor| |rootsOf| |size?| |radicalEigenvalues| |closedCurve| |inf| + |printStats!| |monomial?| |setErrorBound| |fortranReal| + |rightDiscriminant| |laurent| |select!| |makeRecord| |hermiteH| + |mathieu22| |functionIsFracPolynomial?| |SturmHabichtMultiple| + |setOrder| |cyclic| |cycleTail| |selectOptimizationRoutines| |puiseux| + |createPrimitivePoly| |factorial| |hitherPlane| |setleaves!| + |sylvesterMatrix| |fmecg| |trigs2explogs| |midpoint| UP2UTS |ravel| + |cartesian| |setScreenResolution| |dmpToHdmp| |OMclose| |integer?| + |primeFactor| |OMmakeConn| |truncate| |fortranDoubleComplex| FG2F + |s17aff| |reshape| |inR?| |whatInfinity| |tan2cot| + |isAbsolutelyIrreducible?| |useSingleFactorBound| + |integralLastSubResultant| |e04jaf| |delete| |cyclicSubmodule| |cup| + |hcrf| |UP2ifCan| |idealiserMatrix| |rarrow| |viewSizeDefault| + |multiplyCoefficients| |var1StepsDefault| |setlast!| |OMconnOutDevice| + |numberOfFactors| |setClosed| |zeroDim?| |pmintegrate| |zeroOf| + |leftTrace| |range| |atanhIfCan| |squareFreeLexTriangular| + |wholeRagits| |exactQuotient| |lagrange| |symmetricSquare| + |bandedHessian| |localUnquote| |mightHaveRoots| |trapezoidal| |sup| + |tryFunctionalDecomposition| |eof?| |arg1| |horizConcat| |byte| + |putGraph| |entries| |semiResultantEuclidean2| NOT |complexZeros| + |e02gaf| |setelt| |integralBasisAtInfinity| |listOfLists| + |principalAncestors| |arg2| |acothIfCan| |subTriSet?| |makeResult| + |cot2trig| |update| |constantToUnaryFunction| |printTypes| OR + |arguments| |tubePoints| |dn| |updatF| |rightDivide| + |regularRepresentation| |gethi| |removeCoshSq| |currentScope| + |bottom!| |discriminantEuclidean| AND |innerint| + |createPrimitiveNormalPoly| |copy| |characteristicPolynomial| + |radicalSolve| |constantOpIfCan| |ksec| |realEigenvalues| |qqq| + |fractionFreeGauss!| |multisect| |spherical| |every?| |d01aqf| |trunc| + |drawComplex| |rst| |var1Steps| |degree| |gbasis| |unexpand| + |oblateSpheroidal| |leftRecip| |dark| |cycleRagits| |nextPartition| + |lhs| |HenselLift| |match?| |f04atf| |makeSUP| |c06gqf| |simplifyExp| + |quadraticNorm| |autoCoerce| |withPredicates| |besselI| |printHeader| + |separateDegrees| |rhs| |mergeFactors| |enterPointData| |Gamma| + |position| |screenResolution3D| |cyclotomic| |charClass| |identity| + |quasiComponent| |continue| |chineseRemainder| |d01akf| |totolex| + |divisors| |nthRoot| |probablyZeroDim?| |scanOneDimSubspaces| + |skewSFunction| |d02raf| |e01bgf| |collect| |expr| |monomRDEsys| + |reducedForm| |topPredicate| |leader| |symbolTableOf| |nthExponent| + |indicialEquation| |shellSort| |signAround| |fixedPointExquo| |result| + |rightExactQuotient| |ListOfTerms| |presub| |rotatez| |showRegion| + |rational| |selectODEIVPRoutines| GE |properties| |logical?| + |inverseColeman| |nlde| |power| |splitSquarefree| |tree| |d02gaf| + |monicRightFactorIfCan| |parseString| |taylorQuoByVar| GT + |getProperty| |mkPrim| |linearDependence| |qualifier| |f04arf| + |translate| |createRandomElement| |rootPoly| |critMonD1| + |wronskianMatrix| |middle| * LE |whileLoop| |lazy?| |minset| + |factorSquareFreePolynomial| |variable| |separant| |binomThmExpt| + |max| |scopes| |safeCeiling| |constantOperator| |bivariateSLPEBR| + |build| LT |leadingSupport| |aLinear| |bitLength| |debug| + |removeSinSq| |iterators| |innerSolve1| |resultantnaif| + |combineFeatureCompatibility| |decompose| |rightOne| |normInvertible?| + |goodnessOfFit| |increasePrecision| |ranges| |elements| |fi2df| + |vertConcat| |integralRepresents| |bombieriNorm| |factorOfDegree| + |symmetricDifference| |zeroDimPrime?| |mirror| |setFieldInfo| + |internalDecompose| |rationalFunction| |element?| |d03eef| + |algintegrate| |univcase| |OMputEndBVar| |predicates| |cTan| + |twoFactor| |clipPointsDefault| |fixedPoints| |maxPoints| |generator| + |part?| |getlo| |remainder| |aQuadratic| |rightPower| |OMgetAttr| + |parts| |makeMulti| |iiacosh| |rationalPoint?| |quote| |modulus| + |kmax| |slash| |addPoint| |sub| |coordinate| |harmonic| |vconcat| + |supDimElseRittWu?| |fortranCompilerName| |numberOfComputedEntries| + |fillPascalTriangle| |dimensions| |impliesOperands| |scale| |next| + |newSubProgram| |latex| |generalizedContinuumHypothesisAssumed?| + |rewriteIdealWithHeadRemainder| |csch2sinh| |positive?| |point?| + |exprHasLogarithmicWeights| |bothWays| |quatern| |ode2| |makeop| + |stiffnessAndStabilityOfODEIF| |leftCharacteristicPolynomial| |equiv| + |quartic| |mesh| |curveColorPalette| |oddInfiniteProduct| |e04dgf| + |argscript| |norm| |removeDuplicates!| |generic| |minimalPolynomial| + |interpret| |hasTopPredicate?| |remove!| |failed| |iiperm| + |leadingBasisTerm| |e02dff| |space| |reduction| |leastAffineMultiple| + |andOperands| |fill!| |hypergeometric0F1| |makeSin| |monomialIntPoly| + |KrullNumber| |sn| |f04faf| |trapezoidalo| |s17agf| |iidprod| |call| + |OMconnInDevice| |singular?| |uniform01| |e02agf| |shiftLeft| + |createNormalPrimitivePoly| |setMaxPoints| |normalise| + |expextendedint| |cCot| |directory| |wholePart| |argument| |queue| + |cylindrical| |fortranLogical| |hMonic| |wholeRadix| |factorset| + |listexp| |getButtonValue| |moreAlgebraic?| |rowEchLocal| |symFunc| + |hessian| |sinhcosh| |computeBasis| |areEquivalent?| |contract| + |returnTypeOf| |dmp2rfi| |simpleBounds?| |more?| |yCoordinates| + |cSinh| |d02ejf| |leftExactQuotient| |dim| |resultantEuclidean| + |sqfrFactor| |rotatex| |setOfMinN| |leftMult| |iicosh| |supersub| + |bivariatePolynomials| |e02bbf| |f01ref| |seriesSolve| + |physicalLength!| |function| |normalized?| |d02kef| |prime?| + |OMputBind| |leftMinimalPolynomial| |componentUpperBound| |clearCache| + |mapBivariate| |constant| |solveInField| |incrementKthElement| + |cyclic?| |singleFactorBound| |csc2sin| |reindex| |open?| + |inverseIntegralMatrixAtInfinity| |zCoord| |Hausdorff| |homogeneous?| + |listOfMonoms| |eval| |SFunction| |stFuncN| + |stiffnessAndStabilityFactor| |categories| |leftScalarTimes!| |one?| + |f2df| |algSplitSimple| |algint| |insert| |id| |moebiusMu| + |RemainderList| |coleman| |setfirst!| |nsqfree| |c06ecf| |reify| + |routines| |radicalOfLeftTraceForm| |nor| |mathieu12| |htrigs| + |OMputEndBind| |certainlySubVariety?| |removeConstantTerm| |Ci| + |palginfieldint| |term?| |LiePoly| |e02daf| |ipow| + |fullPartialFraction| |pseudoQuotient| |c05nbf| |table| + |brillhartTrials| |OMgetAtp| |log| |lazyEvaluate| |incr| |aQuartic| + |lazyGintegrate| |in?| |identityMatrix| |sequence| |fractRagits| + |setvalue!| |new| |merge!| |asecIfCan| |comment| |multMonom| |s18dcf| + |Is| |s17adf| |nextLatticePermutation| |argumentList!| |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) ((-102) |has| |#1| (-1087)) ((-605 (-853)) -3986 (|has| |#1| (-1087)) (|has| |#1| (-605 (-853)))) ((-308 |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) ((-487 |#1|) . T) ((-512 |#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) ((-1087) |has| |#1| (-1087)) ((-1200) . T)) +((-1978 (((-59 |#2|) (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|) 16)) (-2651 ((|#2| (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|) 18)) (-3124 (((-59 |#2|) (-1 |#2| |#1|) (-59 |#1|)) 13))) +(((-58 |#1| |#2|) (-10 -7 (-15 -1978 ((-59 |#2|) (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -2651 (|#2| (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -3124 ((-59 |#2|) (-1 |#2| |#1|) (-59 |#1|)))) (-1200) (-1200)) (T -58)) +((-3124 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-59 *5)) (-4 *5 (-1200)) (-4 *6 (-1200)) (-5 *2 (-59 *6)) (-5 *1 (-58 *5 *6)))) (-2651 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-59 *5)) (-4 *5 (-1200)) (-4 *2 (-1200)) (-5 *1 (-58 *5 *2)))) (-1978 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-59 *6)) (-4 *6 (-1200)) (-4 *5 (-1200)) (-5 *2 (-59 *5)) (-5 *1 (-58 *6 *5))))) +(-10 -7 (-15 -1978 ((-59 |#2|) (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -2651 (|#2| (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -3124 ((-59 |#2|) (-1 |#2| |#1|) (-59 |#1|)))) +((-2526 (((-112) $ $) NIL 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T) ((-899) -12 (|has| |#1| (-306)) (|has| |#1| (-899))) ((-910) -3986 (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-992) -12 (|has| |#1| (-992)) (|has| |#1| (-1185))) ((-1028 (-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((-1028 (-558)) |has| |#1| (-1028 (-558))) ((-1028 |#1|) . T) ((-1045 #0#) -3986 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-1045 |#1|) . T) ((-1045 $) . T) ((-1039) . T) ((-1046) . T) ((-1099) . T) ((-1087) . T) ((-1138) |has| |#1| (-348)) ((-1185) |has| |#1| (-1185)) ((-1188) |has| |#1| (-1185)) ((-1200) . 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(-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3998 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3998 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3998 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3998 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3998 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3998 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3998 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3998 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3998 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3998 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3998 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3998 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3998 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3998 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3998 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3998 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3998 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3998 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3998 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . T) ((-1253 |#2|) |has| |#2| (-362))) -((-2675 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-3048 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-3167 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) -(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -2675 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3048 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3167 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-762) (-1200) (-1200)) (T -238)) -((-3167 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *7 (-1200)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-3048 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *2 (-1200)) (-5 *1 (-238 *5 *6 *2)))) (-2675 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-762)) (-4 *7 (-1200)) (-4 *5 (-1200)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3986 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3986 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3986 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3986 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3986 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3986 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3986 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3986 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3986 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . T) ((-1253 |#2|) |has| |#2| (-362))) +((-1978 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-2651 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-3124 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) +(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -1978 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -2651 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3124 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-762) (-1200) (-1200)) (T -238)) +((-3124 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *7 (-1200)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-2651 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *2 (-1200)) (-5 *1 (-238 *5 *6 *2)))) (-1978 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-762)) (-4 *7 (-1200)) (-4 *5 (-1200)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #0#) -3986 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 |#1|) . T) ((-608 |#2|) . T) ((-608 |#3|) . T) ((-608 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450))) ((-605 (-853)) . 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T) ((-638 |#2|) |has| |#1| (-362)) ((-638 $) . T) ((-631 (-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-631 (-558)))) ((-631 |#2|) |has| |#1| (-362)) ((-708 #1#) -3986 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-708 |#1|) |has| |#1| (-171)) ((-708 |#2|) |has| |#1| (-362)) ((-708 $) -3986 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-717) . 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T) ((-23) . T) ((-47 |#1| #0=(-762)) . T) ((-25) . T) ((-38 #1=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3998 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3998 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3998 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 #2=(-1069)) . T) ((-608 |#1|) . T) ((-608 $) -3998 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-605 (-853)) . 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T) ((-638 $) . T) ((-631 (-558)) |has| |#1| (-631 (-558))) ((-631 |#1|) . T) ((-708 #1#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) -3998 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-717) . T) ((-841) |has| |#1| (-841)) ((-890 #2#) . T) ((-890 (-1163)) |has| |#1| (-890 (-1163))) ((-876 (-378)) -12 (|has| (-1069) (-876 (-378))) (|has| |#1| (-876 (-378)))) ((-876 (-558)) -12 (|has| (-1069) (-876 (-558))) (|has| |#1| (-876 (-558)))) ((-939 |#1| #0# #2#) . T) ((-899) |has| |#1| (-899)) ((-910) |has| |#1| (-362)) ((-1028 (-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((-1028 (-558)) |has| |#1| (-1028 (-558))) ((-1028 #2#) . T) ((-1028 |#1|) . T) ((-1045 #1#) |has| |#1| (-38 (-406 (-558)))) ((-1045 |#1|) . T) ((-1045 $) -3998 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-1039) . T) ((-1046) . T) ((-1099) . T) ((-1087) . 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T) ((-23) . T) ((-47 |#1| #0=(-762)) . T) ((-25) . T) ((-38 #1=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3986 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 #2=(-1069)) . T) ((-608 |#1|) . T) ((-608 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-605 (-853)) . T) ((-171) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-606 (-534)) -12 (|has| (-1069) (-606 (-534))) (|has| |#1| (-606 (-534)))) ((-606 (-882 (-378))) -12 (|has| (-1069) (-606 (-882 (-378)))) (|has| |#1| (-606 (-882 (-378))))) ((-606 (-882 (-558))) -12 (|has| (-1069) (-606 (-882 (-558)))) (|has| |#1| (-606 (-882 (-558))))) ((-230 |#1|) . T) ((-232) . T) ((-285 (-406 $) (-406 $)) |has| |#1| (-550)) ((-285 |#1| |#1|) . T) ((-285 $ $) . T) ((-289) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-306) |has| |#1| (-362)) ((-308 $) . T) ((-325 |#1| #0#) . T) ((-376 |#1|) . T) ((-410 |#1|) . T) ((-450) -3986 (|has| |#1| (-899)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-512 #2# |#1|) . T) ((-512 #2# $) . T) ((-512 $ $) . T) ((-550) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-638 #1#) |has| |#1| (-38 (-406 (-558)))) ((-638 |#1|) . T) ((-638 $) . T) ((-631 (-558)) |has| |#1| (-631 (-558))) ((-631 |#1|) . T) ((-708 #1#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-717) . T) ((-841) |has| |#1| (-841)) ((-890 #2#) . T) ((-890 (-1163)) |has| |#1| (-890 (-1163))) ((-876 (-378)) -12 (|has| (-1069) (-876 (-378))) (|has| |#1| (-876 (-378)))) ((-876 (-558)) -12 (|has| (-1069) (-876 (-558))) (|has| |#1| (-876 (-558)))) ((-939 |#1| #0# #2#) . T) ((-899) |has| |#1| (-899)) ((-910) |has| |#1| (-362)) ((-1028 (-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((-1028 (-558)) |has| |#1| (-1028 (-558))) ((-1028 #2#) . T) ((-1028 |#1|) . T) ((-1045 #1#) |has| |#1| (-38 (-406 (-558)))) ((-1045 |#1|) . T) ((-1045 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-1039) . T) ((-1046) . T) ((-1099) . T) ((-1087) . T) ((-1138) |has| |#1| (-1138)) ((-1204) |has| |#1| (-899))) +((-3826 (((-635 (-1069)) $) 28)) (-3651 (($ $) 25)) (-3804 (($ |#2| |#3|) NIL) (($ $ (-1069) |#3|) 22) (($ $ (-635 (-1069)) (-635 |#3|)) 21)) (-3612 (($ $) 14)) (-3627 ((|#2| $) 12)) (-4017 ((|#3| $) 10))) +(((-1223 |#1| |#2| |#3|) (-10 -8 (-15 -3826 ((-635 (-1069)) |#1|)) (-15 -3804 (|#1| |#1| (-635 (-1069)) (-635 |#3|))) (-15 -3804 (|#1| |#1| (-1069) |#3|)) (-15 -3651 (|#1| |#1|)) (-15 -3804 (|#1| |#2| |#3|)) (-15 -4017 (|#3| |#1|)) (-15 -3612 (|#1| |#1|)) (-15 -3627 (|#2| |#1|))) (-1224 |#2| |#3|) (-1039) (-783)) (T -1223)) +NIL +(-10 -8 (-15 -3826 ((-635 (-1069)) |#1|)) (-15 -3804 (|#1| |#1| (-635 (-1069)) (-635 |#3|))) (-15 -3804 (|#1| |#1| (-1069) |#3|)) (-15 -3651 (|#1| |#1|)) (-15 -3804 (|#1| |#2| |#3|)) (-15 -4017 (|#3| |#1|)) (-15 -3612 (|#1| |#1|)) (-15 -3627 (|#2| |#1|))) +((-2526 (((-112) $ $) 7)) (-3776 (((-112) $) 16)) (-3826 (((-635 (-1069)) $) 77)) (-4109 (((-1163) $) 106)) (-3689 (((-2 (|:| -2938 $) (|:| 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) |has| |#1| (-550)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3998 (|has| |#1| (-550)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #0#) |has| |#1| (-38 (-406 (-558)))) ((-608 (-558)) . T) ((-608 |#1|) |has| |#1| (-171)) ((-608 $) |has| |#1| (-550)) ((-605 (-853)) . T) ((-171) -3998 (|has| |#1| (-550)) (|has| |#1| (-171))) ((-232) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-285 $ $) |has| |#2| (-1099)) ((-289) |has| |#1| (-550)) ((-550) |has| |#1| (-550)) ((-638 #0#) |has| |#1| (-38 (-406 (-558)))) ((-638 |#1|) . T) ((-638 $) . T) ((-708 #0#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) |has| |#1| (-550)) ((-717) . 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T) ((-23) . T) ((-47 |#1| #0=(-406 (-558))) . T) ((-25) . T) ((-38 #1=(-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3986 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-35) |has| |#1| (-38 (-406 (-558)))) ((-95) |has| |#1| (-38 (-406 (-558)))) ((-102) . T) ((-111 #1# #1#) -3986 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3986 (|has| |#1| (-550)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3986 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 |#1|) |has| |#1| (-171)) ((-608 $) -3986 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-605 (-853)) . 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"TEX1" 2866564 NIL TEX1 (NIL T) -7 NIL NIL) (-1178 2866030 2866093 2866183 "TEMUTL" 2866314 T TEMUTL (NIL) -7 NIL NIL) (-1177 2864184 2864464 2864789 "TBCMPPK" 2865753 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1176 2856072 2862344 2862400 "TBAGG" 2862800 NIL TBAGG (NIL T T) -9 NIL 2863011) (-1175 2851142 2852630 2854384 "TBAGG-" 2854389 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1174 2850526 2850633 2850778 "TANEXP" 2851031 NIL TANEXP (NIL T) -7 NIL NIL) (-1173 2844027 2850383 2850476 "TABLE" 2850481 NIL TABLE (NIL T T) -8 NIL NIL) (-1172 2843439 2843538 2843676 "TABLEAU" 2843924 NIL TABLEAU (NIL T) -8 NIL NIL) (-1171 2838047 2839267 2840515 "TABLBUMP" 2842225 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1170 2837475 2837575 2837703 "SYSTEM" 2837941 T SYSTEM (NIL) -7 NIL NIL) (-1169 2833938 2834633 2835416 "SYSSOLP" 2836726 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1168 2830272 2831199 2831915 "SYNTAX" 2833244 T SYNTAX (NIL) -8 NIL NIL) (-1167 2827430 2828032 2828664 "SYMTAB" 2829662 T SYMTAB (NIL) -8 NIL NIL) (-1166 2822679 2823581 2824564 "SYMS" 2826469 T SYMS (NIL) -8 NIL NIL) (-1165 2819951 2822137 2822367 "SYMPOLY" 2822484 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1164 2819468 2819543 2819666 "SYMFUNC" 2819863 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1163 2815520 2816780 2817593 "SYMBOL" 2818677 T SYMBOL (NIL) -8 NIL NIL) (-1162 2809059 2810748 2812468 "SWITCH" 2813822 T SWITCH (NIL) -8 NIL NIL) (-1161 2802329 2807880 2808183 "SUTS" 2808814 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1160 2794430 2801576 2801849 "SUPXS" 2802114 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1159 2785960 2794048 2794174 "SUP" 2794339 NIL SUP (NIL T) -8 NIL NIL) (-1158 2785119 2785246 2785463 "SUPFRACF" 2785828 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1157 2784740 2784799 2784912 "SUP2" 2785054 NIL SUP2 (NIL T T) -7 NIL NIL) (-1156 2783153 2783427 2783790 "SUMRF" 2784439 NIL SUMRF (NIL T) -7 NIL NIL) (-1155 2782467 2782533 2782732 "SUMFS" 2783074 NIL SUMFS (NIL T T) -7 NIL NIL) (-1154 2766474 2781644 2781895 "SULS" 2782274 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1153 2766103 2766296 2766366 "SUCHTAST" 2766426 T SUCHTAST (NIL) -8 NIL NIL) (-1152 2765425 2765628 2765768 "SUCH" 2766011 NIL SUCH (NIL T T) -8 NIL NIL) (-1151 2759319 2760331 2761290 "SUBSPACE" 2764513 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1150 2758749 2758839 2759003 "SUBRESP" 2759207 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1149 2752118 2753414 2754725 "STTF" 2757485 NIL STTF (NIL T) -7 NIL NIL) (-1148 2746291 2747411 2748558 "STTFNC" 2751018 NIL STTFNC (NIL T) -7 NIL NIL) (-1147 2737606 2739473 2741267 "STTAYLOR" 2744532 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1146 2730850 2737470 2737553 "STRTBL" 2737558 NIL STRTBL (NIL T) -8 NIL NIL) (-1145 2726241 2730805 2730836 "STRING" 2730841 T STRING (NIL) -8 NIL NIL) (-1144 2721129 2725614 2725644 "STRICAT" 2725703 T STRICAT (NIL) -9 NIL 2725765) (-1143 2713939 2718748 2719359 "STREAM" 2720553 NIL STREAM (NIL T) -8 NIL NIL) (-1142 2713449 2713526 2713670 "STREAM3" 2713856 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1141 2712431 2712614 2712849 "STREAM2" 2713262 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1140 2712119 2712171 2712264 "STREAM1" 2712373 NIL STREAM1 (NIL T) -7 NIL NIL) (-1139 2711135 2711316 2711547 "STINPROD" 2711935 NIL STINPROD (NIL T) -7 NIL NIL) (-1138 2710713 2710897 2710927 "STEP" 2711007 T STEP (NIL) -9 NIL 2711085) (-1137 2704256 2710612 2710689 "STBL" 2710694 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1136 2699430 2703477 2703520 "STAGG" 2703673 NIL STAGG (NIL T) -9 NIL 2703762) (-1135 2697132 2697734 2698606 "STAGG-" 2698611 NIL STAGG- (NIL T T) -8 NIL NIL) (-1134 2695327 2696902 2696994 "STACK" 2697075 NIL STACK (NIL T) -8 NIL NIL) (-1133 2688052 2693468 2693924 "SREGSET" 2694957 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1132 2680478 2681846 2683359 "SRDCMPK" 2686658 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1131 2673445 2677918 2677948 "SRAGG" 2679251 T SRAGG (NIL) -9 NIL 2679859) (-1130 2672462 2672717 2673096 "SRAGG-" 2673101 NIL SRAGG- (NIL T) -8 NIL NIL) (-1129 2666957 2671409 2671830 "SQMATRIX" 2672088 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1128 2660706 2663675 2664402 "SPLTREE" 2666302 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1127 2656696 2657362 2658008 "SPLNODE" 2660132 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1126 2655743 2655976 2656006 "SPFCAT" 2656450 T SPFCAT (NIL) -9 NIL NIL) (-1125 2654480 2654690 2654954 "SPECOUT" 2655501 T SPECOUT (NIL) -7 NIL NIL) (-1124 2646132 2647876 2647906 "SPADXPT" 2652298 T SPADXPT (NIL) -9 NIL 2654332) (-1123 2645893 2645933 2646002 "SPADPRSR" 2646085 T SPADPRSR (NIL) -7 NIL NIL) (-1122 2644076 2645848 2645879 "SPADAST" 2645884 T SPADAST (NIL) -8 NIL NIL) (-1121 2636047 2637794 2637837 "SPACEC" 2642210 NIL SPACEC (NIL T) -9 NIL 2644026) (-1120 2634218 2635979 2636028 "SPACE3" 2636033 NIL SPACE3 (NIL T) -8 NIL NIL) (-1119 2632970 2633141 2633432 "SORTPAK" 2634023 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1118 2631020 2631323 2631742 "SOLVETRA" 2632634 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1117 2630031 2630253 2630527 "SOLVESER" 2630793 NIL SOLVESER (NIL T) -7 NIL NIL) (-1116 2625251 2626132 2627134 "SOLVERAD" 2629083 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1115 2621066 2621675 2622404 "SOLVEFOR" 2624618 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1114 2615363 2620415 2620512 "SNTSCAT" 2620517 NIL SNTSCAT (NIL T T T T) -9 NIL 2620587) (-1113 2609506 2613686 2614077 "SMTS" 2615053 NIL SMTS (NIL T T T) -8 NIL NIL) (-1112 2603957 2609394 2609471 "SMP" 2609476 NIL SMP (NIL T T) -8 NIL NIL) (-1111 2602116 2602417 2602815 "SMITH" 2603654 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1110 2595011 2599167 2599270 "SMATCAT" 2600621 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601171) (-1109 2591951 2592774 2593952 "SMATCAT-" 2593957 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1108 2589664 2591187 2591230 "SKAGG" 2591491 NIL SKAGG (NIL T) -9 NIL 2591626) (-1107 2586035 2589109 2589304 "SINT" 2589491 T SINT (NIL) -8 NIL NIL) (-1106 2585807 2585845 2585911 "SIMPAN" 2585991 T SIMPAN (NIL) -7 NIL NIL) (-1105 2585114 2585342 2585482 "SIG" 2585689 T SIG (NIL) -8 NIL NIL) (-1104 2583952 2584173 2584448 "SIGNRF" 2584873 NIL SIGNRF (NIL T) -7 NIL NIL) (-1103 2582757 2582908 2583199 "SIGNEF" 2583781 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1102 2582090 2582340 2582464 "SIGAST" 2582655 T SIGAST (NIL) -8 NIL NIL) (-1101 2579780 2580234 2580740 "SHP" 2581631 NIL SHP (NIL T NIL) -7 NIL NIL) (-1100 2573686 2579681 2579757 "SHDP" 2579762 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1099 2573285 2573451 2573481 "SGROUP" 2573574 T SGROUP (NIL) -9 NIL 2573636) (-1098 2573143 2573169 2573242 "SGROUP-" 2573247 NIL SGROUP- (NIL T) -8 NIL NIL) (-1097 2569979 2570676 2571399 "SGCF" 2572442 T SGCF (NIL) -7 NIL NIL) (-1096 2564374 2569426 2569523 "SFRTCAT" 2569528 NIL SFRTCAT (NIL T T T T) -9 NIL 2569567) (-1095 2557798 2558813 2559949 "SFRGCD" 2563357 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1094 2550926 2551997 2553183 "SFQCMPK" 2556731 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1093 2550548 2550637 2550747 "SFORT" 2550867 NIL SFORT (NIL T T) -8 NIL NIL) (-1092 2549693 2550388 2550509 "SEXOF" 2550514 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1091 2548827 2549574 2549642 "SEX" 2549647 T SEX (NIL) -8 NIL NIL) (-1090 2544366 2545055 2545150 "SEXCAT" 2548087 NIL SEXCAT (NIL T T T T T) -9 NIL 2548665) (-1089 2541546 2544300 2544348 "SET" 2544353 NIL SET (NIL T) -8 NIL NIL) (-1088 2539797 2540259 2540564 "SETMN" 2541287 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1087 2539403 2539529 2539559 "SETCAT" 2539676 T SETCAT (NIL) -9 NIL 2539761) (-1086 2539183 2539235 2539334 "SETCAT-" 2539339 NIL SETCAT- (NIL T) -8 NIL NIL) (-1085 2535570 2537644 2537687 "SETAGG" 2538557 NIL SETAGG (NIL T) -9 NIL 2538897) (-1084 2535028 2535144 2535381 "SETAGG-" 2535386 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1083 2534498 2534724 2534825 "SEQAST" 2534949 T SEQAST (NIL) -8 NIL NIL) (-1082 2533697 2533991 2534052 "SEGXCAT" 2534338 NIL SEGXCAT (NIL T T) -9 NIL 2534458) (-1081 2532753 2533363 2533545 "SEG" 2533550 NIL SEG (NIL T) -8 NIL NIL) (-1080 2531732 2531946 2531989 "SEGCAT" 2532511 NIL SEGCAT (NIL T) -9 NIL 2532732) (-1079 2530781 2531111 2531311 "SEGBIND" 2531567 NIL SEGBIND (NIL T) -8 NIL NIL) (-1078 2530402 2530461 2530574 "SEGBIND2" 2530716 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1077 2530003 2530203 2530280 "SEGAST" 2530347 T SEGAST (NIL) -8 NIL NIL) (-1076 2529222 2529348 2529552 "SEG2" 2529847 NIL SEG2 (NIL T T) -7 NIL NIL) (-1075 2528659 2529157 2529204 "SDVAR" 2529209 NIL SDVAR (NIL T) -8 NIL NIL) (-1074 2520949 2528429 2528559 "SDPOL" 2528564 NIL SDPOL (NIL T) -8 NIL NIL) (-1073 2519542 2519808 2520127 "SCPKG" 2520664 NIL SCPKG (NIL T) -7 NIL NIL) (-1072 2518678 2518858 2519058 "SCOPE" 2519364 T SCOPE (NIL) -8 NIL NIL) (-1071 2517899 2518032 2518211 "SCACHE" 2518533 NIL SCACHE (NIL T) -7 NIL NIL) (-1070 2517571 2517731 2517761 "SASTCAT" 2517766 T SASTCAT (NIL) -9 NIL 2517779) (-1069 2517085 2517406 2517482 "SAOS" 2517517 T SAOS (NIL) -8 NIL NIL) (-1068 2516650 2516685 2516858 "SAERFFC" 2517044 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1067 2510624 2516547 2516627 "SAE" 2516632 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1066 2510217 2510252 2510411 "SAEFACT" 2510583 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1065 2508538 2508852 2509253 "RURPK" 2509883 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1064 2507174 2507453 2507765 "RULESET" 2508372 NIL RULESET (NIL T T T) -8 NIL NIL) (-1063 2504361 2504864 2505329 "RULE" 2506855 NIL RULE (NIL T T T) -8 NIL NIL) (-1062 2504000 2504155 2504238 "RULECOLD" 2504313 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1061 2503498 2503717 2503811 "RSTRCAST" 2503928 T RSTRCAST (NIL) -8 NIL NIL) (-1060 2498347 2499141 2500061 "RSETGCD" 2502697 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1059 2487604 2492656 2492753 "RSETCAT" 2496872 NIL RSETCAT (NIL T T T T) -9 NIL 2497969) (-1058 2485531 2486070 2486894 "RSETCAT-" 2486899 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1057 2477918 2479293 2480813 "RSDCMPK" 2484130 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1056 2475923 2476364 2476438 "RRCC" 2477524 NIL RRCC (NIL T T) -9 NIL 2477868) (-1055 2475274 2475448 2475727 "RRCC-" 2475732 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1054 2474744 2474970 2475071 "RPTAST" 2475195 T RPTAST (NIL) -8 NIL NIL) (-1053 2448750 2458337 2458404 "RPOLCAT" 2469068 NIL RPOLCAT (NIL T T T) -9 NIL 2472227) (-1052 2440250 2442588 2445710 "RPOLCAT-" 2445715 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1051 2431297 2438461 2438943 "ROUTINE" 2439790 T ROUTINE (NIL) -8 NIL NIL) (-1050 2428130 2430923 2431063 "ROMAN" 2431179 T ROMAN (NIL) -8 NIL NIL) (-1049 2426405 2426990 2427250 "ROIRC" 2427935 NIL ROIRC (NIL T T) -8 NIL NIL) (-1048 2422798 2425041 2425071 "RNS" 2425375 T RNS (NIL) -9 NIL 2425648) (-1047 2421307 2421690 2422224 "RNS-" 2422299 NIL RNS- (NIL T) -8 NIL NIL) (-1046 2420756 2421138 2421168 "RNG" 2421173 T RNG (NIL) -9 NIL 2421194) (-1045 2420148 2420510 2420553 "RMODULE" 2420615 NIL RMODULE (NIL T) -9 NIL 2420657) (-1044 2418984 2419078 2419414 "RMCAT2" 2420049 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1043 2415861 2418330 2418627 "RMATRIX" 2418746 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1042 2408803 2411037 2411152 "RMATCAT" 2414511 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415493) (-1041 2408178 2408325 2408632 "RMATCAT-" 2408637 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1040 2407745 2407820 2407948 "RINTERP" 2408097 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1039 2406878 2407398 2407428 "RING" 2407484 T RING (NIL) -9 NIL 2407570) (-1038 2406670 2406714 2406811 "RING-" 2406816 NIL RING- (NIL T) -8 NIL NIL) (-1037 2405511 2405748 2406006 "RIDIST" 2406434 T RIDIST (NIL) -7 NIL NIL) (-1036 2396827 2404979 2405185 "RGCHAIN" 2405359 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1035 2396203 2396583 2396624 "RGBCSPC" 2396682 NIL RGBCSPC (NIL T) -9 NIL 2396734) (-1034 2395387 2395742 2395783 "RGBCMDL" 2396015 NIL RGBCMDL (NIL T) -9 NIL 2396129) (-1033 2392381 2392995 2393665 "RF" 2394751 NIL RF (NIL T) -7 NIL NIL) (-1032 2392027 2392090 2392193 "RFFACTOR" 2392312 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1031 2391752 2391787 2391884 "RFFACT" 2391986 NIL RFFACT (NIL T) -7 NIL NIL) (-1030 2389869 2390233 2390615 "RFDIST" 2391392 T RFDIST (NIL) -7 NIL NIL) (-1029 2389322 2389414 2389577 "RETSOL" 2389771 NIL RETSOL (NIL T T) -7 NIL NIL) (-1028 2388958 2389038 2389081 "RETRACT" 2389214 NIL RETRACT (NIL T) -9 NIL 2389301) (-1027 2388807 2388832 2388919 "RETRACT-" 2388924 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1026 2388436 2388629 2388699 "RETAST" 2388759 T RETAST (NIL) -8 NIL NIL) (-1025 2381290 2388089 2388216 "RESULT" 2388331 T RESULT (NIL) -8 NIL NIL) (-1024 2379916 2380559 2380758 "RESRING" 2381193 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1023 2379552 2379601 2379699 "RESLATC" 2379853 NIL RESLATC (NIL T) -7 NIL NIL) (-1022 2379258 2379292 2379399 "REPSQ" 2379511 NIL REPSQ (NIL T) -7 NIL NIL) (-1021 2376680 2377260 2377862 "REP" 2378678 T REP (NIL) -7 NIL NIL) (-1020 2376378 2376412 2376523 "REPDB" 2376639 NIL REPDB (NIL T) -7 NIL NIL) (-1019 2370288 2371667 2372890 "REP2" 2375190 NIL REP2 (NIL T) -7 NIL NIL) (-1018 2366665 2367346 2368154 "REP1" 2369515 NIL REP1 (NIL T) -7 NIL NIL) (-1017 2359391 2364806 2365262 "REGSET" 2366295 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1016 2358204 2358539 2358789 "REF" 2359176 NIL REF (NIL T) -8 NIL NIL) (-1015 2357581 2357684 2357851 "REDORDER" 2358088 NIL REDORDER (NIL T T) -7 NIL NIL) (-1014 2353586 2356794 2357021 "RECLOS" 2357409 NIL RECLOS (NIL T) -8 NIL NIL) (-1013 2352638 2352819 2353034 "REALSOLV" 2353393 T REALSOLV (NIL) -7 NIL NIL) (-1012 2352484 2352525 2352555 "REAL" 2352560 T REAL (NIL) -9 NIL 2352595) (-1011 2348967 2349769 2350653 "REAL0Q" 2351649 NIL REAL0Q (NIL T) -7 NIL NIL) (-1010 2344568 2345556 2346617 "REAL0" 2347948 NIL REAL0 (NIL T) -7 NIL NIL) (-1009 2344066 2344285 2344379 "RDUCEAST" 2344496 T RDUCEAST (NIL) -8 NIL NIL) (-1008 2343471 2343543 2343750 "RDIV" 2343988 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-1007 2342539 2342713 2342926 "RDIST" 2343293 NIL RDIST (NIL T) -7 NIL NIL) (-1006 2341136 2341423 2341795 "RDETRS" 2342247 NIL RDETRS (NIL T T) -7 NIL NIL) (-1005 2338948 2339402 2339940 "RDETR" 2340678 NIL RDETR (NIL T T) -7 NIL NIL) (-1004 2337559 2337837 2338241 "RDEEFS" 2338664 NIL RDEEFS (NIL T T) -7 NIL NIL) (-1003 2336054 2336360 2336792 "RDEEF" 2337247 NIL RDEEF (NIL T T) -7 NIL NIL) (-1002 2330315 2333190 2333220 "RCFIELD" 2334515 T RCFIELD (NIL) -9 NIL 2335245) (-1001 2328379 2328883 2329579 "RCFIELD-" 2329654 NIL RCFIELD- (NIL T) -8 NIL NIL) (-1000 2324695 2326480 2326523 "RCAGG" 2327607 NIL RCAGG (NIL T) -9 NIL 2328072) (-999 2324325 2324419 2324580 "RCAGG-" 2324585 NIL RCAGG- (NIL T T) -8 NIL NIL) (-998 2323665 2323777 2323940 "RATRET" 2324209 NIL RATRET (NIL T) -7 NIL NIL) (-997 2323222 2323289 2323408 "RATFACT" 2323593 NIL RATFACT (NIL T) -7 NIL NIL) (-996 2322537 2322657 2322807 "RANDSRC" 2323092 T RANDSRC (NIL) -7 NIL NIL) (-995 2322274 2322318 2322389 "RADUTIL" 2322486 T RADUTIL (NIL) -7 NIL NIL) (-994 2315436 2321116 2321424 "RADIX" 2321998 NIL RADIX (NIL NIL) -8 NIL NIL) (-993 2307093 2315280 2315408 "RADFF" 2315413 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-992 2306745 2306820 2306848 "RADCAT" 2307005 T RADCAT (NIL) -9 NIL NIL) (-991 2306530 2306578 2306675 "RADCAT-" 2306680 NIL RADCAT- (NIL T) -8 NIL NIL) (-990 2304681 2306305 2306394 "QUEUE" 2306474 NIL QUEUE (NIL T) -8 NIL NIL) (-989 2301257 2304618 2304663 "QUAT" 2304668 NIL QUAT (NIL T) -8 NIL NIL) (-988 2300895 2300938 2301065 "QUATCT2" 2301208 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-987 2294642 2297944 2297984 "QUATCAT" 2298764 NIL QUATCAT (NIL T) -9 NIL 2299530) (-986 2290786 2291823 2293210 "QUATCAT-" 2293304 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-985 2288306 2289870 2289911 "QUAGG" 2290286 NIL QUAGG (NIL T) -9 NIL 2290461) (-984 2287938 2288131 2288199 "QQUTAST" 2288258 T QQUTAST (NIL) -8 NIL NIL) (-983 2286863 2287336 2287508 "QFORM" 2287810 NIL QFORM (NIL NIL T) -8 NIL NIL) (-982 2278075 2283280 2283320 "QFCAT" 2283978 NIL QFCAT (NIL T) -9 NIL 2284979) (-981 2273647 2274848 2276439 "QFCAT-" 2276533 NIL QFCAT- (NIL T T) -8 NIL NIL) (-980 2273285 2273328 2273455 "QFCAT2" 2273598 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-979 2272745 2272855 2272985 "QEQUAT" 2273175 T QEQUAT (NIL) -8 NIL NIL) (-978 2265893 2266964 2268148 "QCMPACK" 2271678 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-977 2263469 2263890 2264318 "QALGSET" 2265548 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-976 2262714 2262888 2263120 "QALGSET2" 2263289 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-975 2261405 2261628 2261945 "PWFFINTB" 2262487 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-974 2259587 2259755 2260109 "PUSHVAR" 2261219 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-973 2255505 2256559 2256600 "PTRANFN" 2258484 NIL PTRANFN (NIL T) -9 NIL NIL) (-972 2253907 2254198 2254520 "PTPACK" 2255216 NIL PTPACK (NIL T) -7 NIL NIL) (-971 2253539 2253596 2253705 "PTFUNC2" 2253844 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-970 2248066 2252411 2252452 "PTCAT" 2252748 NIL PTCAT (NIL T) -9 NIL 2252901) (-969 2247724 2247759 2247883 "PSQFR" 2248025 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-968 2246319 2246617 2246951 "PSEUDLIN" 2247422 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-967 2233089 2235453 2237777 "PSETPK" 2244079 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-966 2226133 2228847 2228943 "PSETCAT" 2231964 NIL PSETCAT (NIL T T T T) -9 NIL 2232778) (-965 2223969 2224603 2225424 "PSETCAT-" 2225429 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-964 2223318 2223483 2223511 "PSCURVE" 2223779 T PSCURVE (NIL) -9 NIL 2223946) (-963 2219674 2221156 2221221 "PSCAT" 2222065 NIL PSCAT (NIL T T T) -9 NIL 2222305) (-962 2218737 2218953 2219353 "PSCAT-" 2219358 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-961 2217469 2218102 2218307 "PRTITION" 2218552 T PRTITION (NIL) -8 NIL NIL) (-960 2216971 2217190 2217282 "PRTDAST" 2217397 T PRTDAST (NIL) -8 NIL NIL) (-959 2206069 2208275 2210463 "PRS" 2214833 NIL PRS (NIL T T) -7 NIL NIL) (-958 2203927 2205419 2205459 "PRQAGG" 2205642 NIL PRQAGG (NIL T) -9 NIL 2205744) (-957 2203313 2203542 2203570 "PROPLOG" 2203755 T PROPLOG (NIL) -9 NIL 2203877) (-956 2200483 2201127 2201591 "PROPFRML" 2202881 NIL PROPFRML (NIL T) -8 NIL NIL) (-955 2199943 2200053 2200183 "PROPERTY" 2200373 T PROPERTY (NIL) -8 NIL NIL) (-954 2194028 2198109 2198929 "PRODUCT" 2199169 NIL PRODUCT (NIL T T) -8 NIL NIL) (-953 2191341 2193486 2193720 "PR" 2193839 NIL PR (NIL T T) -8 NIL NIL) (-952 2191137 2191169 2191228 "PRINT" 2191302 T PRINT (NIL) -7 NIL NIL) (-951 2190477 2190594 2190746 "PRIMES" 2191017 NIL PRIMES (NIL T) -7 NIL NIL) (-950 2188542 2188943 2189409 "PRIMELT" 2190056 NIL PRIMELT (NIL T) -7 NIL NIL) (-949 2188271 2188320 2188348 "PRIMCAT" 2188472 T PRIMCAT (NIL) -9 NIL NIL) (-948 2184432 2188209 2188254 "PRIMARR" 2188259 NIL PRIMARR (NIL T) -8 NIL NIL) (-947 2183439 2183617 2183845 "PRIMARR2" 2184250 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-946 2183082 2183138 2183249 "PREASSOC" 2183377 NIL PREASSOC (NIL T T) -7 NIL NIL) (-945 2182557 2182690 2182718 "PPCURVE" 2182923 T PPCURVE (NIL) -9 NIL 2183059) (-944 2182179 2182352 2182435 "PORTNUM" 2182494 T PORTNUM (NIL) -8 NIL NIL) (-943 2179538 2179937 2180529 "POLYROOT" 2181760 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-942 2173483 2179142 2179302 "POLY" 2179411 NIL POLY (NIL T) -8 NIL NIL) (-941 2172866 2172924 2173158 "POLYLIFT" 2173419 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-940 2169141 2169590 2170219 "POLYCATQ" 2172411 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-939 2155958 2161316 2161381 "POLYCAT" 2164895 NIL POLYCAT (NIL T T T) -9 NIL 2166823) (-938 2149408 2151269 2153653 "POLYCAT-" 2153658 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-937 2148995 2149063 2149183 "POLY2UP" 2149334 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-936 2148627 2148684 2148793 "POLY2" 2148932 NIL POLY2 (NIL T T) -7 NIL NIL) (-935 2147312 2147551 2147827 "POLUTIL" 2148401 NIL POLUTIL (NIL T T) -7 NIL NIL) (-934 2145667 2145944 2146275 "POLTOPOL" 2147034 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-933 2141185 2145603 2145649 "POINT" 2145654 NIL POINT (NIL T) -8 NIL NIL) (-932 2139372 2139729 2140104 "PNTHEORY" 2140830 T PNTHEORY (NIL) -7 NIL NIL) (-931 2137791 2138088 2138500 "PMTOOLS" 2139070 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-930 2137384 2137462 2137579 "PMSYM" 2137707 NIL PMSYM (NIL T) -7 NIL NIL) (-929 2136894 2136963 2137137 "PMQFCAT" 2137309 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-928 2136249 2136359 2136515 "PMPRED" 2136771 NIL PMPRED (NIL T) -7 NIL NIL) (-927 2135645 2135731 2135892 "PMPREDFS" 2136150 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-926 2134288 2134496 2134881 "PMPLCAT" 2135407 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-925 2133820 2133899 2134051 "PMLSAGG" 2134203 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-924 2133295 2133371 2133552 "PMKERNEL" 2133738 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-923 2132912 2132987 2133100 "PMINS" 2133214 NIL PMINS (NIL T) -7 NIL NIL) (-922 2132340 2132409 2132625 "PMFS" 2132837 NIL PMFS (NIL T T T) -7 NIL NIL) (-921 2131568 2131686 2131891 "PMDOWN" 2132217 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-920 2130731 2130890 2131072 "PMASS" 2131406 T PMASS (NIL) -7 NIL NIL) (-919 2130005 2130116 2130279 "PMASSFS" 2130617 NIL PMASSFS (NIL T T) -7 NIL NIL) (-918 2129660 2129728 2129822 "PLOTTOOL" 2129931 T PLOTTOOL (NIL) -7 NIL NIL) (-917 2124282 2125471 2126619 "PLOT" 2128532 T PLOT (NIL) -8 NIL NIL) (-916 2120096 2121130 2122051 "PLOT3D" 2123381 T PLOT3D (NIL) -8 NIL NIL) (-915 2119008 2119185 2119420 "PLOT1" 2119900 NIL PLOT1 (NIL T) -7 NIL NIL) (-914 2094402 2099074 2103925 "PLEQN" 2114274 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-913 2093720 2093842 2094022 "PINTERP" 2094267 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-912 2093413 2093460 2093563 "PINTERPA" 2093667 NIL PINTERPA (NIL T T) -7 NIL NIL) (-911 2092698 2093219 2093306 "PI" 2093346 T PI (NIL) -8 NIL NIL) (-910 2091095 2092036 2092064 "PID" 2092246 T PID (NIL) -9 NIL 2092380) (-909 2090820 2090857 2090945 "PICOERCE" 2091052 NIL PICOERCE (NIL T) -7 NIL NIL) (-908 2090140 2090279 2090455 "PGROEB" 2090676 NIL PGROEB (NIL T) -7 NIL NIL) (-907 2085727 2086541 2087446 "PGE" 2089255 T PGE (NIL) -7 NIL NIL) (-906 2083851 2084097 2084463 "PGCD" 2085444 NIL PGCD (NIL T T T T) -7 NIL NIL) (-905 2083189 2083292 2083453 "PFRPAC" 2083735 NIL PFRPAC (NIL T) -7 NIL NIL) (-904 2079869 2081737 2082090 "PFR" 2082868 NIL PFR (NIL T) -8 NIL NIL) (-903 2078258 2078502 2078827 "PFOTOOLS" 2079616 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-902 2076791 2077030 2077381 "PFOQ" 2078015 NIL PFOQ (NIL T T T) -7 NIL NIL) (-901 2075264 2075476 2075839 "PFO" 2076575 NIL PFO (NIL T T T T T) -7 NIL NIL) (-900 2071852 2075153 2075222 "PF" 2075227 NIL PF (NIL NIL) -8 NIL NIL) (-899 2069286 2070523 2070551 "PFECAT" 2071136 T PFECAT (NIL) -9 NIL 2071520) (-898 2068731 2068885 2069099 "PFECAT-" 2069104 NIL PFECAT- (NIL T) -8 NIL NIL) (-897 2067335 2067586 2067887 "PFBRU" 2068480 NIL PFBRU (NIL T T) -7 NIL NIL) (-896 2065202 2065553 2065985 "PFBR" 2066986 NIL PFBR (NIL T T T T) -7 NIL NIL) (-895 2061119 2062578 2063254 "PERM" 2064559 NIL PERM (NIL T) -8 NIL NIL) (-894 2056385 2057326 2058196 "PERMGRP" 2060282 NIL PERMGRP (NIL T) -8 NIL NIL) (-893 2054517 2055448 2055489 "PERMCAT" 2055935 NIL PERMCAT (NIL T) -9 NIL 2056240) (-892 2054170 2054211 2054335 "PERMAN" 2054470 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-891 2051706 2053835 2053957 "PENDTREE" 2054081 NIL PENDTREE (NIL T) -8 NIL NIL) (-890 2049799 2050533 2050574 "PDRING" 2051231 NIL PDRING (NIL T) -9 NIL 2051517) (-889 2048902 2049120 2049482 "PDRING-" 2049487 NIL PDRING- (NIL T T) -8 NIL NIL) (-888 2046144 2046895 2047563 "PDEPROB" 2048254 T PDEPROB (NIL) -8 NIL NIL) (-887 2043691 2044193 2044748 "PDEPACK" 2045609 T PDEPACK (NIL) -7 NIL NIL) (-886 2042603 2042793 2043044 "PDECOMP" 2043490 NIL PDECOMP (NIL T T) -7 NIL NIL) (-885 2040208 2041025 2041053 "PDECAT" 2041840 T PDECAT (NIL) -9 NIL 2042553) (-884 2039959 2039992 2040082 "PCOMP" 2040169 NIL PCOMP (NIL T T) -7 NIL NIL) (-883 2038164 2038760 2039057 "PBWLB" 2039688 NIL PBWLB (NIL T) -8 NIL NIL) (-882 2030669 2032237 2033575 "PATTERN" 2036847 NIL PATTERN (NIL T) -8 NIL NIL) (-881 2030301 2030358 2030467 "PATTERN2" 2030606 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-880 2028058 2028446 2028903 "PATTERN1" 2029890 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-879 2025453 2026007 2026488 "PATRES" 2027623 NIL PATRES (NIL T T) -8 NIL NIL) (-878 2025017 2025084 2025216 "PATRES2" 2025380 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-877 2022900 2023305 2023712 "PATMATCH" 2024684 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-876 2022436 2022619 2022660 "PATMAB" 2022767 NIL PATMAB (NIL T) -9 NIL 2022850) (-875 2020981 2021290 2021548 "PATLRES" 2022241 NIL PATLRES (NIL T T T) -8 NIL NIL) (-874 2020527 2020650 2020691 "PATAB" 2020696 NIL PATAB (NIL T) -9 NIL 2020868) (-873 2018008 2018540 2019113 "PARTPERM" 2019974 T PARTPERM (NIL) -7 NIL NIL) (-872 2017629 2017692 2017794 "PARSURF" 2017939 NIL PARSURF (NIL T) -8 NIL NIL) (-871 2017261 2017318 2017427 "PARSU2" 2017566 NIL PARSU2 (NIL T T) -7 NIL NIL) (-870 2017025 2017065 2017132 "PARSER" 2017214 T PARSER (NIL) -7 NIL NIL) (-869 2016646 2016709 2016811 "PARSCURV" 2016956 NIL PARSCURV (NIL T) -8 NIL NIL) (-868 2016278 2016335 2016444 "PARSC2" 2016583 NIL PARSC2 (NIL T T) -7 NIL NIL) (-867 2015917 2015975 2016072 "PARPCURV" 2016214 NIL PARPCURV (NIL T) -8 NIL NIL) (-866 2015549 2015606 2015715 "PARPC2" 2015854 NIL PARPC2 (NIL T T) -7 NIL NIL) (-865 2015069 2015155 2015274 "PAN2EXPR" 2015450 T PAN2EXPR (NIL) -7 NIL NIL) (-864 2013875 2014190 2014418 "PALETTE" 2014861 T PALETTE (NIL) -8 NIL NIL) (-863 2012343 2012880 2013240 "PAIR" 2013561 NIL PAIR (NIL T T) -8 NIL NIL) (-862 2006249 2011602 2011796 "PADICRC" 2012198 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-861 1999513 2005595 2005779 "PADICRAT" 2006097 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-860 1997863 1999450 1999495 "PADIC" 1999500 NIL PADIC (NIL NIL) -8 NIL NIL) (-859 1995073 1996603 1996643 "PADICCT" 1997224 NIL PADICCT (NIL NIL) -9 NIL 1997506) (-858 1994030 1994230 1994498 "PADEPAC" 1994860 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-857 1993242 1993375 1993581 "PADE" 1993892 NIL PADE (NIL T T T) -7 NIL NIL) (-856 1991664 1992450 1992730 "OWP" 1993046 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-855 1990737 1991269 1991441 "OVAR" 1991532 NIL OVAR (NIL NIL) -8 NIL NIL) (-854 1990001 1990122 1990283 "OUT" 1990596 T OUT (NIL) -7 NIL NIL) (-853 1978908 1981110 1983310 "OUTFORM" 1987821 T OUTFORM (NIL) -8 NIL NIL) (-852 1978329 1978505 1978632 "OUTBFILE" 1978801 T OUTBFILE (NIL) -8 NIL NIL) (-851 1977966 1978049 1978077 "OUTBCON" 1978228 T OUTBCON (NIL) -9 NIL 1978313) (-850 1977806 1977841 1977917 "OUTBCON-" 1977922 NIL OUTBCON- (NIL T) -8 NIL NIL) (-849 1977214 1977535 1977624 "OSI" 1977737 T OSI (NIL) -8 NIL NIL) (-848 1976770 1977082 1977110 "OSGROUP" 1977115 T OSGROUP (NIL) -9 NIL 1977137) (-847 1975515 1975742 1976027 "ORTHPOL" 1976517 NIL ORTHPOL (NIL T) -7 NIL NIL) (-846 1973101 1975350 1975471 "OREUP" 1975476 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-845 1970539 1972792 1972919 "ORESUP" 1973043 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-844 1968067 1968567 1969128 "OREPCTO" 1970028 NIL OREPCTO (NIL T T) -7 NIL NIL) (-843 1961891 1964058 1964099 "OREPCAT" 1966447 NIL OREPCAT (NIL T) -9 NIL 1967551) (-842 1959038 1959820 1960878 "OREPCAT-" 1960883 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-841 1958215 1958487 1958515 "ORDSET" 1958824 T ORDSET (NIL) -9 NIL 1958988) (-840 1957734 1957856 1958049 "ORDSET-" 1958054 NIL ORDSET- (NIL T) -8 NIL NIL) (-839 1956368 1957125 1957153 "ORDRING" 1957355 T ORDRING (NIL) -9 NIL 1957480) (-838 1956013 1956107 1956251 "ORDRING-" 1956256 NIL ORDRING- (NIL T) -8 NIL NIL) (-837 1955419 1955856 1955884 "ORDMON" 1955889 T ORDMON (NIL) -9 NIL 1955910) (-836 1954581 1954728 1954923 "ORDFUNS" 1955268 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-835 1953945 1954338 1954366 "ORDFIN" 1954431 T ORDFIN (NIL) -9 NIL 1954505) (-834 1950537 1952531 1952940 "ORDCOMP" 1953569 NIL ORDCOMP (NIL T) -8 NIL NIL) (-833 1949803 1949930 1950116 "ORDCOMP2" 1950397 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-832 1946411 1947294 1948108 "OPTPROB" 1949009 T OPTPROB (NIL) -8 NIL NIL) (-831 1943213 1943852 1944556 "OPTPACK" 1945727 T OPTPACK (NIL) -7 NIL NIL) (-830 1940926 1941666 1941694 "OPTCAT" 1942513 T OPTCAT (NIL) -9 NIL 1943163) (-829 1940369 1940603 1940708 "OPSIG" 1940841 T OPSIG (NIL) -8 NIL NIL) (-828 1940137 1940176 1940242 "OPQUERY" 1940323 T OPQUERY (NIL) -7 NIL NIL) (-827 1937303 1938448 1938952 "OP" 1939666 NIL OP (NIL T) -8 NIL NIL) (-826 1936838 1937009 1937050 "OPERCAT" 1937185 NIL OPERCAT (NIL T) -9 NIL 1937253) (-825 1936684 1936711 1936797 "OPERCAT-" 1936802 NIL OPERCAT- (NIL T T) -8 NIL NIL) (-824 1933529 1935481 1935850 "ONECOMP" 1936348 NIL ONECOMP (NIL T) -8 NIL NIL) (-823 1932834 1932949 1933123 "ONECOMP2" 1933401 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-822 1932253 1932359 1932489 "OMSERVER" 1932724 T OMSERVER (NIL) -7 NIL NIL) (-821 1929141 1931693 1931733 "OMSAGG" 1931794 NIL OMSAGG (NIL T) -9 NIL 1931858) (-820 1927764 1928027 1928309 "OMPKG" 1928879 T OMPKG (NIL) -7 NIL NIL) (-819 1927194 1927297 1927325 "OM" 1927624 T OM (NIL) -9 NIL NIL) (-818 1925776 1926743 1926912 "OMLO" 1927075 NIL OMLO (NIL T T) -8 NIL NIL) (-817 1924701 1924848 1925075 "OMEXPR" 1925602 NIL OMEXPR (NIL T) -7 NIL NIL) (-816 1924019 1924247 1924383 "OMERR" 1924585 T OMERR (NIL) -8 NIL NIL) (-815 1923197 1923440 1923600 "OMERRK" 1923879 T OMERRK (NIL) -8 NIL NIL) (-814 1922675 1922874 1922982 "OMENC" 1923109 T OMENC (NIL) -8 NIL NIL) (-813 1916570 1917755 1918926 "OMDEV" 1921524 T OMDEV (NIL) -8 NIL NIL) (-812 1915639 1915810 1916004 "OMCONN" 1916396 T OMCONN (NIL) -8 NIL NIL) (-811 1914260 1915202 1915230 "OINTDOM" 1915235 T OINTDOM (NIL) -9 NIL 1915256) (-810 1910066 1911250 1911966 "OFMONOID" 1913576 NIL OFMONOID (NIL T) -8 NIL NIL) (-809 1909504 1910003 1910048 "ODVAR" 1910053 NIL ODVAR (NIL T) -8 NIL NIL) (-808 1906962 1909249 1909404 "ODR" 1909409 NIL ODR (NIL T T NIL) -8 NIL NIL) (-807 1899306 1906738 1906864 "ODPOL" 1906869 NIL ODPOL (NIL T) -8 NIL NIL) (-806 1893182 1899178 1899283 "ODP" 1899288 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-805 1891948 1892163 1892438 "ODETOOLS" 1892956 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-804 1888917 1889573 1890289 "ODESYS" 1891281 NIL ODESYS (NIL T T) -7 NIL NIL) (-803 1883799 1884707 1885732 "ODERTRIC" 1887992 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-802 1883225 1883307 1883501 "ODERED" 1883711 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-801 1880113 1880661 1881338 "ODERAT" 1882648 NIL ODERAT (NIL T T) -7 NIL NIL) (-800 1877073 1877537 1878134 "ODEPRRIC" 1879642 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-799 1875043 1875612 1876098 "ODEPROB" 1876607 T ODEPROB (NIL) -8 NIL NIL) (-798 1871565 1872048 1872695 "ODEPRIM" 1874522 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-797 1870814 1870916 1871176 "ODEPAL" 1871457 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-796 1866976 1867767 1868631 "ODEPACK" 1869970 T ODEPACK (NIL) -7 NIL NIL) (-795 1866009 1866116 1866345 "ODEINT" 1866865 NIL ODEINT (NIL T T) -7 NIL NIL) (-794 1860110 1861535 1862982 "ODEIFTBL" 1864582 T ODEIFTBL (NIL) -8 NIL NIL) (-793 1855445 1856231 1857190 "ODEEF" 1859269 NIL ODEEF (NIL T T) -7 NIL NIL) (-792 1854780 1854869 1855099 "ODECONST" 1855350 NIL ODECONST (NIL T T T) -7 NIL NIL) (-791 1852931 1853566 1853594 "ODECAT" 1854199 T ODECAT (NIL) -9 NIL 1854730) (-790 1849838 1852643 1852762 "OCT" 1852844 NIL OCT (NIL T) -8 NIL NIL) (-789 1849476 1849519 1849646 "OCTCT2" 1849789 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-788 1844250 1846650 1846690 "OC" 1847787 NIL OC (NIL T) -9 NIL 1848645) (-787 1841477 1842225 1843215 "OC-" 1843309 NIL OC- (NIL T T) -8 NIL NIL) (-786 1840855 1841297 1841325 "OCAMON" 1841330 T OCAMON (NIL) -9 NIL 1841351) (-785 1840412 1840727 1840755 "OASGP" 1840760 T OASGP (NIL) -9 NIL 1840780) (-784 1839699 1840162 1840190 "OAMONS" 1840230 T OAMONS (NIL) -9 NIL 1840273) (-783 1839139 1839546 1839574 "OAMON" 1839579 T OAMON (NIL) -9 NIL 1839599) (-782 1838443 1838935 1838963 "OAGROUP" 1838968 T OAGROUP (NIL) -9 NIL 1838988) (-781 1838133 1838183 1838271 "NUMTUBE" 1838387 NIL NUMTUBE (NIL T) -7 NIL NIL) (-780 1831706 1833224 1834760 "NUMQUAD" 1836617 T NUMQUAD (NIL) -7 NIL NIL) (-779 1827462 1828450 1829475 "NUMODE" 1830701 T NUMODE (NIL) -7 NIL NIL) (-778 1824843 1825697 1825725 "NUMINT" 1826648 T NUMINT (NIL) -9 NIL 1827412) (-777 1823791 1823988 1824206 "NUMFMT" 1824645 T NUMFMT (NIL) -7 NIL NIL) (-776 1810150 1813095 1815627 "NUMERIC" 1821298 NIL NUMERIC (NIL T) -7 NIL NIL) (-775 1804547 1809599 1809694 "NTSCAT" 1809699 NIL NTSCAT (NIL T T T T) -9 NIL 1809738) (-774 1803741 1803906 1804099 "NTPOLFN" 1804386 NIL NTPOLFN (NIL T) -7 NIL NIL) (-773 1791581 1800566 1801378 "NSUP" 1802962 NIL NSUP (NIL T) -8 NIL NIL) (-772 1791213 1791270 1791379 "NSUP2" 1791518 NIL NSUP2 (NIL T T) -7 NIL NIL) (-771 1781210 1790987 1791120 "NSMP" 1791125 NIL NSMP (NIL T T) -8 NIL NIL) (-770 1779642 1779943 1780300 "NREP" 1780898 NIL NREP (NIL T) -7 NIL NIL) (-769 1778233 1778485 1778843 "NPCOEF" 1779385 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-768 1777299 1777414 1777630 "NORMRETR" 1778114 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-767 1775340 1775630 1776039 "NORMPK" 1777007 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-766 1775025 1775053 1775177 "NORMMA" 1775306 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-765 1774852 1774982 1775011 "NONE" 1775016 T NONE (NIL) -8 NIL NIL) (-764 1774641 1774670 1774739 "NONE1" 1774816 NIL NONE1 (NIL T) -7 NIL NIL) (-763 1774124 1774186 1774372 "NODE1" 1774573 NIL NODE1 (NIL T T) -7 NIL NIL) (-762 1772464 1773287 1773542 "NNI" 1773889 T NNI (NIL) -8 NIL NIL) (-761 1770884 1771197 1771561 "NLINSOL" 1772132 NIL NLINSOL (NIL T) -7 NIL NIL) (-760 1767152 1768120 1769019 "NIPROB" 1770005 T NIPROB (NIL) -8 NIL NIL) (-759 1765909 1766143 1766445 "NFINTBAS" 1766914 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-758 1765353 1765560 1765601 "NETCLT" 1765765 NIL NETCLT (NIL T) -9 NIL 1765854) (-757 1764061 1764292 1764573 "NCODIV" 1765121 NIL NCODIV (NIL T T) -7 NIL NIL) (-756 1763823 1763860 1763935 "NCNTFRAC" 1764018 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-755 1762003 1762367 1762787 "NCEP" 1763448 NIL NCEP (NIL T) -7 NIL NIL) (-754 1760914 1761653 1761681 "NASRING" 1761791 T NASRING (NIL) -9 NIL 1761865) (-753 1760709 1760753 1760847 "NASRING-" 1760852 NIL NASRING- (NIL T) -8 NIL NIL) (-752 1759862 1760361 1760389 "NARNG" 1760506 T NARNG (NIL) -9 NIL 1760597) (-751 1759554 1759621 1759755 "NARNG-" 1759760 NIL NARNG- (NIL T) -8 NIL NIL) (-750 1758433 1758640 1758875 "NAGSP" 1759339 T NAGSP (NIL) -7 NIL NIL) (-749 1749705 1751389 1753062 "NAGS" 1756780 T NAGS (NIL) -7 NIL NIL) (-748 1748253 1748561 1748892 "NAGF07" 1749394 T NAGF07 (NIL) -7 NIL NIL) (-747 1742791 1744082 1745389 "NAGF04" 1746966 T NAGF04 (NIL) -7 NIL NIL) (-746 1735759 1737373 1739006 "NAGF02" 1741178 T NAGF02 (NIL) -7 NIL NIL) (-745 1730983 1732083 1733200 "NAGF01" 1734662 T NAGF01 (NIL) -7 NIL NIL) (-744 1724611 1726177 1727762 "NAGE04" 1729418 T NAGE04 (NIL) -7 NIL NIL) (-743 1715780 1717901 1720031 "NAGE02" 1722501 T NAGE02 (NIL) -7 NIL NIL) (-742 1711733 1712680 1713644 "NAGE01" 1714836 T NAGE01 (NIL) -7 NIL NIL) (-741 1709528 1710062 1710620 "NAGD03" 1711195 T NAGD03 (NIL) -7 NIL NIL) (-740 1701278 1703206 1705160 "NAGD02" 1707594 T NAGD02 (NIL) -7 NIL NIL) (-739 1695089 1696514 1697954 "NAGD01" 1699858 T NAGD01 (NIL) -7 NIL NIL) (-738 1691298 1692120 1692957 "NAGC06" 1694272 T NAGC06 (NIL) -7 NIL NIL) (-737 1689763 1690095 1690451 "NAGC05" 1690962 T NAGC05 (NIL) -7 NIL NIL) (-736 1689139 1689258 1689402 "NAGC02" 1689639 T NAGC02 (NIL) -7 NIL NIL) (-735 1688199 1688756 1688796 "NAALG" 1688875 NIL NAALG (NIL T) -9 NIL 1688936) (-734 1688034 1688063 1688153 "NAALG-" 1688158 NIL NAALG- (NIL T T) -8 NIL NIL) (-733 1681984 1683092 1684279 "MULTSQFR" 1686930 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-732 1681303 1681378 1681562 "MULTFACT" 1681896 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-731 1674396 1678266 1678319 "MTSCAT" 1679389 NIL MTSCAT (NIL T T) -9 NIL 1679903) (-730 1674108 1674162 1674254 "MTHING" 1674336 NIL MTHING (NIL T) -7 NIL NIL) (-729 1673900 1673933 1673993 "MSYSCMD" 1674068 T MSYSCMD (NIL) -7 NIL NIL) (-728 1670012 1672655 1672975 "MSET" 1673613 NIL MSET (NIL T) -8 NIL NIL) (-727 1667107 1669573 1669614 "MSETAGG" 1669619 NIL MSETAGG (NIL T) -9 NIL 1669653) (-726 1662990 1664486 1665231 "MRING" 1666407 NIL MRING (NIL T T) -8 NIL NIL) (-725 1662556 1662623 1662754 "MRF2" 1662917 NIL MRF2 (NIL T T T) -7 NIL NIL) (-724 1662174 1662209 1662353 "MRATFAC" 1662515 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-723 1659786 1660081 1660512 "MPRFF" 1661879 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-722 1653846 1659640 1659737 "MPOLY" 1659742 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-721 1653336 1653371 1653579 "MPCPF" 1653805 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-720 1652850 1652893 1653077 "MPC3" 1653287 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-719 1652045 1652126 1652347 "MPC2" 1652765 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-718 1650346 1650683 1651073 "MONOTOOL" 1651705 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-717 1649597 1649888 1649916 "MONOID" 1650135 T MONOID (NIL) -9 NIL 1650282) (-716 1649143 1649262 1649443 "MONOID-" 1649448 NIL MONOID- (NIL T) -8 NIL NIL) (-715 1640002 1645910 1645969 "MONOGEN" 1646643 NIL MONOGEN (NIL T T) -9 NIL 1647099) (-714 1637220 1637955 1638955 "MONOGEN-" 1639074 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-713 1636079 1636499 1636527 "MONADWU" 1636919 T MONADWU (NIL) -9 NIL 1637157) (-712 1635451 1635610 1635858 "MONADWU-" 1635863 NIL MONADWU- (NIL T) -8 NIL NIL) (-711 1634836 1635054 1635082 "MONAD" 1635289 T MONAD (NIL) -9 NIL 1635401) (-710 1634521 1634599 1634731 "MONAD-" 1634736 NIL MONAD- (NIL T) -8 NIL NIL) (-709 1632837 1633434 1633713 "MOEBIUS" 1634274 NIL MOEBIUS (NIL T) -8 NIL NIL) (-708 1632229 1632607 1632647 "MODULE" 1632652 NIL MODULE (NIL T) -9 NIL 1632678) (-707 1631797 1631893 1632083 "MODULE-" 1632088 NIL MODULE- (NIL T T) -8 NIL NIL) (-706 1629512 1630161 1630488 "MODRING" 1631621 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-705 1626498 1627617 1628138 "MODOP" 1629041 NIL MODOP (NIL T T) -8 NIL NIL) (-704 1625113 1625565 1625842 "MODMONOM" 1626361 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-703 1614920 1623404 1623818 "MODMON" 1624750 NIL MODMON (NIL T T) -8 NIL NIL) (-702 1612111 1613764 1614040 "MODFIELD" 1614795 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-701 1611115 1611392 1611582 "MMLFORM" 1611941 T MMLFORM (NIL) -8 NIL NIL) (-700 1610641 1610684 1610863 "MMAP" 1611066 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-699 1608858 1609591 1609632 "MLO" 1610055 NIL MLO (NIL T) -9 NIL 1610297) (-698 1606225 1606740 1607342 "MLIFT" 1608339 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-697 1605616 1605700 1605854 "MKUCFUNC" 1606136 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-696 1605215 1605285 1605408 "MKRECORD" 1605539 NIL MKRECORD (NIL T T) -7 NIL NIL) (-695 1604263 1604424 1604652 "MKFUNC" 1605026 NIL MKFUNC (NIL T) -7 NIL NIL) (-694 1603651 1603755 1603911 "MKFLCFN" 1604146 NIL MKFLCFN (NIL T) -7 NIL NIL) (-693 1603194 1603561 1603620 "MKCHSET" 1603625 NIL MKCHSET (NIL T) -8 NIL NIL) (-692 1602471 1602573 1602758 "MKBCFUNC" 1603087 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-691 1599213 1602025 1602161 "MINT" 1602355 T MINT (NIL) -8 NIL NIL) (-690 1598025 1598268 1598545 "MHROWRED" 1598968 NIL MHROWRED (NIL T) -7 NIL NIL) (-689 1593451 1596560 1596965 "MFLOAT" 1597640 T MFLOAT (NIL) -8 NIL NIL) (-688 1592808 1592884 1593055 "MFINFACT" 1593363 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-687 1589123 1589971 1590855 "MESH" 1591944 T MESH (NIL) -7 NIL NIL) (-686 1587513 1587825 1588178 "MDDFACT" 1588810 NIL MDDFACT (NIL T) -7 NIL NIL) (-685 1584355 1586672 1586713 "MDAGG" 1586968 NIL MDAGG (NIL T) -9 NIL 1587111) (-684 1574133 1583648 1583855 "MCMPLX" 1584168 T MCMPLX (NIL) -8 NIL NIL) (-683 1573274 1573420 1573620 "MCDEN" 1573982 NIL MCDEN (NIL T T) -7 NIL NIL) (-682 1571164 1571434 1571814 "MCALCFN" 1573004 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-681 1570075 1570248 1570489 "MAYBE" 1570962 NIL MAYBE (NIL T) -8 NIL NIL) (-680 1567687 1568210 1568772 "MATSTOR" 1569546 NIL MATSTOR (NIL T) -7 NIL NIL) (-679 1563693 1567059 1567307 "MATRIX" 1567472 NIL MATRIX (NIL T) -8 NIL NIL) (-678 1559462 1560166 1560902 "MATLIN" 1563050 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-677 1549616 1552754 1552831 "MATCAT" 1557711 NIL MATCAT (NIL T T T) -9 NIL 1559128) (-676 1545980 1546993 1548349 "MATCAT-" 1548354 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-675 1544574 1544727 1545060 "MATCAT2" 1545815 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-674 1542686 1543010 1543394 "MAPPKG3" 1544249 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-673 1541667 1541840 1542062 "MAPPKG2" 1542510 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-672 1540166 1540450 1540777 "MAPPKG1" 1541373 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-671 1539272 1539572 1539749 "MAPPAST" 1540009 T MAPPAST (NIL) -8 NIL NIL) (-670 1538883 1538941 1539064 "MAPHACK3" 1539208 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-669 1538475 1538536 1538650 "MAPHACK2" 1538815 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-668 1537913 1538016 1538158 "MAPHACK1" 1538366 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-667 1536019 1536613 1536917 "MAGMA" 1537641 NIL MAGMA (NIL T) -8 NIL NIL) (-666 1535525 1535743 1535834 "MACROAST" 1535948 T MACROAST (NIL) -8 NIL NIL) (-665 1531992 1533764 1534225 "M3D" 1535097 NIL M3D (NIL T) -8 NIL NIL) (-664 1526146 1530361 1530402 "LZSTAGG" 1531184 NIL LZSTAGG (NIL T) -9 NIL 1531479) (-663 1522120 1523277 1524734 "LZSTAGG-" 1524739 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-662 1519234 1520011 1520498 "LWORD" 1521665 NIL LWORD (NIL T) -8 NIL NIL) (-661 1518837 1519038 1519113 "LSTAST" 1519179 T LSTAST (NIL) -8 NIL NIL) (-660 1512038 1518608 1518742 "LSQM" 1518747 NIL LSQM (NIL NIL T) -8 NIL NIL) (-659 1511262 1511401 1511629 "LSPP" 1511893 NIL LSPP (NIL T T T T) -7 NIL NIL) (-658 1509074 1509375 1509831 "LSMP" 1510951 NIL LSMP (NIL T T T T) -7 NIL NIL) (-657 1505853 1506527 1507257 "LSMP1" 1508376 NIL LSMP1 (NIL T) -7 NIL NIL) (-656 1499778 1505020 1505061 "LSAGG" 1505123 NIL LSAGG (NIL T) -9 NIL 1505201) (-655 1496473 1497397 1498610 "LSAGG-" 1498615 NIL LSAGG- (NIL T T) -8 NIL NIL) (-654 1494099 1495617 1495866 "LPOLY" 1496268 NIL LPOLY (NIL T T) -8 NIL NIL) (-653 1493681 1493766 1493889 "LPEFRAC" 1494008 NIL LPEFRAC (NIL T) -7 NIL NIL) (-652 1492028 1492775 1493028 "LO" 1493513 NIL LO (NIL T T T) -8 NIL NIL) (-651 1491680 1491792 1491820 "LOGIC" 1491931 T LOGIC (NIL) -9 NIL 1492012) (-650 1491542 1491565 1491636 "LOGIC-" 1491641 NIL LOGIC- (NIL T) -8 NIL NIL) (-649 1490735 1490875 1491068 "LODOOPS" 1491398 NIL LODOOPS (NIL T T) -7 NIL NIL) (-648 1488193 1490651 1490717 "LODO" 1490722 NIL LODO (NIL T NIL) -8 NIL NIL) (-647 1486731 1486966 1487319 "LODOF" 1487940 NIL LODOF (NIL T T) -7 NIL NIL) (-646 1483087 1485484 1485525 "LODOCAT" 1485963 NIL LODOCAT (NIL T) -9 NIL 1486174) (-645 1482820 1482878 1483005 "LODOCAT-" 1483010 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-644 1480175 1482661 1482779 "LODO2" 1482784 NIL LODO2 (NIL T T) -8 NIL NIL) (-643 1477645 1480112 1480157 "LODO1" 1480162 NIL LODO1 (NIL T) -8 NIL NIL) (-642 1476505 1476670 1476982 "LODEEF" 1477468 NIL LODEEF (NIL T T T) -7 NIL NIL) (-641 1471791 1474635 1474676 "LNAGG" 1475623 NIL LNAGG (NIL T) -9 NIL 1476067) (-640 1470938 1471152 1471494 "LNAGG-" 1471499 NIL LNAGG- (NIL T T) -8 NIL NIL) (-639 1467101 1467863 1468502 "LMOPS" 1470353 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-638 1466496 1466858 1466899 "LMODULE" 1466960 NIL LMODULE (NIL T) -9 NIL 1467002) (-637 1463742 1466141 1466264 "LMDICT" 1466406 NIL LMDICT (NIL T) -8 NIL NIL) (-636 1463468 1463650 1463710 "LITERAL" 1463715 NIL LITERAL (NIL T) -8 NIL NIL) (-635 1456695 1462414 1462712 "LIST" 1463203 NIL LIST (NIL T) -8 NIL NIL) (-634 1456220 1456294 1456433 "LIST3" 1456615 NIL LIST3 (NIL T T T) -7 NIL NIL) (-633 1455227 1455405 1455633 "LIST2" 1456038 NIL LIST2 (NIL T T) -7 NIL NIL) (-632 1453361 1453673 1454072 "LIST2MAP" 1454874 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-631 1452091 1452727 1452768 "LINEXP" 1453023 NIL LINEXP (NIL T) -9 NIL 1453172) (-630 1450738 1450998 1451295 "LINDEP" 1451843 NIL LINDEP (NIL T T) -7 NIL NIL) (-629 1447505 1448224 1449001 "LIMITRF" 1449993 NIL LIMITRF (NIL T) -7 NIL NIL) (-628 1445781 1446076 1446492 "LIMITPS" 1447200 NIL LIMITPS (NIL T T) -7 NIL NIL) (-627 1440236 1445292 1445520 "LIE" 1445602 NIL LIE (NIL T T) -8 NIL NIL) (-626 1439285 1439728 1439768 "LIECAT" 1439908 NIL LIECAT (NIL T) -9 NIL 1440059) (-625 1439126 1439153 1439241 "LIECAT-" 1439246 NIL LIECAT- (NIL T T) -8 NIL NIL) (-624 1431738 1438575 1438740 "LIB" 1438981 T LIB (NIL) -8 NIL NIL) (-623 1427375 1428256 1429191 "LGROBP" 1430855 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-622 1425241 1425515 1425877 "LF" 1427096 NIL LF (NIL T T) -7 NIL NIL) (-621 1424081 1424773 1424801 "LFCAT" 1425008 T LFCAT (NIL) -9 NIL 1425147) (-620 1420985 1421613 1422301 "LEXTRIPK" 1423445 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-619 1417756 1418555 1419058 "LEXP" 1420565 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-618 1417259 1417477 1417569 "LETAST" 1417684 T LETAST (NIL) -8 NIL NIL) (-617 1415657 1415970 1416371 "LEADCDET" 1416941 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-616 1414847 1414921 1415150 "LAZM3PK" 1415578 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-615 1409803 1412924 1413462 "LAUPOL" 1414359 NIL LAUPOL (NIL T T) -8 NIL NIL) (-614 1409368 1409412 1409580 "LAPLACE" 1409753 NIL LAPLACE (NIL T T) -7 NIL NIL) (-613 1407342 1408469 1408720 "LA" 1409201 NIL LA (NIL T T T) -8 NIL NIL) (-612 1406423 1406973 1407014 "LALG" 1407076 NIL LALG (NIL T) -9 NIL 1407135) (-611 1406137 1406196 1406332 "LALG-" 1406337 NIL LALG- (NIL T T) -8 NIL NIL) (-610 1405972 1405996 1406037 "KVTFROM" 1406099 NIL KVTFROM (NIL T) -9 NIL NIL) (-609 1404772 1405189 1405418 "KTVLOGIC" 1405763 T KTVLOGIC (NIL) -8 NIL NIL) (-608 1404607 1404631 1404672 "KRCFROM" 1404734 NIL KRCFROM (NIL T) -9 NIL NIL) (-607 1403511 1403698 1403997 "KOVACIC" 1404407 NIL KOVACIC (NIL T T) -7 NIL NIL) (-606 1403346 1403370 1403411 "KONVERT" 1403473 NIL KONVERT (NIL T) -9 NIL NIL) (-605 1403181 1403205 1403246 "KOERCE" 1403308 NIL KOERCE (NIL T) -9 NIL NIL) (-604 1400915 1401675 1402068 "KERNEL" 1402820 NIL KERNEL (NIL T) -8 NIL NIL) (-603 1400417 1400498 1400628 "KERNEL2" 1400829 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-602 1394268 1398956 1399010 "KDAGG" 1399387 NIL KDAGG (NIL T T) -9 NIL 1399593) (-601 1393797 1393921 1394126 "KDAGG-" 1394131 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-600 1386972 1393458 1393613 "KAFILE" 1393675 NIL KAFILE (NIL T) -8 NIL NIL) (-599 1381427 1386483 1386711 "JORDAN" 1386793 NIL JORDAN (NIL T T) -8 NIL NIL) (-598 1380833 1381076 1381197 "JOINAST" 1381326 T JOINAST (NIL) -8 NIL NIL) (-597 1380679 1380738 1380793 "JAVACODE" 1380798 T JAVACODE (NIL) -8 NIL NIL) (-596 1376978 1378884 1378938 "IXAGG" 1379867 NIL IXAGG (NIL T T) -9 NIL 1380326) (-595 1375897 1376203 1376622 "IXAGG-" 1376627 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-594 1371477 1375819 1375878 "IVECTOR" 1375883 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-593 1370243 1370480 1370746 "ITUPLE" 1371244 NIL ITUPLE (NIL T) -8 NIL NIL) (-592 1368679 1368856 1369162 "ITRIGMNP" 1370065 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-591 1367424 1367628 1367911 "ITFUN3" 1368455 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-590 1367056 1367113 1367222 "ITFUN2" 1367361 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-589 1364893 1365918 1366217 "ITAYLOR" 1366790 NIL ITAYLOR (NIL T) -8 NIL NIL) (-588 1353876 1359030 1360193 "ISUPS" 1363763 NIL ISUPS (NIL T) -8 NIL NIL) (-587 1352980 1353120 1353356 "ISUMP" 1353723 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-586 1348244 1352781 1352860 "ISTRING" 1352933 NIL ISTRING (NIL NIL) -8 NIL NIL) (-585 1347747 1347965 1348057 "ISAST" 1348172 T ISAST (NIL) -8 NIL NIL) (-584 1346957 1347038 1347254 "IRURPK" 1347661 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-583 1345893 1346094 1346334 "IRSN" 1346737 T IRSN (NIL) -7 NIL NIL) (-582 1343922 1344277 1344713 "IRRF2F" 1345531 NIL IRRF2F (NIL T) -7 NIL NIL) (-581 1343669 1343707 1343783 "IRREDFFX" 1343878 NIL IRREDFFX (NIL T) -7 NIL NIL) (-580 1342284 1342543 1342842 "IROOT" 1343402 NIL IROOT (NIL T) -7 NIL NIL) (-579 1338916 1339968 1340660 "IR" 1341624 NIL IR (NIL T) -8 NIL NIL) (-578 1336529 1337024 1337590 "IR2" 1338394 NIL IR2 (NIL T T) -7 NIL NIL) (-577 1335601 1335714 1335935 "IR2F" 1336412 NIL IR2F (NIL T T) -7 NIL NIL) (-576 1335392 1335426 1335486 "IPRNTPK" 1335561 T IPRNTPK (NIL) -7 NIL NIL) (-575 1332011 1335281 1335350 "IPF" 1335355 NIL IPF (NIL NIL) -8 NIL NIL) (-574 1330374 1331936 1331993 "IPADIC" 1331998 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-573 1329705 1329932 1330069 "IP4ADDR" 1330257 T IP4ADDR (NIL) -8 NIL NIL) (-572 1329205 1329409 1329519 "IOMODE" 1329615 T IOMODE (NIL) -8 NIL NIL) (-571 1328563 1328802 1328929 "IOBFILE" 1329098 T IOBFILE (NIL) -8 NIL NIL) (-570 1328327 1328467 1328495 "IOBCON" 1328500 T IOBCON (NIL) -9 NIL 1328521) (-569 1327824 1327882 1328072 "INVLAPLA" 1328263 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-568 1317473 1319826 1322212 "INTTR" 1325488 NIL INTTR (NIL T T) -7 NIL NIL) (-567 1313817 1314559 1315423 "INTTOOLS" 1316658 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-566 1313403 1313494 1313611 "INTSLPE" 1313720 T INTSLPE (NIL) -7 NIL NIL) (-565 1311398 1313326 1313385 "INTRVL" 1313390 NIL INTRVL (NIL T) -8 NIL NIL) (-564 1309000 1309512 1310087 "INTRF" 1310883 NIL INTRF (NIL T) -7 NIL NIL) (-563 1308411 1308508 1308650 "INTRET" 1308898 NIL INTRET (NIL T) -7 NIL NIL) (-562 1306408 1306797 1307267 "INTRAT" 1308019 NIL INTRAT (NIL T T) -7 NIL NIL) (-561 1303636 1304219 1304845 "INTPM" 1305893 NIL INTPM (NIL T T) -7 NIL NIL) (-560 1300339 1300938 1301683 "INTPAF" 1303022 NIL INTPAF (NIL T T T) -7 NIL NIL) (-559 1295518 1296480 1297531 "INTPACK" 1299308 T INTPACK (NIL) -7 NIL NIL) (-558 1292430 1295247 1295374 "INT" 1295411 T INT (NIL) -8 NIL NIL) (-557 1291682 1291834 1292042 "INTHERTR" 1292272 NIL INTHERTR (NIL T T) -7 NIL NIL) (-556 1291121 1291201 1291389 "INTHERAL" 1291596 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-555 1288967 1289410 1289867 "INTHEORY" 1290684 T INTHEORY (NIL) -7 NIL NIL) (-554 1280275 1281896 1283675 "INTG0" 1287319 NIL INTG0 (NIL T T T) -7 NIL NIL) (-553 1260848 1265638 1270448 "INTFTBL" 1275485 T INTFTBL (NIL) -8 NIL NIL) (-552 1260097 1260235 1260408 "INTFACT" 1260707 NIL INTFACT (NIL T) -7 NIL NIL) (-551 1257482 1257928 1258492 "INTEF" 1259651 NIL INTEF (NIL T T) -7 NIL NIL) (-550 1255949 1256654 1256682 "INTDOM" 1256983 T INTDOM (NIL) -9 NIL 1257190) (-549 1255318 1255492 1255734 "INTDOM-" 1255739 NIL INTDOM- (NIL T) -8 NIL NIL) (-548 1251813 1253702 1253756 "INTCAT" 1254555 NIL INTCAT (NIL T) -9 NIL 1254875) (-547 1251286 1251388 1251516 "INTBIT" 1251705 T INTBIT (NIL) -7 NIL NIL) (-546 1249957 1250111 1250425 "INTALG" 1251131 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-545 1249414 1249504 1249674 "INTAF" 1249861 NIL INTAF (NIL T T) -7 NIL NIL) (-544 1242868 1249224 1249364 "INTABL" 1249369 NIL INTABL (NIL T T T) -8 NIL NIL) (-543 1237883 1240557 1240585 "INS" 1241519 T INS (NIL) -9 NIL 1242184) (-542 1235123 1235894 1236868 "INS-" 1236941 NIL INS- (NIL T) -8 NIL NIL) (-541 1233898 1234125 1234423 "INPSIGN" 1234876 NIL INPSIGN (NIL T T) -7 NIL NIL) (-540 1233016 1233133 1233330 "INPRODPF" 1233778 NIL INPRODPF (NIL T T) -7 NIL NIL) (-539 1231910 1232027 1232264 "INPRODFF" 1232896 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-538 1230910 1231062 1231322 "INNMFACT" 1231746 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-537 1230107 1230204 1230392 "INMODGCD" 1230809 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-536 1228616 1228860 1229184 "INFSP" 1229852 NIL INFSP (NIL T T T) -7 NIL NIL) (-535 1227800 1227917 1228100 "INFPROD0" 1228496 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-534 1224682 1225865 1226380 "INFORM" 1227293 T INFORM (NIL) -8 NIL NIL) (-533 1224292 1224352 1224450 "INFORM1" 1224617 NIL INFORM1 (NIL T) -7 NIL NIL) (-532 1223815 1223904 1224018 "INFINITY" 1224198 T INFINITY (NIL) -7 NIL NIL) (-531 1223260 1223533 1223641 "INETCLTS" 1223727 T INETCLTS (NIL) -8 NIL NIL) (-530 1221877 1222126 1222447 "INEP" 1223008 NIL INEP (NIL T T T) -7 NIL NIL) (-529 1221153 1221774 1221839 "INDE" 1221844 NIL INDE (NIL T) -8 NIL NIL) (-528 1220717 1220785 1220902 "INCRMAPS" 1221080 NIL INCRMAPS (NIL T) -7 NIL NIL) (-527 1219735 1219986 1220192 "INBFILE" 1220531 T INBFILE (NIL) -8 NIL NIL) (-526 1215046 1215971 1216915 "INBFF" 1218823 NIL INBFF (NIL T) -7 NIL NIL) (-525 1214715 1214791 1214819 "INBCON" 1214952 T INBCON (NIL) -9 NIL 1215030) (-524 1214555 1214590 1214666 "INBCON-" 1214671 NIL INBCON- (NIL T) -8 NIL NIL) (-523 1214057 1214276 1214368 "INAST" 1214483 T INAST (NIL) -8 NIL NIL) (-522 1213511 1213736 1213842 "IMPTAST" 1213971 T IMPTAST (NIL) -8 NIL NIL) (-521 1210005 1213355 1213459 "IMATRIX" 1213464 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-520 1208717 1208840 1209155 "IMATQF" 1209861 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-519 1206937 1207164 1207501 "IMATLIN" 1208473 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-518 1201563 1206861 1206919 "ILIST" 1206924 NIL ILIST (NIL T NIL) -8 NIL NIL) (-517 1199516 1201423 1201536 "IIARRAY2" 1201541 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-516 1194949 1199427 1199491 "IFF" 1199496 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-515 1194323 1194566 1194682 "IFAST" 1194853 T IFAST (NIL) -8 NIL NIL) (-514 1189366 1193615 1193803 "IFARRAY" 1194180 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-513 1188573 1189270 1189343 "IFAMON" 1189348 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-512 1188157 1188222 1188276 "IEVALAB" 1188483 NIL IEVALAB (NIL T T) -9 NIL NIL) (-511 1187832 1187900 1188060 "IEVALAB-" 1188065 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-510 1187490 1187746 1187809 "IDPO" 1187814 NIL IDPO (NIL T T) -8 NIL NIL) (-509 1186767 1187379 1187454 "IDPOAMS" 1187459 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-508 1186101 1186656 1186731 "IDPOAM" 1186736 NIL IDPOAM (NIL T T) -8 NIL NIL) (-507 1185186 1185436 1185489 "IDPC" 1185902 NIL IDPC (NIL T T) -9 NIL 1186051) (-506 1184682 1185078 1185151 "IDPAM" 1185156 NIL IDPAM (NIL T T) -8 NIL NIL) (-505 1184085 1184574 1184647 "IDPAG" 1184652 NIL IDPAG (NIL T T) -8 NIL NIL) (-504 1183853 1184000 1184050 "IDENT" 1184055 T IDENT (NIL) -8 NIL NIL) (-503 1180108 1180956 1181851 "IDECOMP" 1183010 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-502 1172982 1174031 1175078 "IDEAL" 1179144 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-501 1172146 1172258 1172457 "ICDEN" 1172866 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-500 1171245 1171626 1171773 "ICARD" 1172019 T ICARD (NIL) -8 NIL NIL) (-499 1169305 1169618 1170023 "IBPTOOLS" 1170922 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-498 1164939 1168925 1169038 "IBITS" 1169224 NIL IBITS (NIL NIL) -8 NIL NIL) (-497 1161662 1162238 1162933 "IBATOOL" 1164356 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-496 1159442 1159903 1160436 "IBACHIN" 1161197 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-495 1157319 1159288 1159391 "IARRAY2" 1159396 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-494 1153472 1157245 1157302 "IARRAY1" 1157307 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-493 1147466 1151884 1152365 "IAN" 1153011 T IAN (NIL) -8 NIL NIL) (-492 1146977 1147034 1147207 "IALGFACT" 1147403 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-491 1146505 1146618 1146646 "HYPCAT" 1146853 T HYPCAT (NIL) -9 NIL NIL) (-490 1146043 1146160 1146346 "HYPCAT-" 1146351 NIL HYPCAT- (NIL T) -8 NIL NIL) (-489 1145665 1145838 1145921 "HOSTNAME" 1145980 T HOSTNAME (NIL) -8 NIL NIL) (-488 1145510 1145547 1145588 "HOMOTOP" 1145593 NIL HOMOTOP (NIL T) -9 NIL 1145626) (-487 1142189 1143520 1143561 "HOAGG" 1144542 NIL HOAGG (NIL T) -9 NIL 1145221) (-486 1140783 1141182 1141708 "HOAGG-" 1141713 NIL HOAGG- (NIL T T) -8 NIL NIL) (-485 1134825 1140380 1140528 "HEXADEC" 1140655 T HEXADEC (NIL) -8 NIL NIL) (-484 1133573 1133795 1134058 "HEUGCD" 1134602 NIL HEUGCD (NIL T) -7 NIL NIL) (-483 1132676 1133410 1133540 "HELLFDIV" 1133545 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-482 1130904 1132453 1132541 "HEAP" 1132620 NIL HEAP (NIL T) -8 NIL NIL) (-481 1130195 1130456 1130590 "HEADAST" 1130790 T HEADAST (NIL) -8 NIL NIL) (-480 1124115 1130110 1130172 "HDP" 1130177 NIL HDP (NIL NIL T) -8 NIL NIL) (-479 1117866 1123750 1123902 "HDMP" 1124016 NIL HDMP (NIL NIL T) -8 NIL NIL) (-478 1117191 1117330 1117494 "HB" 1117722 T HB (NIL) -7 NIL NIL) (-477 1110688 1117037 1117141 "HASHTBL" 1117146 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-476 1110191 1110409 1110501 "HASAST" 1110616 T HASAST (NIL) -8 NIL NIL) (-475 1108003 1109813 1109995 "HACKPI" 1110029 T HACKPI (NIL) -8 NIL NIL) (-474 1103698 1107856 1107969 "GTSET" 1107974 NIL GTSET (NIL T T T T) -8 NIL NIL) (-473 1097224 1103576 1103674 "GSTBL" 1103679 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-472 1089537 1096255 1096520 "GSERIES" 1097015 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-471 1088704 1089095 1089123 "GROUP" 1089326 T GROUP (NIL) -9 NIL 1089460) (-470 1088070 1088229 1088480 "GROUP-" 1088485 NIL GROUP- (NIL T) -8 NIL NIL) (-469 1086439 1086758 1087145 "GROEBSOL" 1087747 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-468 1085379 1085641 1085692 "GRMOD" 1086221 NIL GRMOD (NIL T T) -9 NIL 1086389) (-467 1085147 1085183 1085311 "GRMOD-" 1085316 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-466 1080473 1081501 1082501 "GRIMAGE" 1084167 T GRIMAGE (NIL) -8 NIL NIL) (-465 1078940 1079200 1079524 "GRDEF" 1080169 T GRDEF (NIL) -7 NIL NIL) (-464 1078384 1078500 1078641 "GRAY" 1078819 T GRAY (NIL) -7 NIL NIL) (-463 1077597 1077977 1078028 "GRALG" 1078181 NIL GRALG (NIL T T) -9 NIL 1078274) (-462 1077258 1077331 1077494 "GRALG-" 1077499 NIL GRALG- (NIL T T T) -8 NIL NIL) (-461 1074062 1076843 1077021 "GPOLSET" 1077165 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-460 1073416 1073473 1073731 "GOSPER" 1073999 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-459 1069175 1069854 1070380 "GMODPOL" 1073115 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-458 1068180 1068364 1068602 "GHENSEL" 1068987 NIL GHENSEL (NIL T T) -7 NIL NIL) (-457 1062231 1063074 1064101 "GENUPS" 1067264 NIL GENUPS (NIL T T) -7 NIL NIL) (-456 1061928 1061979 1062068 "GENUFACT" 1062174 NIL GENUFACT (NIL T) -7 NIL NIL) (-455 1061340 1061417 1061582 "GENPGCD" 1061846 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-454 1060814 1060849 1061062 "GENMFACT" 1061299 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-453 1059382 1059637 1059944 "GENEEZ" 1060557 NIL GENEEZ (NIL T T) -7 NIL NIL) (-452 1053295 1058993 1059155 "GDMP" 1059305 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-451 1042672 1047066 1048172 "GCNAALG" 1052278 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-450 1041099 1041927 1041955 "GCDDOM" 1042210 T GCDDOM (NIL) -9 NIL 1042367) (-449 1040569 1040696 1040911 "GCDDOM-" 1040916 NIL GCDDOM- (NIL T) -8 NIL NIL) (-448 1039241 1039426 1039730 "GB" 1040348 NIL GB (NIL T T T T) -7 NIL NIL) (-447 1027861 1030187 1032579 "GBINTERN" 1036932 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-446 1025698 1025990 1026411 "GBF" 1027536 NIL GBF (NIL T T T T) -7 NIL NIL) (-445 1024479 1024644 1024911 "GBEUCLID" 1025514 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-444 1023828 1023953 1024102 "GAUSSFAC" 1024350 T GAUSSFAC (NIL) -7 NIL NIL) (-443 1022195 1022497 1022811 "GALUTIL" 1023547 NIL GALUTIL (NIL T) -7 NIL NIL) (-442 1020503 1020777 1021101 "GALPOLYU" 1021922 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-441 1017868 1018158 1018565 "GALFACTU" 1020200 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-440 1009674 1011173 1012781 "GALFACT" 1016300 NIL GALFACT (NIL T) -7 NIL NIL) (-439 1007062 1007720 1007748 "FVFUN" 1008904 T FVFUN (NIL) -9 NIL 1009624) (-438 1006328 1006510 1006538 "FVC" 1006829 T FVC (NIL) -9 NIL 1007012) (-437 1005970 1006125 1006206 "FUNCTION" 1006280 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-436 1003741 1004292 1004758 "FT" 1005524 T FT (NIL) -8 NIL NIL) (-435 1002559 1003042 1003245 "FTEM" 1003558 T FTEM (NIL) -8 NIL NIL) (-434 1000815 1001104 1001508 "FSUPFACT" 1002250 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-433 999212 999501 999833 "FST" 1000503 T FST (NIL) -8 NIL NIL) (-432 998383 998489 998684 "FSRED" 999094 NIL FSRED (NIL T T) -7 NIL NIL) (-431 997062 997317 997671 "FSPRMELT" 998098 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-430 994147 994585 995084 "FSPECF" 996625 NIL FSPECF (NIL T T) -7 NIL NIL) (-429 976207 984650 984690 "FS" 988538 NIL FS (NIL T) -9 NIL 990827) (-428 964857 967847 971903 "FS-" 972200 NIL FS- (NIL T T) -8 NIL NIL) (-427 964371 964425 964602 "FSINT" 964798 NIL FSINT (NIL T T) -7 NIL NIL) (-426 962698 963364 963667 "FSERIES" 964150 NIL FSERIES (NIL T T) -8 NIL NIL) (-425 961712 961828 962059 "FSCINT" 962578 NIL FSCINT (NIL T T) -7 NIL NIL) (-424 957946 960656 960697 "FSAGG" 961067 NIL FSAGG (NIL T) -9 NIL 961326) (-423 955708 956309 957105 "FSAGG-" 957200 NIL FSAGG- (NIL T T) -8 NIL NIL) (-422 954750 954893 955120 "FSAGG2" 955561 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-421 952405 952684 953238 "FS2UPS" 954468 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-420 951987 952030 952185 "FS2" 952356 NIL FS2 (NIL T T T T) -7 NIL NIL) (-419 950844 951015 951324 "FS2EXPXP" 951812 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-418 950270 950385 950537 "FRUTIL" 950724 NIL FRUTIL (NIL T) -7 NIL NIL) (-417 941725 945765 947123 "FR" 948944 NIL FR (NIL T) -8 NIL NIL) (-416 936800 939443 939483 "FRNAALG" 940879 NIL FRNAALG (NIL T) -9 NIL 941486) (-415 932478 933549 934824 "FRNAALG-" 935574 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-414 932116 932159 932286 "FRNAAF2" 932429 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-413 930523 930970 931265 "FRMOD" 931928 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-412 928302 928906 929223 "FRIDEAL" 930314 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-411 927497 927584 927873 "FRIDEAL2" 928209 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-410 926630 927044 927085 "FRETRCT" 927090 NIL FRETRCT (NIL T) -9 NIL 927266) (-409 925742 925973 926324 "FRETRCT-" 926329 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-408 922954 924130 924189 "FRAMALG" 925071 NIL FRAMALG (NIL T T) -9 NIL 925363) (-407 921088 921543 922173 "FRAMALG-" 922396 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-406 915046 920563 920839 "FRAC" 920844 NIL FRAC (NIL T) -8 NIL NIL) (-405 914682 914739 914846 "FRAC2" 914983 NIL FRAC2 (NIL T T) -7 NIL NIL) (-404 914318 914375 914482 "FR2" 914619 NIL FR2 (NIL T T) -7 NIL NIL) (-403 908991 911843 911871 "FPS" 912990 T FPS (NIL) -9 NIL 913547) (-402 908440 908549 908713 "FPS-" 908859 NIL FPS- (NIL T) -8 NIL NIL) (-401 905894 907529 907557 "FPC" 907782 T FPC (NIL) -9 NIL 907924) (-400 905687 905727 905824 "FPC-" 905829 NIL FPC- (NIL T) -8 NIL NIL) (-399 904565 905175 905216 "FPATMAB" 905221 NIL FPATMAB (NIL T) -9 NIL 905373) (-398 902265 902741 903167 "FPARFRAC" 904202 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-397 897658 898157 898839 "FORTRAN" 901697 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-396 895374 895874 896413 "FORT" 897139 T FORT (NIL) -7 NIL NIL) (-395 893050 893612 893640 "FORTFN" 894700 T FORTFN (NIL) -9 NIL 895324) (-394 892814 892864 892892 "FORTCAT" 892951 T FORTCAT (NIL) -9 NIL 893013) (-393 890947 891430 891820 "FORMULA" 892444 T FORMULA (NIL) -8 NIL NIL) (-392 890735 890765 890834 "FORMULA1" 890911 NIL FORMULA1 (NIL T) -7 NIL NIL) (-391 890258 890310 890483 "FORDER" 890677 NIL FORDER (NIL T T T T) -7 NIL NIL) (-390 889354 889518 889711 "FOP" 890085 T FOP (NIL) -7 NIL NIL) (-389 887962 888634 888808 "FNLA" 889236 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-388 886717 887106 887134 "FNCAT" 887594 T FNCAT (NIL) -9 NIL 887854) (-387 886283 886676 886704 "FNAME" 886709 T FNAME (NIL) -8 NIL NIL) (-386 884946 885875 885903 "FMTC" 885908 T FMTC (NIL) -9 NIL 885944) (-385 881308 882469 883098 "FMONOID" 884350 NIL FMONOID (NIL T) -8 NIL NIL) (-384 880527 881050 881199 "FM" 881204 NIL FM (NIL T T) -8 NIL NIL) (-383 877951 878597 878625 "FMFUN" 879769 T FMFUN (NIL) -9 NIL 880477) (-382 877220 877401 877429 "FMC" 877719 T FMC (NIL) -9 NIL 877901) (-381 874414 875248 875302 "FMCAT" 876497 NIL FMCAT (NIL T T) -9 NIL 876992) (-380 873307 874180 874280 "FM1" 874359 NIL FM1 (NIL T T) -8 NIL NIL) (-379 871081 871497 871991 "FLOATRP" 872858 NIL FLOATRP (NIL T) -7 NIL NIL) (-378 864705 868810 869431 "FLOAT" 870480 T FLOAT (NIL) -8 NIL NIL) (-377 862143 862643 863221 "FLOATCP" 864172 NIL FLOATCP (NIL T) -7 NIL NIL) (-376 860952 861756 861797 "FLINEXP" 861802 NIL FLINEXP (NIL T) -9 NIL 861895) (-375 860106 860341 860669 "FLINEXP-" 860674 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-374 859182 859326 859550 "FLASORT" 859958 NIL FLASORT (NIL T T) -7 NIL NIL) (-373 856399 857241 857293 "FLALG" 858520 NIL FLALG (NIL T T) -9 NIL 858987) (-372 850183 853885 853926 "FLAGG" 855188 NIL FLAGG (NIL T) -9 NIL 855840) (-371 848909 849248 849738 "FLAGG-" 849743 NIL FLAGG- (NIL T T) -8 NIL NIL) (-370 847951 848094 848321 "FLAGG2" 848762 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-369 844926 845900 845959 "FINRALG" 847087 NIL FINRALG (NIL T T) -9 NIL 847595) (-368 844086 844315 844654 "FINRALG-" 844659 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-367 843492 843705 843733 "FINITE" 843929 T FINITE (NIL) -9 NIL 844036) (-366 835950 838111 838151 "FINAALG" 841818 NIL FINAALG (NIL T) -9 NIL 843271) (-365 831291 832332 833476 "FINAALG-" 834855 NIL FINAALG- (NIL T T) -8 NIL NIL) (-364 830686 831046 831149 "FILE" 831221 NIL FILE (NIL T) -8 NIL NIL) (-363 829370 829682 829736 "FILECAT" 830420 NIL FILECAT (NIL T T) -9 NIL 830636) (-362 827238 828732 828760 "FIELD" 828800 T FIELD (NIL) -9 NIL 828880) (-361 825858 826243 826754 "FIELD-" 826759 NIL FIELD- (NIL T) -8 NIL NIL) (-360 823736 824493 824840 "FGROUP" 825544 NIL FGROUP (NIL T) -8 NIL NIL) (-359 822826 822990 823210 "FGLMICPK" 823568 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-358 818693 822751 822808 "FFX" 822813 NIL FFX (NIL T NIL) -8 NIL NIL) (-357 818294 818355 818490 "FFSLPE" 818626 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-356 814287 815066 815862 "FFPOLY" 817530 NIL FFPOLY (NIL T) -7 NIL NIL) (-355 813791 813827 814036 "FFPOLY2" 814245 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-354 809677 813710 813773 "FFP" 813778 NIL FFP (NIL T NIL) -8 NIL NIL) (-353 805110 809588 809652 "FF" 809657 NIL FF (NIL NIL NIL) -8 NIL NIL) (-352 800271 804453 804643 "FFNBX" 804964 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-351 795245 799406 799664 "FFNBP" 800125 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-350 789913 794529 794740 "FFNB" 795078 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-349 788745 788943 789258 "FFINTBAS" 789710 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-348 784973 787152 787180 "FFIELDC" 787800 T FFIELDC (NIL) -9 NIL 788176) (-347 783636 784006 784503 "FFIELDC-" 784508 NIL FFIELDC- (NIL T) -8 NIL NIL) (-346 783206 783251 783375 "FFHOM" 783578 NIL FFHOM (NIL T T T) -7 NIL NIL) (-345 780904 781388 781905 "FFF" 782721 NIL FFF (NIL T) -7 NIL NIL) (-344 776557 780646 780747 "FFCGX" 780847 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-343 772224 776289 776396 "FFCGP" 776500 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-342 767442 771951 772059 "FFCG" 772160 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-341 749275 758313 758399 "FFCAT" 763564 NIL FFCAT (NIL T T T) -9 NIL 765015) (-340 744473 745520 746834 "FFCAT-" 748064 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-339 743884 743927 744162 "FFCAT2" 744424 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-338 733096 736856 738076 "FEXPR" 742736 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-337 732096 732531 732572 "FEVALAB" 732656 NIL FEVALAB (NIL T) -9 NIL 732917) (-336 731255 731465 731803 "FEVALAB-" 731808 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-335 729848 730638 730841 "FDIV" 731154 NIL FDIV (NIL T T T T) -8 NIL NIL) (-334 726914 727629 727744 "FDIVCAT" 729312 NIL FDIVCAT (NIL T T T T) -9 NIL 729749) (-333 726676 726703 726873 "FDIVCAT-" 726878 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-332 725896 725983 726260 "FDIV2" 726583 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-331 724582 724841 725130 "FCPAK1" 725627 T FCPAK1 (NIL) -7 NIL NIL) (-330 723710 724082 724223 "FCOMP" 724473 NIL FCOMP (NIL T) -8 NIL NIL) (-329 707446 710860 714398 "FC" 720192 T FC (NIL) -8 NIL NIL) (-328 700025 704010 704050 "FAXF" 705852 NIL FAXF (NIL T) -9 NIL 706544) (-327 697304 697959 698784 "FAXF-" 699249 NIL FAXF- (NIL T T) -8 NIL NIL) (-326 692404 696680 696856 "FARRAY" 697161 NIL FARRAY (NIL T) -8 NIL NIL) (-325 687657 689689 689742 "FAMR" 690765 NIL FAMR (NIL T T) -9 NIL 691225) (-324 686547 686849 687284 "FAMR-" 687289 NIL FAMR- (NIL T T T) -8 NIL NIL) (-323 685743 686469 686522 "FAMONOID" 686527 NIL FAMONOID (NIL T) -8 NIL NIL) (-322 683555 684239 684292 "FAMONC" 685233 NIL FAMONC (NIL T T) -9 NIL 685619) (-321 682247 683309 683446 "FAGROUP" 683451 NIL FAGROUP (NIL T) -8 NIL NIL) (-320 680042 680361 680764 "FACUTIL" 681928 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-319 679141 679326 679548 "FACTFUNC" 679852 NIL FACTFUNC (NIL T) -7 NIL NIL) (-318 671546 678392 678604 "EXPUPXS" 678997 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-317 669029 669569 670155 "EXPRTUBE" 670980 T EXPRTUBE (NIL) -7 NIL NIL) (-316 665223 665815 666552 "EXPRODE" 668368 NIL EXPRODE (NIL T T) -7 NIL NIL) (-315 650597 663878 664306 "EXPR" 664827 NIL EXPR (NIL T) -8 NIL NIL) (-314 645004 645591 646404 "EXPR2UPS" 649895 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-313 644640 644697 644804 "EXPR2" 644941 NIL EXPR2 (NIL T T) -7 NIL NIL) (-312 636045 643772 644069 "EXPEXPAN" 644477 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-311 635872 636002 636031 "EXIT" 636036 T EXIT (NIL) -8 NIL NIL) (-310 635379 635596 635687 "EXITAST" 635801 T EXITAST (NIL) -8 NIL NIL) (-309 635006 635068 635181 "EVALCYC" 635311 NIL EVALCYC (NIL T) -7 NIL NIL) (-308 634547 634665 634706 "EVALAB" 634876 NIL EVALAB (NIL T) -9 NIL 634980) (-307 634028 634150 634371 "EVALAB-" 634376 NIL EVALAB- (NIL T T) -8 NIL NIL) (-306 631496 632764 632792 "EUCDOM" 633347 T EUCDOM (NIL) -9 NIL 633697) (-305 629901 630343 630933 "EUCDOM-" 630938 NIL EUCDOM- (NIL T) -8 NIL NIL) (-304 617441 620199 622949 "ESTOOLS" 627171 T ESTOOLS (NIL) -7 NIL NIL) (-303 617073 617130 617239 "ESTOOLS2" 617378 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-302 616824 616866 616946 "ESTOOLS1" 617025 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-301 610729 612457 612485 "ES" 615253 T ES (NIL) -9 NIL 616662) (-300 605677 606963 608780 "ES-" 608944 NIL ES- (NIL T) -8 NIL NIL) (-299 602052 602812 603592 "ESCONT" 604917 T ESCONT (NIL) -7 NIL NIL) (-298 601797 601829 601911 "ESCONT1" 602014 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-297 601472 601522 601622 "ES2" 601741 NIL ES2 (NIL T T) -7 NIL NIL) (-296 601102 601160 601269 "ES1" 601408 NIL ES1 (NIL T T) -7 NIL NIL) (-295 600318 600447 600623 "ERROR" 600946 T ERROR (NIL) -7 NIL NIL) (-294 593821 600177 600268 "EQTBL" 600273 NIL EQTBL (NIL T T) -8 NIL NIL) (-293 586378 589135 590584 "EQ" 592405 NIL -3354 (NIL T) -8 NIL NIL) (-292 586010 586067 586176 "EQ2" 586315 NIL EQ2 (NIL T T) -7 NIL NIL) (-291 581302 582348 583441 "EP" 584949 NIL EP (NIL T) -7 NIL NIL) (-290 579884 580185 580502 "ENV" 581005 T ENV (NIL) -8 NIL NIL) (-289 579063 579583 579611 "ENTIRER" 579616 T ENTIRER (NIL) -9 NIL 579662) (-288 575565 577018 577388 "EMR" 578862 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-287 574709 574894 574948 "ELTAGG" 575328 NIL ELTAGG (NIL T T) -9 NIL 575539) (-286 574428 574490 574631 "ELTAGG-" 574636 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-285 574217 574246 574300 "ELTAB" 574384 NIL ELTAB (NIL T T) -9 NIL NIL) (-284 573343 573489 573688 "ELFUTS" 574068 NIL ELFUTS (NIL T T) -7 NIL NIL) (-283 573085 573141 573169 "ELEMFUN" 573274 T ELEMFUN (NIL) -9 NIL NIL) (-282 572955 572976 573044 "ELEMFUN-" 573049 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-281 567846 571055 571096 "ELAGG" 572036 NIL ELAGG (NIL T) -9 NIL 572499) (-280 566131 566565 567228 "ELAGG-" 567233 NIL ELAGG- (NIL T T) -8 NIL NIL) (-279 564788 565068 565363 "ELABEXPR" 565856 T ELABEXPR (NIL) -8 NIL NIL) (-278 557654 559455 560282 "EFUPXS" 564064 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-277 551104 552905 553715 "EFULS" 556930 NIL EFULS (NIL T T T) -8 NIL NIL) (-276 548526 548884 549363 "EFSTRUC" 550736 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-275 537598 539163 540723 "EF" 547041 NIL EF (NIL T T) -7 NIL NIL) (-274 536699 537083 537232 "EAB" 537469 T EAB (NIL) -8 NIL NIL) (-273 535908 536658 536686 "E04UCFA" 536691 T E04UCFA (NIL) -8 NIL NIL) (-272 535117 535867 535895 "E04NAFA" 535900 T E04NAFA (NIL) -8 NIL NIL) (-271 534326 535076 535104 "E04MBFA" 535109 T E04MBFA (NIL) -8 NIL NIL) (-270 533535 534285 534313 "E04JAFA" 534318 T E04JAFA (NIL) -8 NIL NIL) (-269 532746 533494 533522 "E04GCFA" 533527 T E04GCFA (NIL) -8 NIL NIL) (-268 531957 532705 532733 "E04FDFA" 532738 T E04FDFA (NIL) -8 NIL NIL) (-267 531166 531916 531944 "E04DGFA" 531949 T E04DGFA (NIL) -8 NIL NIL) (-266 525344 526691 528055 "E04AGNT" 529822 T E04AGNT (NIL) -7 NIL NIL) (-265 524050 524530 524570 "DVARCAT" 525045 NIL DVARCAT (NIL T) -9 NIL 525244) (-264 523254 523466 523780 "DVARCAT-" 523785 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-263 516154 523053 523182 "DSMP" 523187 NIL DSMP (NIL T T T) -8 NIL NIL) (-262 510964 512099 513167 "DROPT" 515106 T DROPT (NIL) -8 NIL NIL) (-261 510629 510688 510786 "DROPT1" 510899 NIL DROPT1 (NIL T) -7 NIL NIL) (-260 505744 506870 508007 "DROPT0" 509512 T DROPT0 (NIL) -7 NIL NIL) (-259 504089 504414 504800 "DRAWPT" 505378 T DRAWPT (NIL) -7 NIL NIL) (-258 498676 499599 500678 "DRAW" 503063 NIL DRAW (NIL T) -7 NIL NIL) (-257 498309 498362 498480 "DRAWHACK" 498617 NIL DRAWHACK (NIL T) -7 NIL NIL) (-256 497040 497309 497600 "DRAWCX" 498038 T DRAWCX (NIL) -7 NIL NIL) (-255 496556 496624 496775 "DRAWCURV" 496966 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-254 487027 488986 491101 "DRAWCFUN" 494461 T DRAWCFUN (NIL) -7 NIL NIL) (-253 483840 485722 485763 "DQAGG" 486392 NIL DQAGG (NIL T) -9 NIL 486665) (-252 472119 478818 478901 "DPOLCAT" 480753 NIL DPOLCAT (NIL T T T T) -9 NIL 481298) (-251 466958 468304 470262 "DPOLCAT-" 470267 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-250 460113 466819 466917 "DPMO" 466922 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-249 453171 459893 460060 "DPMM" 460065 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-248 452835 453090 453138 "DOMCTOR" 453143 T DOMCTOR (NIL) -8 NIL NIL) (-247 452130 452357 452494 "DOMAIN" 452718 T DOMAIN (NIL) -8 NIL NIL) (-246 445881 451765 451917 "DMP" 452031 NIL DMP (NIL NIL T) -8 NIL NIL) (-245 445481 445537 445681 "DLP" 445819 NIL DLP (NIL T) -7 NIL NIL) (-244 439351 444808 444998 "DLIST" 445323 NIL DLIST (NIL T) -8 NIL NIL) (-243 436195 438204 438245 "DLAGG" 438795 NIL DLAGG (NIL T) -9 NIL 439025) (-242 435008 435638 435666 "DIVRING" 435758 T DIVRING (NIL) -9 NIL 435841) (-241 434245 434435 434735 "DIVRING-" 434740 NIL DIVRING- (NIL T) -8 NIL NIL) (-240 432347 432704 433110 "DISPLAY" 433859 T DISPLAY (NIL) -7 NIL NIL) (-239 426289 432261 432324 "DIRPROD" 432329 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-238 425137 425340 425605 "DIRPROD2" 426082 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-237 414400 420352 420405 "DIRPCAT" 420815 NIL DIRPCAT (NIL NIL T) -9 NIL 421655) (-236 411726 412368 413249 "DIRPCAT-" 413586 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-235 411013 411173 411359 "DIOSP" 411560 T DIOSP (NIL) -7 NIL NIL) (-234 407715 409925 409966 "DIOPS" 410400 NIL DIOPS (NIL T) -9 NIL 410629) (-233 407264 407378 407569 "DIOPS-" 407574 NIL DIOPS- (NIL T T) -8 NIL NIL) (-232 406156 406750 406778 "DIFRING" 406965 T DIFRING (NIL) -9 NIL 407075) (-231 405802 405879 406031 "DIFRING-" 406036 NIL DIFRING- (NIL T) -8 NIL NIL) (-230 403607 404845 404886 "DIFEXT" 405249 NIL DIFEXT (NIL T) -9 NIL 405543) (-229 401892 402320 402986 "DIFEXT-" 402991 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-228 399214 401424 401465 "DIAGG" 401470 NIL DIAGG (NIL T) -9 NIL 401490) (-227 398598 398755 399007 "DIAGG-" 399012 NIL DIAGG- (NIL T T) -8 NIL NIL) (-226 394063 397557 397834 "DHMATRIX" 398367 NIL DHMATRIX (NIL T) -8 NIL NIL) (-225 389675 390584 391594 "DFSFUN" 393073 T DFSFUN (NIL) -7 NIL NIL) (-224 384791 388606 388918 "DFLOAT" 389383 T DFLOAT (NIL) -8 NIL NIL) (-223 383019 383300 383696 "DFINTTLS" 384499 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-222 380084 381040 381440 "DERHAM" 382685 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-221 377933 379859 379948 "DEQUEUE" 380028 NIL DEQUEUE (NIL T) -8 NIL NIL) (-220 377148 377281 377477 "DEGRED" 377795 NIL DEGRED (NIL T T) -7 NIL NIL) (-219 373543 374288 375141 "DEFINTRF" 376376 NIL DEFINTRF (NIL T) -7 NIL NIL) (-218 371070 371539 372138 "DEFINTEF" 373062 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-217 370447 370690 370805 "DEFAST" 370975 T DEFAST (NIL) -8 NIL NIL) (-216 364489 370044 370192 "DECIMAL" 370319 T DECIMAL (NIL) -8 NIL NIL) (-215 362001 362459 362965 "DDFACT" 364033 NIL DDFACT (NIL T T) -7 NIL NIL) (-214 361597 361640 361791 "DBLRESP" 361952 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-213 359496 359830 360190 "DBASE" 361364 NIL DBASE (NIL T) -8 NIL NIL) (-212 358765 358976 359122 "DATAARY" 359395 NIL DATAARY (NIL NIL T) -8 NIL NIL) (-211 357898 358724 358752 "D03FAFA" 358757 T D03FAFA (NIL) -8 NIL NIL) (-210 357032 357857 357885 "D03EEFA" 357890 T D03EEFA (NIL) -8 NIL NIL) (-209 354982 355448 355937 "D03AGNT" 356563 T D03AGNT (NIL) -7 NIL NIL) (-208 354298 354941 354969 "D02EJFA" 354974 T D02EJFA (NIL) -8 NIL NIL) (-207 353614 354257 354285 "D02CJFA" 354290 T D02CJFA (NIL) -8 NIL NIL) (-206 352930 353573 353601 "D02BHFA" 353606 T D02BHFA (NIL) -8 NIL NIL) (-205 352246 352889 352917 "D02BBFA" 352922 T D02BBFA (NIL) -8 NIL NIL) (-204 345444 347032 348638 "D02AGNT" 350660 T D02AGNT (NIL) -7 NIL NIL) (-203 343213 343735 344281 "D01WGTS" 344918 T D01WGTS (NIL) -7 NIL NIL) (-202 342308 343172 343200 "D01TRNS" 343205 T D01TRNS (NIL) -8 NIL NIL) (-201 341403 342267 342295 "D01GBFA" 342300 T D01GBFA (NIL) -8 NIL NIL) (-200 340498 341362 341390 "D01FCFA" 341395 T D01FCFA (NIL) -8 NIL NIL) (-199 339593 340457 340485 "D01ASFA" 340490 T D01ASFA (NIL) -8 NIL NIL) (-198 338688 339552 339580 "D01AQFA" 339585 T D01AQFA (NIL) -8 NIL NIL) (-197 337783 338647 338675 "D01APFA" 338680 T D01APFA (NIL) -8 NIL NIL) (-196 336878 337742 337770 "D01ANFA" 337775 T D01ANFA (NIL) -8 NIL NIL) (-195 335973 336837 336865 "D01AMFA" 336870 T D01AMFA (NIL) -8 NIL NIL) (-194 335068 335932 335960 "D01ALFA" 335965 T D01ALFA (NIL) -8 NIL NIL) (-193 334163 335027 335055 "D01AKFA" 335060 T D01AKFA (NIL) -8 NIL NIL) (-192 333258 334122 334150 "D01AJFA" 334155 T D01AJFA (NIL) -8 NIL NIL) (-191 326555 328106 329667 "D01AGNT" 331717 T D01AGNT (NIL) -7 NIL NIL) (-190 325892 326020 326172 "CYCLOTOM" 326423 T CYCLOTOM (NIL) -7 NIL NIL) (-189 322627 323340 324067 "CYCLES" 325185 T CYCLES (NIL) -7 NIL NIL) (-188 321939 322073 322244 "CVMP" 322488 NIL CVMP (NIL T) -7 NIL NIL) (-187 319710 319968 320344 "CTRIGMNP" 321667 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-186 319433 319669 319697 "CTOR" 319702 T CTOR (NIL) -8 NIL NIL) (-185 318969 319164 319265 "CTORKIND" 319352 T CTORKIND (NIL) -8 NIL NIL) (-184 318440 318668 318696 "CTORCAT" 318816 T CTORCAT (NIL) -9 NIL 318899) (-183 318135 318215 318341 "CTORCAT-" 318346 NIL CTORCAT- (NIL T) -8 NIL NIL) (-182 317651 317838 317936 "CTORCALL" 318057 T CTORCALL (NIL) -8 NIL NIL) (-181 317025 317124 317277 "CSTTOOLS" 317548 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-180 312824 313481 314239 "CRFP" 316337 NIL CRFP (NIL T T) -7 NIL NIL) (-179 312326 312545 312637 "CRCEAST" 312752 T CRCEAST (NIL) -8 NIL NIL) (-178 311373 311558 311786 "CRAPACK" 312130 NIL CRAPACK (NIL T) -7 NIL NIL) (-177 310757 310858 311062 "CPMATCH" 311249 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-176 310482 310510 310616 "CPIMA" 310723 NIL CPIMA (NIL T T T) -7 NIL NIL) (-175 306846 307518 308236 "COORDSYS" 309817 NIL COORDSYS (NIL T) -7 NIL NIL) (-174 306230 306359 306509 "CONTOUR" 306716 T CONTOUR (NIL) -8 NIL NIL) (-173 302156 304233 304725 "CONTFRAC" 305770 NIL CONTFRAC (NIL T) -8 NIL NIL) (-172 302036 302057 302085 "CONDUIT" 302122 T CONDUIT (NIL) -9 NIL NIL) (-171 301209 301729 301757 "COMRING" 301762 T COMRING (NIL) -9 NIL 301814) (-170 300290 300567 300751 "COMPPROP" 301045 T COMPPROP (NIL) -8 NIL NIL) (-169 299951 299986 300114 "COMPLPAT" 300249 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-168 290008 299760 299869 "COMPLEX" 299874 NIL COMPLEX (NIL T) -8 NIL NIL) (-167 289644 289701 289808 "COMPLEX2" 289945 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-166 289362 289397 289495 "COMPFACT" 289603 NIL COMPFACT (NIL T T) -7 NIL NIL) (-165 273535 283755 283795 "COMPCAT" 284799 NIL COMPCAT (NIL T) -9 NIL 286184) (-164 263051 265974 269601 "COMPCAT-" 269957 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-163 262780 262808 262911 "COMMUPC" 263017 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-162 262575 262608 262667 "COMMONOP" 262741 T COMMONOP (NIL) -7 NIL NIL) (-161 262158 262326 262413 "COMM" 262508 T COMM (NIL) -8 NIL NIL) (-160 261762 261962 262037 "COMMAAST" 262103 T COMMAAST (NIL) -8 NIL NIL) (-159 261011 261205 261233 "COMBOPC" 261571 T COMBOPC (NIL) -9 NIL 261746) (-158 259907 260117 260359 "COMBINAT" 260801 NIL COMBINAT (NIL T) -7 NIL NIL) (-157 256105 256678 257318 "COMBF" 259329 NIL COMBF (NIL T T) -7 NIL NIL) (-156 254891 255221 255456 "COLOR" 255890 T COLOR (NIL) -8 NIL NIL) (-155 254394 254612 254704 "COLONAST" 254819 T COLONAST (NIL) -8 NIL NIL) (-154 254034 254081 254206 "CMPLXRT" 254341 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-153 253509 253734 253833 "CLLCTAST" 253955 T CLLCTAST (NIL) -8 NIL NIL) (-152 249011 250039 251119 "CLIP" 252449 T CLIP (NIL) -7 NIL NIL) (-151 247393 248117 248356 "CLIF" 248838 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-150 243615 245539 245580 "CLAGG" 246509 NIL CLAGG (NIL T) -9 NIL 247045) (-149 242037 242494 243077 "CLAGG-" 243082 NIL CLAGG- (NIL T T) -8 NIL NIL) (-148 241581 241666 241806 "CINTSLPE" 241946 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-147 239082 239553 240101 "CHVAR" 241109 NIL CHVAR (NIL T T T) -7 NIL NIL) (-146 238325 238845 238873 "CHARZ" 238878 T CHARZ (NIL) -9 NIL 238893) (-145 238079 238119 238197 "CHARPOL" 238279 NIL CHARPOL (NIL T) -7 NIL NIL) (-144 237206 237759 237787 "CHARNZ" 237834 T CHARNZ (NIL) -9 NIL 237890) (-143 235195 235896 236231 "CHAR" 236891 T CHAR (NIL) -8 NIL NIL) (-142 234921 234982 235010 "CFCAT" 235121 T CFCAT (NIL) -9 NIL NIL) (-141 234166 234277 234459 "CDEN" 234805 NIL CDEN (NIL T T T) -7 NIL NIL) (-140 230158 233319 233599 "CCLASS" 233906 T CCLASS (NIL) -8 NIL NIL) (-139 229465 229608 229771 "CATEGORY" 230015 T -10 (NIL) -8 NIL NIL) (-138 229129 229384 229432 "CATCTOR" 229437 T CATCTOR (NIL) -8 NIL NIL) (-137 228603 228829 228928 "CATAST" 229050 T CATAST (NIL) -8 NIL NIL) (-136 228106 228324 228416 "CASEAST" 228531 T CASEAST (NIL) -8 NIL NIL) (-135 223158 224135 224888 "CARTEN" 227409 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-134 222266 222414 222635 "CARTEN2" 223005 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-133 220608 221416 221673 "CARD" 222029 T CARD (NIL) -8 NIL NIL) (-132 220211 220412 220487 "CAPSLAST" 220553 T CAPSLAST (NIL) -8 NIL NIL) (-131 219583 219911 219939 "CACHSET" 220071 T CACHSET (NIL) -9 NIL 220148) (-130 219079 219375 219403 "CABMON" 219453 T CABMON (NIL) -9 NIL 219509) (-129 218107 218535 218708 "BYTE" 218926 T BYTE (NIL) -8 NIL NIL) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-3 3184509 3184514 3184519 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3184494 3184499 3184504 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3184479 3184484 3184489 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3184464 3184469 3184474 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1274 3183640 3184339 3184416 "ZMOD" 3184421 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1273 3182750 3182914 3183123 "ZLINDEP" 3183472 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1272 3172054 3173818 3175790 "ZDSOLVE" 3180880 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1271 3171300 3171441 3171630 "YSTREAM" 3171900 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1270 3169111 3170601 3170805 "XRPOLY" 3171143 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1269 3165699 3166982 3167557 "XPR" 3168583 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1268 3163455 3165030 3165234 "XPOLY" 3165530 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1267 3161246 3162580 3162635 "XPOLYC" 3162923 NIL XPOLYC (NIL T T) -9 NIL 3163036 NIL) (-1266 3157664 3159763 3160151 "XPBWPOLY" 3160904 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1265 3153575 3155827 3155869 "XF" 3156490 NIL XF (NIL T) -9 NIL 3156890 NIL) (-1264 3153196 3153284 3153453 "XF-" 3153458 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1263 3148530 3149785 3149840 "XFALG" 3152012 NIL XFALG (NIL T T) -9 NIL 3152801 NIL) (-1262 3147663 3147767 3147972 "XEXPPKG" 3148422 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1261 3145807 3147513 3147609 "XDPOLY" 3147614 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1260 3144752 3145318 3145361 "XALG" 3145366 NIL XALG (NIL T) -9 NIL 3145477 NIL) (-1259 3138221 3142729 3143223 "WUTSET" 3144344 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1258 3136512 3137273 3137596 "WP" 3138032 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1257 3136141 3136334 3136404 "WHILEAST" 3136464 T WHILEAST (NIL) -8 NIL NIL NIL) (-1256 3135640 3135858 3135952 "WHEREAST" 3136069 T WHEREAST (NIL) -8 NIL NIL NIL) (-1255 3134526 3134724 3135019 "WFFINTBS" 3135437 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1254 3132430 3132857 3133319 "WEIER" 3134098 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1253 3131577 3132001 3132043 "VSPACE" 3132179 NIL VSPACE (NIL T) -9 NIL 3132253 NIL) (-1252 3131415 3131442 3131533 "VSPACE-" 3131538 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1251 3131223 3131266 3131334 "VOID" 3131369 T VOID (NIL) -8 NIL NIL NIL) (-1250 3129359 3129718 3130124 "VIEW" 3130839 T VIEW (NIL) -7 NIL NIL NIL) (-1249 3125784 3126422 3127159 "VIEWDEF" 3128644 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1248 3115120 3117332 3119505 "VIEW3D" 3123633 T VIEW3D (NIL) -8 NIL NIL NIL) (-1247 3107402 3109031 3110610 "VIEW2D" 3113563 T VIEW2D (NIL) -8 NIL NIL NIL) (-1246 3102806 3107172 3107264 "VECTOR" 3107345 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1245 3101383 3101642 3101960 "VECTOR2" 3102536 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1244 3094910 3099167 3099210 "VECTCAT" 3100203 NIL VECTCAT (NIL T) -9 NIL 3100789 NIL) (-1243 3093924 3094178 3094568 "VECTCAT-" 3094573 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1242 3093405 3093575 3093695 "VARIABLE" 3093839 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1241 3093338 3093343 3093373 "UTYPE" 3093378 T UTYPE (NIL) -9 NIL NIL NIL) (-1240 3092168 3092322 3092584 "UTSODETL" 3093164 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1239 3089608 3090068 3090592 "UTSODE" 3091709 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1238 3081484 3087234 3087723 "UTS" 3089177 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1237 3072727 3078051 3078094 "UTSCAT" 3079206 NIL UTSCAT (NIL T) -9 NIL 3079963 NIL) (-1236 3070082 3070797 3071786 "UTSCAT-" 3071791 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1235 3069709 3069752 3069885 "UTS2" 3070033 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1234 3063982 3066547 3066590 "URAGG" 3068660 NIL URAGG (NIL T) -9 NIL 3069383 NIL) (-1233 3060921 3061784 3062907 "URAGG-" 3062912 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1232 3056645 3059535 3060007 "UPXSSING" 3060585 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1231 3048747 3055892 3056165 "UPXS" 3056430 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1230 3041860 3048651 3048723 "UPXSCONS" 3048728 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1229 3032105 3038855 3038917 "UPXSCCA" 3039491 NIL UPXSCCA (NIL T T) -9 NIL 3039724 NIL) (-1228 3031743 3031828 3032002 "UPXSCCA-" 3032007 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1227 3021841 3028364 3028407 "UPXSCAT" 3029055 NIL UPXSCAT (NIL T) -9 NIL 3029663 NIL) (-1226 3021271 3021350 3021529 "UPXS2" 3021756 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1225 3019925 3020178 3020529 "UPSQFREE" 3021014 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1224 3013713 3016727 3016782 "UPSCAT" 3017943 NIL UPSCAT (NIL T T) -9 NIL 3018717 NIL) (-1223 3012917 3013124 3013451 "UPSCAT-" 3013456 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1222 2998767 3006765 3006808 "UPOLYC" 3008909 NIL UPOLYC (NIL T) -9 NIL 3010130 NIL) (-1221 2990096 2992521 2995668 "UPOLYC-" 2995673 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1220 2989723 2989766 2989899 "UPOLYC2" 2990047 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1219 2981297 2989406 2989535 "UP" 2989642 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1218 2980636 2980743 2980907 "UPMP" 2981186 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1217 2980189 2980270 2980409 "UPDIVP" 2980549 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1216 2978757 2979006 2979322 "UPDECOMP" 2979938 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1215 2977992 2978104 2978289 "UPCDEN" 2978641 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1214 2977511 2977580 2977729 "UP2" 2977917 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1213 2976028 2976715 2976992 "UNISEG" 2977269 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1212 2975243 2975370 2975575 "UNISEG2" 2975871 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1211 2974303 2974483 2974709 "UNIFACT" 2975059 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1210 2958270 2973480 2973731 "ULS" 2974110 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1209 2946310 2958174 2958246 "ULSCONS" 2958251 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1208 2928926 2940868 2940930 "ULSCCAT" 2941568 NIL ULSCCAT (NIL T T) -9 NIL 2941856 NIL) (-1207 2927976 2928221 2928609 "ULSCCAT-" 2928614 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1206 2917851 2924288 2924331 "ULSCAT" 2925194 NIL ULSCAT (NIL T) -9 NIL 2925924 NIL) (-1205 2917281 2917360 2917539 "ULS2" 2917766 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1204 2915684 2916607 2916637 "UFD" 2916849 T UFD (NIL) -9 NIL 2916963 NIL) (-1203 2915478 2915524 2915619 "UFD-" 2915624 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1202 2914560 2914743 2914959 "UDVO" 2915284 T UDVO (NIL) -7 NIL NIL NIL) (-1201 2912376 2912785 2913256 "UDPO" 2914124 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1200 2912309 2912314 2912344 "TYPE" 2912349 T TYPE (NIL) -9 NIL NIL NIL) (-1199 2912096 2912264 2912295 "TYPEAST" 2912300 T TYPEAST (NIL) -8 NIL NIL NIL) (-1198 2911067 2911269 2911509 "TWOFACT" 2911890 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1197 2910139 2910476 2910711 "TUPLE" 2910867 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1196 2907830 2908349 2908888 "TUBETOOL" 2909622 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1195 2906679 2906884 2907125 "TUBE" 2907623 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1194 2901443 2905651 2905934 "TS" 2906431 NIL TS (NIL T) -8 NIL NIL NIL) (-1193 2890110 2894202 2894299 "TSETCAT" 2899568 NIL TSETCAT (NIL T T T T) -9 NIL 2901099 NIL) (-1192 2884845 2886442 2888333 "TSETCAT-" 2888338 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1191 2879108 2879954 2880896 "TRMANIP" 2883981 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1190 2878549 2878612 2878775 "TRIMAT" 2879040 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1189 2876345 2876582 2876946 "TRIGMNIP" 2878298 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1188 2875865 2875978 2876008 "TRIGCAT" 2876221 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1187 2875534 2875613 2875754 "TRIGCAT-" 2875759 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1186 2872431 2874392 2874673 "TREE" 2875288 NIL TREE (NIL T) -8 NIL NIL NIL) (-1185 2871705 2872233 2872263 "TRANFUN" 2872298 T TRANFUN (NIL) -9 NIL 2872364 NIL) (-1184 2870984 2871175 2871455 "TRANFUN-" 2871460 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1183 2870788 2870820 2870881 "TOPSP" 2870945 T TOPSP (NIL) -7 NIL NIL NIL) (-1182 2870136 2870251 2870405 "TOOLSIGN" 2870669 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1181 2868797 2869313 2869552 "TEXTFILE" 2869919 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1180 2866736 2867250 2867679 "TEX" 2868390 T TEX (NIL) -8 NIL NIL NIL) (-1179 2866517 2866548 2866620 "TEX1" 2866699 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1178 2866165 2866228 2866318 "TEMUTL" 2866449 T TEMUTL (NIL) -7 NIL NIL NIL) (-1177 2864319 2864599 2864924 "TBCMPPK" 2865888 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1176 2856207 2862479 2862535 "TBAGG" 2862935 NIL TBAGG (NIL T T) -9 NIL 2863146 NIL) (-1175 2851277 2852765 2854519 "TBAGG-" 2854524 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1174 2850661 2850768 2850913 "TANEXP" 2851166 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1173 2844162 2850518 2850611 "TABLE" 2850616 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1172 2843574 2843673 2843811 "TABLEAU" 2844059 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1171 2838182 2839402 2840650 "TABLBUMP" 2842360 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1170 2837610 2837710 2837838 "SYSTEM" 2838076 T SYSTEM (NIL) -7 NIL NIL NIL) (-1169 2834073 2834768 2835551 "SYSSOLP" 2836861 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1168 2830407 2831334 2832050 "SYNTAX" 2833379 T SYNTAX (NIL) -8 NIL NIL NIL) (-1167 2827565 2828167 2828799 "SYMTAB" 2829797 T SYMTAB (NIL) -8 NIL NIL NIL) (-1166 2822814 2823716 2824699 "SYMS" 2826604 T SYMS (NIL) -8 NIL NIL NIL) (-1165 2820086 2822272 2822502 "SYMPOLY" 2822619 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1164 2819603 2819678 2819801 "SYMFUNC" 2819998 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1163 2815655 2816915 2817728 "SYMBOL" 2818812 T SYMBOL (NIL) -8 NIL NIL NIL) (-1162 2809194 2810883 2812603 "SWITCH" 2813957 T SWITCH (NIL) -8 NIL NIL NIL) (-1161 2802464 2808015 2808318 "SUTS" 2808949 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2794565 2801711 2801984 "SUPXS" 2802249 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2786095 2794183 2794309 "SUP" 2794474 NIL SUP (NIL T) -8 NIL NIL NIL) (-1158 2785254 2785381 2785598 "SUPFRACF" 2785963 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1157 2784875 2784934 2785047 "SUP2" 2785189 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1156 2783288 2783562 2783925 "SUMRF" 2784574 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1155 2782602 2782668 2782867 "SUMFS" 2783209 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1154 2766609 2781779 2782030 "SULS" 2782409 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1153 2766238 2766431 2766501 "SUCHTAST" 2766561 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1152 2765560 2765763 2765903 "SUCH" 2766146 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1151 2759454 2760466 2761425 "SUBSPACE" 2764648 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1150 2758884 2758974 2759138 "SUBRESP" 2759342 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1149 2752253 2753549 2754860 "STTF" 2757620 NIL STTF (NIL T) -7 NIL NIL NIL) (-1148 2746426 2747546 2748693 "STTFNC" 2751153 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1147 2737741 2739608 2741402 "STTAYLOR" 2744667 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1146 2730985 2737605 2737688 "STRTBL" 2737693 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1145 2726376 2730940 2730971 "STRING" 2730976 T STRING (NIL) -8 NIL NIL NIL) (-1144 2721264 2725749 2725779 "STRICAT" 2725838 T STRICAT (NIL) -9 NIL 2725900 NIL) (-1143 2714074 2718883 2719494 "STREAM" 2720688 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1142 2713584 2713661 2713805 "STREAM3" 2713991 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1141 2712566 2712749 2712984 "STREAM2" 2713397 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1140 2712254 2712306 2712399 "STREAM1" 2712508 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1139 2711270 2711451 2711682 "STINPROD" 2712070 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1138 2710848 2711032 2711062 "STEP" 2711142 T STEP (NIL) -9 NIL 2711220 NIL) (-1137 2704391 2710747 2710824 "STBL" 2710829 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1136 2699565 2703612 2703655 "STAGG" 2703808 NIL STAGG (NIL T) -9 NIL 2703897 NIL) (-1135 2697267 2697869 2698741 "STAGG-" 2698746 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1134 2695462 2697037 2697129 "STACK" 2697210 NIL STACK (NIL T) -8 NIL NIL NIL) (-1133 2688187 2693603 2694059 "SREGSET" 2695092 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1132 2680613 2681981 2683494 "SRDCMPK" 2686793 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2673580 2678053 2678083 "SRAGG" 2679386 T SRAGG (NIL) -9 NIL 2679994 NIL) (-1130 2672597 2672852 2673231 "SRAGG-" 2673236 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1129 2667092 2671544 2671965 "SQMATRIX" 2672223 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1128 2660841 2663810 2664537 "SPLTREE" 2666437 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1127 2656831 2657497 2658143 "SPLNODE" 2660267 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1126 2655878 2656111 2656141 "SPFCAT" 2656585 T SPFCAT (NIL) -9 NIL NIL NIL) (-1125 2654615 2654825 2655089 "SPECOUT" 2655636 T SPECOUT (NIL) -7 NIL NIL NIL) (-1124 2646267 2648011 2648041 "SPADXPT" 2652433 T SPADXPT (NIL) -9 NIL 2654467 NIL) (-1123 2646028 2646068 2646137 "SPADPRSR" 2646220 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1122 2644211 2645983 2646014 "SPADAST" 2646019 T SPADAST (NIL) -8 NIL NIL NIL) (-1121 2636182 2637929 2637972 "SPACEC" 2642345 NIL SPACEC (NIL T) -9 NIL 2644161 NIL) (-1120 2634353 2636114 2636163 "SPACE3" 2636168 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1119 2633105 2633276 2633567 "SORTPAK" 2634158 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1118 2631155 2631458 2631877 "SOLVETRA" 2632769 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1117 2630166 2630388 2630662 "SOLVESER" 2630928 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1116 2625386 2626267 2627269 "SOLVERAD" 2629218 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1115 2621201 2621810 2622539 "SOLVEFOR" 2624753 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1114 2615498 2620550 2620647 "SNTSCAT" 2620652 NIL SNTSCAT (NIL T T T T) -9 NIL 2620722 NIL) (-1113 2609641 2613821 2614212 "SMTS" 2615188 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1112 2604092 2609529 2609606 "SMP" 2609611 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1111 2602251 2602552 2602950 "SMITH" 2603789 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1110 2595146 2599302 2599405 "SMATCAT" 2600756 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601306 NIL) (-1109 2592086 2592909 2594087 "SMATCAT-" 2594092 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1108 2589799 2591322 2591365 "SKAGG" 2591626 NIL SKAGG (NIL T) -9 NIL 2591761 NIL) (-1107 2586141 2589215 2589410 "SINT" 2589597 T SINT (NIL) -8 NIL NIL 2589770) (-1106 2585913 2585951 2586017 "SIMPAN" 2586097 T SIMPAN (NIL) -7 NIL NIL NIL) (-1105 2585220 2585448 2585588 "SIG" 2585795 T SIG (NIL) -8 NIL NIL NIL) (-1104 2584058 2584279 2584554 "SIGNRF" 2584979 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1103 2582863 2583014 2583305 "SIGNEF" 2583887 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1102 2582196 2582446 2582570 "SIGAST" 2582761 T SIGAST (NIL) -8 NIL NIL NIL) (-1101 2579886 2580340 2580846 "SHP" 2581737 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1100 2573792 2579787 2579863 "SHDP" 2579868 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1099 2573391 2573557 2573587 "SGROUP" 2573680 T SGROUP (NIL) -9 NIL 2573742 NIL) (-1098 2573249 2573275 2573348 "SGROUP-" 2573353 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1097 2570085 2570782 2571505 "SGCF" 2572548 T SGCF (NIL) -7 NIL NIL NIL) (-1096 2564480 2569532 2569629 "SFRTCAT" 2569634 NIL SFRTCAT (NIL T T T T) -9 NIL 2569673 NIL) (-1095 2557904 2558919 2560055 "SFRGCD" 2563463 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1094 2551032 2552103 2553289 "SFQCMPK" 2556837 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2550654 2550743 2550853 "SFORT" 2550973 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1092 2549799 2550494 2550615 "SEXOF" 2550620 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1091 2548933 2549680 2549748 "SEX" 2549753 T SEX (NIL) -8 NIL NIL NIL) (-1090 2544472 2545161 2545256 "SEXCAT" 2548193 NIL SEXCAT (NIL T T T T T) -9 NIL 2548771 NIL) (-1089 2541652 2544406 2544454 "SET" 2544459 NIL SET (NIL T) -8 NIL NIL NIL) (-1088 2539903 2540365 2540670 "SETMN" 2541393 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1087 2539509 2539635 2539665 "SETCAT" 2539782 T SETCAT (NIL) -9 NIL 2539867 NIL) (-1086 2539289 2539341 2539440 "SETCAT-" 2539445 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1085 2535676 2537750 2537793 "SETAGG" 2538663 NIL SETAGG (NIL T) -9 NIL 2539003 NIL) (-1084 2535134 2535250 2535487 "SETAGG-" 2535492 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1083 2534604 2534830 2534931 "SEQAST" 2535055 T SEQAST (NIL) -8 NIL NIL NIL) (-1082 2533803 2534097 2534158 "SEGXCAT" 2534444 NIL SEGXCAT (NIL T T) -9 NIL 2534564 NIL) (-1081 2532859 2533469 2533651 "SEG" 2533656 NIL SEG (NIL T) -8 NIL NIL NIL) (-1080 2531838 2532052 2532095 "SEGCAT" 2532617 NIL SEGCAT (NIL T) -9 NIL 2532838 NIL) (-1079 2530887 2531217 2531417 "SEGBIND" 2531673 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1078 2530508 2530567 2530680 "SEGBIND2" 2530822 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1077 2530109 2530309 2530386 "SEGAST" 2530453 T SEGAST (NIL) -8 NIL NIL NIL) (-1076 2529328 2529454 2529658 "SEG2" 2529953 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1075 2528765 2529263 2529310 "SDVAR" 2529315 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1074 2521055 2528535 2528665 "SDPOL" 2528670 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1073 2519648 2519914 2520233 "SCPKG" 2520770 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1072 2518784 2518964 2519164 "SCOPE" 2519470 T SCOPE (NIL) -8 NIL NIL NIL) (-1071 2518005 2518138 2518317 "SCACHE" 2518639 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1070 2517677 2517837 2517867 "SASTCAT" 2517872 T SASTCAT (NIL) -9 NIL 2517885 NIL) (-1069 2517191 2517512 2517588 "SAOS" 2517623 T SAOS (NIL) -8 NIL NIL NIL) (-1068 2516756 2516791 2516964 "SAERFFC" 2517150 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1067 2510730 2516653 2516733 "SAE" 2516738 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1066 2510323 2510358 2510517 "SAEFACT" 2510689 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1065 2508644 2508958 2509359 "RURPK" 2509989 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1064 2507280 2507559 2507871 "RULESET" 2508478 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1063 2504467 2504970 2505435 "RULE" 2506961 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1062 2504106 2504261 2504344 "RULECOLD" 2504419 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1061 2503604 2503823 2503917 "RSTRCAST" 2504034 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1060 2498453 2499247 2500167 "RSETGCD" 2502803 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1059 2487710 2492762 2492859 "RSETCAT" 2496978 NIL RSETCAT (NIL T T T T) -9 NIL 2498075 NIL) (-1058 2485637 2486176 2487000 "RSETCAT-" 2487005 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1057 2478024 2479399 2480919 "RSDCMPK" 2484236 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2476029 2476470 2476544 "RRCC" 2477630 NIL RRCC (NIL T T) -9 NIL 2477974 NIL) (-1055 2475380 2475554 2475833 "RRCC-" 2475838 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1054 2474850 2475076 2475177 "RPTAST" 2475301 T RPTAST (NIL) -8 NIL NIL NIL) (-1053 2448856 2458443 2458510 "RPOLCAT" 2469174 NIL RPOLCAT (NIL T T T) -9 NIL 2472333 NIL) (-1052 2440356 2442694 2445816 "RPOLCAT-" 2445821 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1051 2431403 2438567 2439049 "ROUTINE" 2439896 T ROUTINE (NIL) -8 NIL NIL NIL) (-1050 2428236 2431029 2431169 "ROMAN" 2431285 T ROMAN (NIL) -8 NIL NIL NIL) (-1049 2426511 2427096 2427356 "ROIRC" 2428041 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1048 2422904 2425147 2425177 "RNS" 2425481 T RNS (NIL) -9 NIL 2425754 NIL) (-1047 2421413 2421796 2422330 "RNS-" 2422405 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1046 2420862 2421244 2421274 "RNG" 2421279 T RNG (NIL) -9 NIL 2421300 NIL) (-1045 2420254 2420616 2420659 "RMODULE" 2420721 NIL RMODULE (NIL T) -9 NIL 2420763 NIL) (-1044 2419090 2419184 2419520 "RMCAT2" 2420155 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1043 2415967 2418436 2418733 "RMATRIX" 2418852 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1042 2408909 2411143 2411258 "RMATCAT" 2414617 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415599 NIL) (-1041 2408284 2408431 2408738 "RMATCAT-" 2408743 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1040 2407851 2407926 2408054 "RINTERP" 2408203 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1039 2406984 2407504 2407534 "RING" 2407590 T RING (NIL) -9 NIL 2407676 NIL) (-1038 2406776 2406820 2406917 "RING-" 2406922 NIL RING- (NIL T) -8 NIL NIL NIL) (-1037 2405617 2405854 2406112 "RIDIST" 2406540 T RIDIST (NIL) -7 NIL NIL NIL) (-1036 2396933 2405085 2405291 "RGCHAIN" 2405465 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1035 2396309 2396689 2396730 "RGBCSPC" 2396788 NIL RGBCSPC (NIL T) -9 NIL 2396840 NIL) (-1034 2395493 2395848 2395889 "RGBCMDL" 2396121 NIL RGBCMDL (NIL T) -9 NIL 2396235 NIL) (-1033 2392487 2393101 2393771 "RF" 2394857 NIL RF (NIL T) -7 NIL NIL NIL) (-1032 2392133 2392196 2392299 "RFFACTOR" 2392418 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1031 2391858 2391893 2391990 "RFFACT" 2392092 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1030 2389975 2390339 2390721 "RFDIST" 2391498 T RFDIST (NIL) -7 NIL NIL NIL) (-1029 2389428 2389520 2389683 "RETSOL" 2389877 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1028 2389064 2389144 2389187 "RETRACT" 2389320 NIL RETRACT (NIL T) -9 NIL 2389407 NIL) (-1027 2388913 2388938 2389025 "RETRACT-" 2389030 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1026 2388542 2388735 2388805 "RETAST" 2388865 T RETAST (NIL) -8 NIL NIL NIL) (-1025 2381396 2388195 2388322 "RESULT" 2388437 T RESULT (NIL) -8 NIL NIL NIL) (-1024 2380022 2380665 2380864 "RESRING" 2381299 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1023 2379658 2379707 2379805 "RESLATC" 2379959 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1022 2379364 2379398 2379505 "REPSQ" 2379617 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1021 2376786 2377366 2377968 "REP" 2378784 T REP (NIL) -7 NIL NIL NIL) (-1020 2376484 2376518 2376629 "REPDB" 2376745 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1019 2370394 2371773 2372996 "REP2" 2375296 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1018 2366771 2367452 2368260 "REP1" 2369621 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1017 2359497 2364912 2365368 "REGSET" 2366401 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2358310 2358645 2358895 "REF" 2359282 NIL REF (NIL T) -8 NIL NIL NIL) (-1015 2357687 2357790 2357957 "REDORDER" 2358194 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1014 2353692 2356900 2357127 "RECLOS" 2357515 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1013 2352744 2352925 2353140 "REALSOLV" 2353499 T REALSOLV (NIL) -7 NIL NIL NIL) (-1012 2352590 2352631 2352661 "REAL" 2352666 T REAL (NIL) -9 NIL 2352701 NIL) (-1011 2349073 2349875 2350759 "REAL0Q" 2351755 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1010 2344674 2345662 2346723 "REAL0" 2348054 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1009 2344172 2344391 2344485 "RDUCEAST" 2344602 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1008 2343577 2343649 2343856 "RDIV" 2344094 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1007 2342645 2342819 2343032 "RDIST" 2343399 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1006 2341242 2341529 2341901 "RDETRS" 2342353 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1005 2339054 2339508 2340046 "RDETR" 2340784 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1004 2337665 2337943 2338347 "RDEEFS" 2338770 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1003 2336160 2336466 2336898 "RDEEF" 2337353 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1002 2330421 2333296 2333326 "RCFIELD" 2334621 T RCFIELD (NIL) -9 NIL 2335351 NIL) (-1001 2328485 2328989 2329685 "RCFIELD-" 2329760 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1000 2324801 2326586 2326629 "RCAGG" 2327713 NIL RCAGG (NIL T) -9 NIL 2328178 NIL) (-999 2324431 2324525 2324686 "RCAGG-" 2324691 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-998 2323771 2323883 2324046 "RATRET" 2324315 NIL RATRET (NIL T) -7 NIL NIL NIL) (-997 2323328 2323395 2323514 "RATFACT" 2323699 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-996 2322643 2322763 2322913 "RANDSRC" 2323198 T RANDSRC (NIL) -7 NIL NIL NIL) (-995 2322380 2322424 2322495 "RADUTIL" 2322592 T RADUTIL (NIL) -7 NIL NIL NIL) (-994 2315542 2321222 2321530 "RADIX" 2322104 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-993 2307199 2315386 2315514 "RADFF" 2315519 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-992 2306851 2306926 2306954 "RADCAT" 2307111 T RADCAT (NIL) -9 NIL NIL NIL) (-991 2306636 2306684 2306781 "RADCAT-" 2306786 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-990 2304787 2306411 2306500 "QUEUE" 2306580 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-989 2301363 2304724 2304769 "QUAT" 2304774 NIL QUAT (NIL T) -8 NIL NIL NIL) (-988 2301001 2301044 2301171 "QUATCT2" 2301314 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294748 2298050 2298090 "QUATCAT" 2298870 NIL QUATCAT (NIL T) -9 NIL 2299636 NIL) (-986 2290892 2291929 2293316 "QUATCAT-" 2293410 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-985 2288412 2289976 2290017 "QUAGG" 2290392 NIL QUAGG (NIL T) -9 NIL 2290567 NIL) (-984 2288044 2288237 2288305 "QQUTAST" 2288364 T QQUTAST (NIL) -8 NIL NIL NIL) (-983 2286969 2287442 2287614 "QFORM" 2287916 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-982 2278181 2283386 2283426 "QFCAT" 2284084 NIL QFCAT (NIL T) -9 NIL 2285085 NIL) (-981 2273753 2274954 2276545 "QFCAT-" 2276639 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-980 2273391 2273434 2273561 "QFCAT2" 2273704 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-979 2272851 2272961 2273091 "QEQUAT" 2273281 T QEQUAT (NIL) -8 NIL NIL NIL) (-978 2265999 2267070 2268254 "QCMPACK" 2271784 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-977 2263575 2263996 2264424 "QALGSET" 2265654 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-976 2262820 2262994 2263226 "QALGSET2" 2263395 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-975 2261511 2261734 2262051 "PWFFINTB" 2262593 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-974 2259693 2259861 2260215 "PUSHVAR" 2261325 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-973 2255611 2256665 2256706 "PTRANFN" 2258590 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-972 2254013 2254304 2254626 "PTPACK" 2255322 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-971 2253645 2253702 2253811 "PTFUNC2" 2253950 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-970 2248172 2252517 2252558 "PTCAT" 2252854 NIL PTCAT (NIL T) -9 NIL 2253007 NIL) (-969 2247830 2247865 2247989 "PSQFR" 2248131 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-968 2246425 2246723 2247057 "PSEUDLIN" 2247528 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-967 2233195 2235559 2237883 "PSETPK" 2244185 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-966 2226239 2228953 2229049 "PSETCAT" 2232070 NIL PSETCAT (NIL T T T T) -9 NIL 2232884 NIL) (-965 2224075 2224709 2225530 "PSETCAT-" 2225535 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-964 2223424 2223589 2223617 "PSCURVE" 2223885 T PSCURVE (NIL) -9 NIL 2224052 NIL) (-963 2219780 2221262 2221327 "PSCAT" 2222171 NIL PSCAT (NIL T T T) -9 NIL 2222411 NIL) (-962 2218843 2219059 2219459 "PSCAT-" 2219464 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2217575 2218208 2218413 "PRTITION" 2218658 T PRTITION (NIL) -8 NIL NIL NIL) (-960 2217077 2217296 2217388 "PRTDAST" 2217503 T PRTDAST (NIL) -8 NIL NIL NIL) (-959 2206175 2208381 2210569 "PRS" 2214939 NIL PRS (NIL T T) -7 NIL NIL NIL) (-958 2204033 2205525 2205565 "PRQAGG" 2205748 NIL PRQAGG (NIL T) -9 NIL 2205850 NIL) (-957 2203419 2203648 2203676 "PROPLOG" 2203861 T PROPLOG (NIL) -9 NIL 2203983 NIL) (-956 2200589 2201233 2201697 "PROPFRML" 2202987 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-955 2200049 2200159 2200289 "PROPERTY" 2200479 T PROPERTY (NIL) -8 NIL NIL NIL) (-954 2194134 2198215 2199035 "PRODUCT" 2199275 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-953 2191447 2193592 2193826 "PR" 2193945 NIL PR (NIL T T) -8 NIL NIL NIL) (-952 2191243 2191275 2191334 "PRINT" 2191408 T PRINT (NIL) -7 NIL NIL NIL) (-951 2190583 2190700 2190852 "PRIMES" 2191123 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-950 2188648 2189049 2189515 "PRIMELT" 2190162 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-949 2188377 2188426 2188454 "PRIMCAT" 2188578 T PRIMCAT (NIL) -9 NIL NIL NIL) (-948 2184538 2188315 2188360 "PRIMARR" 2188365 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-947 2183545 2183723 2183951 "PRIMARR2" 2184356 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-946 2183188 2183244 2183355 "PREASSOC" 2183483 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-945 2182663 2182796 2182824 "PPCURVE" 2183029 T PPCURVE (NIL) -9 NIL 2183165 NIL) (-944 2182285 2182458 2182541 "PORTNUM" 2182600 T PORTNUM (NIL) -8 NIL NIL NIL) (-943 2179644 2180043 2180635 "POLYROOT" 2181866 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-942 2173589 2179248 2179408 "POLY" 2179517 NIL POLY (NIL T) -8 NIL NIL NIL) (-941 2172972 2173030 2173264 "POLYLIFT" 2173525 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-940 2169247 2169696 2170325 "POLYCATQ" 2172517 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-939 2156064 2161422 2161487 "POLYCAT" 2165001 NIL POLYCAT (NIL T T T) -9 NIL 2166929 NIL) (-938 2149514 2151375 2153759 "POLYCAT-" 2153764 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-937 2149101 2149169 2149289 "POLY2UP" 2149440 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-936 2148733 2148790 2148899 "POLY2" 2149038 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-935 2147418 2147657 2147933 "POLUTIL" 2148507 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-934 2145773 2146050 2146381 "POLTOPOL" 2147140 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-933 2141291 2145709 2145755 "POINT" 2145760 NIL POINT (NIL T) -8 NIL NIL NIL) (-932 2139478 2139835 2140210 "PNTHEORY" 2140936 T PNTHEORY (NIL) -7 NIL NIL NIL) (-931 2137897 2138194 2138606 "PMTOOLS" 2139176 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-930 2137490 2137568 2137685 "PMSYM" 2137813 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-929 2137000 2137069 2137243 "PMQFCAT" 2137415 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-928 2136355 2136465 2136621 "PMPRED" 2136877 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-927 2135751 2135837 2135998 "PMPREDFS" 2136256 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-926 2134394 2134602 2134987 "PMPLCAT" 2135513 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-925 2133926 2134005 2134157 "PMLSAGG" 2134309 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-924 2133401 2133477 2133658 "PMKERNEL" 2133844 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-923 2133018 2133093 2133206 "PMINS" 2133320 NIL PMINS (NIL T) -7 NIL NIL NIL) (-922 2132446 2132515 2132731 "PMFS" 2132943 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-921 2131674 2131792 2131997 "PMDOWN" 2132323 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-920 2130837 2130996 2131178 "PMASS" 2131512 T PMASS (NIL) -7 NIL NIL NIL) (-919 2130111 2130222 2130385 "PMASSFS" 2130723 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-918 2129766 2129834 2129928 "PLOTTOOL" 2130037 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-917 2124388 2125577 2126725 "PLOT" 2128638 T PLOT (NIL) -8 NIL NIL NIL) (-916 2120202 2121236 2122157 "PLOT3D" 2123487 T PLOT3D (NIL) -8 NIL NIL NIL) (-915 2119114 2119291 2119526 "PLOT1" 2120006 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-914 2094508 2099180 2104031 "PLEQN" 2114380 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-913 2093826 2093948 2094128 "PINTERP" 2094373 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-912 2093519 2093566 2093669 "PINTERPA" 2093773 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-911 2092767 2093288 2093375 "PI" 2093415 T PI (NIL) -8 NIL NIL 2093482) (-910 2091164 2092105 2092133 "PID" 2092315 T PID (NIL) -9 NIL 2092449 NIL) (-909 2090889 2090926 2091014 "PICOERCE" 2091121 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-908 2090209 2090348 2090524 "PGROEB" 2090745 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-907 2085796 2086610 2087515 "PGE" 2089324 T PGE (NIL) -7 NIL NIL NIL) (-906 2083920 2084166 2084532 "PGCD" 2085513 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-905 2083258 2083361 2083522 "PFRPAC" 2083804 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-904 2079938 2081806 2082159 "PFR" 2082937 NIL PFR (NIL T) -8 NIL NIL NIL) (-903 2078327 2078571 2078896 "PFOTOOLS" 2079685 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-902 2076860 2077099 2077450 "PFOQ" 2078084 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-901 2075333 2075545 2075908 "PFO" 2076644 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-900 2071921 2075222 2075291 "PF" 2075296 NIL PF (NIL NIL) -8 NIL NIL NIL) (-899 2069355 2070592 2070620 "PFECAT" 2071205 T PFECAT (NIL) -9 NIL 2071589 NIL) (-898 2068800 2068954 2069168 "PFECAT-" 2069173 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-897 2067404 2067655 2067956 "PFBRU" 2068549 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-896 2065271 2065622 2066054 "PFBR" 2067055 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-895 2061187 2062647 2063323 "PERM" 2064628 NIL PERM (NIL T) -8 NIL NIL NIL) (-894 2056453 2057394 2058264 "PERMGRP" 2060350 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-893 2054585 2055516 2055557 "PERMCAT" 2056003 NIL PERMCAT (NIL T) -9 NIL 2056308 NIL) (-892 2054238 2054279 2054403 "PERMAN" 2054538 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-891 2051774 2053903 2054025 "PENDTREE" 2054149 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-890 2049867 2050601 2050642 "PDRING" 2051299 NIL PDRING (NIL T) -9 NIL 2051585 NIL) (-889 2048970 2049188 2049550 "PDRING-" 2049555 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-888 2046212 2046963 2047631 "PDEPROB" 2048322 T PDEPROB (NIL) -8 NIL NIL NIL) (-887 2043759 2044261 2044816 "PDEPACK" 2045677 T PDEPACK (NIL) -7 NIL NIL NIL) (-886 2042671 2042861 2043112 "PDECOMP" 2043558 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-885 2040276 2041093 2041121 "PDECAT" 2041908 T PDECAT (NIL) -9 NIL 2042621 NIL) (-884 2040027 2040060 2040150 "PCOMP" 2040237 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-883 2038232 2038828 2039125 "PBWLB" 2039756 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-882 2030737 2032305 2033643 "PATTERN" 2036915 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-881 2030369 2030426 2030535 "PATTERN2" 2030674 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-880 2028126 2028514 2028971 "PATTERN1" 2029958 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-879 2025521 2026075 2026556 "PATRES" 2027691 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-878 2025085 2025152 2025284 "PATRES2" 2025448 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-877 2022968 2023373 2023780 "PATMATCH" 2024752 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-876 2022504 2022687 2022728 "PATMAB" 2022835 NIL PATMAB (NIL T) -9 NIL 2022918 NIL) (-875 2021049 2021358 2021616 "PATLRES" 2022309 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-874 2020595 2020718 2020759 "PATAB" 2020764 NIL PATAB (NIL T) -9 NIL 2020936 NIL) (-873 2018076 2018608 2019181 "PARTPERM" 2020042 T PARTPERM (NIL) -7 NIL NIL NIL) (-872 2017697 2017760 2017862 "PARSURF" 2018007 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-871 2017329 2017386 2017495 "PARSU2" 2017634 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-870 2017093 2017133 2017200 "PARSER" 2017282 T PARSER (NIL) -7 NIL NIL NIL) (-869 2016714 2016777 2016879 "PARSCURV" 2017024 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-868 2016346 2016403 2016512 "PARSC2" 2016651 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-867 2015985 2016043 2016140 "PARPCURV" 2016282 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-866 2015617 2015674 2015783 "PARPC2" 2015922 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-865 2015137 2015223 2015342 "PAN2EXPR" 2015518 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-864 2013943 2014258 2014486 "PALETTE" 2014929 T PALETTE (NIL) -8 NIL NIL NIL) (-863 2012411 2012948 2013308 "PAIR" 2013629 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-862 2006317 2011670 2011864 "PADICRC" 2012266 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-861 1999581 2005663 2005847 "PADICRAT" 2006165 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-860 1997931 1999518 1999563 "PADIC" 1999568 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-859 1995141 1996671 1996711 "PADICCT" 1997292 NIL PADICCT (NIL NIL) -9 NIL 1997574 NIL) (-858 1994098 1994298 1994566 "PADEPAC" 1994928 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-857 1993310 1993443 1993649 "PADE" 1993960 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-856 1991732 1992518 1992798 "OWP" 1993114 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-855 1990805 1991337 1991509 "OVAR" 1991600 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-854 1990069 1990190 1990351 "OUT" 1990664 T OUT (NIL) -7 NIL NIL NIL) (-853 1978976 1981178 1983378 "OUTFORM" 1987889 T OUTFORM (NIL) -8 NIL NIL NIL) (-852 1978397 1978573 1978700 "OUTBFILE" 1978869 T OUTBFILE (NIL) -8 NIL NIL NIL) (-851 1978034 1978117 1978145 "OUTBCON" 1978296 T OUTBCON (NIL) -9 NIL 1978381 NIL) (-850 1977874 1977909 1977985 "OUTBCON-" 1977990 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-849 1977282 1977603 1977692 "OSI" 1977805 T OSI (NIL) -8 NIL NIL NIL) (-848 1976838 1977150 1977178 "OSGROUP" 1977183 T OSGROUP (NIL) -9 NIL 1977205 NIL) (-847 1975583 1975810 1976095 "ORTHPOL" 1976585 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-846 1973169 1975418 1975539 "OREUP" 1975544 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-845 1970607 1972860 1972987 "ORESUP" 1973111 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-844 1968135 1968635 1969196 "OREPCTO" 1970096 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-843 1961959 1964126 1964167 "OREPCAT" 1966515 NIL OREPCAT (NIL T) -9 NIL 1967619 NIL) (-842 1959106 1959888 1960946 "OREPCAT-" 1960951 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-841 1958283 1958555 1958583 "ORDSET" 1958892 T ORDSET (NIL) -9 NIL 1959056 NIL) (-840 1957802 1957924 1958117 "ORDSET-" 1958122 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-839 1956436 1957193 1957221 "ORDRING" 1957423 T ORDRING (NIL) -9 NIL 1957548 NIL) (-838 1956081 1956175 1956319 "ORDRING-" 1956324 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-837 1955487 1955924 1955952 "ORDMON" 1955957 T ORDMON (NIL) -9 NIL 1955978 NIL) (-836 1954649 1954796 1954991 "ORDFUNS" 1955336 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-835 1954013 1954406 1954434 "ORDFIN" 1954499 T ORDFIN (NIL) -9 NIL 1954573 NIL) (-834 1950605 1952599 1953008 "ORDCOMP" 1953637 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-833 1949871 1949998 1950184 "ORDCOMP2" 1950465 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1946479 1947362 1948176 "OPTPROB" 1949077 T OPTPROB (NIL) -8 NIL NIL NIL) (-831 1943281 1943920 1944624 "OPTPACK" 1945795 T OPTPACK (NIL) -7 NIL NIL NIL) (-830 1940994 1941734 1941762 "OPTCAT" 1942581 T OPTCAT (NIL) -9 NIL 1943231 NIL) (-829 1940437 1940671 1940776 "OPSIG" 1940909 T OPSIG (NIL) -8 NIL NIL NIL) (-828 1940205 1940244 1940310 "OPQUERY" 1940391 T OPQUERY (NIL) -7 NIL NIL NIL) (-827 1937371 1938516 1939020 "OP" 1939734 NIL OP (NIL T) -8 NIL NIL NIL) (-826 1936906 1937077 1937118 "OPERCAT" 1937253 NIL OPERCAT (NIL T) -9 NIL 1937321 NIL) (-825 1936752 1936779 1936865 "OPERCAT-" 1936870 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-824 1933597 1935549 1935918 "ONECOMP" 1936416 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-823 1932902 1933017 1933191 "ONECOMP2" 1933469 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-822 1932321 1932427 1932557 "OMSERVER" 1932792 T OMSERVER (NIL) -7 NIL NIL NIL) (-821 1929209 1931761 1931801 "OMSAGG" 1931862 NIL OMSAGG (NIL T) -9 NIL 1931926 NIL) (-820 1927832 1928095 1928377 "OMPKG" 1928947 T OMPKG (NIL) -7 NIL NIL NIL) (-819 1927262 1927365 1927393 "OM" 1927692 T OM (NIL) -9 NIL NIL NIL) (-818 1925844 1926811 1926980 "OMLO" 1927143 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-817 1924769 1924916 1925143 "OMEXPR" 1925670 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-816 1924087 1924315 1924451 "OMERR" 1924653 T OMERR (NIL) -8 NIL NIL NIL) (-815 1923265 1923508 1923668 "OMERRK" 1923947 T OMERRK (NIL) -8 NIL NIL NIL) (-814 1922743 1922942 1923050 "OMENC" 1923177 T OMENC (NIL) -8 NIL NIL NIL) (-813 1916638 1917823 1918994 "OMDEV" 1921592 T OMDEV (NIL) -8 NIL NIL NIL) (-812 1915707 1915878 1916072 "OMCONN" 1916464 T OMCONN (NIL) -8 NIL NIL NIL) (-811 1914328 1915270 1915298 "OINTDOM" 1915303 T OINTDOM (NIL) -9 NIL 1915324 NIL) (-810 1910134 1911318 1912034 "OFMONOID" 1913644 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-809 1909572 1910071 1910116 "ODVAR" 1910121 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-808 1907030 1909317 1909472 "ODR" 1909477 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-807 1899374 1906806 1906932 "ODPOL" 1906937 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-806 1893250 1899246 1899351 "ODP" 1899356 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-805 1892016 1892231 1892506 "ODETOOLS" 1893024 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-804 1888985 1889641 1890357 "ODESYS" 1891349 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-803 1883867 1884775 1885800 "ODERTRIC" 1888060 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-802 1883293 1883375 1883569 "ODERED" 1883779 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-801 1880181 1880729 1881406 "ODERAT" 1882716 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-800 1877141 1877605 1878202 "ODEPRRIC" 1879710 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-799 1875111 1875680 1876166 "ODEPROB" 1876675 T ODEPROB (NIL) -8 NIL NIL NIL) (-798 1871633 1872116 1872763 "ODEPRIM" 1874590 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-797 1870882 1870984 1871244 "ODEPAL" 1871525 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-796 1867044 1867835 1868699 "ODEPACK" 1870038 T ODEPACK (NIL) -7 NIL NIL NIL) (-795 1866077 1866184 1866413 "ODEINT" 1866933 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-794 1860178 1861603 1863050 "ODEIFTBL" 1864650 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-793 1855513 1856299 1857258 "ODEEF" 1859337 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-792 1854848 1854937 1855167 "ODECONST" 1855418 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-791 1852999 1853634 1853662 "ODECAT" 1854267 T ODECAT (NIL) -9 NIL 1854798 NIL) (-790 1849906 1852711 1852830 "OCT" 1852912 NIL OCT (NIL T) -8 NIL NIL NIL) (-789 1849544 1849587 1849714 "OCTCT2" 1849857 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-788 1844318 1846718 1846758 "OC" 1847855 NIL OC (NIL T) -9 NIL 1848713 NIL) (-787 1841545 1842293 1843283 "OC-" 1843377 NIL OC- (NIL T T) -8 NIL NIL NIL) (-786 1840923 1841365 1841393 "OCAMON" 1841398 T OCAMON (NIL) -9 NIL 1841419 NIL) (-785 1840480 1840795 1840823 "OASGP" 1840828 T OASGP (NIL) -9 NIL 1840848 NIL) (-784 1839767 1840230 1840258 "OAMONS" 1840298 T OAMONS (NIL) -9 NIL 1840341 NIL) (-783 1839207 1839614 1839642 "OAMON" 1839647 T OAMON (NIL) -9 NIL 1839667 NIL) (-782 1838511 1839003 1839031 "OAGROUP" 1839036 T OAGROUP (NIL) -9 NIL 1839056 NIL) (-781 1838201 1838251 1838339 "NUMTUBE" 1838455 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-780 1831774 1833292 1834828 "NUMQUAD" 1836685 T NUMQUAD (NIL) -7 NIL NIL NIL) (-779 1827530 1828518 1829543 "NUMODE" 1830769 T NUMODE (NIL) -7 NIL NIL NIL) (-778 1824911 1825765 1825793 "NUMINT" 1826716 T NUMINT (NIL) -9 NIL 1827480 NIL) (-777 1823859 1824056 1824274 "NUMFMT" 1824713 T NUMFMT (NIL) -7 NIL NIL NIL) (-776 1810218 1813163 1815695 "NUMERIC" 1821366 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-775 1804615 1809667 1809762 "NTSCAT" 1809767 NIL NTSCAT (NIL T T T T) -9 NIL 1809806 NIL) (-774 1803809 1803974 1804167 "NTPOLFN" 1804454 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-773 1791649 1800634 1801446 "NSUP" 1803030 NIL NSUP (NIL T) -8 NIL NIL NIL) (-772 1791281 1791338 1791447 "NSUP2" 1791586 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-771 1781278 1791055 1791188 "NSMP" 1791193 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-770 1779710 1780011 1780368 "NREP" 1780966 NIL NREP (NIL T) -7 NIL NIL NIL) (-769 1778301 1778553 1778911 "NPCOEF" 1779453 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-768 1777367 1777482 1777698 "NORMRETR" 1778182 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-767 1775408 1775698 1776107 "NORMPK" 1777075 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-766 1775093 1775121 1775245 "NORMMA" 1775374 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-765 1774920 1775050 1775079 "NONE" 1775084 T NONE (NIL) -8 NIL NIL NIL) (-764 1774709 1774738 1774807 "NONE1" 1774884 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-763 1774192 1774254 1774440 "NODE1" 1774641 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-762 1772463 1773286 1773541 "NNI" 1773888 T NNI (NIL) -8 NIL NIL 1774123) (-761 1770883 1771196 1771560 "NLINSOL" 1772131 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-760 1767151 1768119 1769018 "NIPROB" 1770004 T NIPROB (NIL) -8 NIL NIL NIL) (-759 1765908 1766142 1766444 "NFINTBAS" 1766913 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-758 1765352 1765559 1765600 "NETCLT" 1765764 NIL NETCLT (NIL T) -9 NIL 1765853 NIL) (-757 1764060 1764291 1764572 "NCODIV" 1765120 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-756 1763822 1763859 1763934 "NCNTFRAC" 1764017 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-755 1762002 1762366 1762786 "NCEP" 1763447 NIL NCEP (NIL T) -7 NIL NIL NIL) (-754 1760913 1761652 1761680 "NASRING" 1761790 T NASRING (NIL) -9 NIL 1761864 NIL) (-753 1760708 1760752 1760846 "NASRING-" 1760851 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-752 1759861 1760360 1760388 "NARNG" 1760505 T NARNG (NIL) -9 NIL 1760596 NIL) (-751 1759553 1759620 1759754 "NARNG-" 1759759 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-750 1758432 1758639 1758874 "NAGSP" 1759338 T NAGSP (NIL) -7 NIL NIL NIL) (-749 1749704 1751388 1753061 "NAGS" 1756779 T NAGS (NIL) -7 NIL NIL NIL) (-748 1748252 1748560 1748891 "NAGF07" 1749393 T NAGF07 (NIL) -7 NIL NIL NIL) (-747 1742790 1744081 1745388 "NAGF04" 1746965 T NAGF04 (NIL) -7 NIL NIL NIL) (-746 1735758 1737372 1739005 "NAGF02" 1741177 T NAGF02 (NIL) -7 NIL NIL NIL) (-745 1730982 1732082 1733199 "NAGF01" 1734661 T NAGF01 (NIL) -7 NIL NIL NIL) (-744 1724610 1726176 1727761 "NAGE04" 1729417 T NAGE04 (NIL) -7 NIL NIL NIL) (-743 1715779 1717900 1720030 "NAGE02" 1722500 T NAGE02 (NIL) -7 NIL NIL NIL) (-742 1711732 1712679 1713643 "NAGE01" 1714835 T NAGE01 (NIL) -7 NIL NIL NIL) (-741 1709527 1710061 1710619 "NAGD03" 1711194 T NAGD03 (NIL) -7 NIL NIL NIL) (-740 1701277 1703205 1705159 "NAGD02" 1707593 T NAGD02 (NIL) -7 NIL NIL NIL) (-739 1695088 1696513 1697953 "NAGD01" 1699857 T NAGD01 (NIL) -7 NIL NIL NIL) (-738 1691297 1692119 1692956 "NAGC06" 1694271 T NAGC06 (NIL) -7 NIL NIL NIL) (-737 1689762 1690094 1690450 "NAGC05" 1690961 T NAGC05 (NIL) -7 NIL NIL NIL) (-736 1689138 1689257 1689401 "NAGC02" 1689638 T NAGC02 (NIL) -7 NIL NIL NIL) (-735 1688198 1688755 1688795 "NAALG" 1688874 NIL NAALG (NIL T) -9 NIL 1688935 NIL) (-734 1688033 1688062 1688152 "NAALG-" 1688157 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-733 1681983 1683091 1684278 "MULTSQFR" 1686929 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-732 1681302 1681377 1681561 "MULTFACT" 1681895 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-731 1674395 1678265 1678318 "MTSCAT" 1679388 NIL MTSCAT (NIL T T) -9 NIL 1679902 NIL) (-730 1674107 1674161 1674253 "MTHING" 1674335 NIL MTHING (NIL T) -7 NIL NIL NIL) (-729 1673899 1673932 1673992 "MSYSCMD" 1674067 T MSYSCMD (NIL) -7 NIL NIL NIL) (-728 1670011 1672654 1672974 "MSET" 1673612 NIL MSET (NIL T) -8 NIL NIL NIL) (-727 1667106 1669572 1669613 "MSETAGG" 1669618 NIL MSETAGG (NIL T) -9 NIL 1669652 NIL) (-726 1662989 1664485 1665230 "MRING" 1666406 NIL MRING (NIL T T) -8 NIL NIL NIL) (-725 1662555 1662622 1662753 "MRF2" 1662916 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-724 1662173 1662208 1662352 "MRATFAC" 1662514 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-723 1659785 1660080 1660511 "MPRFF" 1661878 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-722 1653845 1659639 1659736 "MPOLY" 1659741 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-721 1653335 1653370 1653578 "MPCPF" 1653804 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-720 1652849 1652892 1653076 "MPC3" 1653286 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-719 1652044 1652125 1652346 "MPC2" 1652764 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-718 1650345 1650682 1651072 "MONOTOOL" 1651704 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-717 1649596 1649887 1649915 "MONOID" 1650134 T MONOID (NIL) -9 NIL 1650281 NIL) (-716 1649142 1649261 1649442 "MONOID-" 1649447 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-715 1640001 1645909 1645968 "MONOGEN" 1646642 NIL MONOGEN (NIL T T) -9 NIL 1647098 NIL) (-714 1637219 1637954 1638954 "MONOGEN-" 1639073 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-713 1636078 1636498 1636526 "MONADWU" 1636918 T MONADWU (NIL) -9 NIL 1637156 NIL) (-712 1635450 1635609 1635857 "MONADWU-" 1635862 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-711 1634835 1635053 1635081 "MONAD" 1635288 T MONAD (NIL) -9 NIL 1635400 NIL) (-710 1634520 1634598 1634730 "MONAD-" 1634735 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-709 1632836 1633433 1633712 "MOEBIUS" 1634273 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-708 1632228 1632606 1632646 "MODULE" 1632651 NIL MODULE (NIL T) -9 NIL 1632677 NIL) (-707 1631796 1631892 1632082 "MODULE-" 1632087 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-706 1629511 1630160 1630487 "MODRING" 1631620 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1626497 1627616 1628137 "MODOP" 1629040 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-704 1625112 1625564 1625841 "MODMONOM" 1626360 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-703 1614919 1623403 1623817 "MODMON" 1624749 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-702 1612110 1613763 1614039 "MODFIELD" 1614794 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-701 1611114 1611391 1611581 "MMLFORM" 1611940 T MMLFORM (NIL) -8 NIL NIL NIL) (-700 1610640 1610683 1610862 "MMAP" 1611065 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-699 1608857 1609590 1609631 "MLO" 1610054 NIL MLO (NIL T) -9 NIL 1610296 NIL) (-698 1606224 1606739 1607341 "MLIFT" 1608338 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-697 1605615 1605699 1605853 "MKUCFUNC" 1606135 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-696 1605214 1605284 1605407 "MKRECORD" 1605538 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-695 1604262 1604423 1604651 "MKFUNC" 1605025 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-694 1603650 1603754 1603910 "MKFLCFN" 1604145 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-693 1603193 1603560 1603619 "MKCHSET" 1603624 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-692 1602470 1602572 1602757 "MKBCFUNC" 1603086 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-691 1599212 1602024 1602160 "MINT" 1602354 T MINT (NIL) -8 NIL NIL NIL) (-690 1598024 1598267 1598544 "MHROWRED" 1598967 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-689 1593450 1596559 1596964 "MFLOAT" 1597639 T MFLOAT (NIL) -8 NIL NIL NIL) (-688 1592807 1592883 1593054 "MFINFACT" 1593362 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-687 1589122 1589970 1590854 "MESH" 1591943 T MESH (NIL) -7 NIL NIL NIL) (-686 1587512 1587824 1588177 "MDDFACT" 1588809 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-685 1584354 1586671 1586712 "MDAGG" 1586967 NIL MDAGG (NIL T) -9 NIL 1587110 NIL) (-684 1574132 1583647 1583854 "MCMPLX" 1584167 T MCMPLX (NIL) -8 NIL NIL NIL) (-683 1573273 1573419 1573619 "MCDEN" 1573981 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-682 1571163 1571433 1571813 "MCALCFN" 1573003 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-681 1570074 1570247 1570488 "MAYBE" 1570961 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-680 1567686 1568209 1568771 "MATSTOR" 1569545 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-679 1563692 1567058 1567306 "MATRIX" 1567471 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-678 1559461 1560165 1560901 "MATLIN" 1563049 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-677 1549615 1552753 1552830 "MATCAT" 1557710 NIL MATCAT (NIL T T T) -9 NIL 1559127 NIL) (-676 1545979 1546992 1548348 "MATCAT-" 1548353 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-675 1544573 1544726 1545059 "MATCAT2" 1545814 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-674 1542685 1543009 1543393 "MAPPKG3" 1544248 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-673 1541666 1541839 1542061 "MAPPKG2" 1542509 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-672 1540165 1540449 1540776 "MAPPKG1" 1541372 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-671 1539271 1539571 1539748 "MAPPAST" 1540008 T MAPPAST (NIL) -8 NIL NIL NIL) (-670 1538882 1538940 1539063 "MAPHACK3" 1539207 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-669 1538474 1538535 1538649 "MAPHACK2" 1538814 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-668 1537912 1538015 1538157 "MAPHACK1" 1538365 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-667 1536018 1536612 1536916 "MAGMA" 1537640 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-666 1535524 1535742 1535833 "MACROAST" 1535947 T MACROAST (NIL) -8 NIL NIL NIL) (-665 1531991 1533763 1534224 "M3D" 1535096 NIL M3D (NIL T) -8 NIL NIL NIL) (-664 1526145 1530360 1530401 "LZSTAGG" 1531183 NIL LZSTAGG (NIL T) -9 NIL 1531478 NIL) (-663 1522119 1523276 1524733 "LZSTAGG-" 1524738 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-662 1519233 1520010 1520497 "LWORD" 1521664 NIL LWORD (NIL T) -8 NIL NIL NIL) (-661 1518836 1519037 1519112 "LSTAST" 1519178 T LSTAST (NIL) -8 NIL NIL NIL) (-660 1512037 1518607 1518741 "LSQM" 1518746 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-659 1511261 1511400 1511628 "LSPP" 1511892 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-658 1509073 1509374 1509830 "LSMP" 1510950 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-657 1505852 1506526 1507256 "LSMP1" 1508375 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-656 1499777 1505019 1505060 "LSAGG" 1505122 NIL LSAGG (NIL T) -9 NIL 1505200 NIL) (-655 1496472 1497396 1498609 "LSAGG-" 1498614 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-654 1494098 1495616 1495865 "LPOLY" 1496267 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-653 1493680 1493765 1493888 "LPEFRAC" 1494007 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-652 1492027 1492774 1493027 "LO" 1493512 NIL LO (NIL T T T) -8 NIL NIL NIL) (-651 1491679 1491791 1491819 "LOGIC" 1491930 T LOGIC (NIL) -9 NIL 1492011 NIL) (-650 1491541 1491564 1491635 "LOGIC-" 1491640 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-649 1490734 1490874 1491067 "LODOOPS" 1491397 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-648 1488192 1490650 1490716 "LODO" 1490721 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-647 1486730 1486965 1487318 "LODOF" 1487939 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-646 1483086 1485483 1485524 "LODOCAT" 1485962 NIL LODOCAT (NIL T) -9 NIL 1486173 NIL) (-645 1482819 1482877 1483004 "LODOCAT-" 1483009 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-644 1480174 1482660 1482778 "LODO2" 1482783 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-643 1477644 1480111 1480156 "LODO1" 1480161 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-642 1476504 1476669 1476981 "LODEEF" 1477467 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-641 1471790 1474634 1474675 "LNAGG" 1475622 NIL LNAGG (NIL T) -9 NIL 1476066 NIL) (-640 1470937 1471151 1471493 "LNAGG-" 1471498 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-639 1467100 1467862 1468501 "LMOPS" 1470352 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-638 1466495 1466857 1466898 "LMODULE" 1466959 NIL LMODULE (NIL T) -9 NIL 1467001 NIL) (-637 1463741 1466140 1466263 "LMDICT" 1466405 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-636 1463467 1463649 1463709 "LITERAL" 1463714 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-635 1456694 1462413 1462711 "LIST" 1463202 NIL LIST (NIL T) -8 NIL NIL NIL) (-634 1456219 1456293 1456432 "LIST3" 1456614 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-633 1455226 1455404 1455632 "LIST2" 1456037 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-632 1453360 1453672 1454071 "LIST2MAP" 1454873 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-631 1452090 1452726 1452767 "LINEXP" 1453022 NIL LINEXP (NIL T) -9 NIL 1453171 NIL) (-630 1450737 1450997 1451294 "LINDEP" 1451842 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-629 1447504 1448223 1449000 "LIMITRF" 1449992 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-628 1445780 1446075 1446491 "LIMITPS" 1447199 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-627 1440235 1445291 1445519 "LIE" 1445601 NIL LIE (NIL T T) -8 NIL NIL NIL) (-626 1439284 1439727 1439767 "LIECAT" 1439907 NIL LIECAT (NIL T) -9 NIL 1440058 NIL) (-625 1439125 1439152 1439240 "LIECAT-" 1439245 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-624 1431737 1438574 1438739 "LIB" 1438980 T LIB (NIL) -8 NIL NIL NIL) (-623 1427374 1428255 1429190 "LGROBP" 1430854 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-622 1425240 1425514 1425876 "LF" 1427095 NIL LF (NIL T T) -7 NIL NIL NIL) (-621 1424080 1424772 1424800 "LFCAT" 1425007 T LFCAT (NIL) -9 NIL 1425146 NIL) (-620 1420984 1421612 1422300 "LEXTRIPK" 1423444 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-619 1417755 1418554 1419057 "LEXP" 1420564 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-618 1417258 1417476 1417568 "LETAST" 1417683 T LETAST (NIL) -8 NIL NIL NIL) (-617 1415656 1415969 1416370 "LEADCDET" 1416940 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-616 1414846 1414920 1415149 "LAZM3PK" 1415577 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-615 1409801 1412923 1413461 "LAUPOL" 1414358 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-614 1409366 1409410 1409578 "LAPLACE" 1409751 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-613 1407340 1408467 1408718 "LA" 1409199 NIL LA (NIL T T T) -8 NIL NIL NIL) (-612 1406421 1406971 1407012 "LALG" 1407074 NIL LALG (NIL T) -9 NIL 1407133 NIL) (-611 1406135 1406194 1406330 "LALG-" 1406335 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-610 1405970 1405994 1406035 "KVTFROM" 1406097 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-609 1404770 1405187 1405416 "KTVLOGIC" 1405761 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-608 1404605 1404629 1404670 "KRCFROM" 1404732 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-607 1403509 1403696 1403995 "KOVACIC" 1404405 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-606 1403344 1403368 1403409 "KONVERT" 1403471 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-605 1403179 1403203 1403244 "KOERCE" 1403306 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-604 1400913 1401673 1402066 "KERNEL" 1402818 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-603 1400415 1400496 1400626 "KERNEL2" 1400827 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-602 1394266 1398954 1399008 "KDAGG" 1399385 NIL KDAGG (NIL T T) -9 NIL 1399591 NIL) (-601 1393795 1393919 1394124 "KDAGG-" 1394129 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386970 1393456 1393611 "KAFILE" 1393673 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-599 1381425 1386481 1386709 "JORDAN" 1386791 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-598 1380831 1381074 1381195 "JOINAST" 1381324 T JOINAST (NIL) -8 NIL NIL NIL) (-597 1380677 1380736 1380791 "JAVACODE" 1380796 T JAVACODE (NIL) -8 NIL NIL NIL) (-596 1376976 1378882 1378936 "IXAGG" 1379865 NIL IXAGG (NIL T T) -9 NIL 1380324 NIL) (-595 1375895 1376201 1376620 "IXAGG-" 1376625 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-594 1371475 1375817 1375876 "IVECTOR" 1375881 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-593 1370241 1370478 1370744 "ITUPLE" 1371242 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-592 1368677 1368854 1369160 "ITRIGMNP" 1370063 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-591 1367422 1367626 1367909 "ITFUN3" 1368453 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-590 1367054 1367111 1367220 "ITFUN2" 1367359 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-589 1364891 1365916 1366215 "ITAYLOR" 1366788 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-588 1353874 1359028 1360191 "ISUPS" 1363761 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-587 1352978 1353118 1353354 "ISUMP" 1353721 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-586 1348242 1352779 1352858 "ISTRING" 1352931 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-585 1347745 1347963 1348055 "ISAST" 1348170 T ISAST (NIL) -8 NIL NIL NIL) (-584 1346955 1347036 1347252 "IRURPK" 1347659 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-583 1345891 1346092 1346332 "IRSN" 1346735 T IRSN (NIL) -7 NIL NIL NIL) (-582 1343920 1344275 1344711 "IRRF2F" 1345529 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-581 1343667 1343705 1343781 "IRREDFFX" 1343876 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-580 1342282 1342541 1342840 "IROOT" 1343400 NIL IROOT (NIL T) -7 NIL NIL NIL) (-579 1338914 1339966 1340658 "IR" 1341622 NIL IR (NIL T) -8 NIL NIL NIL) (-578 1336527 1337022 1337588 "IR2" 1338392 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-577 1335599 1335712 1335933 "IR2F" 1336410 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-576 1335390 1335424 1335484 "IPRNTPK" 1335559 T IPRNTPK (NIL) -7 NIL NIL NIL) (-575 1332009 1335279 1335348 "IPF" 1335353 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-574 1330372 1331934 1331991 "IPADIC" 1331996 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-573 1329703 1329930 1330067 "IP4ADDR" 1330255 T IP4ADDR (NIL) -8 NIL NIL NIL) (-572 1329203 1329407 1329517 "IOMODE" 1329613 T IOMODE (NIL) -8 NIL NIL NIL) (-571 1328561 1328800 1328927 "IOBFILE" 1329096 T IOBFILE (NIL) -8 NIL NIL NIL) (-570 1328325 1328465 1328493 "IOBCON" 1328498 T IOBCON (NIL) -9 NIL 1328519 NIL) (-569 1327822 1327880 1328070 "INVLAPLA" 1328261 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-568 1317471 1319824 1322210 "INTTR" 1325486 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-567 1313815 1314557 1315421 "INTTOOLS" 1316656 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-566 1313401 1313492 1313609 "INTSLPE" 1313718 T INTSLPE (NIL) -7 NIL NIL NIL) (-565 1311396 1313324 1313383 "INTRVL" 1313388 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-564 1308998 1309510 1310085 "INTRF" 1310881 NIL INTRF (NIL T) -7 NIL NIL NIL) (-563 1308409 1308506 1308648 "INTRET" 1308896 NIL INTRET (NIL T) -7 NIL NIL NIL) (-562 1306406 1306795 1307265 "INTRAT" 1308017 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-561 1303634 1304217 1304843 "INTPM" 1305891 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-560 1300337 1300936 1301681 "INTPAF" 1303020 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-559 1295516 1296478 1297529 "INTPACK" 1299306 T INTPACK (NIL) -7 NIL NIL NIL) (-558 1292428 1295245 1295372 "INT" 1295409 T INT (NIL) -8 NIL NIL NIL) (-557 1291680 1291832 1292040 "INTHERTR" 1292270 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-556 1291119 1291199 1291387 "INTHERAL" 1291594 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-555 1288965 1289408 1289865 "INTHEORY" 1290682 T INTHEORY (NIL) -7 NIL NIL NIL) (-554 1280273 1281894 1283673 "INTG0" 1287317 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-553 1260846 1265636 1270446 "INTFTBL" 1275483 T INTFTBL (NIL) -8 NIL NIL NIL) (-552 1260095 1260233 1260406 "INTFACT" 1260705 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-551 1257480 1257926 1258490 "INTEF" 1259649 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-550 1255947 1256652 1256680 "INTDOM" 1256981 T INTDOM (NIL) -9 NIL 1257188 NIL) (-549 1255316 1255490 1255732 "INTDOM-" 1255737 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-548 1251811 1253700 1253754 "INTCAT" 1254553 NIL INTCAT (NIL T) -9 NIL 1254873 NIL) (-547 1251284 1251386 1251514 "INTBIT" 1251703 T INTBIT (NIL) -7 NIL NIL NIL) (-546 1249955 1250109 1250423 "INTALG" 1251129 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-545 1249412 1249502 1249672 "INTAF" 1249859 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-544 1242866 1249222 1249362 "INTABL" 1249367 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-543 1237881 1240555 1240583 "INS" 1241517 T INS (NIL) -9 NIL 1242182 NIL) (-542 1235121 1235892 1236866 "INS-" 1236939 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233896 1234123 1234421 "INPSIGN" 1234874 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1233014 1233131 1233328 "INPRODPF" 1233776 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231908 1232025 1232262 "INPRODFF" 1232894 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230908 1231060 1231320 "INNMFACT" 1231744 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1230105 1230202 1230390 "INMODGCD" 1230807 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228614 1228858 1229182 "INFSP" 1229850 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227798 1227915 1228098 "INFPROD0" 1228494 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224680 1225863 1226378 "INFORM" 1227291 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224290 1224350 1224448 "INFORM1" 1224615 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223813 1223902 1224016 "INFINITY" 1224196 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223258 1223531 1223639 "INETCLTS" 1223725 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221875 1222124 1222445 "INEP" 1223006 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221151 1221772 1221837 "INDE" 1221842 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220715 1220783 1220900 "INCRMAPS" 1221078 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219733 1219984 1220190 "INBFILE" 1220529 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1215044 1215969 1216913 "INBFF" 1218821 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214713 1214789 1214817 "INBCON" 1214950 T INBCON (NIL) -9 NIL 1215028 NIL) (-524 1214553 1214588 1214664 "INBCON-" 1214669 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1214055 1214274 1214366 "INAST" 1214481 T INAST (NIL) -8 NIL NIL NIL) (-522 1213509 1213734 1213840 "IMPTAST" 1213969 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1210003 1213353 1213457 "IMATRIX" 1213462 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208715 1208838 1209153 "IMATQF" 1209859 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206935 1207162 1207499 "IMATLIN" 1208471 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201561 1206859 1206917 "ILIST" 1206922 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199514 1201421 1201534 "IIARRAY2" 1201539 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194947 1199425 1199489 "IFF" 1199494 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194321 1194564 1194680 "IFAST" 1194851 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189364 1193613 1193801 "IFARRAY" 1194178 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188571 1189268 1189341 "IFAMON" 1189346 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188155 1188220 1188274 "IEVALAB" 1188481 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187830 1187898 1188058 "IEVALAB-" 1188063 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187488 1187744 1187807 "IDPO" 1187812 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186765 1187377 1187452 "IDPOAMS" 1187457 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1186099 1186654 1186729 "IDPOAM" 1186734 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185184 1185434 1185487 "IDPC" 1185900 NIL IDPC (NIL T T) -9 NIL 1186049 NIL) (-506 1184680 1185076 1185149 "IDPAM" 1185154 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1184083 1184572 1184645 "IDPAG" 1184650 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183851 1183998 1184048 "IDENT" 1184053 T IDENT (NIL) -8 NIL NIL NIL) (-503 1180106 1180954 1181849 "IDECOMP" 1183008 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172980 1174029 1175076 "IDEAL" 1179142 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172144 1172256 1172455 "ICDEN" 1172864 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171243 1171624 1171771 "ICARD" 1172017 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169303 1169616 1170021 "IBPTOOLS" 1170920 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164937 1168923 1169036 "IBITS" 1169222 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161660 1162236 1162931 "IBATOOL" 1164354 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159440 1159901 1160434 "IBACHIN" 1161195 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157317 1159286 1159389 "IARRAY2" 1159394 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153470 1157243 1157300 "IARRAY1" 1157305 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147464 1151882 1152363 "IAN" 1153009 T IAN (NIL) -8 NIL NIL NIL) (-492 1146975 1147032 1147205 "IALGFACT" 1147401 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146503 1146616 1146644 "HYPCAT" 1146851 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1146041 1146158 1146344 "HYPCAT-" 1146349 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145663 1145836 1145919 "HOSTNAME" 1145978 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145508 1145545 1145586 "HOMOTOP" 1145591 NIL HOMOTOP (NIL T) -9 NIL 1145624 NIL) (-487 1142187 1143518 1143559 "HOAGG" 1144540 NIL HOAGG (NIL T) -9 NIL 1145219 NIL) (-486 1140781 1141180 1141706 "HOAGG-" 1141711 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134823 1140378 1140526 "HEXADEC" 1140653 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133571 1133793 1134056 "HEUGCD" 1134600 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132674 1133408 1133538 "HELLFDIV" 1133543 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130902 1132451 1132539 "HEAP" 1132618 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130193 1130454 1130588 "HEADAST" 1130788 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1124113 1130108 1130170 "HDP" 1130175 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117864 1123748 1123900 "HDMP" 1124014 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117189 1117328 1117492 "HB" 1117720 T HB (NIL) -7 NIL NIL NIL) (-477 1110686 1117035 1117139 "HASHTBL" 1117144 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110189 1110407 1110499 "HASAST" 1110614 T HASAST (NIL) -8 NIL NIL NIL) (-475 1108001 1109811 1109993 "HACKPI" 1110027 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103696 1107854 1107967 "GTSET" 1107972 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097222 1103574 1103672 "GSTBL" 1103677 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089535 1096253 1096518 "GSERIES" 1097013 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088702 1089093 1089121 "GROUP" 1089324 T GROUP (NIL) -9 NIL 1089458 NIL) (-470 1088068 1088227 1088478 "GROUP-" 1088483 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086437 1086756 1087143 "GROEBSOL" 1087745 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085377 1085639 1085690 "GRMOD" 1086219 NIL GRMOD (NIL T T) -9 NIL 1086387 NIL) (-467 1085145 1085181 1085309 "GRMOD-" 1085314 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080471 1081499 1082499 "GRIMAGE" 1084165 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078938 1079198 1079522 "GRDEF" 1080167 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078382 1078498 1078639 "GRAY" 1078817 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077595 1077975 1078026 "GRALG" 1078179 NIL GRALG (NIL T T) -9 NIL 1078272 NIL) (-462 1077256 1077329 1077492 "GRALG-" 1077497 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1074060 1076841 1077019 "GPOLSET" 1077163 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073414 1073471 1073729 "GOSPER" 1073997 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069173 1069852 1070378 "GMODPOL" 1073113 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068178 1068362 1068600 "GHENSEL" 1068985 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062229 1063072 1064099 "GENUPS" 1067262 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061926 1061977 1062066 "GENUFACT" 1062172 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061338 1061415 1061580 "GENPGCD" 1061844 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060812 1060847 1061060 "GENMFACT" 1061297 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059380 1059635 1059942 "GENEEZ" 1060555 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053293 1058991 1059153 "GDMP" 1059303 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042670 1047064 1048170 "GCNAALG" 1052276 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1041097 1041925 1041953 "GCDDOM" 1042208 T GCDDOM (NIL) -9 NIL 1042365 NIL) (-449 1040567 1040694 1040909 "GCDDOM-" 1040914 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039239 1039424 1039728 "GB" 1040346 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027859 1030185 1032577 "GBINTERN" 1036930 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025696 1025988 1026409 "GBF" 1027534 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024477 1024642 1024909 "GBEUCLID" 1025512 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023826 1023951 1024100 "GAUSSFAC" 1024348 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022193 1022495 1022809 "GALUTIL" 1023545 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020501 1020775 1021099 "GALPOLYU" 1021920 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017866 1018156 1018563 "GALFACTU" 1020198 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009672 1011171 1012779 "GALFACT" 1016298 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1007060 1007718 1007746 "FVFUN" 1008902 T FVFUN (NIL) -9 NIL 1009622 NIL) (-438 1006326 1006508 1006536 "FVC" 1006827 T FVC (NIL) -9 NIL 1007010 NIL) (-437 1005968 1006123 1006204 "FUNCTION" 1006278 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003739 1004290 1004756 "FT" 1005522 T FT (NIL) -8 NIL NIL NIL) (-435 1002557 1003040 1003243 "FTEM" 1003556 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000813 1001102 1001506 "FSUPFACT" 1002248 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999210 999499 999831 "FST" 1000501 T FST (NIL) -8 NIL NIL NIL) (-432 998381 998487 998682 "FSRED" 999092 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997060 997315 997669 "FSPRMELT" 998096 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994145 994583 995082 "FSPECF" 996623 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976205 984648 984688 "FS" 988536 NIL FS (NIL T) -9 NIL 990825 NIL) (-428 964855 967845 971901 "FS-" 972198 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964369 964423 964600 "FSINT" 964796 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962696 963362 963665 "FSERIES" 964148 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961710 961826 962057 "FSCINT" 962576 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957944 960654 960695 "FSAGG" 961065 NIL FSAGG (NIL T) -9 NIL 961324 NIL) (-423 955706 956307 957103 "FSAGG-" 957198 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954748 954891 955118 "FSAGG2" 955559 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952403 952682 953236 "FS2UPS" 954466 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951985 952028 952183 "FS2" 952354 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950842 951013 951322 "FS2EXPXP" 951810 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950268 950383 950535 "FRUTIL" 950722 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941723 945763 947121 "FR" 948942 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936798 939441 939481 "FRNAALG" 940877 NIL FRNAALG (NIL T) -9 NIL 941484 NIL) (-415 932476 933547 934822 "FRNAALG-" 935572 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932114 932157 932284 "FRNAAF2" 932427 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930521 930968 931263 "FRMOD" 931926 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928300 928904 929221 "FRIDEAL" 930312 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927495 927582 927871 "FRIDEAL2" 928207 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926628 927042 927083 "FRETRCT" 927088 NIL FRETRCT (NIL T) -9 NIL 927264 NIL) (-409 925740 925971 926322 "FRETRCT-" 926327 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922952 924128 924187 "FRAMALG" 925069 NIL FRAMALG (NIL T T) -9 NIL 925361 NIL) (-407 921086 921541 922171 "FRAMALG-" 922394 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915044 920561 920837 "FRAC" 920842 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914680 914737 914844 "FRAC2" 914981 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914316 914373 914480 "FR2" 914617 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908989 911841 911869 "FPS" 912988 T FPS (NIL) -9 NIL 913545 NIL) (-402 908438 908547 908711 "FPS-" 908857 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905892 907527 907555 "FPC" 907780 T FPC (NIL) -9 NIL 907922 NIL) (-400 905685 905725 905822 "FPC-" 905827 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904563 905173 905214 "FPATMAB" 905219 NIL FPATMAB (NIL T) -9 NIL 905371 NIL) (-398 902263 902739 903165 "FPARFRAC" 904200 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897657 898155 898837 "FORTRAN" 901695 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895373 895873 896412 "FORT" 897138 T FORT (NIL) -7 NIL NIL NIL) (-395 893049 893611 893639 "FORTFN" 894699 T FORTFN (NIL) -9 NIL 895323 NIL) (-394 892813 892863 892891 "FORTCAT" 892950 T FORTCAT (NIL) -9 NIL 893012 NIL) (-393 890946 891429 891819 "FORMULA" 892443 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890734 890764 890833 "FORMULA1" 890910 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890257 890309 890482 "FORDER" 890676 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889353 889517 889710 "FOP" 890084 T FOP (NIL) -7 NIL NIL NIL) (-389 887961 888633 888807 "FNLA" 889235 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886716 887105 887133 "FNCAT" 887593 T FNCAT (NIL) -9 NIL 887853 NIL) (-387 886282 886675 886703 "FNAME" 886708 T FNAME (NIL) -8 NIL NIL NIL) (-386 884945 885874 885902 "FMTC" 885907 T FMTC (NIL) -9 NIL 885943 NIL) (-385 881307 882468 883097 "FMONOID" 884349 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880526 881049 881198 "FM" 881203 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877950 878596 878624 "FMFUN" 879768 T FMFUN (NIL) -9 NIL 880476 NIL) (-382 877219 877400 877428 "FMC" 877718 T FMC (NIL) -9 NIL 877900 NIL) (-381 874413 875247 875301 "FMCAT" 876496 NIL FMCAT (NIL T T) -9 NIL 876991 NIL) (-380 873306 874179 874279 "FM1" 874358 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871080 871496 871990 "FLOATRP" 872857 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864704 868809 869430 "FLOAT" 870479 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862142 862642 863220 "FLOATCP" 864171 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860951 861755 861796 "FLINEXP" 861801 NIL FLINEXP (NIL T) -9 NIL 861894 NIL) (-375 860105 860340 860668 "FLINEXP-" 860673 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859181 859325 859549 "FLASORT" 859957 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856398 857240 857292 "FLALG" 858519 NIL FLALG (NIL T T) -9 NIL 858986 NIL) (-372 850182 853884 853925 "FLAGG" 855187 NIL FLAGG (NIL T) -9 NIL 855839 NIL) (-371 848908 849247 849737 "FLAGG-" 849742 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847950 848093 848320 "FLAGG2" 848761 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844925 845899 845958 "FINRALG" 847086 NIL FINRALG (NIL T T) -9 NIL 847594 NIL) (-368 844085 844314 844653 "FINRALG-" 844658 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843491 843704 843732 "FINITE" 843928 T FINITE (NIL) -9 NIL 844035 NIL) (-366 835949 838110 838150 "FINAALG" 841817 NIL FINAALG (NIL T) -9 NIL 843270 NIL) (-365 831290 832331 833475 "FINAALG-" 834854 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830685 831045 831148 "FILE" 831220 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829369 829681 829735 "FILECAT" 830419 NIL FILECAT (NIL T T) -9 NIL 830635 NIL) (-362 827237 828731 828759 "FIELD" 828799 T FIELD (NIL) -9 NIL 828879 NIL) (-361 825857 826242 826753 "FIELD-" 826758 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823735 824492 824839 "FGROUP" 825543 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822825 822989 823209 "FGLMICPK" 823567 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818692 822750 822807 "FFX" 822812 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818293 818354 818489 "FFSLPE" 818625 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814286 815065 815861 "FFPOLY" 817529 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813790 813826 814035 "FFPOLY2" 814244 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809676 813709 813772 "FFP" 813777 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805109 809587 809651 "FF" 809656 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800270 804452 804642 "FFNBX" 804963 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795244 799405 799663 "FFNBP" 800124 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789912 794528 794739 "FFNB" 795077 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788744 788942 789257 "FFINTBAS" 789709 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784972 787151 787179 "FFIELDC" 787799 T FFIELDC (NIL) -9 NIL 788175 NIL) (-347 783635 784005 784502 "FFIELDC-" 784507 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783205 783250 783374 "FFHOM" 783577 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780903 781387 781904 "FFF" 782720 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776556 780645 780746 "FFCGX" 780846 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772223 776288 776395 "FFCGP" 776499 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767441 771950 772058 "FFCG" 772159 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749274 758312 758398 "FFCAT" 763563 NIL FFCAT (NIL T T T) -9 NIL 765014 NIL) (-340 744472 745519 746833 "FFCAT-" 748063 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743883 743926 744161 "FFCAT2" 744423 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733095 736855 738075 "FEXPR" 742735 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732095 732530 732571 "FEVALAB" 732655 NIL FEVALAB (NIL T) -9 NIL 732916 NIL) (-336 731254 731464 731802 "FEVALAB-" 731807 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729847 730637 730840 "FDIV" 731153 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726913 727628 727743 "FDIVCAT" 729311 NIL FDIVCAT (NIL T T T T) -9 NIL 729748 NIL) (-333 726675 726702 726872 "FDIVCAT-" 726877 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725895 725982 726259 "FDIV2" 726582 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724581 724840 725129 "FCPAK1" 725626 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723709 724081 724222 "FCOMP" 724472 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707446 710859 714397 "FC" 720191 T FC (NIL) -8 NIL NIL NIL) (-328 700025 704010 704050 "FAXF" 705852 NIL FAXF (NIL T) -9 NIL 706544 NIL) (-327 697304 697959 698784 "FAXF-" 699249 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692404 696680 696856 "FARRAY" 697161 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687657 689689 689742 "FAMR" 690765 NIL FAMR (NIL T T) -9 NIL 691225 NIL) (-324 686547 686849 687284 "FAMR-" 687289 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685743 686469 686522 "FAMONOID" 686527 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683555 684239 684292 "FAMONC" 685233 NIL FAMONC (NIL T T) -9 NIL 685619 NIL) (-321 682247 683309 683446 "FAGROUP" 683451 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680042 680361 680764 "FACUTIL" 681928 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679141 679326 679548 "FACTFUNC" 679852 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671546 678392 678604 "EXPUPXS" 678997 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669029 669569 670155 "EXPRTUBE" 670980 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665223 665815 666552 "EXPRODE" 668368 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650597 663878 664306 "EXPR" 664827 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645004 645591 646404 "EXPR2UPS" 649895 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644640 644697 644804 "EXPR2" 644941 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636045 643772 644069 "EXPEXPAN" 644477 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635872 636002 636031 "EXIT" 636036 T EXIT (NIL) -8 NIL NIL NIL) (-310 635379 635596 635687 "EXITAST" 635801 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635006 635068 635181 "EVALCYC" 635311 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634547 634665 634706 "EVALAB" 634876 NIL EVALAB (NIL T) -9 NIL 634980 NIL) (-307 634028 634150 634371 "EVALAB-" 634376 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631496 632764 632792 "EUCDOM" 633347 T EUCDOM (NIL) -9 NIL 633697 NIL) (-305 629901 630343 630933 "EUCDOM-" 630938 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617441 620199 622949 "ESTOOLS" 627171 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617073 617130 617239 "ESTOOLS2" 617378 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616824 616866 616946 "ESTOOLS1" 617025 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610729 612457 612485 "ES" 615253 T ES (NIL) -9 NIL 616662 NIL) (-300 605677 606963 608780 "ES-" 608944 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602052 602812 603592 "ESCONT" 604917 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601797 601829 601911 "ESCONT1" 602014 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601472 601522 601622 "ES2" 601741 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601102 601160 601269 "ES1" 601408 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600318 600447 600623 "ERROR" 600946 T ERROR (NIL) -7 NIL NIL NIL) (-294 593821 600177 600268 "EQTBL" 600273 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586378 589135 590584 "EQ" 592405 NIL -3278 (NIL T) -8 NIL NIL NIL) (-292 586010 586067 586176 "EQ2" 586315 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581302 582348 583441 "EP" 584949 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579884 580185 580502 "ENV" 581005 T ENV (NIL) -8 NIL NIL NIL) (-289 579063 579583 579611 "ENTIRER" 579616 T ENTIRER (NIL) -9 NIL 579662 NIL) (-288 575565 577018 577388 "EMR" 578862 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574709 574894 574948 "ELTAGG" 575328 NIL ELTAGG (NIL T T) -9 NIL 575539 NIL) (-286 574428 574490 574631 "ELTAGG-" 574636 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574217 574246 574300 "ELTAB" 574384 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573343 573489 573688 "ELFUTS" 574068 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573085 573141 573169 "ELEMFUN" 573274 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572955 572976 573044 "ELEMFUN-" 573049 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567846 571055 571096 "ELAGG" 572036 NIL ELAGG (NIL T) -9 NIL 572499 NIL) (-280 566131 566565 567228 "ELAGG-" 567233 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564788 565068 565363 "ELABEXPR" 565856 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557654 559455 560282 "EFUPXS" 564064 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551104 552905 553715 "EFULS" 556930 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548526 548884 549363 "EFSTRUC" 550736 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537598 539163 540723 "EF" 547041 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536699 537083 537232 "EAB" 537469 T EAB (NIL) -8 NIL NIL NIL) (-273 535908 536658 536686 "E04UCFA" 536691 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535117 535867 535895 "E04NAFA" 535900 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534326 535076 535104 "E04MBFA" 535109 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533535 534285 534313 "E04JAFA" 534318 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532746 533494 533522 "E04GCFA" 533527 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531957 532705 532733 "E04FDFA" 532738 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531166 531916 531944 "E04DGFA" 531949 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525344 526691 528055 "E04AGNT" 529822 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524050 524530 524570 "DVARCAT" 525045 NIL DVARCAT (NIL T) -9 NIL 525244 NIL) (-264 523254 523466 523780 "DVARCAT-" 523785 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516154 523053 523182 "DSMP" 523187 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510964 512099 513167 "DROPT" 515106 T DROPT (NIL) -8 NIL NIL NIL) (-261 510629 510688 510786 "DROPT1" 510899 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505744 506870 508007 "DROPT0" 509512 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504089 504414 504800 "DRAWPT" 505378 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498676 499599 500678 "DRAW" 503063 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498309 498362 498480 "DRAWHACK" 498617 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497040 497309 497600 "DRAWCX" 498038 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496556 496624 496775 "DRAWCURV" 496966 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487027 488986 491101 "DRAWCFUN" 494461 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483840 485722 485763 "DQAGG" 486392 NIL DQAGG (NIL T) -9 NIL 486665 NIL) (-252 472119 478818 478901 "DPOLCAT" 480753 NIL DPOLCAT (NIL T T T T) -9 NIL 481298 NIL) (-251 466958 468304 470262 "DPOLCAT-" 470267 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460113 466819 466917 "DPMO" 466922 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453171 459893 460060 "DPMM" 460065 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452835 453090 453138 "DOMCTOR" 453143 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452130 452357 452494 "DOMAIN" 452718 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445881 451765 451917 "DMP" 452031 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445481 445537 445681 "DLP" 445819 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439351 444808 444998 "DLIST" 445323 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436195 438204 438245 "DLAGG" 438795 NIL DLAGG (NIL T) -9 NIL 439025 NIL) (-242 435008 435638 435666 "DIVRING" 435758 T DIVRING (NIL) -9 NIL 435841 NIL) (-241 434245 434435 434735 "DIVRING-" 434740 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432347 432704 433110 "DISPLAY" 433859 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426289 432261 432324 "DIRPROD" 432329 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425137 425340 425605 "DIRPROD2" 426082 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414400 420352 420405 "DIRPCAT" 420815 NIL DIRPCAT (NIL NIL T) -9 NIL 421655 NIL) (-236 411726 412368 413249 "DIRPCAT-" 413586 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411013 411173 411359 "DIOSP" 411560 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407715 409925 409966 "DIOPS" 410400 NIL DIOPS (NIL T) -9 NIL 410629 NIL) (-233 407264 407378 407569 "DIOPS-" 407574 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406156 406750 406778 "DIFRING" 406965 T DIFRING (NIL) -9 NIL 407075 NIL) (-231 405802 405879 406031 "DIFRING-" 406036 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403607 404845 404886 "DIFEXT" 405249 NIL DIFEXT (NIL T) -9 NIL 405543 NIL) (-229 401892 402320 402986 "DIFEXT-" 402991 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399214 401424 401465 "DIAGG" 401470 NIL DIAGG (NIL T) -9 NIL 401490 NIL) (-227 398598 398755 399007 "DIAGG-" 399012 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394063 397557 397834 "DHMATRIX" 398367 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389675 390584 391594 "DFSFUN" 393073 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384791 388606 388918 "DFLOAT" 389383 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383019 383300 383696 "DFINTTLS" 384499 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380084 381040 381440 "DERHAM" 382685 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377933 379859 379948 "DEQUEUE" 380028 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377148 377281 377477 "DEGRED" 377795 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373543 374288 375141 "DEFINTRF" 376376 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371070 371539 372138 "DEFINTEF" 373062 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370447 370690 370805 "DEFAST" 370975 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364489 370044 370192 "DECIMAL" 370319 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362001 362459 362965 "DDFACT" 364033 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361597 361640 361791 "DBLRESP" 361952 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359496 359830 360190 "DBASE" 361364 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358765 358976 359122 "DATAARY" 359395 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357898 358724 358752 "D03FAFA" 358757 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357032 357857 357885 "D03EEFA" 357890 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354982 355448 355937 "D03AGNT" 356563 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354298 354941 354969 "D02EJFA" 354974 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353614 354257 354285 "D02CJFA" 354290 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352930 353573 353601 "D02BHFA" 353606 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352246 352889 352917 "D02BBFA" 352922 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345444 347032 348638 "D02AGNT" 350660 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343213 343735 344281 "D01WGTS" 344918 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342308 343172 343200 "D01TRNS" 343205 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341403 342267 342295 "D01GBFA" 342300 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340498 341362 341390 "D01FCFA" 341395 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339593 340457 340485 "D01ASFA" 340490 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338688 339552 339580 "D01AQFA" 339585 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337783 338647 338675 "D01APFA" 338680 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336878 337742 337770 "D01ANFA" 337775 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335973 336837 336865 "D01AMFA" 336870 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335068 335932 335960 "D01ALFA" 335965 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334163 335027 335055 "D01AKFA" 335060 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333258 334122 334150 "D01AJFA" 334155 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326555 328106 329667 "D01AGNT" 331717 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325892 326020 326172 "CYCLOTOM" 326423 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322627 323340 324067 "CYCLES" 325185 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321939 322073 322244 "CVMP" 322488 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319710 319968 320344 "CTRIGMNP" 321667 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319433 319669 319697 "CTOR" 319702 T CTOR (NIL) -8 NIL NIL NIL) (-185 318969 319164 319265 "CTORKIND" 319352 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318440 318668 318696 "CTORCAT" 318816 T CTORCAT (NIL) -9 NIL 318899 NIL) (-183 318135 318215 318341 "CTORCAT-" 318346 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317651 317838 317936 "CTORCALL" 318057 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317025 317124 317277 "CSTTOOLS" 317548 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312824 313481 314239 "CRFP" 316337 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312326 312545 312637 "CRCEAST" 312752 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311373 311558 311786 "CRAPACK" 312130 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310757 310858 311062 "CPMATCH" 311249 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310482 310510 310616 "CPIMA" 310723 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306846 307518 308236 "COORDSYS" 309817 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306230 306359 306509 "CONTOUR" 306716 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302156 304233 304725 "CONTFRAC" 305770 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302036 302057 302085 "CONDUIT" 302122 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301209 301729 301757 "COMRING" 301762 T COMRING (NIL) -9 NIL 301814 NIL) (-170 300290 300567 300751 "COMPPROP" 301045 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299951 299986 300114 "COMPLPAT" 300249 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290008 299760 299869 "COMPLEX" 299874 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289644 289701 289808 "COMPLEX2" 289945 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289362 289397 289495 "COMPFACT" 289603 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273535 283755 283795 "COMPCAT" 284799 NIL COMPCAT (NIL T) -9 NIL 286184 NIL) (-164 263051 265974 269601 "COMPCAT-" 269957 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262780 262808 262911 "COMMUPC" 263017 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262575 262608 262667 "COMMONOP" 262741 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262158 262326 262413 "COMM" 262508 T COMM (NIL) -8 NIL NIL NIL) (-160 261762 261962 262037 "COMMAAST" 262103 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261011 261205 261233 "COMBOPC" 261571 T COMBOPC (NIL) -9 NIL 261746 NIL) (-158 259907 260117 260359 "COMBINAT" 260801 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256105 256678 257318 "COMBF" 259329 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254891 255221 255456 "COLOR" 255890 T COLOR (NIL) -8 NIL NIL NIL) (-155 254394 254612 254704 "COLONAST" 254819 T COLONAST (NIL) -8 NIL NIL NIL) (-154 254034 254081 254206 "CMPLXRT" 254341 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253509 253734 253833 "CLLCTAST" 253955 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 249011 250039 251119 "CLIP" 252449 T CLIP (NIL) -7 NIL NIL NIL) (-151 247393 248117 248356 "CLIF" 248838 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243615 245539 245580 "CLAGG" 246509 NIL CLAGG (NIL T) -9 NIL 247045 NIL) (-149 242037 242494 243077 "CLAGG-" 243082 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241581 241666 241806 "CINTSLPE" 241946 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 239082 239553 240101 "CHVAR" 241109 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238325 238845 238873 "CHARZ" 238878 T CHARZ (NIL) -9 NIL 238893 NIL) (-145 238079 238119 238197 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"BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 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NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
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(-1087)) (-5 *1 (-672 *3))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-1246 *5)) (-4 *5 (-631 *4)) (-4 *4 (-550)) - (-5 *2 (-1246 *4)) (-5 *1 (-630 *4 *5))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-635 (-406 (-942 (-558))))) (-5 *2 (-635 (-635 (-293 (-942 *4))))) (-5 *1 (-379 *4)) @@ -9832,7 +7888,7 @@ (|partial| -12 (-5 *5 (-1163)) (-4 *6 (-13 (-841) (-306) (-1028 (-558)) (-631 (-558)) (-146))) (-4 *4 (-13 (-29 *6) (-1185) (-949))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -1794 (-635 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2867 (-635 *4)))) (-5 *1 (-642 *6 *4 *3)) (-4 *3 (-646 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1163)) (-5 *5 (-635 *2)) @@ -9843,40 +7899,40 @@ (-12 (-5 *3 (-679 *5)) (-4 *5 (-362)) (-5 *2 (-2 (|:| |particular| (-3 (-1246 *5) "failed")) - (|:| -1794 (-635 (-1246 *5))))) + (|:| -2867 (-635 (-1246 *5))))) (-5 *1 (-657 *5)) (-5 *4 (-1246 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-635 (-635 *5))) (-4 *5 (-362)) (-5 *2 (-2 (|:| |particular| (-3 (-1246 *5) "failed")) 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(-6 -4383)))) (-5 *2 (-635 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -1794 (-635 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -2867 (-635 *7))))) (-5 *1 (-658 *5 *6 *7 *3)) (-5 *4 (-635 *7)) (-4 *3 (-677 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -9894,7 +7950,7 @@ (-4 *7 (-13 (-29 *6) (-1185) (-949))) (-4 *6 (-13 (-841) (-306) (-1028 (-558)) (-631 (-558)) (-146))) (-5 *2 - (-2 (|:| |particular| (-1246 *7)) (|:| -1794 (-635 (-1246 *7))))) + (-2 (|:| |particular| (-1246 *7)) (|:| -2867 (-635 (-1246 *7))))) (-5 *1 (-793 *6 *7)) (-5 *4 (-1246 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-679 *6)) (-5 *4 (-1163)) @@ -9906,27 +7962,27 @@ (-5 *5 (-1163)) (-4 *7 (-13 (-29 *6) (-1185) (-949))) (-4 *6 (-13 (-841) (-306) (-1028 (-558)) (-631 (-558)) (-146))) (-5 *2 - (-2 (|:| |particular| (-1246 *7)) (|:| -1794 (-635 (-1246 *7))))) + (-2 (|:| |particular| (-1246 *7)) (|:| -2867 (-635 (-1246 *7))))) (-5 *1 (-793 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-635 *7)) (-5 *4 (-635 (-114))) 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*2)) (-5 *4 (-114)) (-5 *5 (-635 *2)) @@ -9962,10 +8018,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -1794 (-635 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -2867 (-635 *6))) "failed") *7 *6)) (-4 *6 (-362)) (-4 *7 (-646 *6)) - (-5 *2 (-2 (|:| |particular| (-1246 *6)) (|:| -1794 (-679 *6)))) + (-5 *2 (-2 (|:| |particular| (-1246 *6)) (|:| -2867 (-679 *6)))) (-5 *1 (-804 *6 *7)) (-5 *3 (-679 *6)) (-5 *4 (-1246 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1025)) (-5 *1 (-887)))) ((*1 *2 *3 *4) @@ -10038,305 +8094,275 @@ ((*1 *2 *3) (-12 (-4 *4 (-550)) (-5 *2 (-635 (-293 (-406 (-942 *4))))) (-5 *1 (-1169 *4)) (-5 *3 (-293 (-406 (-942 *4))))))) -(((*1 *2) - (-12 (-4 *1 (-341 *3 *4 *5)) (-4 *3 (-1204)) (-4 *4 (-1222 *3)) - (-4 *5 (-1222 (-406 *4))) (-5 *2 (-679 (-406 *4)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-252 *3 *4 *5 *6)) (-4 *3 (-1039)) (-4 *4 (-841)) - (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-762)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-252 *4 *3 *5 *6)) 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continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1143 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3951 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-553))))) +(((*1 *2 *3 *4 *5) + (-12 (-4 *6 (-1222 *9)) (-4 *7 (-784)) (-4 *8 (-841)) (-4 *9 (-306)) + (-4 *10 (-939 *9 *7 *8)) + (-5 *2 + (-2 (|:| |deter| (-635 (-1159 *10))) + (|:| |dterm| + (-635 (-635 (-2 (|:| -2643 (-762)) (|:| |pcoef| *10))))) + (|:| |nfacts| (-635 *6)) (|:| |nlead| (-635 *10)))) + (-5 *1 (-769 *6 *7 *8 *9 *10)) (-5 *3 (-1159 *10)) (-5 *4 (-635 *6)) + (-5 *5 (-635 *10))))) +(((*1 *2 *2 *2 *2 *2 *3) + (-12 (-5 *2 (-679 *4)) (-5 *3 (-762)) (-4 *4 (-1039)) + (-5 *1 (-680 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 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+ ((*1 *2 *3) (-12 (-5 *3 (-1145)) (-5 *2 (-1251)) (-5 *1 (-701)))) + ((*1 *2 *1) (-12 (-5 *2 (-1251)) (-5 *1 (-1180)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-558)) (-5 *2 (-1251)) (-5 *1 (-1180))))) (((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4382)) (-4 *1 (-150 *2)) (-4 *2 (-1200)) (-4 *2 (-1087)))) @@ -16382,114 +16750,27 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1127 *3 *4)) (-4 *3 (-13 (-1087) (-34))) (-4 *4 (-13 (-1087) (-34))) (-5 *1 (-1128 *3 *4))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *2 (-1143 (-635 (-558)))) (-5 *1 (-873)) (-5 *3 (-558)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1143 (-635 (-558)))) (-5 *1 (-873)) (-5 *3 (-558)))) - ((*1 *2 *3 *3) - (-12 (-5 *2 (-1143 (-635 (-558)))) (-5 *1 (-873)) (-5 *3 (-558))))) -(((*1 *1) (-5 *1 (-140)))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-558)) (-5 *4 (-679 (-224))) (-5 *2 (-1025)) - (-5 *1 (-746))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1087)) (-4 *6 (-1087)) - (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-674 *4 *5 *6)) (-4 *5 (-1087))))) -(((*1 *2 *1) (-12 (-5 *2 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(-12 (-5 *2 (-315 (-224))) (-5 *1 (-209))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-224)) (-5 *4 (-558)) (-5 *2 (-1025)) (-5 *1 (-749))))) -(((*1 *1 *1 *1) (-4 *1 (-543)))) -(((*1 *1 *1) (-12 (-4 *1 (-985 *2)) (-4 *2 (-1200))))) -(((*1 *1 *2) - (-12 (-5 *2 (-635 *3)) (-4 *3 (-1087)) (-4 *1 (-1085 *3)))) - ((*1 *1) (-12 (-4 *1 (-1085 *2)) (-4 *2 (-1087))))) + (-12 + (-5 *2 + (-2 (|:| -4173 (-635 (-853))) (|:| -3962 (-635 (-853))) + (|:| |presup| (-635 (-853))) (|:| -4074 (-635 (-853))) + (|:| |args| (-635 (-853))))) + (-5 *1 (-1163)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-635 (-635 (-853)))) (-5 *1 (-1163))))) +(((*1 *2 *1) (-12 (-5 *2 (-1251)) (-5 *1 (-247))))) (((*1 *1) (-4 *1 (-348))) ((*1 *2 *3) (-12 (-5 *3 (-635 *5)) (-4 *5 (-429 *4)) @@ -16514,750 +16795,258 @@ (-12 (-5 *3 (-635 (-942 *5))) (-5 *4 (-635 (-1163))) (-4 *5 (-13 (-362) (-146))) (-5 *2 - (-2 (|:| -2023 (-635 (-558))) (|:| |poly| (-635 (-1159 *5))) + (-2 (|:| -3201 (-635 (-558))) (|:| |poly| (-635 (-1159 *5))) (|:| |prim| (-1159 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\ No newline at end of file |