diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1336 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9128 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32305 |
5 files changed, 22491 insertions, 22488 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 22a8f118..42ca82cb 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294384 . 3507854467) +(2294384 . 3508426629) (-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 `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1608) +(-32 R -4340) ((|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 -1069) (QUOTE (-560))))) @@ -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 \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -1608 UP UPUP -3385) +(-40 -4340 UP UPUP -2179) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2229 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2229 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2229 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2229 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2229 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2229 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1608) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2219 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2219 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2219 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2219 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2219 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2219 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -4340) ((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'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 (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|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."))) ((-4508 . T) (-4509 . T)) -((-2229 (-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|))))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-871))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|))))))) +((-2219 (-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#2|))))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-871))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1608) +(-54 |Base| R -4340) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,64 +171,64 @@ NIL (-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's."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -3976) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2113) ((|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 -(-62 -3976) +(-62 -2113) ((|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 -(-63 -3976) +(-63 -2113) ((|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 -(-64 -3976) +(-64 -2113) ((|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 -(-65 -3976) +(-65 -2113) ((|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 -3976) +(-66 -2113) ((|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 -3976) +(-67 -2113) ((|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 -3976) +(-68 -2113) ((|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 -3976) +(-69 -2113) ((|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 -3976) +(-70 -2113) ((|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 -3976) +(-71 -2113) ((|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 -3976) +(-72 -2113) ((|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 -3976) +(-73 -2113) ((|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 -3976) +(-74 -2113) ((|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 -(-75 -3976) +(-75 -2113) ((|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 @@ -240,51 +240,51 @@ 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 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 -(-78 -3976) +(-78 -2113) ((|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 -(-79 -3976) +(-79 -2113) ((|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 -3976) +(-80 -2113) ((|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 -3976) +(-81 -2113) ((|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 -3976) +(-82 -2113) ((|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 -(-83 -3976) +(-83 -2113) ((|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 -(-84 -3976) +(-84 -2113) ((|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 -(-85 -3976) +(-85 -2113) ((|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 -(-86 -3976) +(-86 -2113) ((|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 -(-87 -3976) +(-87 -2113) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -3976) +(-88 -2113) ((|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 -(-89 -3976) +(-89 -2113) ((|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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 pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2229 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2219 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-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| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -396,7 +396,7 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -1608 UP) +(-117 -4340 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 @@ -407,7 +407,7 @@ NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2229 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2219 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 @@ -423,7 +423,7 @@ NIL (-123 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"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -455,7 +455,7 @@ NIL (-131) ((|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 `n'. The array can then store up to `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.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2229 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2229 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-2219 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2219 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2219 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -476,11 +476,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4510 "*") . T)) NIL -(-137 |minix| -3432 R) +(-137 |minix| -2969 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -3432 S T$) +(-138 |minix| -2969 S T$) ((|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 @@ -503,7 +503,7 @@ NIL (-143) ((|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}."))) ((-4508 . T) (-4498 . T) (-4509 . T)) -((-2229 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2219 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 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{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4505 . T)) NIL -(-150 -1608 UP UPUP) +(-150 -4340 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 @@ -568,7 +568,7 @@ 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 -(-160 R -1608) +(-160 R -4340) ((|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})/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.} 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.} 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.} n!/(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 @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4501 -2229 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-3102 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4501 -2219 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-4435 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-169 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."))) @@ -614,8 +614,8 @@ NIL NIL (-171 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}."))) -((-4501 -2229 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-3102 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2229 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2229 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4507)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4501 -2219 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-4435 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2219 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2219 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4507)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-363))))) (-172 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1608) +(-191 R -4340) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1608 UP UPUP R) +(-219 -4340 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 -(-220 -1608 FP) +(-220 -4340 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 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 (-221) ((|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2229 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2219 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -1608) +(-223 R -4340) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) ((-4505 . T)) NIL -(-228 R -1608) +(-228 R -4340) ((|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 (-229) ((|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}."))) -((-3092 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4423 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-230) ((|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{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * 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*\\%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*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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)}.}"))) @@ -855,7 +855,7 @@ NIL (-231 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}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 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 @@ -904,19 +904,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-244 S -3432 R) +(-244 S -2969 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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 (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4505)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1132)))) -(-245 -3432 R) +(-245 -2969 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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"))) ((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . T)) NIL -(-246 -3432 R) +(-246 -2969 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."))) ((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (-2229 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-376))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1080)))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-815))) (-2229 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381))) (-2229 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-175)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE 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(QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) +(-247 -2969 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 @@ -939,7 +939,7 @@ NIL (-252 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}"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 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'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 @@ -951,7 +951,7 @@ NIL (-255 |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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T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\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| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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} := 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 @@ -1031,7 +1031,7 @@ NIL (-275 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"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-276 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}.")) (|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 @@ -1076,11 +1076,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1'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 -(-287 R -1608) +(-287 R -4340) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -1608) +(-288 R -4340) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1132,7 +1132,7 @@ 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 -(-301 S R |Mod| -2211 -4091 |exactQuo|) +(-301 S R |Mod| -4336 -3462 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{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.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4505 -2229 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) -((|HasCategory| |#1| (QUOTE (-376))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2229 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2229 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2229 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4505 -2219 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) +((|HasCategory| |#1| (QUOTE (-376))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2219 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2219 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2219 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -1159,7 +1159,7 @@ NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|)))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#2|)))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102)))) (-308) ((|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 @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1608 S) +(-311 -4340 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1608) +(-312 E -4340) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -(-322 -1608) +(-322 -4340) ((|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 @@ -1231,11 +1231,11 @@ NIL (-325 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))}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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(|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))) (-2219 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 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(QUOTE (-1080))) (|HasCategory| $ (|%list| (QUOTE -1069) (QUOTE (-560))))) (-327 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 @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -1608) +(-329 R -4340) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1255,7 +1255,7 @@ NIL (-331 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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2229 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2219 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-332 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},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ NIL (-339 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."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1608) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -4340) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -1608) +(-341 -4340) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -1608 UP UPUP R) +(-346 -4340 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}'s are integers and the \\spad{P}'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 @@ -1320,11 +1320,11 @@ 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 -(-348 S -1608 UP UPUP R) +(-348 S -4340 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}'s are integers and the \\spad{P}'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 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 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 -(-349 -1608 UP UPUP R) +(-349 -4340 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}'s are integers and the \\spad{P}'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 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 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 @@ -1343,12 +1343,12 @@ NIL (-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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) -(-354 S -1608 UP UPUP) +((-2219 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +(-354 S -4340 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -1608 UP UPUP) +(-355 -4340 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1359,15 +1359,15 @@ NIL (-357 |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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2219 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2219 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2219 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(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 @@ -1384,42 +1384,42 @@ 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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-364 R UP -1608) +(-364 R UP -4340) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-365 |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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2219 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2219 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2219 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2219 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|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(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(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(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(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(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(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 -(-370 -1608 GF) +(-370 -4340 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}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 -(-371 -1608 FP FPP) +(-371 -4340 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2219 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 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{ls}."))) NIL @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|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{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}."))) -((-4491 . T) (-4499 . T) (-3092 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4491 . T) (-4499 . T) (-4423 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "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 -(-406 -1608 UP UPUP R) +(-406 -4340 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 @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -3976 |returnType| -1557 |symbols|) +(-412 -2113 |returnType| -2520 |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 -(-413 -1608 UP) +(-413 -4340 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4491)) (|HasAttribute| |#1| (QUOTE -4499))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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'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\"."))) -((-3092 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4423 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-419 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 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."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 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."))) NIL @@ -1615,7 +1615,7 @@ NIL (-421 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4495 -12 (|has| |#1| (-6 -4506)) (|has| |#1| (-466)) (|has| |#1| (-6 -4495))) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -1608 UP A) +(-427 R -4340 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)}."))) ((-4505 . T)) NIL @@ -1644,7 +1644,7 @@ 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 -(-429 R -1608 UP A |ibasis|) +(-429 R -4340 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 -1069) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo'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|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4505 -2229 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) +((-4505 -2219 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -1608) +(-442 R -4340) ((|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 @@ -1704,19 +1704,19 @@ 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"))) ((-4495 -12 (|has| |#1| (-6 -4495)) (|has| |#2| (-6 -4495))) (-4502 . T) (-4503 . T) (-4505 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4495)) (|HasAttribute| |#2| (QUOTE -4495)))) -(-444 R -1608) +(-444 R -4340) ((|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 -(-445 R -1608) +(-445 R -4340) ((|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 -(-446 R -1608) +(-446 R -4340) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -1608) +(-447 R -4340) ((|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 @@ -1724,7 +1724,7 @@ 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 -(-449 R -1608 UP) +(-449 R -4340 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 -1069) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ 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's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein'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'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 -(-457 R UP -1608) +(-457 R UP -4340) ((|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 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'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'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's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri'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 @@ -1803,7 +1803,7 @@ NIL (-468 |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"))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 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's conditional."))) NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\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 -(-485 |lv| -1608 R) +(-485 |lv| -4340 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 @@ -1883,11 +1883,11 @@ NIL (-488 |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.")) (|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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . 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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)}"))) ((-4509 . T) (-4508 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |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."))) ((-4508 . T) (-4509 . 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Hall as given in Serre's book Lie Groups -- 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{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 @@ -1911,11 +1911,11 @@ NIL (-495 |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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The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1935,7 +1935,7 @@ NIL (-501) ((|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2229 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2219 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -1608 UP |AlExt| |AlPol|) +(-508 -4340 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP'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 @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 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'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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -1608) +(-513 R UP -4340) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the 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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1608 |Expon| |VarSet| |DPoly|) +(-518 -4340 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1207))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 @@ -2059,15 +2059,15 @@ NIL (-532 |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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2229 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-2219 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 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,{} m*h and 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 @@ -2079,7 +2079,7 @@ NIL (-537 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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2112,7 +2112,7 @@ 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 ((-12 (|HasCategory| (-793) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132))))) -(-546 K -1608 |Par|) +(-546 K -4340 |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 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 @@ -2136,7 +2136,7 @@ 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 -(-552 K -1608 |Par|) +(-552 K -4340 |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 @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|)))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102)))) -(-566 R -1608) +((-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#2|)))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102)))) +(-566 R -4340) ((|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 -(-567 R0 -1608 UP UPUP R) +(-567 R0 -4340 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 @@ -2206,7 +2206,7 @@ NIL NIL (-569 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{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3092 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4423 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-570 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."))) @@ -2216,7 +2216,7 @@ 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."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-572 R -1608) +(-572 R -4340) ((|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},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2228,7 +2228,7 @@ 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 -(-575 R -1608 L) +(-575 R -4340 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ 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 -(-577 -1608 UP UPUP R) +(-577 -4340 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 -(-578 -1608 UP) +(-578 -4340 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 @@ -2248,15 +2248,15 @@ 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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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 -(-580 R -1608 L) +(-580 R -4340 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -1608) +(-581 R -4340) ((|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 -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1608 UP) +(-582 -4340 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,27 +2264,27 @@ 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 -(-584 -1608) +(-584 -4340) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-585 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."))) -((-3092 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4423 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-586) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-587 R -1608) +(-587 R -4340) ((|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 -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1608 UP) +(-588 -4340 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -1608) +(-589 R -4340) ((|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 @@ -2316,15 +2316,15 @@ 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 -(-597 -1608) +(-597 -4340) ((|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 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}."))) ((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1207))))) -(-598 E -1608) +(-598 E -4340) ((|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 -(-599 R -1608) +(-599 R -4340) ((|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},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2229 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2229 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2219 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2219 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2219 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 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 @@ -2367,7 +2367,7 @@ NIL (-609 |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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |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}.")) (|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.}"))) (((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -2384,7 +2384,7 @@ 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 -(-614 R -1608 FG) +(-614 R -4340 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4505 -2229 (-1378 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2229 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2219 (-2818 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2219 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-102)))) (-628 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 @@ -2464,7 +2464,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1608 UP) +(-634 -4340 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2492,7 +2492,7 @@ NIL ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4505 . T)) NIL -(-641 R -1608) +(-641 R -4340) ((|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 @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -1608) +(-648 R -4340) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,18 +2528,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -1608) +(-650 |lv| -4340) ((|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 (-651) ((|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}.")) (|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."))) ((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -1689) (QUOTE (-51))))))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -3463) (QUOTE (-51))))))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (QUOTE (-1132)))) (-652 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)."))) -((-4505 -2229 (-1378 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2229 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2219 (-2818 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2219 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 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{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 @@ -2563,7 +2563,7 @@ NIL (-658 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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1370 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-2807 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) ((-4503 . T) (-4502 . T)) @@ -2583,7 +2583,7 @@ NIL (-663 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} is the empty list."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2607,7 +2607,7 @@ NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2628,11 +2628,11 @@ NIL ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|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{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-813)))) -(-675 R -1608 L) +(-675 R -4340 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 -(-676 A -3002) +(-676 A -3412) ((|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}}"))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ 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}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-681 -1608 UP) +(-681 -4340 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)))) @@ -2684,11 +2684,11 @@ 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}."))) ((-4509 . T) (-4508 . T)) NIL -(-689 -1608 |Row| |Col| M) +(-689 -4340 |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 -(-690 -1608) +(-690 -4340) ((|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'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 @@ -2699,7 +2699,7 @@ NIL (-692 |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."))) ((-4505 . T) (-4508 . T) (-4502 . T) (-4503 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2229 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2219 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2775,7 +2775,7 @@ NIL (-711 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."))) ((-4508 . T) (-4509 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 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{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 @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-714 S -1608 FLAF FLAS) +(-714 S -4340 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,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{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}."))) 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(|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 -(-720 OV E -1608 PG) +(-720 OV E -4340 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 (-721) ((|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}"))) -((-3092 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4423 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-722 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."))) @@ -2840,7 +2840,7 @@ 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 \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-728 S -2535 I) +(-728 S -3002 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 @@ -2860,14 +2860,14 @@ 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 -(-733 R |Mod| -2211 -4091 |exactQuo|) +(-733 R |Mod| -4336 -3462 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-734 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -2211 -4091 |exactQuo|) +(-737 R |Mod| -4336 -3462 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4505 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4503 . T) (-4502 . T)) NIL -(-740 -1608) +(-740 -4340) ((|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]]}."))) ((-4505 . T)) NIL @@ -2924,7 +2924,7 @@ 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 -(-749 -1608 UP) +(-749 -4340 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 @@ -2943,7 +2943,7 @@ NIL (-753 |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."))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 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 @@ -3076,11 +3076,11 @@ 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 -(-787 -1608) +(-787 -4340) ((|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 -(-788 P -1608) +(-788 P -4340) ((|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''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -1608) +(-790 UP -4340) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3104,7 +3104,7 @@ 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."))) (((-4510 "*") . T)) NIL -(-794 R -1608) +(-794 R -4340) ((|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 @@ -3124,7 +3124,7 @@ 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}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},{}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 -(-799 -1608 |ExtF| |SUEx| |ExtP| |n|) +(-799 -4340 |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 @@ -3139,11 +3139,11 @@ NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3211,8 +3211,8 @@ NIL (-820 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2229 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2229 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) -(-821 -2229 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2219 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2219 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) +(-821 -2219 R OS S) ((|constructor| (NIL "\\spad{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 @@ -3220,11 +3220,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-823 R -1608 L) +(-823 R -4340 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-824 R -1608) +(-824 R -4340) ((|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 @@ -3232,7 +3232,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE'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 -(-826 R -1608) +(-826 R -4340) ((|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 @@ -3240,11 +3240,11 @@ 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'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'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'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'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'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'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'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's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-828 -1608 UP UPUP R) +(-828 -4340 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 -(-829 -1608 UP L LQ) +(-829 -4340 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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 @@ -3252,38 +3252,38 @@ 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 -(-831 -1608 UP L LQ) +(-831 -4340 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-832 -1608 UP) +(-832 -4340 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}'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}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-833 -1608 L UP A LO) +(-833 -4340 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 -(-834 -1608 UP) +(-834 -4340 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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-835 -1608 LO) +(-835 -4340 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 -(-836 -1608 LODO) +(-836 -4340 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(((-4510 "*") |has| |#2| (-376)) (-4501 |has| |#2| (-376)) (-4506 |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4505 . T) (-4503 . T) (-4502 . T)) @@ -3347,7 +3347,7 @@ NIL (-854 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."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2229 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2229 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2219 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2219 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-855 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL @@ -3387,7 +3387,7 @@ NIL (-864 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2229 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2229 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2219 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2219 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-865 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3396,7 +3396,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -3432 S) +(-867 -2969 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 @@ -3440,11 +3440,11 @@ 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{\\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{\\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{\\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{\\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 (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-878 R |sigma| -1462) +(-878 R |sigma| -3892) ((|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."))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-879 |x| R |sigma| -1462) +(-879 |x| R |sigma| -3892) ((|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}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3511,15 +3511,15 @@ NIL (-895 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2229 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) +((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2219 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) (-896 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2229 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2219 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-897 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-898) ((|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'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's lowest value."))) NIL @@ -3579,7 +3579,7 @@ NIL (-912 |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 (-1370 (|HasCategory| |#2| (QUOTE (-1080)))) (-1370 (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-1370 (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207))))) +((-12 (-2807 (|HasCategory| |#2| (QUOTE (-1080)))) (-2807 (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-2807 (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207))))) (-913 R S) ((|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'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},{}\\spad{e1}),{}...,{}(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 @@ -3592,7 +3592,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-916 R -2535) +(-916 R -3002) ((|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 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 @@ -3620,7 +3620,7 @@ 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 -(-923 UP -1608) +(-923 UP -4340) ((|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 @@ -3651,11 +3651,11 @@ NIL (-930 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-931 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.")) (|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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4505 . T)) -((-2229 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) +((-2219 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (-932 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 @@ -3688,7 +3688,7 @@ NIL ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-940 R0 -1608 UP UPUP R) +(-940 R0 -4340 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 @@ -3716,7 +3716,7 @@ 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'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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik'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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-947 -1608) +(-947 -4340) ((|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 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 @@ -3732,11 +3732,11 @@ NIL ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-951 |xx| -1608) +(-951 |xx| -4340) ((|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 -(-952 -1608 P) +(-952 -4340 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3764,7 +3764,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\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.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-959 R -1608) +(-959 R -4340) ((|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 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3772,7 +3772,7 @@ 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 -(-961 S R -1608) +(-961 S R -4340) ((|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 @@ -3792,11 +3792,11 @@ 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 -911) (|devaluate| |#1|)))) -(-966 -2535) +(-966 -3002) ((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-967 R -1608 -2535) +(-967 R -4340 -3002) ((|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 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 @@ -3819,7 +3819,7 @@ NIL (-972 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-973 |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 @@ -3831,7 +3831,7 @@ NIL (-975 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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-976 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3848,7 +3848,7 @@ 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 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 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 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 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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL -(-980 E V R P -1608) +(-980 E V R P -4340) ((|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},{}...,{}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 @@ -3856,7 +3856,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-982 E V R P -1608) +(-982 E V R P -4340) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3871,7 +3871,7 @@ NIL (-985 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) (-986 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL @@ -3879,7 +3879,7 @@ NIL (-987 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-988 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3888,7 +3888,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-990 -1608) +(-990 -4340) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3903,7 +3903,7 @@ NIL (-993 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"))) ((-4505 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-994) ((|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| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3992,7 +3992,7 @@ 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 -(-1016 K R UP -1608) +(-1016 K R UP -4340) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -4039,7 +4039,7 @@ NIL (-1027 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.}"))) ((-4501 |has| |#1| (-302)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) (-1028 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4055,7 +4055,7 @@ NIL (-1031 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1032 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4064,14 +4064,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1034 -1608 UP UPUP |radicnd| |n|) +(-1034 -4340 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . 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(|fractRadix| (($ (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2229 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2219 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1036) ((|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 @@ -4104,19 +4104,19 @@ 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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}"))) ((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) NIL -(-1044 R -1608) +(-1044 R -4340) ((|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 -(-1045 R -1608) +(-1045 R -4340) ((|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 -(-1046 -1608 UP) +(-1046 -4340 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 -(-1047 -1608 UP) +(-1047 -4340 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 @@ -4151,8 +4151,8 @@ NIL (-1055 |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"))) ((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) -((-2229 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) -(-1056 -1608 L) +((-2219 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) +(-1056 -4340 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4188,14 +4188,14 @@ 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 -(-1065 -1608 |Expon| |VarSet| |FPol| |LFPol|) +(-1065 -4340 |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"))) (((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1066) ((|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.}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -1689) (QUOTE (-51))))))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -3463) (QUOTE (-51))))))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (QUOTE (-102)))) (-1067) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4252,7 +4252,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4505 . T)) NIL -(-1081 |xx| -1608) +(-1081 |xx| -4340) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4271,7 +4271,7 @@ NIL (-1085 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4508 . T) (-4503 . T) (-4502 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2229 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2219 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) (-1086 |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 @@ -4307,7 +4307,7 @@ NIL (-1094) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4508 . T) (-4509 . 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When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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 @@ -4352,7 +4352,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1106 |Base| R -1608) +(-1106 |Base| R -4340) ((|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},{}...,{}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 @@ -4360,7 +4360,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1108 |Base| R -1608) +(-1108 |Base| R -4340) ((|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 @@ -4371,7 +4371,7 @@ NIL (-1110 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."))) ((-4501 |has| |#1| (-376)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (-1111 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4403,7 +4403,7 @@ NIL (-1118 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"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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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 @@ -4443,7 +4443,7 @@ NIL (-1128 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)}}"))) ((-4508 . T) (-4498 . T) (-4509 . 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Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |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 \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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|#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-871))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-2219 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1132)))) (|HasAttribute| |#3| (QUOTE -4505)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1145 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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 @@ -4520,7 +4520,7 @@ 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 `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1148 R -1608) +(-1148 R -4340) ((|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 @@ -4555,16 +4555,16 @@ NIL (-1156 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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2229 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1157 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1158 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}"))) ((-4509 . T) (-4508 . T)) NIL -(-1159 UP -1608) +(-1159 UP -4340) ((|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 @@ -4619,11 +4619,11 @@ NIL (-1172 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2229 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2229 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2219 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2219 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) (-1173 |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}."))) ((-4505 . T) (-4497 |has| |#2| (-6 (-4510 "*"))) (-4508 . T) (-4502 . T) (-4503 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2229 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2229 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2219 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1174 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4643,7 +4643,7 @@ NIL (-1178 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1179 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 @@ -4655,7 +4655,7 @@ NIL (-1181 |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."))) ((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|)))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#2|)))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132)))) (-1182) ((|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}'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 @@ -4671,7 +4671,7 @@ NIL (-1185 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."))) ((-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1186 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4687,11 +4687,11 @@ NIL (-1189) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2229 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2229 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2219 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2219 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2219 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1190 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#1|)))))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#1|)))))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (QUOTE (-102)))) (-1191 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by 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 b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4722,9 +4722,9 @@ NIL NIL (-1198 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4735,7 +4735,7 @@ NIL (-1201 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4747,11 +4747,11 @@ NIL (-1204 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2229 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2219 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1205 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1206) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4767,7 +4767,7 @@ NIL (-1209 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2229 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2219 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4506))) (-1210) ((|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 @@ -4807,7 +4807,7 @@ NIL (-1219 |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}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3865) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1689) (|devaluate| |#2|)))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2229 (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1885) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3463) (|devaluate| |#2|)))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2219 (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (QUOTE (-102)))) (-1220 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4867,7 +4867,7 @@ NIL (-1234 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4509 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1235 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4876,7 +4876,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1237 R -1608) +(-1237 R -4340) ((|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 @@ -4884,14 +4884,14 @@ 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 -(-1239 R -1608) +(-1239 R -4340) ((|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 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 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 -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (|devaluate| |#1|))))) (-1240 |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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1241 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\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)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL @@ -4912,7 +4912,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter'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 (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) -(-1246 -1608) +(-1246 -4340) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4958,8 +4958,8 @@ NIL NIL (-1257 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} 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{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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(|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-147)))))) (-1263 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 @@ -4995,7 +4995,7 @@ NIL (-1266 |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}"))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4504 |has| |#2| (-376)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2229 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| 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(|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2219 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2219 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2219 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1267 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\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| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -5031,7 +5031,7 @@ NIL (-1275 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{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}.")) (|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 -927) (QUOTE (-1207)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#2|) (QUOTE (-1207)))))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#2|) (QUOTE (-1207)))))) (-1276 |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{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}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -5043,7 +5043,7 @@ NIL (-1278 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2229 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2219 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1279 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL @@ -5063,11 +5063,11 @@ NIL (-1283 |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)}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2229 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2229 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2219 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2219 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1284 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))}."))) (((-4510 "*") |has| (-1278 |#2| |#3| |#4|) (-175)) (-4501 |has| (-1278 |#2| |#3| |#4|) (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-2229 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-2219 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-571)))) (-1285 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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5079,7 +5079,7 @@ NIL (-1287 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2229 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2489) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2229 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2219 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3782) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2219 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1288 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -5087,7 +5087,7 @@ NIL (-1289 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 (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%list| (QUOTE -2748) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -2248) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%list| (QUOTE -2601) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4394) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1290 |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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -5096,7 +5096,7 @@ NIL ((|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 -(-1292 -1608 UP L UTS) +(-1292 -4340 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 (-571)))) @@ -5119,7 +5119,7 @@ NIL (-1297 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."))) ((-4509 . T) (-4508 . T)) -((-2229 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2229 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2229 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2229 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2219 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2219 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2219 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2219 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1298 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\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| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\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 @@ -5156,7 +5156,7 @@ 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]*v + A[2]\\spad{*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 -(-1307 K R UP -1608) +(-1307 K R UP -4340) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5188,11 +5188,11 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1315 S -1608) +(-1315 S -4340) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1316 -1608) +(-1316 -4340) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 585f52b7..e87e3e75 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3507854472) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) #0#) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-321 (-2 (|:| -3865 |#1|) (|:| -1689 |#2|))))) -((((-560)) . T) (($) -2229 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3508426635) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) #0#) |has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-321 (-2 (|:| -1885 |#1|) (|:| -3463 |#2|))))) +((((-560)) . T) (($) -2219 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-560)) . T)) -((($ $) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) +((($ $) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T)) -((($) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-939)) ((((-887)) . T)) ((((-887)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1189)) . T) (((-229)) . T) (((-391)) . T) (((-915 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-887)) . T)) -(-2229 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2229 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2219 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2219 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2229 (|has| |#1| (-21)) (|has| |#1| (-870))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) -(-2229 (|has| |#1| (-842)) (|has| |#1| (-871))) +(-2219 (|has| |#1| (-21)) (|has| |#1| (-870))) +((($ $) . T) ((#0=(-421 (-560)) #0#) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +(-2219 (|has| |#1| (-842)) (|has| |#1| (-871))) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-326 |#1|)) . T) (((-560)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-560)) . T) (((-893 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((($) . T) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-887)) . T)) ((((-1212)) . T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1212)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -(-2229 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(((|#2| (-496 (-2387 |#1|) (-793))) . T)) -((((-1207)) -2229 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +(-2219 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(((|#2| (-496 (-3764 |#1|) (-793))) . T)) +((((-1207)) -2219 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1| (-545 (-1207))) . T)) ((((-1189)) . T) (((-987 (-130))) . T) (((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((#0=(-893 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2229 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -4012 |#1|) (|:| -1553 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2219 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -2028 |#1|) (|:| -4035 |#2|))) . T)) ((($) . T)) ((((-887)) |has| |#1| (-632 (-887))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-560)) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1207)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-887)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2229 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2219 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (|has| |#1| (-1132)) (((|#1|) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((($) -2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((($) -2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((((-118 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) @@ -116,14 +116,14 @@ ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2229 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2219 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2229 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1264 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2229 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2219 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-887)) . T)) @@ -241,13 +241,13 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2229 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -((($ $) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1132)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-887)) . T) (((-1212)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((((-1212)) . 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T)) (((|#1| (-1002)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1182)) -((((-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))) . T)) +((((-2 (|:| -1885 (-1189)) (|:| -3463 |#1|))) . T)) (|has| (-1284 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1284 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-840 (-1207))) . T) (($) -2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-840 (-1207))) . T) (($) -2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . 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T)) @@ -840,8 +840,8 @@ (|has| |#3| (-1080)) (|has| |#3| (-815)) (|has| |#3| (-815)) -((((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2229 (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#2|) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2229 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2219 (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#2|) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2219 (|has| |#1| (-376)) (|has| |#1| (-571)))) (((|#2|) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -855,37 +855,37 @@ ((((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((($) . T) (((-421 (-560))) . 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T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) (|has| |#1| (-843)) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1| $) |has| |#1| (-298 |#1| |#1|))) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) @@ -1065,49 +1065,49 @@ (((|#4|) |has| |#4| (-1132))) (((|#3|) |has| |#3| (-1132))) (|has| |#3| (-381)) -((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) +((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) ((((-887)) . 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T)) -(-2229 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) +(-2219 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) (((|#1|) |has| |#1| (-175))) (|has| $ (-149)) (|has| $ (-149)) ((((-1212)) . T)) (((|#1|) |has| |#1| (-175))) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) ((($ $) |has| |#1| (-298 $ $)) ((|#1| $) |has| |#1| (-298 |#1| |#1|))) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1207)) . T)) (|has| |#1| (-571)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2387 |#1|) (-793)) (-888 |#1|)) . T)) +(((|#2| (-246 (-3764 |#1|) (-793)) (-888 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2229 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2219 (|has| |#1| (-363)) (|has| |#1| (-381))) ((((-1173 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) -(((|#2|) . T) (((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (|has| |#3| (-815)) (|has| |#3| (-815)) ((((-887)) . T)) @@ -1176,18 +1176,18 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) -((((-1207)) -2229 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) +((((-1207)) -2219 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-630 $)) . T)) (((|#1| (-421 (-560))) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) -((((-560)) -2229 (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1132)) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) +((((-560)) -2219 (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1132)) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1195,15 +1195,15 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-321 (-2 (|:| -3865 |#1|) (|:| -1689 |#2|))))) -(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) (((-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))) |has| (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|)) (-321 (-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) |has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-321 (-2 (|:| -1885 |#1|) (|:| -3463 |#2|))))) +(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) (((-2 (|:| -1885 (-1189)) (|:| -3463 |#1|))) |has| (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|)) (-321 (-2 (|:| -1885 (-1189)) (|:| -3463 |#1|))))) ((((-887)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-1207) (-51)) . T)) -((((-1207)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((((-1207)) -2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-843)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1120 |#1|) (-1132)) -(((|#2| |#2|) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) -(((|#2|) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2| |#2|) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) ((((-560)) . T)) ((((-1212)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1212)) . T)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -(-2229 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2219 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((|#1|) . T) (($) . T)) (((|#2|) |has| |#2| (-175))) -((($) -2229 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) |has| |#2| (-175)) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2219 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) |has| |#2| (-175)) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-893 |#1|)) . T)) -(-2229 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) +(-2219 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (|has| |#2| (-1182)) -(((#0=(-51)) . T) (((-2 (|:| -3865 (-1207)) (|:| -1689 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1885 (-1207)) (|:| -3463 #0#))) . T)) (((|#1| |#2|) . T)) (((|#1| (-657 |#2|)) . T)) (|has| |#3| (-1080)) @@ -1269,10 +1269,10 @@ (((|#1| (-560) (-1113)) . T)) (((|#1| (-421 (-560)) (-1113)) . T)) ((((-1207)) . T)) -((($) -2229 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -2229 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2219 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2219 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1207)) -2229 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((($ (-1207)) -2219 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-887)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1207) $) |has| |#1| (-528 (-1207) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1207) |#1|) |has| |#1| (-528 (-1207) |#1|))) ((((-1207)) |has| |#1| (-927 (-1207)))) -(-2229 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2219 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#2|) . T) (((-887)) . T)) ((((-887)) . T)) (((|#2|) . T)) ((((-935 |#1|)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-893 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (|has| |#2| (-1080)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1233)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -1383,39 +1383,39 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T)) ((((-887)) . T)) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +((($ $) . T) ((#0=(-421 (-560)) #0#) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) ((((-549)) |has| |#3| (-633 (-549)))) (((|#1| |#2|) . T)) (|has| |#1| (-870)) (|has| |#1| (-870)) ((((-711 |#3|)) . T) (((-887)) . T)) -((($) . T) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) (((|#1|) . T)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-571))) ((($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((((-887)) . T)) ((((-935 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-870)) -((($) -2229 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2219 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-376)) (((|#1|) . T) (($) . T)) (|has| |#1| (-870)) -((($) . T) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (|has| |#1| (-870)) ((((-520)) . T)) @@ -1443,7 +1443,7 @@ ((((-549)) . T)) ((((-887)) . T)) ((($) . T)) -((((-560) (-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T) (((-1264 (-560)) $) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T) (((-1264 (-560)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-175))) @@ -1453,22 +1453,22 @@ (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#3|) . 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T)) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) -(((|#2| |#2|) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(((|#2| |#2|) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (((|#2|) . T) (((-560)) . T)) ((((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T) ((|#2|) . T)) ((((-887)) . T)) ((((-887)) . T)) ((((-1189) (-1207) (-560) (-229) (-887)) . T)) @@ -1559,9 +1559,9 @@ ((((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((($) . T) (((-421 (-560))) . T)) -(((|#2|) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1069 (-421 (-560)))) (((-560)) |has| #0# (-1069 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-1027 |#1|)) . T) ((|#1|) . T)) -((((-1207)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-840 (-1207))) . 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T)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) (|has| |#1| (-813)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-571))) -((((-1207)) -2229 (-12 (|has| (-1287 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-571))) +((((-1207)) -2219 (-12 (|has| (-1287 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207))))) (((|#1|) |has| |#1| (-175))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2229 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-2219 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-2229 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-2219 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1189) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1719,24 +1719,24 @@ (((|#3|) . T)) ((((-1287 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) ((((-887)) . T)) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-987 |#1|)) . T)) -(((|#4|) -2229 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) -(((|#3|) -2229 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) +(((|#4|) -2219 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) +(((|#3|) -2219 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) (|has| |#2| (-376)) (((|#1|) |has| |#1| (-175))) -(((|#4|) -2229 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) -(((|#3|) -2229 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) +(((|#4|) -2219 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) +(((|#3|) -2219 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) (((|#2|) |has| |#2| (-1080))) (((|#2|) |has| |#2| (-1080))) ((((-1189) |#1|) . T)) @@ -1748,8 +1748,8 @@ ((((-402) (-1189)) . T)) ((($ (-1207)) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-887)) -2229 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1297 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3865 (-1189)) (|:| -1689 #0#))) . T)) +((((-887)) -2219 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1297 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1885 (-1189)) (|:| -3463 #0#))) . T)) (((|#1|) . T)) ((((-887)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) @@ -1758,7 +1758,7 @@ ((((-560)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-2229 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2219 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (|has| |#1| (-376)) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1769,8 +1769,8 @@ (|has| |#1| (-870)) ((((-887)) . T)) (((|#2|) . T)) -((((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2229 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2229 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2219 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-841 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1779,8 +1779,8 @@ ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2387 |#1|) (-793)) (-888 |#1|)) . T)) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-3764 |#1|) (-793)) (-888 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1207)) (-1207)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -1885 (-1189)) (|:| -3463 |#1|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3865 (-1207)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((((-1207) (-51)) . T)) ((((-421 (-560)) |#1|) . T) (($ $) . T)) (((|#1| (-560)) . T)) ((((-935 |#1|)) . T)) -(((|#1|) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) -((((-1207)) -2229 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) +(((|#1|) -2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-1207)) -2219 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#3|) -2229 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2229 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) -((($) -2229 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((|#3|) -2219 (|has| |#3| (-175)) (|has| |#3| (-376)))) +((($) -2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(-2219 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) +((($) -2219 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((($ |#2|) . T)) -((($ (-1207)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) +((($ (-1207)) -2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) ((((-560) |#2|) . T)) -(((|#2|) -2229 (|has| |#2| (-175)) (|has| |#2| (-376)))) +(((|#2|) -2219 (|has| |#2| (-175)) (|has| |#2| (-376)))) (|has| |#1| (-363)) (((|#3| |#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#2|) . T) (((-560)) . T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) -(-2229 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-870)) (|has| |#1| (-870)) (|has| |#1| (-870)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T)) (((|#1|) . T)) (|has| |#1| (-870)) -(((#0=(-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) #0#) |has| (-2 (|:| -3865 (-1189)) (|:| -1689 (-51))) (-321 (-2 (|:| -3865 (-1189)) (|:| -1689 (-51)))))) +(((#0=(-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) #0#) |has| (-2 (|:| -1885 (-1189)) (|:| -3463 (-51))) (-321 (-2 (|:| -1885 (-1189)) (|:| -3463 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#1| (-1132)) ((((-887)) . T) (((-1212)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1113)) . T)) ((((-146)) . T)) -((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2229 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2219 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1917,31 +1917,31 @@ ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) (((|#2|) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2229 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2219 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((($) |has| |#1| (-870))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (|has| |#1| (-939)) ((((-1207)) . T)) ((((-887)) . T)) -((($) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . 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T)) +((((-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) ((((-694 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1975,7 +1975,7 @@ ((((-887)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-887)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((((-1212)) . T)) ((((-421 (-560))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T) (((-560)) . T)) (((|#3|) . T) (((-560)) . T) (((-630 $)) . T)) @@ -1983,12 +1983,12 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#2|) . 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T)) +((($) -2219 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))))) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((((-1002)) . T)) ((((-1002)) . T) (((-887)) . T)) @@ -2058,7 +2058,7 @@ ((($) . T)) (((|#1|) . T)) ((((-114)) . T)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) (((|#1| (-560)) . T)) ((($) . T)) @@ -2081,7 +2081,7 @@ (((|#1| (-1257 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) (|has| |#1| (-1132)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#1| (-793)) . T)) ((((-1189) |#1|) . T)) (((|#1|) . T)) @@ -2102,20 +2102,20 @@ ((((-560)) . T)) ((((-560)) . T)) ((((-887)) . T)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-363))) ((((-887)) . T)) (|has| |#1| (-149)) (((|#3|) . 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T)) @@ -2159,8 +2159,8 @@ (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| (-560) (-1113)) . T)) -(-2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +(-2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#1| (-421 (-560)) (-1113)) . T)) (((|#1| (-793) (-1113)) . T)) (|has| |#1| (-871)) @@ -2174,41 +2174,41 @@ ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-1132)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T) (((-560)) . T)) -((((-560)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-560)) -2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) @@ -2320,37 +2320,37 @@ ((((-721)) . T)) ((((-721)) . T)) (((|#2|) |has| |#2| (-175))) -(-2229 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2219 (|has| |#1| (-240)) (|has| |#1| (-239))) ((((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) -((((-114)) |has| |#1| (-1132)) (((-887)) -2229 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132)))) +((((-114)) |has| |#1| (-1132)) (((-887)) -2219 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) -((((-2 (|:| -3865 (-1189)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1189)) (|:| -3463 (-51)))) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) -((((-1207)) -2229 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) +((((-1207)) -2219 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-721)) . T) (((-421 (-560))) . T) (((-560)) . T)) (((|#1| |#1|) |has| |#1| (-175))) (((|#2|) . T)) -((($) . T) (((-560)) . T) (((-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-560)) . T) (((-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-560) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-321 (-2 (|:| -3865 |#1|) (|:| -1689 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) |has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-321 (-2 (|:| -1885 |#1|) (|:| -3463 |#2|))))) ((((-391)) . T)) ((((-721)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1|) |has| |#1| (-175))) ((((-421 (-975 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1080))) @@ -2362,7 +2362,7 @@ ((((-1207)) |has| |#2| (-927 (-1207)))) (|has| |#1| (-871)) ((((-887)) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (|has| |#1| (-813)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -((($) -2229 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +((($) -2219 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-887)) . T)) (((|#2|) . T) (((-887)) . T)) -((($ (-1207)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((($ (-1207)) -2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-871)) -((((-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))) . T)) +((((-2 (|:| -1885 (-1189)) (|:| -3463 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-321 (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) |has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-321 (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2229 (-12 (|has| (-1287 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2219 (-12 (|has| (-1287 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-887)) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) -((((-1207)) -2229 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +((((-1207)) -2219 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) ((((-663 (-802 |#1| (-888 |#2|)))) . T) (((-887)) . T)) ((((-549)) |has| (-802 |#1| (-888 |#2|)) (-633 (-549)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#1|) |has| |#1| (-175))) ((((-887)) . T)) -(-2229 (|has| |#2| (-466)) (|has| |#2| (-939))) +(-2219 (|has| |#2| (-466)) (|has| |#2| (-939))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) -2229 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1278 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . T)) -(-2229 (-12 (|has| (-1287 |#1| |#2| |#3|) (-149)) (|has| |#1| (-376))) (|has| |#1| (-149))) -(-2229 (-12 (|has| (-1287 |#1| |#2| |#3|) (-147)) (|has| |#1| (-376))) (|has| |#1| (-147))) +(-2219 (-12 (|has| (-1287 |#1| |#2| |#3|) (-149)) (|has| |#1| (-376))) (|has| |#1| (-149))) +(-2219 (-12 (|has| (-1287 |#1| |#2| |#3|) (-147)) (|has| |#1| (-376))) (|has| |#1| (-147))) (|has| |#1| (-376)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -2488,29 +2488,29 @@ ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (|has| |#1| (-871)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T)) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-1173 |#2| |#1|)) . T) ((|#1|) . T) (((-560)) . T)) (((|#1| |#2|) . T)) -((((-560)) . T) ((|#1|) . 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T)) -(-2229 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-102)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) +(-2219 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-102)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) ((((-887)) . T)) ((((-560)) . T)) -(-2229 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2219 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((|#1| $) |has| |#1| (-298 |#1| |#1|))) ((((-421 (-560))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T)) ((((-975 |#1|)) . T) (((-887)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -2229 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) +(((|#1| |#1|) . T) (($ $) -2219 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) ((((-975 |#1|)) . T)) -((((-2 (|:| -3865 (-1207)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))) . T)) ((($) . T)) ((((-560) |#1|) . T)) ((((-1207)) |has| (-421 |#2|) (-927 (-1207)))) -(((|#1|) . T) (($) -2229 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2219 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) ((((-549)) |has| |#2| (-633 (-549)))) ((((-711 |#2|)) . T) (((-887)) . T)) (((|#1|) . T)) @@ -2518,24 +2518,24 @@ (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-893 |#1|)) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2229 (|has| |#2| (-842)) (|has| |#2| (-871))) +(-2219 (|has| |#2| (-842)) (|has| |#2| (-871))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2229 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2219 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T) (((-560)) . T)) -((((-2 (|:| -3865 (-1189)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1189)) (|:| -3463 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2229 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2219 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-870)) @@ -2880,7 +2880,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-186)) . T) (((-887)) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-871)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (|has| |#1| (-842)) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-870)) -((((-1234 |#1|)) . T) (((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-1234 |#1|)) . T) (((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1080)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-363))) (((#0=(-421 (-560)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-376))) ((((-887)) . T)) (|has| |#1| (-1132)) (((|#1|) . T)) -(((|#1|) -2229 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) -(((|#1|) -2229 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2219 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2219 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1207)) -2229 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((($ (-1207)) -2219 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (|has| |#1| (-871)) (|has| |#2| (-240)) ((((-888 |#1|)) . T)) @@ -3011,10 +3011,10 @@ (|has| |#1| (-1132)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2229 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2219 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1051)) ((($) . T)) (|has| |#1| (-939)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-935 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . T)) -((($) -2229 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) |has| |#1| (-870)) (((-560)) -2229 (|has| |#1| (-21)) (|has| |#1| (-870)))) +((($) -2219 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) |has| |#1| (-870)) (((-560)) -2219 (|has| |#1| (-21)) (|has| |#1| (-870)))) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) -(-2229 (|has| |#1| (-381)) (|has| |#1| (-871))) +(-2219 (|has| |#1| (-381)) (|has| |#1| (-871))) (((|#1|) . T)) ((((-793)) . T)) ((((-887)) . T)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-421 |#2|) |#3|) . T)) -(-2229 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +(-2219 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2387 |#1|) (-793))) . T)) +(((|#2| (-246 (-3764 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((((-1189)) . T) (((-887)) . T)) -(((#0=(-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) #0#) |has| (-2 (|:| -3865 (-1207)) (|:| -1689 (-51))) (-321 (-2 (|:| -3865 (-1207)) (|:| -1689 (-51)))))) +(((#0=(-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) #0#) |has| (-2 (|:| -1885 (-1207)) (|:| -3463 (-51))) (-321 (-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))))) ((((-1189)) . T)) (|has| |#1| (-939)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2229 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2219 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -3109,12 +3109,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2229 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-843))) ((((-887)) . T)) (|has| |#1| (-376)) -((((-1207)) -2229 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) +((((-1207)) -2219 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) (|has| |#1| (-376)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-421 (-560))) . T) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T)) -(-2229 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2219 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2229 (|has| |#4| (-815)) (|has| |#4| (-871))) -(-2229 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2219 (|has| |#4| (-815)) (|has| |#4| (-871))) +(-2219 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3167,7 +3167,7 @@ (|has| |#1| (-871)) ((((-887)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1189)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2229 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2219 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1080)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) -((((-2 (|:| -3865 (-1189)) (|:| -1689 |#1|))) . T)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) +((((-2 (|:| -1885 (-1189)) (|:| -3463 |#1|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-560))) |has| |#2| (-1069 (-560))) (((-560)) |has| |#2| (-1069 (-560))) (((-1207)) |has| |#2| (-1069 (-1207))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2229 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2219 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-887)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-1207)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +((((-1207)) -2219 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) (|has| |#1| (-813)) (|has| |#1| (-813)) ((((-887)) . T)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-887)) . T)) ((((-887)) . T)) -(-2229 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2219 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-887)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1207)) -2229 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((((-1207)) -2219 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) ((((-887)) . T)) ((((-560)) . T)) -(-2229 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2219 (|has| |#2| (-815)) (|has| |#2| (-871))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-887)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2229 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) (|has| |#1| (-1182)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2229 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2219 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-887)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-887)) . T)) -((((-1207)) -2229 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2219 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1207) |#1|) . T)) -(((|#1|) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2219 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1207)) . T)) -(((|#1|) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) +(((|#1|) -2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1132)) ((((-802 |#1| (-888 |#2|))) |has| (-802 |#1| (-888 |#2|)) (-321 (-802 |#1| (-888 |#2|))))) -(-2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1119 (-1207)))) . T)) -((($) -2229 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2219 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) -((((-2 (|:| -3865 (-1189)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1189)) (|:| -3463 (-51)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-560)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#2| (-376)) ((((-887)) . T)) ((((-887)) . T)) -(-2229 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2219 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-887)) . T)) ((((-1151)) . T) (((-887)) . T)) ((((-549)) . T) (((-887)) . T)) @@ -3353,14 +3353,14 @@ ((((-560)) . T)) (((|#3|) . T)) ((((-887)) . T)) -(-2229 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) -((((-560)) . 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T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-1119 (-1207))) . T) (($) -2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1297 |#1|) (-1297 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3375,7 +3375,7 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-887)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2229 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2219 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2229 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2219 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-2229 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1207)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2229 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) +(-2219 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (((|#1|) . T)) (((|#1|) . T)) -(-2229 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2219 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) ((((-1113)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) (((|#1|) . T)) @@ -3477,11 +3477,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-842)) (|has| |#2| (-842)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -((($) -2229 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2219 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-560)) |has| |#1| (-911 (-560))) (((-391)) |has| |#1| (-911 (-391)))) (((|#1|) . T)) @@ -3496,7 +3496,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-939))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#2|) -2229 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2219 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1207)) . T)) ((((-893 |#1|)) . 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T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2229 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-887)) . T)) (|has| |#2| (-939)) -((((-2 (|:| -3865 (-1207)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560))))) ((((-887)) . T)) ((((-887)) . T)) @@ -3553,7 +3553,7 @@ ((((-1201 |#1|)) . T) (((-887)) . T)) ((((-887)) . T)) ((((-421 (-560))) |has| |#2| (-1069 (-421 (-560)))) (((-560)) |has| |#2| (-1069 (-560))) ((|#2|) . T) (((-888 |#1|)) . T)) -((((-1207)) -2229 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . 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T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-1207)) . T)) ((($) . T)) @@ -3810,12 +3810,12 @@ (((#0=(-1284 |#1| |#2| |#3| |#4|)) |has| #0# (-321 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2| |#2|) |has| |#1| (-376)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -2229 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2229 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) +((($ $) -2219 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2219 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2| |#2|) |has| |#1| (-376)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-560))) . T) (($) . T)) @@ -3886,7 +3886,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2229 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2219 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) ((((-887)) . T)) @@ -3895,21 +3895,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((($) . 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T)) ((((-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) (|has| |#2| (-1080)) -(-2229 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-2219 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4010,7 +4010,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-2229 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2219 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4019,11 +4019,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1132)) (((-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) -(-2229 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2219 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-939)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1212)) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2229 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2219 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#2|) . T)) -(-2229 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2219 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-887)) -2229 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) +((((-887)) -2219 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2229 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2219 (|has| |#3| (-815)) (|has| |#3| (-871))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1212)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2229 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) +((((-1207)) -2219 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1171 |#1| |#2|)) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) -((((-2 (|:| -3865 (-1207)) (|:| -1689 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) +((((-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1051)) -(((|#2|) . T) (((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) ((($) . T)) ((((-887)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560)))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-391)) . #0=(|has| |#2| (-1051))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1207)) -2229 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2219 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) ((((-887)) . T)) (((|#2|) . T)) ((((-887)) . T)) @@ -4106,15 +4106,15 @@ ((((-1205 |#1| |#2| |#3|)) . T)) ((((-1205 |#1| |#2| |#3|)) . T) (((-1198 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2229 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) -(((|#2|) . T) ((|#3|) -2229 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2219 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) +(((|#2|) . T) ((|#3|) -2219 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-186)) . T) (((-887)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2229 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) +(-2219 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) ((($ (-1207)) |has| |#1| (-1080))) -(-2229 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2219 (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -3865 (-1207)) (|:| -1689 (-51)))) . T)) +((((-2 (|:| -1885 (-1207)) (|:| -3463 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4158,8 +4158,8 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) -(-2229 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2229 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2219 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2219 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((($) . T)) (((|#2| (-545 (-888 |#1|))) . T)) ((((-1212)) . T)) @@ -4174,7 +4174,7 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-887)) -2229 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2219 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1189) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T)) +((((-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . 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T) (($) -2219 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-1113)) . T) ((|#2|) . T) (((-421 (-560))) -2219 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560)))))) +((((-1027 |#1|)) . T) ((|#1|) . T) (((-560)) -2219 (|has| (-1027 |#1|) (-1069 (-560))) (|has| |#1| (-1069 (-560)))) (((-421 (-560))) -2219 (|has| (-1027 |#1|) (-1069 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560)))))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -4216,11 +4216,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1171 |#1| |#2|) #0#) |has| (-1171 |#1| |#2|) (-321 (-1171 |#1| |#2|)))) (((|#1|) . 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196913) ((-1201 . -670) 196802) ((-1156 . -670) 196691) ((-878 . -670) 196665) ((-740 . -632) 196647) ((-561 . -381) T) ((-1319 . -23) T) ((-716 . -929) NIL) ((-1318 . -23) T) ((-505 . -1132) T) ((-391 . -635) 196597) ((-391 . -637) 196579) ((-1065 . -1080) T) ((-889 . -102) T) ((-1219 . -298) 196558) ((-171 . -381) 196509) ((-1035 . -1247) T) ((-1002 . -1247) T) ((-943 . -1247) T) ((-856 . -635) 196463) ((-850 . -635) 196418) ((-44 . -23) T) ((-1327 . -102) T) ((-493 . -298) 196397) ((-597 . -1132) T) ((-1177 . -1140) 196366) ((-443 . -1247) T) ((-1134 . -1135) 196318) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1143) T) ((-1240 . -739) 196215) ((-1227 . -1132) T) ((-1035 . -909) 196197) ((-1035 . -911) 196179) ((-642 . -234) 196163) ((-642 . -274) 196147) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1035 . -1069) 196107) ((-733 . -739) 196072) ((-246 . -390) 196041) ((-391 . -1080) T) ((-227 . -1088) T) ((-119 . -274) 196018) ((-119 . -234) 195995) ((-58 . -298) 195947) 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T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1034 . -239) 194419) ((-930 . -102) 194369) ((-878 . -748) T) ((-803 . -1132) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1132) T) ((-802 . -1096) 194290) ((-475 . -1132) T) ((-468 . -1132) T) ((-597 . -739) 194265) ((-671 . -1132) T) ((-1287 . -47) 194242) ((-1284 . -102) T) ((-1278 . -47) 194212) ((-1257 . -47) 194189) ((-1240 . -175) 194140) ((-1204 . -319) 194119) ((-1198 . -319) 194098) ((-1127 . -635) 194079) ((-1122 . -635) 194060) ((-1110 . -571) 194011) ((-1110 . -1252) 193962) ((-1104 . -635) 193943) ((-1035 . -927) NIL) ((-1097 . -635) 193924) ((-692 . -133) T) ((-646 . -1143) T) ((-1067 . -635) 193905) ((-1050 . -635) 193886) ((-736 . -1087) 193856) ((-734 . -921) 193759) ((-721 . -668) 193709) ((-286 . -1132) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1087) 193693) ((-50 . -1132) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1132) T) ((-532 . -1132) T) 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T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1172 . -632) 190662) ((-1151 . -662) 190649) ((-1151 . -1082) 190636) ((-841 . -748) T) ((-841 . -881) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-935 . -632) 190487) ((-935 . -633) 190469) ((-400 . -748) T) ((-896 . -1087) 190421) ((-896 . -111) 190359) ((-736 . -1080) T) ((-734 . -1273) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -819) T) ((-170 . -1247) T) ((-227 . -1132) T) ((-391 . -814) T) ((-58 . -633) 190236) ((-229 . -816) T) ((-229 . -813) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1110 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1247) T) ((-895 . -939) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1247) T) ((-661 . -1132) T) ((-1257 . -351) 189637) ((-895 . -670) 189582) ((-1257 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1256 . -684) T) ((-1118 . -175) 189155) ((-987 . -385) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-975 . -748) T) ((-1311 . -321) 188723) ((-1287 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1283 . -1087) 188334) ((-1278 . -927) 188240) ((-1262 . -1087) 188048) ((-495 . -748) T) ((-1257 . -927) 187881) ((-1240 . -302) 187860) ((-1217 . -1247) T) ((-1214 . -381) T) ((-1213 . -381) T) ((-1177 . -153) 187844) ((-1151 . -102) T) ((-1146 . -1132) T) ((-1110 . -23) T) ((-1110 . -1143) T) ((-1107 . -102) T) ((-1089 . -632) 187811) ((-1034 . -424) 187783) ((-954 . -984) T) ((-758 . -321) 187721) ((-76 . -1247) T) ((-686 . -397) 187693) ((-171 . -939) 187646) ((-30 . -984) T) ((-114 . -866) T) ((-1 . -632) 187628) ((-1027 . -921) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -927) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-896 . -1080) T) ((-854 . -871) 187324) ((-81 . -1247) T) ((-733 . -302) T) ((-40 . -1088) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1143) T) ((-367 . -1143) T) ((-359 . -1143) T) ((-1035 . -319) T) ((-943 . -319) T) ((-896 . -250) T) ((-108 . -1143) T) ((-896 . -240) 187123) ((-1283 . -111) 186944) ((-1262 . -111) 186733) ((-252 . -1286) 186717) ((-560 . -870) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1035 . -1051) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1082) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1132) T) ((-678 . -662) 186541) ((-1284 . -38) 186433) ((-1266 . -939) 186412) ((-114 . -1132) T) ((-838 . -1247) T) ((-427 . -1247) T) ((-1066 . -102) T) ((-1266 . -670) 186301) ((-895 . -816) NIL) ((-879 . -670) 186275) ((-895 . -813) NIL) ((-838 . -911) NIL) ((-895 . -748) T) ((-1118 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-838 . -1069) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1283 . -635) 185618) ((-1262 . -635) 185366) ((-60 . -1247) T) ((-638 . -871) 185345) ((-514 . -684) T) ((-1177 . -1007) 185314) ((-1055 . -668) 185251) ((-1034 . -466) T) ((-721 . -870) T) ((-525 . -814) T) 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-1132) T) ((-918 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-879 . -748) T) ((-119 . -870) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1066 . -321) 183173) ((-900 . -504) 183154) ((-900 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1178 . -34) T) ((-972 . -1247) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1207 . -635) 182524) ((-343 . -1247) T) ((-488 . -1080) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1151 . -1182) T) ((-1278 . -319) 182433) ((-734 . -1082) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1257 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1247) T) ((-734 . -662) 181995) ((-1257 . -1051) NIL) ((-1110 . -133) T) ((-896 . -819) 181974) ((-146 . -102) T) ((-40 . -1132) T) ((-896 . -814) 181953) ((-663 . -1041) 181937) ((-594 . -1088) T) ((-560 . -1088) T) ((-509 . -1088) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1212 . -1132) T) ((-1151 . -38) 181869) ((-1120 . -632) 181836) ((-108 . -133) T) ((-983 . -1132) T) ((-948 . -1132) T) ((-793 . -1132) T) ((-694 . -1132) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-1318 . -21) T) ((-1318 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-377 . -1247) T) ((-368 . -1087) 181772) ((-366 . -1087) 181724) ((-358 . -1087) 181676) ((-260 . -1247) T) ((-259 . -1247) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1252) 181320) ((-562 . -866) T) ((-326 . -929) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-931 . -874) 180693) ((-130 . -684) T) ((-837 . -660) 180599) ((-839 . -571) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-935 . -1087) 180181) ((-734 . -102) T) ((-721 . -1088) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-935 . -111) 179984) ((-40 . -739) 179929) ((-893 . -1132) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1132) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1247) T) ((-1262 . -814) 179062) 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177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-935 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1204 . -950) 177432) ((-1198 . -950) 177411) ((-1198 . -842) NIL) ((-1027 . -1082) 177307) ((-996 . -1247) T) ((-935 . -250) T) ((-839 . -376) 177286) ((-218 . -1132) T) ((-394 . -23) T) ((-129 . -1132) 177264) ((-123 . -1132) 177242) ((-935 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1027 . -662) 177155) ((-893 . -739) 177142) ((-1327 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1247) T) ((-887 . -1247) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-856 . -670) 177008) ((-850 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1132) T) ((-560 . -1132) T) ((-509 . -1132) T) ((-1201 . -1247) T) ((-252 . -300) 176938) ((-1156 . -1247) T) ((-878 . -1247) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1253 . -874) T) ((-1201 . -911) NIL) ((-55 . -1132) T) ((-1156 . -911) 176719) ((-130 . -871) T) ((-1201 . -1069) 176599) ((-1156 . -1069) 176482) ((-187 . -632) 176464) ((-878 . -1069) 176360) ((-803 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1027 . -102) T) ((-839 . -23) T) ((-734 . -1182) 176085) ((-716 . -1088) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1300 . -1132) T) ((-256 . -1132) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1132) T) ((-721 . -1132) T) ((-374 . -487) T) ((-1240 . -632) 176051) ((-1201 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -426) 175981) ((-143 . -233) 175963) ((-391 . -816) T) ((-391 . -813) T) ((-893 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1297 . -1296) 175758) ((-365 . -416) T) ((-1297 . -1132) 175708) ((-1221 . -1132) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1284 . -668) 175537) ((-326 . -649) 175516) ((-856 . -748) T) 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T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1252) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1252) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1088) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1093 . -1247) T) ((-975 . -1247) T) ((-735 . -1247) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1247) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1128 . -107) 173800) ((-1093 . -911) 173782) ((-975 . -911) 173707) ((-677 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1120 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-975 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-677 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-820 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -939) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1316) 172342) ((-366 . -1316) 172326) ((-358 . -1316) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -814) T) ((-526 . -819) T) ((-525 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1132) T) ((-896 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-975 . -390) 171946) ((-893 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1322 . -1317) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1266 . -1247) T) ((-137 . -484) 169520) ((-879 . -1247) T) ((-678 . -668) 169479) ((-48 . -1132) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1247) T) ((-1266 . -911) NIL) ((-913 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1132) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1266 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1027 . -929) 169096) ((-677 . -133) T) ((-674 . -814) 169075) ((-674 . -819) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-305 . -1305) 168914) ((-1198 . -874) NIL) ((-890 . -102) T) ((-985 . -571) 168893) ((-1240 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-934 . -1132) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1178 . -1247) T) ((-1240 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1327 . -1088) T) ((-1266 . -390) 168084) ((-419 . -1252) 168062) ((-1146 . -632) 168044) ((-325 . -870) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1262 . -813) 167997) ((-1262 . -816) 167950) ((-1283 . -748) T) ((-1262 . -748) T) ((-48 . -739) 167915) ((-229 . -1051) T) ((-1284 . -426) 167881) ((-1266 . -927) 167824) ((-365 . -1305) 167801) ((-1240 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1321 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1321 . -662) 167115) ((-642 . -302) T) ((-597 . -1087) 167090) 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-1247) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1321 . -102) T) ((-1229 . -1247) T) ((-1227 . -635) 166423) ((-1119 . -1247) T) ((-1118 . -1087) 166266) ((-1106 . -1247) T) ((-275 . -939) 166245) ((-255 . -939) 166224) ((-803 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1247) T) ((-1195 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1247) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1189 . -871) T) ((-1119 . -1069) 164755) ((-1106 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-987 . -1247) T) ((-985 . -1143) T) ((-128 . -1041) 164488) ((-872 . -1247) T) ((-895 . -1051) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-676 . -635) 164406) ((-1297 . -503) 164390) ((-1215 . -1247) T) ((-1214 . -1247) T) ((-1173 . -38) 164350) ((-985 . -23) T) ((-935 . -670) 164315) ((-889 . -1132) T) ((-864 . -102) T) ((-839 . -21) T) ((-652 . -1082) 164299) ((-620 . -1082) 164283) ((-839 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1087) 164216) ((-532 . -1087) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1213 . -1247) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-890 . -38) 164089) ((-1118 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1143) T) ((-326 . -1088) 163600) ((-325 . -1088) T) ((-132 . -1247) T) ((-131 . -1247) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1080) T) ((-1327 . -1132) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1022) 162778) ((-118 . -894) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) 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-1132) T) ((-421 . -321) 161010) ((-1173 . -929) 160933) ((-893 . -632) 160915) ((-856 . -1069) 160884) ((-661 . -1087) 160868) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160850) ((-509 . -1033) T) ((-285 . -861) T) ((-284 . -861) T) ((-283 . -861) T) ((-282 . -861) T) ((-48 . -302) T) ((-281 . -861) T) ((-280 . -861) T) ((-279 . -861) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -871) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -871) T) ((-677 . -21) T) ((-677 . -25) T) ((-1321 . -38) 160696) ((-119 . -298) 160647) ((-1297 . -19) 160631) ((-1257 . -874) NIL) ((-1297 . -618) 160608) ((-1311 . -1132) T) ((-365 . -1082) 160553) ((-1108 . -1132) T) ((-1017 . -1132) T) ((-985 . -133) T) ((-839 . -236) 160540) ((-758 . -1132) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -815) T) ((-526 . -816) T) ((-467 . -133) T) ((-421 . -1182) 160463) ((-227 . -1080) T) ((-305 . -102) 160245) ((-143 . -1132) T) ((-721 . -1033) T) ((-1136 . -298) 160201) ((-91 . -1247) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1327 . -175) T) ((-1204 . -376) 160026) ((-1198 . -376) 160005) ((-326 . -1132) T) ((-419 . -133) T) ((-325 . -1132) T) ((-421 . -38) 159957) ((-1164 . -102) T) ((-1284 . -739) 159849) ((-1166 . -1293) T) ((-1127 . -1247) T) ((-1122 . -1247) T) ((-678 . -1088) T) ((-1104 . -1247) T) ((-1097 . -1247) T) ((-1067 . -1247) T) ((-1050 . -1247) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1132) T) ((-137 . -1132) T) ((-115 . -1132) T) ((-882 . -102) T) ((-645 . -1247) T) ((-497 . -1247) T) ((-594 . -632) 159789) ((-560 . -633) 159688) ((-560 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1247) T) ((-496 . -871) 159548) ((-501 . -660) 159530) ((-994 . -632) 159512) ((-1034 . 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-1132) 146013) ((-1255 . -866) T) ((-331 . -1004) 145975) ((-105 . -102) T) ((-48 . -1087) 145940) ((-895 . -874) NIL) ((-1322 . -102) T) ((-395 . -102) T) ((-1284 . -632) 145922) ((-1164 . -1165) 145906) ((-1035 . -660) 145888) ((-900 . -1247) T) ((-48 . -111) 145844) ((-703 . -1247) T) ((-698 . -1247) T) ((-674 . -1247) T) ((-837 . -921) 145711) ((-492 . -1247) T) ((-252 . -1247) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1305) 145695) ((-140 . -1247) T) ((-139 . -1247) T) ((-135 . -1247) T) ((-1248 . -102) T) ((-1055 . -635) 145632) ((-839 . -239) T) ((-1201 . -1252) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1156 . -1252) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1201 . -571) 145127) ((-1156 . -571) 145058) ((-1255 . -1132) T) ((-561 . -874) T) ((-1066 . -298) 145033) ((-1197 . -1114) T) ((-1025 . -1114) T) ((-838 . -133) T) ((-119 . -819) NIL) ((-119 . -814) NIL) ((-368 . -319) T) 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143042) ((-1219 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1224) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1151 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1151 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1257 . -660) 142704) ((-493 . -107) 142654) ((-1024 . -23) T) ((-1322 . -38) 142624) ((-1201 . -1143) T) ((-1156 . -1143) T) ((-1093 . -1252) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-878 . -1143) T) ((-975 . -1252) 142494) ((-495 . -1252) 142473) ((-1093 . -571) T) ((-975 . -571) 142404) ((-1201 . -23) T) ((-1183 . -1114) T) ((-1156 . -23) T) ((-878 . -23) T) ((-495 . -571) 142335) ((-1173 . -739) 142267) ((-692 . -1082) 142251) ((-1177 . -528) 142184) ((-692 . -662) 142168) ((-1066 . -633) NIL) ((-1066 . -632) 142150) ((-96 . -1114) T) ((-1327 . -1087) 142137) ((-890 . -739) 142107) ((-1327 . -111) 142092) ((-1240 . -47) 142061) ((-1198 . -871) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1134 . -1132) T) ((-1034 . -1132) T) ((-63 . -632) 142043) ((-1110 . -921) 141912) ((-1055 . -814) T) ((-1055 . -819) T) ((-1287 . -25) T) ((-1287 . -21) T) ((-1278 . -21) T) ((-1278 . -25) T) ((-893 . -670) 141899) ((-1257 . -21) T) ((-1257 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -950) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1247) T) ((-948 . -816) T) ((-948 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1132) T) ((-516 . -1132) T) ((-793 . -748) T) ((-229 . -376) T) ((-1319 . -1082) 141537) ((-1318 . -1082) 141521) ((-1319 . -662) 141491) ((-1185 . -1132) 141469) ((-895 . -1252) T) ((-1318 . -662) 141439) ((-1119 . -874) T) ((-678 . -632) 141421) ((-895 . -571) T) ((-716 . -381) NIL) ((-44 . -1082) 141405) ((-1327 . -635) 141387) ((-1321 . -1132) T) ((-692 . -102) T) ((-372 . -1305) 141371) ((-367 . -1305) 141355) ((-44 . -662) 141339) ((-359 . -1305) 141323) ((-563 . -102) T) ((-1240 . -1247) T) ((-534 . -871) 141302) ((-733 . -1247) T) ((-987 . -874) 141281) ((-872 . -874) T) ((-501 . -239) T) ((-221 . -239) T) ((-1077 . -1132) T) ((-839 . -466) 141260) ((-154 . -1082) 141244) ((-1077 . -1102) 141173) ((-1058 . -1007) 141142) ((-841 . -1143) T) ((-1034 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1143) T) ((-490 . -1007) 141040) ((-477 . -1007) 141009) ((-1214 . -874) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-918 . -632) 140955) ((-1213 . -874) T) ((-1110 . -746) 140934) ((-1327 . -1080) T) ((-838 . -660) 140882) ((-305 . -1088) 140824) ((-171 . -1252) 140729) ((-229 . -1143) T) ((-336 . -23) T) ((-1198 . -1022) 140681) ((-1284 . -1087) 140586) ((-864 . -1132) T) ((-131 . -874) T) ((-1157 . -762) 140565) ((-1283 . -950) 140544) ((-1262 . -950) 140523) ((-893 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1132) T) ((-270 . -1132) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1262 . -842) 140278) ((-1319 . -102) T) ((-505 . -1247) T) ((-353 . -1316) 140255) ((-1318 . -102) T) ((-1284 . -111) 140147) ((-1144 . -921) 140014) ((-837 . -1082) 139915) ((-837 . -662) 139837) ((-146 . -632) 139819) ((-1024 . -133) T) ((-44 . -102) T) ((-246 . -871) 139770) ((-597 . -1247) T) ((-1266 . -1252) 139749) ((-103 . -503) 139733) ((-1321 . -739) 139703) ((-1118 . -47) 139664) ((-1093 . -1143) T) ((-975 . -1143) T) ((-129 . -34) T) ((-123 . -34) T) ((-1266 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1227 . -1247) T) ((-1201 . -133) T) ((-353 . -381) T) ((-495 . -1143) T) ((-1156 . -133) T) ((-895 . -376) T) ((-468 . -47) 139503) ((-878 . -133) T) ((-334 . -874) 139482) ((-154 . -102) T) ((-1093 . -23) T) ((-975 . -23) T) ((-585 . -571) T) ((-838 . -25) T) ((-838 . -21) T) 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137363) ((-1118 . -1247) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-560 . -816) T) ((-171 . -376) 137289) ((-560 . -813) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1247) T) ((-802 . -1247) T) ((-1177 . -503) 137273) ((-475 . -1247) T) ((-468 . -1247) T) ((-1319 . -1320) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -939) NIL) ((-1318 . -1320) 137228) ((-671 . -1247) T) ((-803 . -911) NIL) ((-802 . -911) 137087) ((-1313 . -25) T) ((-1313 . -21) T) ((-1245 . -102) 137065) ((-1137 . -410) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-803 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1247) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1247) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1247) T) ((-532 . -1247) T) ((-226 . -503) 135750) ((-1297 . -34) T) ((-638 . -668) 135709) ((-301 . -1082) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1151 . -1087) 135582) ((-86 . -632) 135564) ((-50 . -1069) 135548) ((-1118 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -816) T) ((-721 . -813) T) ((-60 . -57) 135478) ((-595 . -1069) 135465) ((-532 . -1069) 135442) ((-174 . -1247) T) ((-336 . -133) T) ((-326 . -1080) 135332) ((-325 . -1080) T) ((-171 . -1143) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1035 . -1022) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1132) 134993) ((-229 . -133) T) ((-1151 . -111) 134978) ((-171 . -23) T) ((-820 . -149) 134957) ((-820 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1185 . -528) 134647) ((-491 . -668) 134597) ((-657 . -866) T) ((-496 . -921) 134464) ((-1164 . -1132) T) ((-229 . -1091) T) ((-837 . -321) 134402) ((-1118 . -927) 134337) ((-803 . -927) 134280) ((-802 . -927) 134264) ((-1319 . -38) 134234) ((-1318 . -38) 134204) ((-1266 . -1143) T) ((-879 . -1143) T) ((-468 . -927) 134181) ((-882 . -1132) T) ((-1266 . -23) T) ((-1151 . -635) 134153) ((-1093 . -133) T) ((-879 . -23) T) ((-585 . -1143) T) ((-642 . -748) T) ((-525 . -874) T) ((-368 . -950) T) ((-366 . -950) T) ((-301 . -102) T) ((-358 . -950) T) ((-1001 . -1114) T) ((-975 . -133) T) ((-838 . -236) 134098) ((-119 . -816) NIL) ((-119 . -813) NIL) ((-119 . -748) T) ((-1077 . -528) 133999) ((-716 . -939) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1247) T) ((-657 . -1132) T) ((-652 . -783) T) ((-620 . -783) T) ((-1257 . -871) NIL) ((-1110 . -1082) 133798) ((-1034 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1132) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-935 . -950) T) ((-1110 . -662) 133600) ((-496 . -1305) 133570) ((-1151 . -1080) T) ((-733 . -319) T) ((-723 . -1088) T) ((-372 . -1082) 133522) ((-367 . -1082) 133474) ((-359 . -1082) 133426) ((-372 . -662) 133378) ((-227 . -1069) 133355) ((-367 . -662) 133307) ((-108 . -1082) 133257) ((-359 . -662) 133209) ((-305 . -739) 133151) ((-661 . -1247) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1151 . -240) T) ((-307 . -153) 132963) ((-1027 . -633) 132924) ((-1027 . -632) 132906) ((-1020 . -632) 132888) ((-118 . -1088) T) ((-678 . -1087) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1085 . -1305) 132801) ((-678 . -111) 132780) ((-692 . -929) 132703) ((-1173 . -503) 132687) ((-1322 . -668) 132646) ((-395 . -668) 132615) ((-64 . -455) T) ((-64 . -410) T) ((-1190 . -102) T) ((-895 . -133) T) ((-498 . -102) 132565) ((-1146 . -1247) T) ((-1254 . -874) T) ((-1327 . -381) T) ((-1110 . -102) T) ((-1092 . -102) T) ((-365 . -739) 132510) ((-896 . -874) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1189 . -102) T) ((-1266 . -133) T) ((-1262 . -874) 131065) ((-1201 . -25) T) ((-1201 . -21) T) ((-1190 . -321) 130860) ((-357 . -1247) T) ((-1156 . -25) T) ((-879 . -133) T) ((-407 . -1247) T) ((-1156 . -21) T) ((-878 . -25) T) ((-878 . -21) T) ((-803 . -319) 130839) ((-1185 . -503) 130823) ((-1181 . -153) 130773) ((-1177 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1177 . -633) 130646) ((-585 . -133) T) ((-638 . -870) 130625) ((-1055 . -813) T) ((-1055 . -816) T) ((-1055 . -748) T) ((-837 . -929) 130494) ((-734 . -1087) 130317) ((-616 . -874) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1069) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -102) T) ((-205 . 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-874) T) ((-1205 . -35) 128490) ((-1205 . -95) 128456) ((-1205 . -1236) 128422) ((-1205 . -1233) 128388) ((-1204 . -1233) 128354) ((-1204 . -1236) 128320) ((-1204 . -95) 128286) ((-1204 . -35) 128252) ((-1198 . -1233) 128218) ((-1198 . -1236) 128184) ((-1189 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1110 . -1182) 128163) ((-40 . -1247) T) ((-1198 . -95) 128129) ((-1065 . -23) T) ((-1198 . -35) 128095) ((-585 . -507) T) ((-1157 . -35) 128061) ((-1157 . -95) 128027) ((-1157 . -1236) 127993) ((-1157 . -1233) 127959) ((-374 . -1143) T) ((-372 . -1182) 127938) ((-367 . -1182) 127917) ((-359 . -1182) 127896) ((-1134 . -298) 127852) ((-983 . -1247) T) ((-948 . -1247) T) ((-108 . -1182) T) ((-854 . -1088) 127831) ((-793 . -1247) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1247) T) ((-734 . -1080) T) ((-1093 . -660) 127602) ((-1110 . -38) 127470) ((-975 . -660) 127418) ((-1035 . -149) T) ((-1035 . -147) NIL) ((-391 . -1143) T) ((-336 . -25) T) ((-334 . -23) T) ((-972 . -871) 127397) ((-734 . -338) 127374) ((-495 . -660) 127322) ((-40 . -1069) 127210) ((-734 . -240) T) ((-723 . -739) 127197) ((-352 . -1132) T) ((-177 . -1132) T) ((-343 . -871) T) ((-419 . -466) 127147) ((-391 . -23) T) ((-372 . -38) 127112) ((-367 . -38) 127077) ((-359 . -38) 127042) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-856 . -1143) T) ((-108 . -38) 126992) ((-850 . -1143) T) ((-795 . -1132) T) ((-118 . -739) 126979) ((-694 . -1069) 126963) ((-630 . -102) T) ((-856 . -23) T) ((-850 . -23) T) ((-1185 . -298) 126915) ((-1144 . -321) 126853) ((-496 . -1082) 126754) ((-1128 . -242) 126738) ((-61 . -411) T) ((-61 . -410) T) ((-1183 . -102) T) ((-110 . -102) T) ((-496 . -662) 126660) ((-40 . -390) 126637) ((-96 . -102) T) ((-677 . -876) 126621) ((-1201 . -236) 126608) ((-1166 . -1114) T) ((-1093 . -21) T) ((-1093 . -25) T) ((-1085 . -1082) 126592) ((-837 . -274) 126561) ((-837 . -234) 126530) ((-975 . -25) T) ((-975 . -21) T) ((-1151 . -381) T) ((-1085 . -662) 126472) ((-638 . -1088) T) ((-1058 . -321) 126410) ((-913 . -632) 126392) ((-692 . -668) 126351) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1082) 126335) ((-910 . -632) 126317) ((-893 . -1247) T) ((-537 . -528) 126250) ((-260 . -871) 126201) ((-259 . -871) 126152) ((-394 . -662) 126122) ((-895 . -660) 126099) ((-490 . -321) 126037) ((-562 . -1247) T) ((-477 . -321) 125975) ((-365 . -302) T) ((-1185 . -1286) 125959) ((-1173 . -632) 125921) ((-1173 . -633) 125882) ((-1171 . -102) T) ((-1027 . -1087) 125778) ((-40 . -927) 125730) ((-1185 . -618) 125707) ((-1327 . -670) 125694) ((-1094 . -153) 125640) ((-501 . -921) NIL) ((-890 . -504) 125617) ((-1027 . -111) 125499) ((-896 . -1252) T) ((-221 . -921) NIL) ((-352 . -739) 125483) ((-890 . -632) 125445) ((-177 . -739) 125377) ((-896 . -571) T) ((-421 . -298) 125335) ((-246 . -239) 125232) ((-108 . -414) 125214) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125196) ((-99 . -748) T) ((-496 . -102) 124928) ((-99 . 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-1233) 84069) ((-1283 . -1236) 84035) ((-1266 . -921) 83938) ((-1201 . -1082) 83761) ((-1173 . -1247) T) ((-1156 . -1082) 83604) ((-878 . -1082) 83588) ((-651 . -618) 83563) ((-1283 . -95) 83529) ((-1283 . -239) 83481) ((-1264 . -102) 83459) ((-1201 . -662) 83288) ((-1156 . -662) 83137) ((-878 . -662) 83107) ((-1262 . -1233) 83073) ((-1118 . -25) T) ((-564 . -1132) T) ((-1118 . -21) T) ((-985 . -1088) T) ((-545 . -814) T) ((-545 . -819) T) ((-119 . -1252) T) ((-890 . -1247) T) ((-642 . -571) T) ((-803 . -25) T) ((-803 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1088) T) ((-737 . -1088) T) ((-692 . -1087) 83057) ((-531 . -1114) T) ((-475 . -25) T) ((-119 . -571) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1262 . -1236) 83023) ((-1183 . -93) T) ((-1173 . -1069) 82919) ((-839 . -302) 82898) ((-1262 . -239) 82757) ((-846 . -1132) T) ((-995 . -998) T) ((-692 . -111) 82736) ((-636 . -1247) T) ((-307 . -528) 82528) ((-1257 . -234) 82480) ((-1257 . -274) 82432) ((-1256 . -381) T) ((-260 . -321) 82370) ((-259 . -321) 82308) ((-1253 . -866) T) ((-1190 . -633) NIL) ((-1190 . -632) 82290) ((-1173 . -390) 82274) ((-1151 . -842) T) ((-1151 . -950) T) ((-96 . -93) T) ((-1144 . -618) 82251) ((-1110 . -633) 82235) ((-1110 . -632) 82217) ((-1035 . -668) 82167) ((-943 . -668) 82104) ((-837 . -300) 82081) ((-498 . -632) 82013) ((-627 . -153) 81960) ((-501 . -739) 81910) ((-419 . -1088) T) ((-496 . -503) 81894) ((-443 . -668) 81853) ((-339 . -871) 81832) ((-352 . -670) 81806) ((-50 . -21) T) ((-50 . -25) T) ((-221 . -739) 81756) ((-171 . -746) 81727) ((-177 . -670) 81659) ((-595 . -21) T) ((-595 . -25) T) ((-532 . -25) T) ((-532 . -21) T) ((-489 . -153) 81609) ((-1092 . -632) 81591) ((-1024 . -102) T) ((-887 . -102) T) ((-838 . -929) 81491) ((-820 . -426) 81454) ((-40 . -133) T) ((-721 . -376) T) ((-723 . -748) T) ((-723 . -816) T) ((-723 . -813) T) ((-215 . -922) T) ((-594 . -1143) T) ((-560 . -1143) T) ((-509 . -1143) T) ((-372 . -632) 81436) ((-367 . -632) 81418) ((-359 . -632) 81400) ((-66 . -411) T) ((-66 . -410) T) ((-108 . -633) 81330) ((-108 . -632) 81272) ((-214 . -922) T) ((-987 . -153) 81256) ((-793 . -133) T) ((-692 . -635) 81174) ((-136 . -748) T) ((-118 . -748) T) ((-1283 . -35) 81140) ((-1085 . -503) 81124) ((-594 . -23) T) ((-560 . -23) T) ((-509 . -23) T) ((-1262 . -95) 81090) ((-1262 . -35) 81056) ((-1201 . -102) T) ((-1156 . -102) T) ((-878 . -102) T) ((-231 . -503) 81040) ((-1319 . -111) 81019) ((-1318 . -111) 80998) ((-44 . -1087) 80982) ((-1321 . -1247) T) ((-1319 . -635) 80928) ((-1319 . -1080) T) ((-1318 . -635) 80857) ((-1318 . -1080) T) ((-1266 . -1273) 80841) ((-879 . -876) 80825) ((-1209 . -302) 80804) ((-1134 . -1247) T) ((-110 . -298) 80754) ((-1034 . -1247) T) ((-131 . -153) 80736) ((-1173 . -927) 80695) ((-44 . -111) 80674) ((-1253 . -1132) T) ((-1212 . -1293) T) ((-1198 . -870) NIL) ((-1197 . -504) 80655) ((-692 . -1080) T) ((-1197 . -632) 80621) ((-1189 . -632) 80603) ((-488 . -239) 80555) ((-1094 . -629) 80530) ((-1025 . -504) 80511) ((-74 . -455) T) ((-74 . -410) T) ((-1094 . -1132) T) ((-154 . -1087) 80495) ((-1025 . -632) 80461) ((-692 . -240) 80440) ((-585 . -569) 80424) ((-368 . -149) 80403) ((-368 . -147) 80354) ((-366 . -149) 80333) ((-366 . -147) 80284) ((-358 . -149) 80263) ((-358 . -147) 80214) ((-275 . -147) 80193) ((-275 . -149) 80172) ((-255 . -149) 80151) ((-119 . -376) T) ((-255 . -147) 80130) ((-1189 . -633) NIL) ((-154 . -111) 80109) ((-1034 . -1069) 79997) ((-1185 . -1247) T) ((-716 . -1252) T) ((-820 . -1088) T) ((-721 . -1143) T) ((-1034 . -390) 79974) ((-520 . -1247) T) ((-516 . -1247) T) ((-935 . -147) T) ((-935 . -149) 79956) ((-893 . -133) T) ((-837 . -1087) 79877) ((-721 . -23) T) ((-716 . -571) T) ((-229 . -1082) 79842) ((-669 . -632) 79774) ((-669 . -633) 79735) ((-651 . -633) NIL) ((-651 . -632) 79717) ((-501 . -175) T) ((-229 . -662) 79682) ((-221 . -175) T) ((-227 . -21) T) ((-227 . -25) T) ((-488 . -1236) 79648) ((-488 . -1233) 79614) ((-285 . -632) 79596) ((-284 . -632) 79578) ((-283 . -632) 79560) ((-282 . -632) 79542) ((-281 . -632) 79524) ((-514 . -673) 79506) ((-280 . -632) 79488) ((-352 . -748) T) ((-279 . -632) 79470) ((-110 . -19) 79452) ((-177 . -748) T) ((-514 . -385) 79434) ((-215 . -632) 79416) ((-534 . -1180) 79400) ((-514 . -125) T) ((-110 . -618) 79375) ((-214 . -632) 79357) ((-488 . -35) 79323) ((-488 . -95) 79289) ((-212 . -632) 79271) ((-211 . -632) 79253) ((-210 . -632) 79235) ((-209 . -632) 79217) ((-206 . -632) 79199) ((-205 . -632) 79181) ((-204 . -632) 79163) ((-203 . -632) 79145) ((-202 . -632) 79127) ((-201 . -632) 79109) ((-200 . -632) 79091) ((-549 . -1135) 79043) ((-199 . -632) 79025) ((-198 . -632) 79007) ((-45 . -503) 78944) ((-197 . -632) 78926) ((-196 . -632) 78908) ((-154 . -635) 78877) ((-1147 . -102) T) ((-837 . -111) 78793) ((-663 . -102) 78723) ((-661 . -21) T) ((-661 . -25) T) ((-496 . -298) 78700) ((-1321 . -1069) 78684) ((-1144 . -632) 78377) ((-1133 . -1132) T) ((-1077 . -1247) T) ((-1201 . -321) 78364) ((-1093 . -1082) 78351) ((-1166 . -1132) T) ((-975 . -1082) 78194) ((-1156 . -321) 78181) ((-1127 . -1114) T) ((-642 . -1143) T) ((-1093 . -662) 78168) ((-1122 . -1114) T) ((-975 . -662) 78017) ((-1118 . -236) 77962) ((-495 . -1082) 77805) ((-1104 . -1114) T) ((-1097 . -1114) T) ((-1067 . -1114) T) ((-1050 . -1114) T) ((-119 . -1143) T) ((-495 . -662) 77654) ((-803 . -236) 77641) ((-841 . -102) T) ((-645 . -1114) T) ((-642 . -23) T) ((-1181 . -528) 77433) ((-497 . -1114) T) ((-985 . -1132) T) ((-400 . -102) T) ((-336 . -102) T) ((-222 . -1114) T) ((-864 . -1247) T) ((-154 . -1080) T) ((-753 . -426) 77417) ((-119 . -23) T) ((-1034 . -927) 77369) ((-757 . -1132) T) ((-737 . -1132) T) ((-1287 . -668) 77279) ((-1278 . -668) 77161) ((-467 . -1132) T) ((-421 . -1247) T) ((-326 . -435) 77145) ((-606 . -93) T) ((-1058 . -633) 77106) ((-270 . -1247) T) ((-1055 . -1252) T) ((-229 . -102) T) ((-1058 . -632) 77068) ((-838 . -274) 77052) ((-838 . -234) 77036) ((-837 . -635) 76834) 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75010) ((-735 . -102) T) ((-307 . -503) 74947) ((-895 . -662) 74892) ((-495 . -102) T) ((-753 . -1088) T) ((-630 . -632) 74874) ((-630 . -633) 74735) ((-421 . -390) 74719) ((-421 . -351) 74703) ((-1201 . -38) 74532) ((-1156 . -38) 74381) ((-331 . -635) 74207) ((-935 . -239) T) ((-652 . -1247) T) ((-620 . -1247) T) ((-878 . -38) 74177) ((-404 . -670) 74161) ((-663 . -321) 74099) ((-1183 . -504) 74080) ((-1183 . -632) 74046) ((-985 . -739) 73943) ((-757 . -739) 73913) ((-638 . -670) 73887) ((-226 . -107) 73871) ((-45 . -298) 73771) ((-323 . -1132) T) ((-301 . -1087) 73758) ((-110 . -632) 73740) ((-110 . -633) 73722) ((-467 . -739) 73692) ((-838 . -262) 73631) ((-711 . -1132) 73609) ((-565 . -1132) T) ((-1205 . -1088) T) ((-1204 . -1088) T) ((-96 . -504) 73590) ((-1198 . -1088) T) ((-301 . -111) 73575) ((-1157 . -1088) T) ((-565 . -629) 73554) ((-96 . -632) 73520) ((-1035 . -870) T) ((-231 . -708) 73478) ((-716 . -1143) T) ((-1240 . -762) 73454) ((-1055 . -376) T) ((-860 . -858) 73436) 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T) ((-895 . -321) 69641) ((-677 . -298) 69620) ((-657 . -1247) T) ((-114 . -684) T) ((-365 . -1247) T) ((-372 . -635) 69557) ((-367 . -635) 69494) ((-359 . -635) 69431) ((-77 . -1247) T) ((-108 . -635) 69381) ((-114 . -113) T) ((-1093 . -38) 69368) ((-686 . -387) 69347) ((-975 . -38) 69196) ((-753 . -1132) T) ((-495 . -38) 69045) ((-82 . -1247) T) ((-606 . -504) 69026) ((-1257 . -870) NIL) ((-1205 . -1132) T) ((-585 . -296) T) ((-1204 . -1132) T) ((-606 . -632) 68992) ((-1198 . -1132) T) ((-1151 . -874) T) ((-1110 . -1080) T) ((-365 . -1069) 68969) ((-839 . -504) 68953) ((-1035 . -1088) T) ((-45 . -632) 68935) ((-45 . -633) NIL) ((-943 . -1088) T) ((-839 . -632) 68904) ((-1178 . -102) 68854) ((-1110 . -250) 68805) ((-443 . -1088) T) ((-372 . -1080) T) ((-367 . -1080) T) ((-377 . -378) 68782) ((-359 . -1080) T) ((-357 . -236) 68769) ((-260 . -245) 68748) ((-259 . -245) 68727) ((-1110 . -240) 68652) ((-1157 . -1132) T) ((-305 . -927) 68611) ((-108 . -1080) T) ((-716 . -133) T) ((-419 . -528) 68453) ((-372 . -240) 68432) ((-372 . -250) T) ((-44 . -742) T) ((-367 . -240) 68411) ((-367 . -250) T) ((-359 . -240) 68390) ((-359 . -250) T) ((-1197 . -635) 68371) ((-171 . -321) 68336) ((-108 . -250) T) ((-108 . -240) T) ((-1025 . -635) 68317) ((-331 . -814) T) ((-893 . -21) T) ((-893 . -25) T) ((-421 . -319) T) ((-514 . -34) T) ((-110 . -300) 68292) ((-1144 . -1087) 68213) ((-895 . -1182) NIL) ((-342 . -632) 68195) ((-421 . -1051) 68173) ((-1144 . -111) 68089) ((-713 . -1293) T) ((-451 . -1132) T) ((-258 . -1132) T) ((-1322 . -748) T) ((-64 . -632) 68071) ((-895 . -38) 68016) ((-616 . -153) 68000) ((-537 . -1247) T) ((-524 . -632) 67940) ((-1266 . -321) 67927) ((-753 . -739) 67776) ((-545 . -815) T) ((-545 . -816) T) ((-560 . -660) 67758) ((-509 . -660) 67718) ((-518 . -1247) T) ((-659 . -1305) 67702) ((-368 . -466) T) ((-366 . -466) T) ((-358 . -466) T) ((-275 . -466) 67653) ((-539 . -1132) T) ((-534 . -1132) 67603) ((-255 . -466) 67554) ((-1181 . -298) 67533) ((-1209 . 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. -1088) T) ((-1240 . -149) 63676) ((-334 . -1082) 63658) ((-1240 . -147) 63637) ((-1215 . -102) T) ((-1214 . -102) T) ((-1213 . -102) T) ((-1205 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1247) T) ((-1204 . -175) 63501) ((-1198 . -175) 63432) ((-1183 . -635) 63413) ((-1157 . -175) 63364) ((-610 . -1088) T) ((-609 . -1088) T) ((-1035 . -1132) T) ((-1002 . -1132) T) ((-391 . -1082) 63329) ((-136 . -1247) T) ((-118 . -1247) T) ((-943 . -1132) T) ((-895 . -929) NIL) ((-391 . -662) 63294) ((-146 . -874) T) ((-820 . -818) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -911) 63237) ((-443 . -1132) T) ((-326 . -1252) 63216) ((-325 . -1252) T) ((-171 . -414) 63200) ((-856 . -1082) 63170) ((-488 . -1004) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-850 . -1082) 63098) ((-108 . -819) T) ((-108 . -814) T) ((-723 . -1069) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-856 . -662) 63029) ((-850 . -662) 62999) ((-1327 . -23) T) ((-136 . -1069) 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. -921) 60880) ((-987 . -321) 60818) ((-856 . -102) T) ((-443 . -739) 60802) ((-229 . -843) T) ((-850 . -102) T) ((-847 . -102) T) ((-1319 . -670) 60776) ((-1283 . -1282) 60755) ((-493 . -153) 60705) ((-1283 . -1276) 60675) ((-1151 . -1252) T) ((-352 . -1069) 60642) ((-1283 . -1280) 60626) ((-1266 . -929) 60533) ((-1262 . -1261) 60512) ((-80 . -632) 60494) ((-931 . -632) 60476) ((-1262 . -1276) 60453) ((-1151 . -571) T) ((-948 . -871) T) ((-793 . -871) T) ((-694 . -871) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1262 . -1259) 60308) ((-1284 . -1143) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1094 . -618) 60154) ((-840 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1316) 60048) ((-367 . -1316) 60032) ((-359 . -1316) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1080) 59973) ((-716 . -660) 59955) ((-1318 . -670) 59929) ((-131 . -321) NIL) ((-1284 . -23) T) 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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 b347770e..8164dd22 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3507854465) +(30 . 3508426628) (4511 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,672 +488,674 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |generalPosition| |taylorRep| - |OMencodingUnknown| |factorByRecursion| |symmetricDifference| - |numberOfPrimitivePoly| |fmecg| |associatedSystem| |bright| - |inputBinaryFile| |physicalLength!| |pade| |ceiling| |writeByte!| - |numberOfVariables| |sortConstraints| |palgextint0| - |drawComplexVectorField| |principalIdeal| |compound?| |OMgetError| - |countRealRootsMultiple| |someBasis| |keys| |moduloP| |abs| - |SturmHabicht| |diagonalProduct| |mainPrimitivePart| |null| - |leadingExponent| |subCase?| |substitute| |oneDimensionalArray| - |groebgen| |nextPrimitiveNormalPoly| |firstNumer| - |stoseInternalLastSubResultant| |not| |balancedFactorisation| - |removeRoughlyRedundantFactorsInPols| |level| |s17acf| |deepestTail| - |nil?| |negative?| |and| |f04jgf| |s17adf| |xCoord| - |linearAssociatedLog| |module| |byteBuffer| |useSingleFactorBound| - |setFieldInfo| |or| |qelt| |shufflein| |dual| |rootPower| |predicates| - |bivariateSLPEBR| |nthFlag| |viewPhiDefault| |qsetelt| |subNodeOf?| - |createLowComplexityNormalBasis| |xor| |jacobi| |numberOfComponents| - |iomode| |OMputFloat| |doubleDisc| |c06fqf| |viewPosDefault| - |basisOfRightNucleus| |xRange| |symmetricTensors| |case| |f07fef| - |semiLastSubResultantEuclidean| |listRepresentation| - |nextsousResultant2| |sorted?| |cSin| |f02aff| |Zero| |infinite?| - |yRange| |Beta| |removeRedundantFactorsInPols| |algebraic?| - |writeInt8!| |value| |plotPolar| |graphImage| |ksec| |readInt16!| - |firstDenom| |alphabetic?| |readInt32!| |One| |zRange| - |noLinearFactor?| |e02akf| |mainContent| |characteristic| |testDim| - |e01sef| |idealiser| |intersect| |fortranComplex| |leftUnits| |map!| - |HenselLift| |light| |associates?| |outputFloating| |factorOfDegree| - |rightQuotient| |qsetelt!| |cyclicGroup| |rationalFunction| |times!| - |primPartElseUnitCanonical!| |empty| |vedf2vef| |po| |rowEchelonLocal| - |prevPrime| |delta| |duplicates| |supDimElseRittWu?| |jvmProtected| - |bag| |seriesSolve| |algebraicVariables| |monicDivide| |critT| - |subResultantGcd| |equality| |besselY| |untab| |mapUnivariate| - |resetVariableOrder| |rightOne| |tanintegrate| |sumOfKthPowerDivisors| - |badValues| |elt| |thenBranch| |laguerre| EQ |denomRicDE| |orbits| - |legendreP| |LiePolyIfCan| |schwerpunkt| 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|RemainderList| - |truncate| |bivariate?| |lowerCase| LODO2FUN |multivariate| |iiexp| - |tanh| |relerror| |setvalue!| |plenaryPower| - |factorSquareFreeByRecursion| |ldf2vmf| |safeCeiling| |precision| - |s17ajf| |variables| |lhs| |incrementBy| |coth| |swapColumns!| - |acschIfCan| |autoCoerce| |factorSquareFreePolynomial| |powern| - |extendIfCan| |colorDef| |localReal?| |createIrreduciblePoly| |s15adf| - |rhs| |sech| |expand| |row| |patternMatch| |minColIndex| |palgLODE0| - |bernoulliB| |jvmFieldrefConstantTag| |rootsOf| |datalist| |e02dcf| - |symmetricGroup| |filterWhile| |csch| |f02bbf| |lookup| - |dihedralGroup| |dmpToP| |stoseInvertible?reg| |certainlySubVariety?| - |branchPoint?| |jvmVolatile| |contractSolve| |width| |filterUntil| - |asinh| |knownInfBasis| |setEpilogue!| |invmod| - |getMultiplicationMatrix| |deepExpand| |fortranCarriageReturn| - |f02fjf| |acosh| |select| |groebner?| |explicitEntries?| - |pleskenSplit| |generalTwoFactor| |pr2dmp| |table| |categoryMode| - |OMgetEndObject| |viewWriteAvailable| |taylor| |withPredicates| - |atanh| |e01bhf| |quasiComponent| |pushuconst| |newTypeLists| - |categories| |constDsolve| |new| |extract!| |open?| |direction| - |laurent| |torsion?| |acoth| |OMsetEncoding| |dmp2rfi| - |zeroDimPrimary?| |headReduce| |paren| |match?| |copyInto!| |puiseux| - |stack| |asech| |reflect| |currentScope| |getZechTable| |addPoint2| - |failed| |f02bjf| |backOldPos| |setOrder| |scopes| |cAcsch| - |changeThreshhold| |createMultiplicationTable| |assign| |setColumn!| - |resultantReduitEuclidean| |derivative| |create| |inv| |multiple| - |symmetric?| |fortranLinkerArgs| |permutationRepresentation| |index?| - |conjugates| |applyQuote| |packageCall| |exprex| |recoverAfterFail| - |commonDenominator| |ground?| |optional| |makeRecord| |status| - |attributeData| |subNode?| |cAcsc| |restorePrecision| - |ScanFloatIgnoreSpaces| |headRemainder| |ground| - |selectIntegrationRoutines| |error| |symbolIfCan| |OMgetBind| - |prolateSpheroidal| |repSq| |freeOf?| |numerator| |axesColorDefault| - |leadingMonomial| |retractable?| |totalfract| |rotate| |simpleBounds?| - |sizeLess?| |any| |dflist| |maxrank| |positive?| |leadingCoefficient| - |reindex| |ruleset| |aQuartic| |squareMatrix| |curve?| |outputForm| - |nextSublist| |minimize| |rectangularMatrix| |primitiveMonomials| - |external?| |setrest!| |identity| |lintgcd| |declare| - |definingEquations| |left| |log2| |cCosh| |reopen!| |reductum| - |identitySquareMatrix| |shift| |chebyshevT| |eof?| |conjugate| - |roughSubIdeal?| |right| |palgLODE| |bsolve| |hdmpToDmp| |escape| - |viewport2D| |palglimint0| |ridHack1| |isAnd| |e04ucf| |zeroSetSplit| - |aromberg| |palglimint| |splitLinear| |lazy?| |qinterval| - |solveLinearlyOverQ| |integralLastSubResultant| |bytes| |henselFact| - |stronglyReduced?| |tail| |fractionFreeGauss!| |returns| - |rootDirectory| |lazyVariations| |characteristicSerie| - |matrixConcat3D| |incrementKthElement| |Nul| |polyred| |cAcoth| - |complex?| |splitConstant| |eval| |linearAssociatedExp| |exponential| - |corrPoly| |expintfldpoly| |readBytes!| |cSec| |d03faf| |vspace| - |getOperands| |order| |lfextlimint| |localIntegralBasis| - |factorsOfDegree| |heap| |setsubMatrix!| |OMclose| |checkPrecision| - |mr| |unvectorise| |rightExactQuotient| |compiledFunction| - |coercePreimagesImages| |coerceL| |setPoly| |numFunEvals| |ldf2lst| - |complexZeros| |OMconnectTCP| |fortranInteger| |toseSquareFreePart| - |thetaCoord| |rur| |contract| |recip| |jvmPublic| - |stoseSquareFreePart| |groebSolve| |upperCase| |distance| |curveColor| - |showTheIFTable| |optpair| |changeWeightLevel| |setClosed| - |leviCivitaSymbol| |headReduced?| |userOrdered?| |diff| |polCase| - |viewZoomDefault| |separateDegrees| |e02bdf| |ode| |powerSum| - |radicalSimplify| |nextPartition| |setStatus!| |rank| |complete| - |selectOrPolynomials| |realElementary| |internalAugment| |crest| - |optAttributes| |principal?| |quadraticForm| |whatInfinity| - |conditionP| |secIfCan| |primeFrobenius| |cot2tan| |isOpen?| |symbol| - |unexpand| |pol| |evaluateInverse| |rightRemainder| |rootKerSimp| - |useEisensteinCriterion?| |clipPointsDefault| |genericPosition| - |coefficient| |cosIfCan| |jvmClassConstantTag| |expression| |makeSin| - |boundOfCauchy| |nodes| |list?| |void| |unitCanonical| |replace| - |normalDenom| |s17aff| |makeYoungTableau| |integer| |dot| - |rightDivide| |changeBase| |exprToXXP| |clikeUniv| |e01sff| |Is| - |f01ref| |OMgetString| |mainValue| |nil| |characteristicPolynomial| - |digits| |initTable!| |length| |cExp| |edf2ef| |fortranLogical| - |ideal| |simpsono| |insertionSort!| |permutation| - |SturmHabichtMultiple| |defineProperty| |scripts| |outputBinaryFile| - |mulmod| |minimumExponent| |irCtor| |tubePointsDefault| |lllip| - |s13adf| |roughUnitIdeal?| |fintegrate| |singRicDE| |radicalRoots| - |ode1| |ipow| |linearDependence| |style| |OMputApp| |approximate| - |writable?| |getRef| |pop!| |f04faf| |airyBi| |f02aaf| |univariate?| - |inRadical?| |dom| |complex| |minIndex| |shanksDiscLogAlgorithm| - |OMbindTCP| |bezoutResultant| |reverse| |leftUnit| |isPower| - |printStatement| |primextintfrac| |extendedIntegrate| |obj| |ddFact| - |primextendedint| |stoseLastSubResultant| |meshFun2Var| |linearForm| - |ParCondList| |setMaxPoints3D| |resultantEuclidean| |subHeight| - |diophantineSystem| |block| |generateIrredPoly| |nor| |quadratic?| - |createNormalPoly| |besselI| |symbolTableOf| |returnTypeOf| - |invmultisect| |associative?| |psolve| |lists| |op| |removeZero| - |maxRowIndex| |normDeriv2| |getMatch| - |removeSuperfluousQuasiComponents| |primeFactor| |lazyPremWithDefault| - |univariatePolynomial| |rotatex| |c06ecf| |makeCos| |primintegrate| - |LyndonWordsList1| |sort!| |OMgetBVar| |univariatePolynomialsGcds| - |addiag| |setVariableOrder| |factorList| |d01apf| |dimensionsOf| - |setDifference| |s18aff| |inc| |OMputInteger| |putColorInfo| - |stronglyReduce| |iiasech| |wordInStrongGenerators| |cCsc| |divisor| - |outputFixed| |printStats!| |cSech| |li| |schema| - |associatedEquations| |character?| |getCode| |upperCase!| - |extractSplittingLeaf| |bitTruth| |prem| |autoReduced?| - |univariatePolynomials| |pointSizeDefault| |neglist| |asimpson| - |rightRecip| |stripCommentsAndBlanks| |denomLODE| |elaborate| |iiacos| - |consnewpol| |sylvesterSequence| |fractionPart| |say| |moreAlgebraic?| - UP2UTS |iicosh| |cyclicEqual?| |bits| |changeName| |d01amf| - |whitePoint| |subTriSet?| |dominantTerm| |read!| - |variationOfParameters| |mat| |simplifyPower| |interval| |lp| - |optimize| |iitanh| |getButtonValue| |root?| |createThreeSpace| - |makeEq| |radix| |normal?| |leftRecip| |exactQuotient| |palgint0| - |polynomialZeros| |discriminant| |composite| |basisOfRightAnnihilator| - |genericRightMinimalPolynomial| |c06gbf| |maxdeg| |nlde| - |exprToGenUPS| |droot| |null?| |genericLeftTrace| |karatsubaOnce| - |concat!| |iicsc| |quoted?| |ScanFloatIgnoreSpacesIfCan| |closed| - |elliptic| |weierstrass| |partialDenominators| |kmax| |fixPredicate| - |idealiserMatrix| |e02baf| |insertMatch| |ravel| |OMputBVar| |e04mbf| - |column| |polyRicDE| |invertibleElseSplit?| |complexElementary| - |e02bcf| |e02dff| |iiacosh| |reshape| |lineColorDefault| |shuffle| - |fortranTypeOf| |semiIndiceSubResultantEuclidean| |zeroDimPrime?| - |swapRows!| |stirling2| |groebnerIdeal| |ratDsolve| |btwFact| - |calcRanges| |linearDependenceOverZ| |colorFunction| |f01qcf| |max| - |outputSpacing| |solveLinear| |constantRight| |s13aaf| |symbol?| - |normFactors| |internalSubQuasiComponent?| |OMputString| - |OMgetEndBind| |particularSolution| |elementary| |members| |npcoef| - |leftOne| |elem?| |nthRoot| |aCubic| |traceMatrix| - |regularRepresentation| |resize| |shallowExpand| |removeZeroes| - |linefeed| |showAll?| |build| |superHeight| |makeop| |hash| - |difference| |startPolynomial| |selectMultiDimensionalRoutines| - |normalElement| |expint| |setLegalFortranSourceExtensions| - |macroExpand| |critB| |count| |prefix| |overlabel| - |semiSubResultantGcdEuclidean1| |leftMult| |listConjugateBases| - |removeDuplicates!| |gcdprim| |element?| |leftDivide| |Ci| - |symmetricPower| |closed?| |separate| |cTan| |integral| |octon| - |OMputError| |category| |eigenvectors| |prefixRagits| - |leftTraceMatrix| |radicalEigenvectors| - |removeRedundantFactorsInContents| |minPoly| |edf2fi| - |primPartElseUnitCanonical| |setfirst!| |domain| |rdHack1| - |complexSolve| |critBonD| |operation| |bitLength| |ratPoly| - |intPatternMatch| |fill!| |subspace| |package| |high| |trueEqual| - |jvmFloatConstantTag| |f02akf| |depth| |position| - |solveLinearPolynomialEquation| |approxNthRoot| |intChoose| |fortran| - |cRationalPower| |mainCharacterization| |radicalEigenvalues| - |atrapezoidal| |low| |univariateSolve| |hasTopPredicate?| |linearPart| - |sech2cosh| |sayLength| |dimension| |char| |primitivePart| |monomRDE| - |rule| |limitedint| |prepareDecompose| |cLog| |center| |sumSquares| - |selectFiniteRoutines| |coerceS| |setButtonValue| |roman| - |stopTableGcd!| |purelyTranscendental?| |fglmIfCan| |modulus| |over| - |enqueue!| |halfExtendedResultant1| |readable?| |unknownEndian| - |fixedPoints| |kovacic| |addBadValue| |setchildren!| |s18aef| - |var1StepsDefault| |degreePartition| |compdegd| |shiftRoots| - |matrixGcd| |quatern| |leftExtendedGcd| |interpretString| |d02raf| - |omError| |cyclic| |float| |equiv| |latex| |mightHaveRoots| - |scripted?| |subst| |complexEigenvalues| |printHeader| |computePowers| - |atom?| |zag| |radicalSolve| |euclideanNormalForm| |forLoop| |terms| - |var2Steps| |getOperator| |selectPolynomials| |prime?| |jacobian| - |e02zaf| |showClipRegion| |iiacoth| |PDESolve| |f02xef| |dim| - |roughBasicSet| GF2FG |inverseColeman| |push| |realZeros| |insert!| - |zeroSquareMatrix| |e04jaf| |jvmFinal| |eigenvector| |systemCommand| - |option?| |rationalApproximation| |mappingAst| |normalForm| - |outlineRender| |f01bsf| |s18dcf| |objects| |linearPolynomials| - |OMgetAtp| |antiCommutative?| |divergence| |vark| |weights| |front| - |patternVariable| |argscript| |base| |messagePrint| |s17dhf| |normal| - |taylorQuoByVar| |rewriteSetWithReduction| |rotatez| |minPol| |irDef| - |options| |property| |lazyPrem| |retract| |script| |constructor| - |leftReducedSystem| |sqfrFactor| |binomial| |swap| |Si| |OMUnknownCD?| - |wholeRadix| |antiAssociative?| |mapmult| |squareTop| GE |s21bdf| - |idealSimplify| |rationalPoints| |epilogue| |basisOfRightNucloid| - |hexDigit?| |d02kef| |string| |linSolve| |drawCurves| |solid| GT - |setref| |oddInfiniteProduct| |getIdentifier| |horizConcat| - |rubiksGroup| |any?| |OMputAttr| |qualifier| |currentSubProgram| |tex| - |redPol| LE |isEquiv| |coefChoose| |hitherPlane| |bottom!| |quote| - |newSubProgram| |bfEntry| |att2Result| |csubst| |distdfact| - |getDatabase| |numberOfFactors| |curveColorPalette| |symmetricProduct| - |s15aef| |isNot| |smith| |basisOfCommutingElements| |checkForZero| - |bindings| |e01bgf| |trim| |typeForm| |rationalPoint?| |pole?| - |leftZero| |isPlus| |noncommutativeJordanAlgebra?| |delete| - |stoseInvertibleSetsqfreg| |minset| |constantOpIfCan| |commutator| - |basisOfMiddleNucleus| |f01brf| |discriminantEuclidean| - |purelyAlgebraicLeadingMonomial?| |lex| |derivationCoordinates| - |normal01| |select!| |iFTable| |rootNormalize| |every?| |polygon?| - |iiGamma| |genericLeftNorm| |shade| |zeroOf| |insertBottom!| |just| - |leaves| |partialQuotients| |factorAndSplit| |expt| |torsionIfCan| - |cotIfCan| |find| |complementaryBasis| |rightRank| |singularitiesOf| - |subresultantVector| |finiteBasis| |rational?| |f04asf| |sinhcosh| - |previous| |gensym| |unrankImproperPartitions0| |f02axf| |isAtom| - |nativeModuleExtension| |LazardQuotient2| |mainMonomial| |isExpt| - |makeprod| |divideExponents| |second| |cycleElt| |retractIfCan| - |padicallyExpand| |primitiveElement| |zoom| |elColumn2!| |makeSketch| - |nextNormalPoly| |explicitlyEmpty?| |rightTraceMatrix| |bernoulli| - |addmod| |third| |integralRepresents| |delay| |s14baf| |OMopenString| - |LazardQuotient| |exprHasAlgebraicWeight| |rightLcm| |sinhIfCan| - |lepol| |adaptive3D?| |cn| |bivariatePolynomials| |curryLeft| - |nonQsign| |setValue!| |setMinPoints3D| |sin?| |var1Steps| - |eigenvalues| |numberOfNormalPoly| |extractProperty| |listLoops| - |laurentRep| |presuper| |selectNonFiniteRoutines| |reduceByQuasiMonic| - |linears| |binding| |nand| |lastSubResultantElseSplit| - |inputOutputBinaryFile| |internalZeroSetSplit| |pile| |shiftLeft| |id| - |randnum| |vectorise| |magnitude| |permutationGroup| |rightMult| - |setLabelValue| |euler| |ptFunc| |stosePrepareSubResAlgo| |ocf2ocdf| - |discreteLog| |palgRDE0| |mkPrim| |vertConcat| |lo| |toroidal| |tower| - |map| |exponential1| |green| |lprop| |argumentList!| - |genericRightDiscriminant| |iterationVar| |verticalTab| - |pmComplexintegrate| |lexGroebner| |step| |callForm?| |rischNormalize| - |integralBasisAtInfinity| |remove!| |s18def| |primes| - |numberOfDivisors| |subResultantsChain| |insertTop!| |f2df| - |graphStates| |rotatey| |constant?| |tensorProduct| |tanh2trigh| - |hdmpToP| |log10| |palgextint| |leftExactQuotient| - |basisOfLeftNucloid| |s17dlf| |mapGen| |genericRightNorm| |unitVector| - |firstUncouplingMatrix| |internalLastSubResultant| |imagJ| |zero?| - |fullDisplay| |bitand| |parabolic| |resetAttributeButtons| |yCoord| - |prologue| |showSummary| |positiveSolve| |inverseIntegralMatrix| - |key?| |sec2cos| |qqq| |jvmNameAndTypeConstantTag| |bitior| |lquo| - |checkRur| |c06gqf| |degree| |OMputEndBVar| |gramschmidt| |readByte!| - |initializeGroupForWordProblem| |normalizedDivide| |reset| - |indicialEquationAtInfinity| |rischDE| |quartic| |s14aaf| - |complexNumeric| |showAttributes| |startTable!| |stFuncN| - |virtualDegree| |splitDenominator| |e02ahf| |update| |overbar| - |socf2socdf| |unparse| |chiSquare| |pomopo!| |mkAnswer| |setTex!| - |quadraticNorm| |sum| |viewDeltaYDefault| |write| |multMonom| |isOr| - |typeList| |dioSolve| |kernels| |putProperty| |bothWays| |box| - |double?| |invertibleSet| |flexible?| |save| |decompose| |rightUnits| - |getGraph| |nsqfree| |OMgetEndAtp| |minRowIndex| |cSinh| - |internalInfRittWu?| |rroot| |jvmStrict| |alphabetic| |lyndonIfCan| - |bounds| |varselect| |mvar| |pmintegrate| |radicalEigenvector| - |e02daf| |solveLinearPolynomialEquationByRecursion| |squareFreePrim| - |mindegTerm| |quoByVar| |setClipValue| |decreasePrecision| |orbit| - |rootBound| |basicSet| |mantissa| |mainVariables| |leftQuotient| - |OMlistCDs| |isList| |numberOfMonomials| |iiacot| |pdf2df| |binary| - |oddlambert| |medialSet| |mirror| |toseLastSubResultant| |eq?| - |musserTrials| |hexDigit| |weakBiRank| |deleteRoutine!| |iipow| - |doubleResultant| |primitive?| |nextIrreduciblePoly| |entry?| - |binomThmExpt| |hconcat| |dmpToHdmp| |monomialIntegrate| |unit| - |e01daf| |outputAsScript| |pushdown| |rightFactorIfCan| |c05adf| - |qPot| |logGamma| |bit?| |csc2sin| |jordanAdmissible?| |f04arf| - |OMParseError?| |maxrow| |viewSizeDefault| |myDegree| |s17agf| - |nextItem| |removeSinhSq| |opeval| |noKaratsuba| |outputArgs| - |failed?| |distribute| |stopTableInvSet!| |jvmInterface| - |monicDecomposeIfCan| |nthExponent| |underscore| |OMconnOutDevice| - |zCoord| |externalList| |sdf2lst| |iifact| |LyndonBasis| - |isConnected?| |modTree| Y |conjug| |SturmHabichtCoefficients| - |f04adf| |revert| |in?| |environment| |totolex| |imagk| |topPredicate| - |encodingDirectory| |semiDiscriminantEuclidean| |size?| |exp1| |cycle| - |numberOfIrreduciblePoly| |d03edf| |bracket| |modifyPointData| - |computeCycleLength| |credPol| |d02cjf| |key| |coerceP| - |createRandomElement| |Lazard| |possiblyNewVariety?| |totalLex| - |rational| |ramifiedAtInfinity?| |generic?| |measure| |parent| - |linGenPos| |padicFraction| |infix| |parametersOf| |d01asf| - |acosIfCan| |cross| |filename| |increment| |solve| |probablyZeroDim?| - |OMgetEndApp| |factorSquareFree| |leadingIdeal| |traverse| - |antiCommutator| |asinhIfCan| |unknown| |d01gaf| |cardinality| - |makeUnit| |iisqrt3| |cAsin| |nextLatticePermutation| |lookupFunction| - |isOp| |rewriteIdealWithHeadRemainder| |invertible?| |decimal| - |dAndcExp| |parse| |errorKind| |isQuotient| |monomRDEsys| |intensity| - |OMgetVariable| |geometric| |setOfMinN| |univcase| |primintfldpoly| - |algebraicDecompose| |kroneckerDelta| |antisymmetricTensors| |support| - |fractRadix| |bipolarCylindrical| |listexp| |flexibleArray| - |BasicMethod| |preprocess| |subscript| |hasHi| |linkToFortran| |cAtan| - |maximumExponent| |invertIfCan| |lift| |stiffnessAndStabilityOfODEIF| - |strongGenerators| |sizePascalTriangle| |continuedFraction| |meatAxe| - |clipSurface| |backspace| |real?| |reduce| |getPickedPoints| |input| - |numerators| |contains?| |setMaxPoints| |maxColIndex| |gcdPolynomial| - |cTanh| |mapUp!| |extractPoint| |algDsolve| |library| |critMonD1| - |transform| |OMputVariable| |symmetricRemainder| |height| |viewport3D| - |nullary| |factor1| |lagrange| |makeMulti| |e02gaf| - |createGenericMatrix| |flagFactor| |OMputEndError| |setleaves!| - |iisech| |relativeApprox| |screenResolution| |rationalPower| - |sylvesterMatrix| |routines| |genericLeftMinimalPolynomial| |name| - |cylindrical| |lflimitedint| |hessian| |inspect| |imaginary| - |children| |polarCoordinates| |readInt8!| |init| |body| |taylorIfCan| - |exprHasWeightCosWXorSinWX| |partialFraction| |expandTrigProducts| - |identification| |rootOfIrreduciblePoly| |queue| |bandedJacobian| - |complexEigenvectors| |lifting1| |minPoints| |rightTrim| - |setAdaptive3D| |divisorCascade| |region| - |stiffnessAndStabilityFactor| |cCos| |doubleFloatFormat| |c06ebf| - |exponents| |polyPart| |leftTrim| |weighted| |setAdaptive| - |getVariableOrder| |index| |isAbsolutelyIrreducible?| |resultant| - |before?| |cyclePartition| |pascalTriangle| |multiple?| |choosemon| - |variable?| |cAsinh| |showFortranOutputStack| |complexExpand| - |coshIfCan| |createZechTable| |logical?| |showTheFTable| - |semiDegreeSubResultantEuclidean| |f01qdf| |d02ejf| |mainExpression| - |pair| |directSum| |iiasin| |splitSquarefree| |upDateBranches| - |nextSubsetGray| |inconsistent?| |subQuasiComponent?| - |stopMusserTrials| |cPower| |rowEch| ** - |removeRoughlyRedundantFactorsInContents| |curry| |reverseLex| - |iidprod| |constantToUnaryFunction| |lambert| |fibonacci| - |leadingCoefficientRicDE| |permanent| |functorData| |factorPolynomial| - |fortranLiteral| |trigs| |iitan| |dn| |directory| |diagonalMatrix| - |quadratic| |makingStats?| |repeatUntilLoop| |port| - |semiSubResultantGcdEuclidean2| |raisePolynomial| |f01mcf| |byte| - |localAbs| |listOfMonoms| |balancedBinaryTree| |copy!| |deriv| - |normalizeAtInfinity| |extendedEuclidean| |representationType| - |solveid| |kind| |divideIfCan!| |show| |FormatArabic| - |SturmHabichtSequence| |lieAdmissible?| |sup| |minimalPolynomial| - |has?| |abelianGroup| |expIfCan| |hasSolution?| - |generalizedEigenvectors| |merge| |cyclicParents| |setUnion| |implies| - |resultantReduit| |t| |zero| |newline| |units| - |stoseInvertible?sqfreg| |printingInfo?| |setFormula!| |morphism| - |trace| |f04qaf| |splitNodeOf!| |makeFloatFunction| |getBadValues| - |skewSFunction| |newLine| |cache| |hostPlatform| |sign| - |associatorDependence| |monomialIntPoly| |enterPointData| |d01aqf| - |matrix| |complexLimit| |varList| |iicsch| |comparison| |ffactor| - |sizeMultiplication| |reducedQPowers| |setEmpty!| |permutations| - |pquo| |gradient| |fortranCharacter| |e02def| |parametric?| |constant| - |quasiRegular| |coordinate| |Gamma| |powerAssociative?| |monomial?| - |rewriteSetByReducingWithParticularGenerators| |OMputBind| |hue| - |product| |member?| |int| |factors| |less?| |setprevious!| - |constantKernel| |sin2csc| |code| |f02wef| |makeCrit| |split| - |exponentialOrder| |universe| |multiplyCoefficients| - |singleFactorBound| |midpoint| |monicRightFactorIfCan| - |tubeRadiusDefault| |safeFloor| |chineseRemainder| |maxPoints| - |pushdterm| |enterInCache| |OMReadError?| |viewWriteDefault| |imagj| - |leftRank| |cAsec| |constantLeft| |df2fi| |rightAlternative?| |tube| - |s19adf| |buildSyntax| |complexNormalize| |finite?| - |basisOfLeftNucleus| |tablePow| |graphs| |complement| |typeLists| - |f01maf| |coerceImages| |recur| |rationalIfCan| |iteratedInitials| - |clearFortranOutputStack| |fortranDouble| |readLineIfCan!| |rename| - |listYoungTableaus| |writeUInt8!| |getExplanations| |asechIfCan| - |shallowCopy| |doubleRank| |testModulus| |simplifyExp| |string?| - |finiteBound| |modifyPoint| |s21bcf| |writeLine!| |radPoly| |gderiv| - |rightMinimalPolynomial| |integral?| |leftRegularRepresentation| - |palgintegrate| |useNagFunctions| |createPrimitivePoly| |signature| - |cyclotomicFactorization| |d02gbf| |unitNormal| |plus| |push!| - |partialNumerators| |cAsech| |e04naf| |findConstructor| |vconcat| - |imports| |e02bef| |primitivePart!| |subscriptedVariables| |nary?| - |adaptive?| |genericRightTraceForm| |number?| |hex| - |jvmMethodrefConstantTag| |jvmSynchronized| |setRow!| |plusInfinity| - |tanSum| |dequeue| |wronskianMatrix| |critpOrder| |exp| - |makeGraphImage| |ScanArabic| |nodeOf?| |s19aaf| - |selectSumOfSquaresRoutines| |minusInfinity| |times| |whileLoop| - |putProperties| |pushup| |printInfo!| |rightRegularRepresentation| - |triangulate| |union| |safetyMargin| |totalGroebner| |contours| - |fractRagits| |radicalOfLeftTraceForm| |setMinPoints| - |functionIsContinuousAtEndPoints| |reseed| |deref| - |multiEuclideanTree| |rischDEsys| |OMopenFile| |child?| |df2st| - |jvmIntegerConstantTag| |dimensions| |arrayStack| |e01bef| - |fortranReal| |quasiMonic?| |clearTheFTable| |pattern| |round| |frst| - |f04mbf| |nthr| |OMgetEndBVar| |semiResultantEuclideannaif| - |doubleComplex?| |fixedPoint| |halfExtendedResultant2| |monom| - |unravel| |outputList| |cschIfCan| |cycleRagits| |youngDiagram| - |harmonic| |float?| |outputGeneral| |cosSinInfo| |reify| |type| - |createMultiplicationMatrix| |leftCharacteristicPolynomial| - |rightRankPolynomial| |basisOfLeftAnnihilator| |f07aef| - |pointColorDefault| |f02agf| |transcendenceDegree| |bezoutMatrix| - |nthExpon| |writeBytes!| |mainVariable?| |OMwrite| |leader| - |sequences| |setPrologue!| |roughBase?| |resetNew| |common| |tValues| - |printInfo| |unitsColorDefault| |Ei| |returnType!| |applyRules| - |readUInt8!| |concat| |scalarMatrix| |primlimitedint| |integralBasis| - |enumerate| |nothing| |s21baf| |minrank| |lazyIrreducibleFactors| - |jvmStringConstantTag| |cond| |resetBadValues| |redmat| |s21bbf| - |phiCoord| |headAst| |mix| |removeSquaresIfCan| |sinIfCan| |s18adf| - |subSet| |closedCurve| |functionIsFracPolynomial?| |controlPanel| - |linearElement| |powmod| |createPrimitiveNormalPoly| |OMgetType| - |mapExponents| |node| |blankSeparate| |B1solve| |indicialEquation| - |semicolonSeparate| |screenResolution3D| |jvmTransient| |ord| - |increasePrecision| |saturate| |nthRootIfCan| |pseudoRemainder| - |innerSolve1| |antisymmetric?| |readUInt16!| |carriageReturn| |arg1| - |showIntensityFunctions| |evenlambert| |Aleph| - |rightCharacteristicPolynomial| |OMencodingBinary| |inverse| - |perspective| |expandPower| |arg2| |bat| |RittWuCompare| |floor| - |polygon| |symmetricSquare| |perfectNthRoot| |hasPredicate?| - |pointLists| |trivialIdeal?| |removeSuperfluousCases| - |nextPrimitivePoly| |leftPower| |conditionsForIdempotents| |getOrder| - |setProperty| |HermiteIntegrate| |rk4f| |pdf2ef| |stopTable!| - |quotientByP| |stop| |inHallBasis?| |compactFraction| |powers| - |conditions| |integer?| |removeRoughlyRedundantFactorsInPol| - |jvmNative| |addPointLast| |numericIfCan| |roughEqualIdeals?| - |semiResultantEuclidean1| |f2st| |zeroDimensional?| |match| |integers| - |blue| |readUInt32!| |var2StepsDefault| |tRange| |clearDenominator| - |perfectSqrt| |tableForDiscreteLogarithm| |delete!| |getlo| - |mapUnivariateIfCan| |getProperties| |firstSubsetGray| |interpolate| - |expandLog| |pureLex| |reorder| |coerceListOfPairs| |Hausdorff| - |removeSinSq| |hermiteH| |cubic| |OMmakeConn| |compose| |iicos| - |fortranCompilerName| |parabolicCylindrical| |critMTonD1| - |ellipticCylindrical| |e01baf| |setStatus| |cup| |evenInfiniteProduct| - |brillhartTrials| |problemPoints| |removeDuplicates| |mapBivariate| - |definingInequation| |UP2ifCan| |reduced?| |algSplitSimple| - |meshPar2Var| |solid?| |indices| |fillPascalTriangle| |OMencodingXML| - |approxSqrt| |bezoutDiscriminant| |rst| |meshPar1Var| - |unrankImproperPartitions1| |leftRemainder| |spherical| - |integralMatrixAtInfinity| |zeroMatrix| |mindeg| |augment| - |printTypes| |c06gsf| |algebraicCoefficients?| |gcdPrimitive| - |functionIsOscillatory| |setPredicates| |check| |jvmAbstract| |c06frf| - |equation| |dark| |nonSingularModel| |clearTable!| |subtractIfCan| - |back| |OMreceive| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| + |Enumeration| |Mapping| |Record| |Union| |less?| |exactQuotient!| + |OMgetFloat| |setPosition| |callForm?| |integral?| |dilog| |scripts| + |double?| |leftTrim| |constantOpIfCan| |jvmStrict| |dimensionsOf| + |equality| |structuralConstants| |Ci| |kind| |youngGroup| + |oddInfiniteProduct| |sin| |plus!| |eigenMatrix| |partition| |init| + |reflect| |innerSolve1| |inRadical?| |listRepresentation| |numerator| + |arrayStack| |hostPlatform| |cos| |mapExponents| |mappingMode| + |exponentialOrder| |clipParametric| |antiCommutator| |algebraicOf| + |mesh?| |leadingBasisTerm| |LiePoly| |sylvesterSequence| |tan| + |removeConstantTerm| |nthRoot| |jvmFieldrefConstantTag| |makeVariable| + |mappingAst| |divisorCascade| |simpson| |optAttributes| |script| + |datalist| |PollardSmallFactor| |squareFreeFactors| |FormatRoman| + |assign| |wholeRagits| |lifting| |argscript| |numberOfPrimitivePoly| + |initializeGroupForWordProblem| |jvmPrivate| |toScale| |approxNthRoot| + |roughBasicSet| |invertible?| |null?| |dn| |superscript| + |brillhartIrreducible?| |cup| |lastSubResultantElseSplit| |df2mf| + |e01daf| |OMputEndError| |reverseLex| |optimize| + |SturmHabichtCoefficients| |alphabetic| |testModulus| |d02raf| + |fintegrate| |tex| |dual| |beauzamyBound| |rightDivide| |blue| |union| + |stoseSquareFreePart| |UP2ifCan| |jvmProtected| |makeViewport2D| |inf| + |pastel| |wronskianMatrix| |isMult| |setScreenResolution3D| + |ip4Address| |lazyEvaluate| |zerosOf| |rotatex| |setDifference| + |optional?| |yCoord| |fracPart| |rischNormalize| |getIdentifier| + |delay| |returnTypeOf| |aromberg| |rowEchLocal| |sh| |iilog| + |transcendenceDegree| |symmetricPower| |overset?| |allRootsOf| + |leftRegularRepresentation| |qfactor| |sts2stst| |asinhIfCan| + |stoseInvertible?| |tanQ| |besselY| |degreeSubResultantEuclidean| + |reverse| |swap!| |e01bef| |sign| + |solveLinearPolynomialEquationByFractions| |invertibleSet| + |commutator| |antisymmetric?| |currentScope| |iicot| |minIndex| + |approxSqrt| |strongGenerators| |ScanFloatIgnoreSpacesIfCan| |pack!| + |prepareSubResAlgo| |integralCoordinates| |blankSeparate| |light| + |readable?| |hash| |postfix| |extend| |normalizedDivide| |point| + |listBranches| |axesColorDefault| |relationsIdeal| |fractionPart| + |aCubic| UTS2UP |universe| |count| |clipBoolean| |normalForm| + |totalDegree| |region| |principal?| |intChoose| |pointPlot| + |setColumn!| GF2FG |rootsOf| |messagePrint| |lazyIntegrate| + |evenInfiniteProduct| |fmecg| |leftFactorIfCan| |setleaves!| + |constructor| |outputAsScript| |decimal| |repeating?| + |genericLeftTrace| |diagonalMatrix| |simplifyExp| |highCommonTerms| + |absolutelyIrreducible?| |primlimintfrac| + |generalizedContinuumHypothesisAssumed| |readUInt32!| |li| |iidprod| + |groebSolve| |s19abf| |bag| |leadingIndex| |singRicDE| |omError| + |inputOutputBinaryFile| |rewriteIdealWithRemainder| |changeBase| + |flexible?| |notelem| |f04adf| |c06ecf| |s18aff| + |numericalOptimization| |rootOf| |critpOrder| + |integralBasisAtInfinity| |scaleRoots| |ratpart| |fractionFreeGauss!| + |s14baf| |reduced?| |cn| EQ |iiperm| |linear?| |choosemon| |prologue| + |randomLC| |category| |horizConcat| |rk4qc| |findCycle| |subPolSet?| + |karatsubaDivide| |basisOfMiddleNucleus| |bezoutMatrix| |lyndonIfCan| + |diag| |shanksDiscLogAlgorithm| |expextendedint| |palgRDE| |domain| + |associatorDependence| |fortranReal| |apply| |palgintegrate| + |invmultisect| |integralMatrix| |iiasec| |getProperty| |readUInt16!| + |yCoordinates| |every?| |closed?| |henselFact| |package| |iiacsch| + |first| |generalInfiniteProduct| |realEigenvectors| + |getSyntaxFormsFromFile| |palglimint| |irForm| |s17dhf| + |unknownEndian| |untab| |select!| |sizePascalTriangle| |elaboration| + |cRationalPower| |rest| |traceMatrix| |B1solve| |associates?| + |leftNorm| |string?| |hcrf| |physicalLength| |retractable?| |d01anf| + |moreAlgebraic?| |factorials| |normalize| + |indiceSubResultantEuclidean| |integerBound| |outlineRender| + |stiffnessAndStabilityFactor| |indicialEquationAtInfinity| |call| + |iisech| |pushdown| |dAndcExp| |OMUnknownSymbol?| + |multiplyCoefficients| |seriesSolve| |quadratic| |associatedSystem| + |brillhartTrials| |quadraticForm| |exprToXXP| |var2StepsDefault| + |resultantReduitEuclidean| |inverseColeman| |e02dcf| |mainKernel| + |OMputInteger| |setLength!| |factorsOfCyclicGroupSize| |ratDenom| + |conjunction| |symFunc| |constantToUnaryFunction| |minPoints3D| + |solveRetract| |makeCos| |newReduc| |cyclic| |root| + |internalZeroSetSplit| |cAcot| |depth| |nullSpace| + |selectOptimizationRoutines| |upperCase| |solveLinearlyOverQ| + |karatsubaOnce| |ran| |rootBound| |normalise| |arg1| |radicalRoots| + |makeGraphImage| |rootNormalize| |associative?| |rubiksGroup| + |remove!| |OMopenString| |sturmSequence| |revert| |variable?| |bounds| + |infRittWu?| |arg2| |positiveSolve| |monicModulo| |monomialIntPoly| + |OMunhandledSymbol| |substring?| |quasiMonic?| |findBinding| + |branchIfCan| |algSplitSimple| |doublyTransitive?| |carriageReturn| + |mapUnivariate| |nthExpon| |wrregime| |e01sef| |prefix| |pseudoDivide| + |useNagFunctions| |is?| |splitLinear| |next| |scalarTypeOf| + |taylorQuoByVar| |tan2trig| |lyndon?| |conditions| |leader| |separate| + |iCompose| |suffix?| |tab1| |pushNewContour| |decompose| + |LowTriBddDenomInv| |finiteBound| |d02gaf| |match| |OMbindTCP| + |fixedPoints| |totalfract| |mainCharacterization| UP2UTS + |regularRepresentation| |indicialEquation| |cCos| |scan| + |continuedFraction| |relativeApprox| |listOfLists| |prefix?| |digit| + |selectODEIVPRoutines| |multinomial| |inputBinaryFile| |rischDE| |An| + |seriesToOutputForm| |rightFactorIfCan| |derivative| |s17dgf| + |btwFact| |pattern| |balancedFactorisation| |problemPoints| + |whatInfinity| |tRange| |clikeUniv| |push| |errorKind| |extract!| + |OMreadFile| |reducedDiscriminant| |pile| |distance| |lambert| + |d01asf| |numeric| |OMputObject| |ode1| |halfExtendedSubResultantGcd2| + |exteriorDifferential| |removeRoughlyRedundantFactorsInPol| |biRank| + |lllp| |tubePlot| |radical| |inverseIntegralMatrix| |equiv| + |ScanArabic| |readInt32!| |d01akf| |ravel| |expenseOfEvaluationIF| + |psolve| |true| |factorsOfDegree| |cAsinh| |removeRedundantFactors| + |cyclotomicDecomposition| |reshape| |c06fqf| |epilogue| + |LazardQuotient| |infix?| |enterInCache| |coth2tanh| |specialTrigs| + |extractBottom!| |boundOfCauchy| |rquo| |createPrimitivePoly| |mask| + |rightUnits| |kmax| |powerAssociative?| |unrankImproperPartitions0| + |map| |triangular?| |cTan| |setFormula!| |green| |aQuadratic| + |simplify| |clearFortranOutputStack| |extractTop!| |roman| |meatAxe| + |tanh2coth| |neglist| |closedCurve?| |branchPointAtInfinity?| + |semicolonSeparate| |OMgetAttr| |rootOfIrreduciblePoly| |OMputApp| + |rotate| |createLowComplexityNormalBasis| |primitive?| + |nextPrimitivePoly| |calcRanges| |distribute| |mulmod| |convert| + |figureUnits| |imagj| |prod| |subset?| |setelt!| |rationalFunction| + |acosIfCan| |s17ajf| |qroot| |conditionP| |irreducibleFactor| + |stoseInternalLastSubResultant| |dec| |s13acf| |makeSketch| |rightGcd| + |open?| |pToDmp| |compose| |arbitrary| |log10| |intPatternMatch| + |jvmNative| |sparsityIF| |ricDsolve| |id| FG2F |parseString| + |firstUncouplingMatrix| |basisOfRightNucloid| |bitand| |viewport3D| + |nthFactor| |prime?| |lo| |f02axf| |createMultiplicationMatrix| + |s15aef| |laurentRep| |noLinearFactor?| |collect| |bitior| + |bivariateSLPEBR| |inconsistent?| |step| |fortranDouble| |curryRight| + |coordinates| |number?| |reduceBasisAtInfinity| |jvmStatic| |block| + |standardBasisOfCyclicSubmodule| |e02adf| |mainCoefficients| + |monomial?| |leftMult| |morphism| |nodes| |second| |d01bbf| + |particularSolution| |linearDependenceOverZ| |writable?| + |stopTableGcd!| |laplacian| |alphanumeric?| |f01rdf| |third| |iisqrt3| + |multMonom| |numericalIntegration| |direction| |center| |queue| + |startTableInvSet!| |key| |mathieu12| |asimpson| |lprop| |backOldPos| + |OMgetInteger| |createIrreduciblePoly| |cross| |swapColumns!| + |minimumExponent| |selectIntegrationRoutines| |categoryFrame| + |completeEval| |reducedForm| |realSolve| |externalList| |filename| + |getStream| |solveInField| |stopTableInvSet!| |subscript| + |nextIrreduciblePoly| |fill!| |functionIsFracPolynomial?| + |mainPrimitivePart| |escape| |iicos| |jacobiIdentity?| |systemCommand| + |stack| |OMgetSymbol| |setStatus!| |addPointLast| |setlast!| + |nextNormalPoly| |times!| |middle| |isAtom| |generators| + |internalLastSubResultant| |parse| |monicCompleteDecompose| |laplace| + |nullary| |toseSquareFreePart| |removeCoshSq| |e04gcf| + |leftCharacteristicPolynomial| |readLineIfCan!| |normal| + |rewriteSetByReducingWithParticularGenerators| |presuper| |hexDigit?| + |iibinom| |leadingTerm| |critM| |pole?| |colorFunction| |homogeneous?| + |leftTrace| |scanOneDimSubspaces| |combineFeatureCompatibility| + |jacobian| |list?| |xCoord| |value| |setprevious!| |drawStyle| + |getRef| |semiResultantEuclidean2| |hex| |rightScalarTimes!| |f04qaf| + |s21bcf| |subQuasiComponent?| |genericRightMinimalPolynomial| |eq| + |increment| |jvmInterface| |purelyTranscendental?| |fprindINFO| + |df2ef| |argumentList!| |mapDown!| |elementary| |iter| |acothIfCan| + |torsion?| |bandedJacobian| |acschIfCan| |listConjugateBases| + |rightRecip| |rischDEsys| |changeNameToObjf| |pToHdmp| |sdf2lst| + |matrixDimensions| |generalPosition| |fortranCompilerName| + |chebyshevU| |setright!| |entry?| |generateIrredPoly| |ref| |s15adf| + |red| |jvmSuper| |viewPhiDefault| |symbolIfCan| |extendedint| |regime| + |nthFlag| |mpsode| |exprHasLogarithmicWeights| |nativeModuleExtension| + Y |topFortranOutputStack| |irCtor| |hasHi| |numericIfCan| |subspace| + |cAsin| |isOr| |viewport2D| |rename| |compdegd| |graphState| |e04ycf| + |innerint| |factor1| |setOrder| |controlPanel| |leftZero| + |irreducibleRepresentation| |OMputBind| |janko2| |complete| + |setRealSteps| |groebnerFactorize| |unitCanonical| |rename!| |rule| + |belong?| |index| |f01qcf| |imagJ| |mainVariable| + |selectNonFiniteRoutines| |entries| |d02kef| |leadingExponent| + |e02zaf| |constantKernel| |units| |OMsetEncoding| + |rightRankPolynomial| |pop!| |internalSubPolSet?| + |genericRightDiscriminant| |splitNodeOf!| |indiceSubResultant| + |chainSubResultants| |algintegrate| |fglmIfCan| |solve| |pair| + |factorSquareFreePolynomial| |jvmMethodrefConstantTag| + |intermediateResultsIF| |stopMusserTrials| |iFTable| + |patternMatchTimes| |sort| |thetaCoord| |c06gbf| |rspace| |d01fcf| + |monicDecomposeIfCan| |groebner| |binomThmExpt| |OMopenFile| + |multisect| |linearAssociatedLog| |genericLeftTraceForm| |iifact| + |LazardQuotient2| |parabolicCylindrical| |complexForm| + |removeDuplicates!| |nor| |nextsousResultant2| |collectUnder| + |explicitlyEmpty?| |random| |row| |child| |shiftRoots| + |complexEigenvectors| |selectfirst| |high| |stripCommentsAndBlanks| + |lexTriangular| |writeLine!| |palglimint0| |code| |listYoungTableaus| + |debug3D| |taylorRep| |linkToFortran| |innerSolve| + |subresultantSequence| |makeTerm| |stFunc2| |tan2cot| |dmp2rfi| + |gcdcofactprim| |subNodeOf?| |OMgetBind| |roughEqualIdeals?| + |lagrange| |iiatan| |typeList| |complexRoots| |probablyZeroDim?| + |rightZero| |hue| |selectOrPolynomials| |OMputAtp| |name| + |coefficients| |linearElement| |members| |isPlus| |overlap| + |algebraicVariables| |tubePointsDefault| |midpoints| |scopes| + |linSolve| |body| |replace| |search| |largest| |result| |sin2csc| + |extension| |OMputEndApp| |input| |f04faf| |point?| |fi2df| |leaf?| + |deepestInitial| |bitCoef| |nextLatticePermutation| |LyndonBasis| + |library| |mainMonomial| |zero?| |decomposeFunc| |reduceByQuasiMonic| + |rightTraceMatrix| BY |makeFloatFunction| |pushdterm| |iterationVar| + |OMReadError?| |baseRDE| |showClipRegion| |e02ajf| |size| + |writeUInt8!| |basisOfLeftAnnihilator| |nthExponent| |jvmSynchronized| + |partialDenominators| |sorted?| |child?| |cPower| |subCase?| |maxdeg| + |algint| |reset| |shrinkable| |powern| |gcdprim| |denomLODE| + |karatsuba| |dioSolve| |OMputEndObject| |patternMatch| |topPredicate| + |addiag| |critMTonD1| |modulus| |pow| |lfunc| |imagK| |quadratic?| + |rur| |selectsecond| |zeroDimPrimary?| |write| |dmpToP| |makeResult| + |resultantnaif| |quasiAlgebraicSet| |trueEqual| |hconcat| |powmod| + |atanIfCan| |ridHack1| |save| |OMgetEndApp| |factorGroebnerBasis| + |lifting1| |prolateSpheroidal| |makeMulti| |showTheRoutinesTable| + |radPoly| |leastMonomial| |noncommutativeJordanAlgebra?| NOT + |laguerreL| |matrixGcd| |OMencodingUnknown| |cAtan| |normalDenom| + |port| |semiResultantEuclidean1| |expintegrate| |acotIfCan| |monic?| + |series| OR |outputMeasure| |edf2df| |product| + |setAttributeButtonStep| |chiSquare1| |eyeDistance| |hyperelliptic| + |e04fdf| |f02wef| AND |isExpt| |squareFreeLexTriangular| |monicDivide| + |realElementary| |verticalTab| |rootPoly| |redPo| |npcoef| |constant| + |heapSort| |getExplanations| |elseBranch| |lllip| |linears| |iiacoth| + |f04axf| |t| |drawCurves| |lookupFunction| |signature| |node| |nlde| + |rightTrace| |fullDisplay| |airyBi| |extendedSubResultantGcd| + |checkPrecision| |df2st| |getBadValues| |validExponential| |cAcsch| + |isConnected?| |min| |nothing| |readInt16!| |ellipticCylindrical| + |prevPrime| |setRow!| |assert| |elaborate| |part?| |zeroDim?| |rowEch| + |minColIndex| |limit| |f07aef| |element?| |pointColor| + |jvmFloatConstantTag| |contract| |sechIfCan| |removeDuplicates| + |subresultantVector| |show| |transpose| |generalSqFr| |OMputEndAtp| + |sumOfSquares| |lazyPseudoRemainder| |createNormalPoly| |besselJ| + |gbasis| |typeLists| |lfintegrate| |quatern| |rightFactorCandidate| + |e02gaf| |dmpToHdmp| |bernoulli| |polyRDE| |categories| |isAnd| + |zeroDimPrime?| |critT| |trace| |over| |repSq| |tower| |putProperty| + |gderiv| |useSingleFactorBound?| |substitute| |f02aaf| |minPoints| + |maximumExponent| |eq?| |extractIndex| |OMlistSymbols| |divideIfCan| + |stoseInvertibleSetsqfreg| |f01rcf| * |factorByRecursion| |member?| + |tanIfCan| |extractIfCan| |setfirst!| |leftOne| + |createPrimitiveNormalPoly| |makeCrit| |e01bhf| |parabolic| + |charthRoot| |internalAugment| |solveid| |stopTable!| |countable?| + |unmakeSUP| |exprToGenUPS| |byte| |parent| |binding| |cCoth| + |rowEchelonLocal| |isOp| |PDESolve| |divisors| |nonSingularModel| + |s17agf| |cycleRagits| |concat| |position!| |antiAssociative?| + |genericPosition| |loadNativeModule| |complexNumeric| |dequeue!| + |changeThreshhold| |modTree| |getConstant| |finiteBasis| |reorder| = + |tanSum| |quotient| |leftLcm| |bigEndian| |cond| + |removeRoughlyRedundantFactorsInContents| |palgLODE0| |equation| + |d01ajf| |noValueMode| |presub| |nullary?| |e02baf| |palgRDE0| + |setUnion| |kernels| |mapBivariate| |formfeed| |vspace| + |prepareDecompose| < |insertRoot!| |modularFactor| |cyclicCopy| + |pascalTriangle| |polygamma| |linearForm| |operator| |typeForm| + |e04ucf| |att2Result| |mapMatrixIfCan| |readInt8!| > |perfectNthRoot| + |twist| |leftDivide| |d03edf| |plusInfinity| |extractSplittingLeaf| + |varList| |univariate| |countRealRootsMultiple| |monomials| + |fortranCharacter| |f01maf| |simpsono| <= |freeOf?| |oblateSpheroidal| + |setEpilogue!| |musserTrials| |minusInfinity| |drawToScale| + |chiSquare| |oneDimensionalArray| |minset| |interval| |int| + |characteristicSet| >= |spherical| |zeroVector| |sub| |setPoly| |mix| + |resultantEuclideannaif| |graphImage| |jvmLongConstantTag| |minordet| + |cyclic?| |leftRank| |cycleElt| |quotientByP| |rdHack1| |factor| + |move| |split| |swapRows!| |relerror| |leftExactQuotient| + |attributeData| |forLoop| |leftDiscriminant| |monicLeftDivide| + |divideIfCan!| |sqrt| |rewriteIdealWithQuasiMonicGenerators| |title| + |droot| |nextItem| |OMputEndBind| |youngDiagram| + |fractRadix| + |readUInt8!| |characteristicSerie| |exptMod| |infinite?| |real| + |stoseInvertibleSet| |dimensionOfIrreducibleRepresentation| + |linGenPos| |coerceListOfPairs| - |separateDegrees| |type| + |nextNormalPrimitivePoly| |genericLeftNorm| |mapmult| |coefficient| + |directSum| |imag| |chebyshevT| |clipWithRanges| |quasiComponent| + |tab| / |computeInt| |e| |schwerpunkt| |moebiusMu| |implies| + |viewDefaults| |directProduct| |clearTheSymbolTable| |elRow1!| + |directory| |clearTable!| |cLog| |csubst| |cscIfCan| |mapdiv| |jacobi| + |numberOfHues| |bitTruth| |predicates| |ParCondList| |isNot| |conical| + |e02def| |taylorIfCan| |var1Steps| |safeFloor| |mkPrim| |padecf| + |brace| |commaSeparate| |symbol?| |cosh2sech| |radicalOfLeftTraceForm| + |knownInfBasis| |s19acf| |littleEndian| |insertionSort!| |hexDigit| + |primitivePart!| |arguments| |pomopo!| |plus| |insertMatch| |destruct| + |hasPredicate?| |multiple?| |rootDirectory| |inrootof| |char| + |getOperands| |iitanh| |pseudoQuotient| |numberOfIrreduciblePoly| + |positiveRemainder| |invmod| |numberOfComputedEntries| |sinh2csch| + |someBasis| |satisfy?| |leftRecip| |more?| |rational?| + |basisOfLeftNucloid| |setvalue!| |expint| |bracket| |inHallBasis?| + |rightQuotient| |se2rfi| |removeSquaresIfCan| |external?| |refine| + |derivationCoordinates| |coerceImages| |totalDifferential| + |removeSinhSq| |setTopPredicate| |mkIntegral| + |integralDerivationMatrix| |integralMatrixAtInfinity| + |leftAlternative?| |times| |d03eef| |numFunEvals| |critMonD1| + |stirling2| |harmonic| |Hausdorff| |bipolarCylindrical| |complexSolve| + |gcdcofact| |matrixConcat3D| |squareTop| |fixPredicate| |monomial| + |getGoodPrime| |eof?| |options| |ksec| |froot| |collectUpper| |float| + |subNode?| |e04dgf| |FormatArabic| |components| |multivariate| + |getMeasure| |padicallyExpand| |terms| |prime| |mathieu11| |distdfact| + |sumSquares| |commutativeEquality| |qelt| |iiasin| |Vectorise| + |OMputFloat| |resultantReduit| |variables| |scalarMatrix| |addMatch| + |string| |pushuconst| |iiacsc| |ParCond| |e02bdf| |qsetelt| |cosIfCan| + |shade| |prem| |monom| |domainTemplate| |endSubProgram| |smith| |lp| + |padicFraction| |exprHasWeightCosWXorSinWX| |parametric?| + |eigenvalues| |xRange| |cAsec| |bubbleSort!| |Beta| |cCsch| + |setMaxPoints3D| |setMinPoints| |subtractIfCan| |getButtonValue| + |permutation| |createLowComplexityTable| |yRange| |OMputBVar| + |weakBiRank| |limitPlus| |normFactors| |atoms| |fixedDivisor| + |OMencodingXML| |acscIfCan| F2FG |graphCurves| |subscriptedVariables| + |zRange| |common| |ode2| |vertConcat| |reduceLODE| |mkAnswer| + |moduloP| |exactQuotient| |bytes| |order| |plenaryPower| |s17dlf| + |setLegalFortranSourceExtensions| |map!| |binarySearchTree| + |getMultiplicationMatrix| |compactFraction| |toseInvertible?| |taylor| + |remainder| |transform| |firstNumer| |xn| |opeval| |showRegion| + |tanNa| |qsetelt!| |cartesian| |modifyPointData| |ldf2lst| + |mainSquareFreePart| |laurent| |sinIfCan| |idealiserMatrix| |setrest!| + |linear| |f04asf| |float?| |removeSinSq| |plot| GE |zeroMatrix| + |critBonD| |sequence| |upperCase?| |airyAi| |e02agf| |recur| |OMread| + RF2UTS |cAcsc| GT |incrementKthElement| |pointLists| |s21bdf| + |var2Steps| |primitiveElement| |conjugate| |operation| |polynomial| + |groebnerIdeal| |ignore?| |recolor| |listexp| LE + |basisOfCommutingElements| |newline| |primlimitedint| |sample| + |bright| |cyclicGroup| |exp| |updateStatus!| |level| |mr| |label| + |sincos| |getDatabase| |selectFiniteRoutines| |digamma| LT |zeroOf| + |nextPrime| |BumInSepFFE| |irreducible?| |splitSquarefree| |one?| + |infix| |partialFraction| |quasiRegular| |ode| |acsch| |cCot| + |jvmClassConstantTag| |autoReduced?| |lazyPseudoQuotient| + |interReduce| |functionIsContinuousAtEndPoints| |newTypeLists| + |increase| |eisensteinIrreducible?| |numberOfNormalPoly| + |constantLeft| |s17aef| |LagrangeInterpolation| |resultantEuclidean| + |internalSubQuasiComponent?| |palgint0| |back| |SturmHabichtMultiple| + |root?| |csch2sinh| |e04mbf| |toroidal| |deleteRoutine!| + |getZechTable| |poisson| |lastSubResultant| |lfextlimint| |mapGen| + |factorSquareFreeByRecursion| |nary?| |lowerCase?| |pdct| |powers| + |bumprow| |d01gaf| SEGMENT |roughSubIdeal?| |lyndon| |rightPower| + |noKaratsuba| |dictionary| |computeCycleLength| |hclf| |OMgetEndAttr| + |abs| |setTex!| |internal?| |outputGeneral| |cycleEntry| |super| + |hermiteH| |critB| |rank| |complexZeros| |deepExpand| |basis| + |trivialIdeal?| |null| |s18adf| |checkForZero| |option| |sinhcosh| + |tryFunctionalDecomposition?| |coerceS| |tanhIfCan| + |useSingleFactorBound| |mindeg| |bitLength| |idealSimplify| + |infieldint| |not| |diagonal| |rationalIfCan| |numberOfFactors| + |besselK| |flexibleArray| |Nul| |sPol| |eulerPhi| + |stoseInvertible?sqfreg| |aLinear| |and| |reseed| |ratDsolve| + |mergeDifference| |showArrayValues| |restorePrecision| |prinshINFO| + |extendedResultant| |OMputVariable| |univariatePolynomials| |zoom| + |or| |underscore| |UpTriBddDenomInv| |coordinate| |expandTrigProducts| + |powerSum| |summation| |getOperator| |lowerCase!| |viewPosDefault| + |integralBasis| |xor| |polynomialZeros| |constDsolve| |ldf2vmf| + |f02ajf| |multiEuclidean| |f01brf| |iipow| |insertBottom!| + |unitNormalize| |makeSin| |upDateBranches| |case| |irVar| + |parametersOf| |outputArgs| |defineProperty| |charClass| + |cyclicSubmodule| |reducedContinuedFraction| |df2fi| |doubleDisc| + |asecIfCan| |unit?| |Zero| |extendIfCan| |showSummary| |mergeFactors| + |interpret| |OMreceive| |comp| |cubic| |lists| |extractProperty| + |singleFactorBound| |fillPascalTriangle| |column| |OMputString| + |integer?| |coleman| |subHeight| |One| |palgLODE| |double| + |drawComplex| |edf2efi| |genericRightNorm| |function| |adaptive?| + |quotedOperators| |differentialVariables| |infiniteProduct| + |lazyPseudoDivide| |integralLastSubResultant| |cardinality| + |explicitlyFinite?| |startTableGcd!| |gensym| |curveColorPalette| + |cosSinInfo| |BasicMethod| |concat!| |rationalPoints| + |createNormalPrimitivePoly| |exponential1| |showAttributes| + |addPoint2| |separant| |localIntegralBasis| |setButtonValue| |imagI| + |overlabel| |in?| |arity| |removeSuperfluousCases| |quadraticNorm| + |SturmHabicht| |e01bgf| |cyclotomic| |dualSignature| |Gamma| + |evaluate| |symmetricGroup| |f02abf| |printingInfo?| |OMconnectTCP| + |subSet| |deref| |iteratedInitials| |wreath| |primaryDecomp| |square?| + |meshPar2Var| |ratPoly| |measure2Result| |setFieldInfo| |delete| + |seed| |elt| |hspace| |condition| |style| |identification| + |ScanFloatIgnoreSpaces| |constantOperator| |mathieu24| + |pointSizeDefault| |elColumn2!| |numberOfComposites| |discriminant| + |generalTwoFactor| |safeCeiling| |moduleSum| |factorial| |lazy?| + |basisOfRightNucleus| |doubleResultant| |rangeIsFinite| |adjoint| + |OMconnOutDevice| |declare!| |functionIsOscillatory| |predicate| + |outputBinaryFile| |failed?| |updatF| |discriminantEuclidean| + |symmetricRemainder| |f04maf| |dim| |selectPolynomials| |enumerate| + |colorDef| |space| |OMmakeConn| |OMputSymbol| |radicalSimplify| + |extractClosed| |nextSubsetGray| |const| |bsolve| |exponential| + |close!| |unitVector| |listLoops| |midpoint| |euclideanSize| + |OMgetObject| |fTable| |OMgetApp| |triangularSystems| |chvar| |debug| + |reify| |linearMatrix| |genericRightTraceForm| |iicsc| |printStats!| + |perspective| |OMgetEndBind| |leftFactor| |jvmDoubleConstantTag| D + |cotIfCan| |cAtanh| |symmetricProduct| |lcm| + |semiSubResultantGcdEuclidean1| |sn| |car| |pdf2df| |hasoln| + |makeUnit| |diophantineSystem| |trim| |iomode| + |numberOfImproperPartitions| |environment| |weights| |d02bhf| |f02bjf| + |lighting| |multiEuclideanTree| |finite?| |semiResultantEuclideannaif| + |removeCosSq| |append| |zeroSetSplitIntoTriangularSystems| |f02bbf| + |conditionsForIdempotents| |OMcloseConn| |diagonalProduct| + |viewDeltaYDefault| |cos2sec| |segment| |iiacosh| |jordanAdmissible?| + |rk4| |leftRemainder| |headRemainder| |gcd| |solid?| + |balancedBinaryTree| |transcendent?| |fortranInteger| |closedCurve| + |composite| |minimumDegree| |rootSimp| |generalizedInverse| |decrease| + |false| |preprocess| |qinterval| |sqfrFactor| |pol| |localReal?| + |mapUnivariateIfCan| |parts| |totalLex| |sech2cosh| |weierstrass| + |parameters| |addMatchRestricted| |irreducibleFactors| + |clearTheIFTable| |toseInvertibleSet| |OMclose| |splitDenominator| + |zCoord| |bezoutDiscriminant| |pr2dmp| |goodPoint| |lflimitedint| + |nextPartition| |purelyAlgebraicLeadingMonomial?| |abelianGroup| + |coth2trigh| |expPot| |resetBadValues| |perfectNthPower?| + |setPredicates| |host| |digits| |jordanAlgebra?| |inc| |cSech| + |cfirst| |factorset| |mindegTerm| |checkRur| |nil?| |hdmpToDmp| + |processTemplate| |polygon?| |coefChoose| |ListOfTerms| |size?| + |trigs2explogs| |monicRightFactorIfCan| |sqfree| |expandPower| + |denominator| |resetNew| |rotatey| |rationalPoint?| |corrPoly| + |viewWriteDefault| |print| |sizeMultiplication| |compile| |cycles| + |range| |exprToUPS| |binary| |modularGcdPrimitive| |computePowers| + |moebius| |find| |resolve| |mkcomm| |useEisensteinCriterion| + |bivariatePolynomials| |certainlySubVariety?| |quoted?| |trapezoidal| + |maxPoints| |front| |randomR| |getVariableOrder| + |basisOfRightAnnihilator| |constantCoefficientRicDE| |doubleComplex?| + |subTriSet?| |shape| |getCurve| |exp1| |lookup| + |semiDiscriminantEuclidean| |nullity| |getOrder| |showTheFTable| + |palgextint0| |basisOfLeftNucleus| |localUnquote| |f04arf| |cAsech| + |alternative?| |totolex| |copy!| |split!| |jvmVolatile| |empty| + |printInfo!| |transcendentalDecompose| |sayLength| |RemainderList| + |lhs| |endOfFile?| |indices| |polar| |binomial| |laguerre| + |unvectorise| |lieAlgebra?| |binaryTournament| |lineColorDefault| + |getProperties| |groebgen| |comment| |rhs| |argumentListOf| + |evaluateInverse| |simplifyLog| |modularGcd| |ddFact| + |radicalEigenvectors| |categoryMode| |e01sbf| + |stoseIntegralLastSubResultant| |superHeight| |f07adf| |expIfCan| + |c06gqf| |alternatingGroup| |setMaxPoints| |rational| |isobaric?| + |hessian| |packageCall| |width| |schema| |quoByVar| |e02ahf| |tValues| + |aQuartic| |check| |signAround| |hitherPlane| |primintfldpoly| |bat| + |multiplyExponents| |mapCoef| |cycleLength| |lintgcd| |sumOfDivisors| + |reducedQPowers| |initTable!| |genericLeftDiscriminant| |dihedral| + |nextsubResultant2| |redmat| |mainDefiningPolynomial| |legendre| + |expintfldpoly| |multiset| |viewDeltaXDefault| |headReduced?| |deriv| + |oddlambert| |removeRedundantFactorsInPols| + |primPartElseUnitCanonical!| |yellow| |declare| |macroExpand| + |complementaryBasis| |dominantTerm| |constant?| |curryLeft| + |setProperty| |shift| |rightRemainder| |max| |negative?| |euler| + |initiallyReduced?| |fixedPoint| |OMParseError?| + |semiResultantReduitEuclidean| |swap| |triangSolve| |ramified?| + |isAbsolutelyIrreducible?| |rightRegularRepresentation| |tablePow| + |elaborateFile| |truncate| |e04naf| |optional| |setClipValue| |bat1| + |drawComplexVectorField| |rCoord| |prindINFO| |initial| |shuffle| + |nextPrimitiveNormalPoly| |firstSubsetGray| |eulerE| |subst| + |jokerMode| |imagE| |symbolTable| |updatD| |atom?| + |removeRedundantFactorsInContents| |squareFreePart| |c06fpf| |stFunc1| + |linearlyDependentOverZ?| |hasSolution?| |RittWuCompare| |vedf2vef| + |rightExactQuotient| |maxColIndex| |ramifiedAtInfinity?| |log| + |bottom!| |dimension| |makeop| |lift| |associatedEquations| + |pushFortranOutputStack| |e02aef| |tryFunctionalDecomposition| + |semiDegreeSubResultantEuclidean| |squareMatrix| |OMgetEndObject| + |inspect| |Lazard2| |exprex| |reduce| |minPoly| + |popFortranOutputStack| |makeViewport3D| |numberOfOperations| |degree| + |definingEquations| |jvmAbstract| |cExp| |setEmpty!| + |algebraicDecompose| |rightUnit| |left| |objects| + |completeEchelonBasis| |outputAsFortran| |compBound| + |unitsColorDefault| |norm| |readBytes!| |read!| |possiblyInfinite?| + |trailingCoefficient| |base| |right| |normalizeAtInfinity| |medialSet| + |createPrimitiveElement| |denomRicDE| |fullPartialFraction| + |showAllElements| |goto| |supRittWu?| |userOrdered?| |rootKerSimp| + |HermiteIntegrate| |outputSpacing| |primextendedint| |ptFunc| |cache| + |rightRank| |say| |bivariate?| |tensorProduct| |areEquivalent?| + |close| |Si| |quasiMonicPolynomials| |factorOfDegree| |lfinfieldint| + |triangulate| |halfExtendedResultant2| |fixedPointExquo| |lex| + |maxrow| |nonQsign| |convergents| |usingTable?| |overbar| |algebraic?| + |gcdPolynomial| |graphs| |lexico| |interpolate| |tubeRadiusDefault| + |findConstructor| |display| |decreasePrecision| |e01saf| |s21bbf| + |resultant| |curve?| |repeating| |digit?| |elements| + |computeCycleEntry| |generalizedEigenvectors| |floor| |principalIdeal| + |upperBound| |log2| |fortranTypeOf| |inverseLaplace| |primitivePart| + |iExquo| |nilFactor| |represents| |compiledFunction| |zag| + |quasiRegular?| |generic?| |imaginary| |quote| |difference| |edf2fi| + |character?| |showScalarValues| |determinant| |GospersMethod| + |viewWriteAvailable| |edf2ef| |permutations| |kroneckerDelta| + |setnext!| |showTheSymbolTable| |leftScalarTimes!| |f01qdf| + |stosePrepareSubResAlgo| |c06frf| |SFunction| |power!| + |recoverAfterFail| |extendedEuclidean| |vector| |mirror| |socf2socdf| + |OMputEndBVar| |safetyMargin| |cSec| |variationOfParameters| + |tanh2trigh| |diff| |useEisensteinCriterion?| |symbol| |rk4f| + |differentiate| |rightDiscriminant| |Ei| |tubeRadius| |elRow2!| + |output| |lowerCase| |scale| |partitions| |previous| |currentEnv| + |expression| |logpart| |readIfCan!| |generic| |orbits| + |createThreeSpace| |test| |singularitiesOf| |unravel| + |viewSizeDefault| |iprint| |integer| |rootProduct| |orbit| |component| + |c06gcf| |cTanh| |properties| |f02adf| |remove| |iisinh| |expandLog| + |setValue!| |OMUnknownCD?| |color| |solveLinear| + |stoseLastSubResultant| |outputForm| |complement| |translate| + |monomRDE| |cot2trig| |vconcat| |before?| |polygon| |merge| |entry| + |intersect| |trace2PowMod| |expr| |singularAtInfinity?| |last| + |divide| |KrullNumber| |startPolynomial| |getCode| |symmetricTensors| + |phiCoord| |sum| |compound?| |cCosh| |assoc| + |semiIndiceSubResultantEuclidean| |message| |children| |newSubProgram| + |hypergeometric0F1| |parents| |normalDeriv| |encodingDirectory| + |inverseIntegralMatrixAtInfinity| |errorInfo| |lazyVariations| + |nextColeman| |ocf2ocdf| |fortranLogical| |withPredicates| |leaves| + |pquo| |e01bff| |iiGamma| |stoseInvertible?reg| + |primPartElseUnitCanonical| |algebraicSort| |coercePreimagesImages| + |radicalSolve| |singular?| |keys| |measure| |mat| |isTimes| + |antisymmetricTensors| |toseLastSubResultant| |connect| |returnType!| + |hostByteOrder| |totalGroebner| |variable| |dark| |infinityNorm| + |subResultantChain| |commonDenominator| |pdf2ef| |representationType| + |leftRankPolynomial| |d02ejf| |makeEq| |iterators| |myDegree| |d03faf| + |badNum| |hdmpToP| |polCase| |po| |head| |fortranComplex| + |explogs2trigs| |imagi| |cdr| |cschIfCan| |stronglyReduced?| LODO2FUN + |s17akf| |deleteProperty!| |wholeRadix| |unparse| |constantRight| + |mapUp!| |central?| |pureLex| |uniform| |associator| |outputList| + |clipPointsDefault| |mapSolve| |legendreP| |cyclePartition| |top| + |nextSublist| |lfextendedint| |binaryFunction| |setMinPoints3D| + |iroot| |continue| |cyclicParents| |meshFun2Var| |OMgetError| + |reopen!| |fortranCarriageReturn| |rootSplit| |limitedint| |imports| + |iflist2Result| |setIntersection| |symmetricSquare| |imagk| + |outputAsTex| |crushedSet| |credPol| |bfEntry| |polarCoordinates| + |basisOfCenter| |coerceL| |f07fef| |upperCase!| |s01eaf| + |dihedralGroup| |discreteLog| |augment| |cap| |gradient| |iiabs| + |rules| |rootRadius| |headAst| |mainMonomials| |cAcos| |simplifyPower| + |ideal| |selectMultiDimensionalRoutines| |putColorInfo| |f01bsf| + |generalizedContinuumHypothesisAssumed?| |divideExponents| |contours| + |polyred| |leadingSupport| |connectTo| |support| |tableau| + |makingStats?| |applyRules| |euclideanNormalForm| |prinb| + |prinpolINFO| |iiexp| |palgextint| |status| |leastPower| + |primintegrate| |rootPower| |diagonal?| |radix| |just| |makeFR| + |basicSet| |squareFree| |OMencodingSGML| |mainExpression| |minimize| + |rightAlternative?| |graeffe| |lSpaceBasis| |viewZoomDefault| + |varselect| |factorSFBRlcUnit| |exportedOperators| |tubePoints| + |extractPoint| |branchPoint?| |polyRicDE| |s18def| |power| |sin?| + |maxPoints3D| |purelyAlgebraic?| |s13aaf| |LiePolyIfCan| + |identitySquareMatrix| |any?| |startStats!| |clearTheFTable| |rst| + |submod| |showIntensityFunctions| |rewriteSetWithReduction| + |quickSort| |d02cjf| |aspFilename| |enterPointData| |cons| |e02bef| + |pointColorPalette| |modifyPoint| |bezoutResultant| |writeBytes!| + |ptree| |fractRagits| |alphabetic?| |f02fjf| |OMputEndAttr| |numer| + |normalized?| |uncouplingMatrices| |odd?| |setErrorBound| + |normalizeIfCan| |iicosh| |normal?| |inGroundField?| |printTypes| + |denom| |radicalEigenvalues| |normalElement| |s18dcf| |stronglyReduce| + |kovacic| |resetVariableOrder| |even?| |fortranDoubleComplex| + |idealiser| |chineseRemainder| |screenResolution| |rem| + |repeatUntilLoop| |inR?| |reducedSystem| |c05nbf| |algDsolve| |cAcoth| + |cSin| |e01sff| |pi| |principalAncestors| |resize| |quo| + |approximants| |mainVariables| |doubleFloatFormat| |quartic| + |setleft!| |rectangularMatrix| |maxint| |s20acf| |infinity| |source| + |horizontalTab| |monomRDEsys| |LyndonWordsList| |replaceKthElement| + |physicalLength!| |latex| |charpol| |partialQuotients| + |basisOfCentroid| |c05adf| |realZeros| |create| |div| |rotatez| + |LyndonWordsList1| |ipow| |content| |tube| |rarrow| |primes| + |capacity| |fibonacci| |exquo| |nonLinearPart| |mvar| |palginfieldint| + |completeSmith| |shiftLeft| |coerceP| |elliptic| |kernel| |round| + |target| |clearDenominator| |exprHasAlgebraicWeight| |write!| ~= + |iiasech| |showFortranOutputStack| |evenlambert| |closed| |key?| + |nodeOf?| |curveColor| |lowerPolynomial| |separateFactors| + |loopPoints| |OMreadStr| |list| |duplicates?| |position| |#| + |rightOne| |printCode| |anfactor| + |removeRoughlyRedundantFactorsInPols| |rowEchelon| |infieldIntegrate| + |draw| |invertibleElseSplit?| |bandedHessian| |c02agf| |removeZero| + |Frobenius| ~ |leftUnit| |leftQuotient| |linearPolynomials| + |definingPolynomial| |coerce| |c06eaf| |groebner?| |atrapezoidal| + |OMputAttr| |cyclotomicFactorization| |f02awf| + |semiSubResultantGcdEuclidean2| |uniform01| |mainVariable?| + |componentUpperBound| |construct| |integral| |writeInt8!| |d01aqf| + |rationalPower| |bumptab1| |getGraph| |sort!| |numberOfCycles| |exQuo| + |d01alf| |simpleBounds?| |c06gsf| |f01qef| |f02aff| |shallowExpand| + |screenResolution3D| |/\\| |maxIndex| |s14aaf| |goodnessOfFit| + |isQuotient| |addBadValue| |clipSurface| |makeObject| |complex?| |Is| + |squareFreePolynomial| |update| |sturmVariationsOf| |completeHermite| + |\\/| |pmintegrate| |minPol| |s21baf| |numberOfFractionalTerms| + |secIfCan| |shellSort| |fortranLiteralLine| |cyclicEqual?| |coef| + |internalIntegrate| |symmetric?| |c06ekf| |SturmHabichtSequence| + |intcompBasis| |c06ebf| |trunc| |factorAndSplit| |qPot| + |numberOfDivisors| |insert!| |intensity| |Aleph| |accuracyIF| |pade| + |nthFractionalTerm| |randnum| |formula| |logIfCan| |frst| |baseRDEsys| + |iisin| |leadingCoefficientRicDE| |f04mcf| |wordInStrongGenerators| + |linearDependence| |mightHaveRoots| |initials| |s19adf| |perfectSqrt| + |initiallyReduce| |genus| |showTheIFTable| |clip| |complexExpand| + |OMlistCDs| |height| |setScreenResolution| |s19aaf| |explicitEntries?| + |mantissa| |wordInGenerators| |composites| |romberg| |curve| + |OMgetAtp| |isImplies| |f04jgf| |currentCategoryFrame| |octon| + |llprop| |low| |numberOfChildren| |rightLcm| |maxRowIndex| + |raisePolynomial| |tanintegrate| |ODESolve| |delta| |sec2cos| + |internalDecompose| |complexElementary| |sylvesterMatrix| |qualifier| + |d02gbf| |signatureAst| |bringDown| |rangePascalTriangle| + |meshPar1Var| |OMwrite| |isPower| |backspace| |plotPolar| + |complexLimit| |f01ref| |nsqfree| |viewThetaDefault| |returns| |irDef| + |OMgetBVar| |mathieu22| |deepCopy| |sizeLess?| |createRandomElement| + |bits| |leftGcd| |operators| |jvmTransient| |lieAdmissible?| + |radicalEigenvector| |gethi| |setchildren!| |primeFrobenius| + |algebraicCoefficients?| |setProperties| |changeVar| |UnVectorise| + |removeZeroes| |innerEigenvectors| |addPoint| |wholePart| + |startTable!| |leftUnits| |logGamma| |internalIntegrate0| + |subResultantsChain| |match?| |zeroSquareMatrix| |fortranLinkerArgs| + |exponents| |rightCharacteristicPolynomial| |cCsc| |minrank| |setelt| + |completeHensel| |splitConstant| |f04mbf| |normalizedAssociate| + |ReduceOrder| |set| |OMgetVariable| |isList| |hermite| |ceiling| + |changeMeasure| |bfKeys| |minus!| |tableForDiscreteLogarithm| + |getMultiplicationTable| |c05pbf| |permanent| |antiCommutative?| + |exists?| |lambda| |readLine!| |constantIfCan| |copy| |vectorise| + |expt| |module| |OMconnInDevice| |explimitedint| |c06fuf| + |oddintegers| |diagonals| |scripted?| |qqq| + |selectSumOfSquaresRoutines| |pushucoef| |characteristic| + |univariateSolve| |cot| |normDeriv2| |optpair| |bipolar| |f01mcf| + |s17adf| |box| |sequences| |autoCoerce| |commutative?| |routines| + |buildSyntax| |currentSubProgram| |sec| |realEigenvalues| |sinhIfCan| + |voidMode| |property| |removeIrreducibleRedundantFactors| |coshIfCan| + |OMputError| |e02bcf| |OMgetString| |extensionDegree| |csc| + |unitNormal| |birth| |sup| |univariatePolynomialsGcds| + |printStatement| |s18aef| |dflist| |iicsch| |unknown| |f02aef| + |coHeight| |asin| |linefeed| |OMgetEndAtp| |divisor| + |sumOfKthPowerDivisors| |e02daf| |companionBlocks| |nrows| |real?| + |ord| |pleskenSplit| |changeName| |insertTop!| |acos| |exponent| + |tail| |polyPart| |rdregime| |htrigs| |computeBasis| |ncols| + |alternating| |jvmUTF8ConstantTag| |lazyGintegrate| |Lazard| |retract| + |atan| |s17ahf| |closeComponent| |palgint| |OMencodingBinary| + |writeByte!| |empty?| |HenselLift| ** |bit?| |gcdPrimitive| |nthr| + |acot| |copies| |permutationRepresentation| |numberOfMonomials| |void| + |generalLambert| |heap| |stFuncN| |cot2tan| |top!| + |wordsForStrongGenerators| |stoseInvertibleSetreg| |asec| |e04jaf| + |geometric| |stirling1| |divergence| |coord| |lazyIrreducibleFactors| + |e02bbf| |delete!| |linearAssociatedExp| |monicRightDivide| |acsc| + |functorData| |lepol| |frobenius| |OMserve| |alphanumeric| + |paraboloidal| |magnitude| |byteBuffer| |hasTopPredicate?| |tanAn| + |printInfo| |sinh| |anticoord| |infLex?| |generator| |localAbs| + |lazyPrem| |jvmNameAndTypeConstantTag| |rombergo| |whileLoop| + |reciprocalPolynomial| |testDim| |genericLeftMinimalPolynomial| |cosh| + |shiftRight| |changeWeightLevel| |minimalPolynomial| + |solveLinearPolynomialEquationByRecursion| |complexEigenvalues| + |setPrologue!| |eigenvectors| |sncndn| |torsionIfCan| |mainValue| + |tanh| |e02akf| |minRowIndex| |createZechTable| |outputFixed| + |subResultantGcdEuclidean| |euclideanGroebner| |points| |ranges| + |retractIfCan| |redPol| |flatten| |numberOfComponents| + |halfExtendedSubResultantGcd1| |coth| |getMatch| |laurentIfCan| + |outputFloating| |mainForm| |inverse| |rotate!| |normal01| |maxrank| + |comparison| |complexNormalize| |weight| |sech| |push!| |putGraph| + |binaryTree| |iiacot| |virtualDegree| |var1StepsDefault| + |getPickedPoints| |bindings| |f2df| |ef2edf| |precision| |d01amf| + |csch| |increasePrecision| |c02aff| |solve1| |perfectSquare?| + |primextintfrac| |weighted| |isOpen?| |e02dff| |rk4a| |failed| |asinh| + |OMgetEndBVar| |denominators| |subMatrix| |vark| |leftPower| + |badValues| |numberOfVariables| |error| |lazyResidueClass| |adaptive| + |possiblyNewVariety?| |acosh| |csc2sin| |jvmFinal| |showAll?| + |listOfMonoms| |cycleTail| |setsubMatrix!| |s17dcf| |OMsupportsCD?| + |linearPart| |atanh| |axes| |index?| |reverse!| |leftReducedSystem| + |mathieu23| |setCondition!| |makeSUP| |permutationGroup| |getlo| + |acoth| |expressIdealMember| |factorPolynomial| |setOfMinN| |d01gbf| + |cycle| |unexpand| |iiatanh| |jvmStringConstantTag| |putProperties| + |cylindrical| |expenseOfEvaluation| |asech| |basisOfNucleus| + |systemSizeIF| |incr| |has?| |squareFreePrim| |contractSolve| + |iiasinh| |lquo| |numerators| |s18acf| |trapezoidalo| |cSinh| + |setClosed| |hi| |hMonic| |roughBase?| |prefixRagits| |insert| + |characteristicPolynomial| |multiple| |isEquiv| |outerProduct| + |adaptive3D?| |asinIfCan| |primeFactor| |setVariableOrder| |puiseux| + |generalizedEigenvector| |printHeader| |factorFraction| |iisqrt2| + |applyQuote| |ffactor| |unprotectedRemoveRedundantFactors| + |removeSuperfluousQuasiComponents| |complexIntegrate| |headReduce| + |tracePowMod| |stop| |logical?| |positive?| |whitePoint| |graphStates| + |mainContent| |countRealRoots| |inv| |internalInfRittWu?| + |factorSquareFree| |degreePartition| |thenBranch| |rightMult| |eval| + |partialNumerators| |saturate| |ground?| |OMgetEndError| + |nthRootIfCan| |zero| |extendedIntegrate| |setAdaptive| |f07fdf| + |f2st| |bombieriNorm| |ruleset| |integerIfCan| |create3Space| |iidsum| + |linearAssociatedOrder| |ground| |sortConstraints| |LyndonCoordinates| + |pushup| |integralAtInfinity?| |s17aff| |eigenvector| |build| + |option?| |makeprod| |leadingMonomial| |And| |leastAffineMultiple| + |genericRightTrace| |leftTraceMatrix| |any| |solid| + |pmComplexintegrate| |complexNumericIfCan| |slex| |appendPoint| + |asechIfCan| |leadingCoefficient| |Or| |pair?| + |jvmInterfaceMethodConstantTag| |node?| |suchThat| |fortranLiteral| + |univcase| |realRoots| |s13adf| |primitiveMonomials| |trigs| |OMsend| + |Not| |reindex| |skewSFunction| |jvmIntegerConstantTag| |unary?| + |conjugates| |factorList| |s17acf| |reductum| |cothIfCan| + |gramschmidt| |contains?| |iiacos| |collectQuasiMonic| + |leviCivitaSymbol| |s14abf| |leadingIdeal| |s20adf| |duplicates| + |e01baf| |identity| |reduction| |normInvertible?| |paren| |acoshIfCan| + F |leftExtendedGcd| |cycleSplit!| |leftMinimalPolynomial| |nthCoef| + |f02akf| |iicoth| |recip| |generate| |firstDenom| |rroot| + |indicialEquations| |pointColorDefault| |setLabelValue| |addmod| + |monomialIntegrate| |createGenericMatrix| |matrix| |surface| + |lazyPremWithDefault| |bumptab| |atanhIfCan| |mdeg| |cAcosh| + |argument| |zeroDimensional?| |rightExtendedGcd| |besselI| |open| + |incrementBy| |selectAndPolynomials| |shallowCopy| |factors| + |semiLastSubResultantEuclidean| |selectPDERoutines| |makeYoungTableau| + |rightMinimalPolynomial| |bothWays| |expand| |unaryFunction| + |pseudoRemainder| |enqueue!| |subResultantGcd| |invertIfCan| |select| + |lexGroebner| |redpps| |makeSeries| |distFact| |nil| |filterWhile| + |d01apf| |twoFactor| |supersub| |integrate| |nand| |fortran| |setref| + |orthonormalBasis| |minGbasis| |OMgetType| |filterUntil| |copyInto!| + |rationalApproximation| |setAdaptive3D| |univariate?| |setImagSteps| + |newLine| |dimensions| |elem?| |linearlyDependent?| |operations| + |limitedIntegrate| |traverse| |createNormalElement| + |symmetricDifference| |crest| |iisec| |createMultiplicationTable| + |consnewpol| |f02xef| |tree| |pointData| |approximate| |dom| |iitan| + |cyclicEntries| |table| |readByte!| |lastSubResultantEuclidean| + |degreeSubResultant| |f04atf| |OMsupportsSymbol?| + |rewriteIdealWithHeadRemainder| |lowerBound| |complex| |bernoulliB| + |obj| |rightNorm| |mapExpon| |new| |identityMatrix| |roughUnitIdeal?| + |shufflein| |unit| |solveLinearPolynomialEquation| + |integralRepresents| |curry| |conjug| |s17def| |patternVariable| + |resetAttributeButtons| |setStatus| |dequeue| |makeRecord| + |flagFactor| |erf| |numFunEvals3D| |elliptic?| |jvmPublic| + |definingInequation| |op| |doubleRank| |deepestTail| |interactiveEnv| + |mesh| |stiffnessAndStabilityOfODEIF| |ScanRoman| |integers| |merge!| + |lazyPquo| |clearCache| |disjunction| |f02agf| |supDimElseRittWu?| + |univariatePolynomial| |interpretString| |unrankImproperPartitions1| + |dfRange| |e02ddf| |dot| |length| |slash| |rightTrim| |symbolTableOf| + |zeroSetSplit| |d02bbf| |halfExtendedResultant1| |viewpoint| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index b8da2257..fade5200 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5471 +1,5471 @@ -(3473054 . 3507854482) -((-1415 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-3150 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-2705 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1264 (-560)) |#2|) 44 T ELT)) (-2313 (($ $) 80 T ELT)) (-3941 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3353 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-1861 (((-663 |#2|) $) 13 T ELT)) (-4091 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-1445 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3654 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-1736 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3568 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-3554 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-1481 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-560)) NIL T ELT) (($ $ (-1264 (-560))) 66 T ELT)) (-3539 (($ $ (-560)) 76 T ELT) (($ $ (-1264 (-560))) 75 T ELT)) (-3309 (((-793) (-1 (-114) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-2829 (($ $ $ (-560)) 69 T ELT)) (-2728 (($ $) 68 T ELT)) (-2505 (($ (-663 |#2|)) 73 T ELT)) (-4326 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-663 $)) 85 T ELT)) (-2489 (((-887) $) 92 T ELT)) (-3504 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-2416 (((-114) $ $) 95 T ELT)) (-2442 (((-114) $ $) 99 T ELT))) -(((-18 |#1| |#2|) (-10 -8 (-15 -2416 ((-114) |#1| |#1|)) (-15 -2489 ((-887) |#1|)) (-15 -2442 ((-114) |#1| |#1|)) (-15 -3150 (|#1| |#1|)) (-15 -3150 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -2313 (|#1| |#1|)) (-15 -2829 (|#1| |#1| |#1| (-560))) (-15 -1415 ((-114) |#1|)) (-15 -4091 (|#1| |#1| |#1|)) (-15 -3353 ((-560) |#2| |#1| (-560))) (-15 -3353 ((-560) |#2| |#1|)) (-15 -3353 ((-560) (-1 (-114) |#2|) |#1|)) (-15 -1415 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -4091 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -2705 (|#2| |#1| (-1264 (-560)) |#2|)) (-15 -1736 (|#1| |#1| |#1| (-560))) (-15 -1736 (|#1| |#2| |#1| (-560))) (-15 -3539 (|#1| |#1| (-1264 (-560)))) (-15 -3539 (|#1| |#1| (-560))) (-15 -3654 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4326 (|#1| (-663 |#1|))) (-15 -4326 (|#1| |#1| |#1|)) (-15 -4326 (|#1| |#2| |#1|)) (-15 -4326 (|#1| |#1| |#2|)) (-15 -1481 (|#1| |#1| (-1264 (-560)))) (-15 -2505 (|#1| (-663 |#2|))) (-15 -3568 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -3941 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3941 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3941 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -1481 (|#2| |#1| (-560))) (-15 -1481 (|#2| |#1| (-560) |#2|)) (-15 -2705 (|#2| |#1| (-560) |#2|)) (-15 -3309 ((-793) |#2| |#1|)) (-15 -1861 ((-663 |#2|) |#1|)) (-15 -3309 ((-793) (-1 (-114) |#2|) |#1|)) (-15 -3554 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -3504 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -1445 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3654 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2728 (|#1| |#1|))) (-19 |#2|) (-1247)) (T -18)) +(3473054 . 3508426648) +((-2161 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-3800 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3947 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1264 (-560)) |#2|) 44 T ELT)) (-4192 (($ $) 80 T ELT)) (-3291 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3763 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-3058 (((-663 |#2|) $) 13 T ELT)) (-3462 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2658 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-1782 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-4229 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3118 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-1575 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-2938 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-560)) NIL T ELT) (($ $ (-1264 (-560))) 66 T ELT)) (-2936 (($ $ (-560)) 76 T ELT) (($ $ (-1264 (-560))) 75 T ELT)) (-1490 (((-793) (-1 (-114) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-4402 (($ $ $ (-560)) 69 T ELT)) (-3970 (($ $) 68 T ELT)) (-3793 (($ (-663 |#2|)) 73 T ELT)) (-2350 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-663 $)) 85 T ELT)) (-3782 (((-887) $) 92 T ELT)) (-3646 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-2362 (((-114) $ $) 95 T ELT)) (-2383 (((-114) $ $) 99 T ELT))) +(((-18 |#1| |#2|) (-10 -8 (-15 -2362 ((-114) |#1| |#1|)) (-15 -3782 ((-887) |#1|)) (-15 -2383 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T) ((-107 #0=(-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T) ((-102) -2229 (|has| |#2| (-1132)) (|has| |#2| (-102)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-1132)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-871)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-102))) ((-632 (-887)) -2229 (|has| |#2| (-1132)) (|has| |#2| (-632 (-887))) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-1132)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-871)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-632 (-887)))) ((-153 #1=(-2 (|:| -3865 |#1|) (|:| -1689 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1264 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . T) ((-321 #1#) -12 (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-321 (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)))) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-1132))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-294 #1#) . T) ((-385 #1#) . T) ((-503 #1#) . T) ((-503 |#2|) . T) ((-618 #2# #1#) . T) ((-618 |#1| |#2|) . T) ((-528 #1# #1#) -12 (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-321 (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)))) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-1132))) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-629 |#1| |#2|) . T) ((-673 #1#) . T) ((-688 #1#) . T) ((-871) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-871)) ((-874) |has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-871)) ((-1041 #1#) . T) ((-1132) -2229 (|has| |#2| (-1132)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-1132)) (|has| (-2 (|:| -3865 |#1|) (|:| -1689 |#2|)) (-871))) ((-1180 #1#) . T) ((-1224 |#1| |#2|) . T) ((-1247) . T) ((-1286 #1#) . 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T) ((-107 #0=(-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T) ((-102) -2219 (|has| |#2| (-1132)) (|has| |#2| (-102)) (|has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-1132)) (|has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-871)) (|has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-102))) ((-632 (-887)) -2219 (|has| |#2| (-1132)) (|has| |#2| (-632 (-887))) (|has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-1132)) (|has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-871)) (|has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-632 (-887)))) ((-153 #1=(-2 (|:| -1885 |#1|) (|:| -3463 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -1885 |#1|) (|:| -3463 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1264 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2229 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1233)) ((-95) |has| |#1| (-1233)) ((-102) . T) ((-111 #0# #0#) -2229 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2229 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2229 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-887)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1051)) ((-633 (-171 (-391))) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-633 #1=(-1201 |#1|)) . 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T) ((-921 $ #3=(-1207)) -2229 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #3#) -2229 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) |has| |#1| (-911 (-391))) ((-911 (-560)) |has| |#1| (-911 (-560))) ((-909 |#1|) . T) ((-939) -12 (|has| |#1| (-319)) (|has| |#1| (-939))) ((-950) -2229 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1033) -12 (|has| |#1| (-1033)) (|has| |#1| (-1233))) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1082 #0#) -2229 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) -2229 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-363)) ((-1233) |has| |#1| (-1233)) ((-1236) |has| |#1| (-1233)) ((-1247) . 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T) ((-236 $) -2229 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2229 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . 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T) ((-102) -2219 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2219 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2219 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-635 (-560)) -2219 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132)))) ((-635 |#2|) |has| |#2| (-1132)) ((-632 (-887)) -2219 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-887))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1297 |#2|)) . T) ((-236 $) -2219 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2219 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-668 (-560)) -2219 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2219 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-670 |#2|) -2219 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2219 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2219 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-871) -2219 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2219 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2219 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-927 (-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) ((-929 #3#) -2219 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-1069 (-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ((-1069 |#2|) |has| |#2| (-1132)) ((-1082 |#2|) -2219 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2219 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1088) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1132) -2219 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1247) . T) ((-1305 |#2|) |has| |#2| (-376))) +((-3749 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-2143 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-2983 (($ (-948)) 62 (|has| |#2| (-1080)) ELT)) (-1459 (((-1303) $ (-560) (-560)) NIL (|has| $ (-6 -4509)) ELT)) (-4012 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-2629 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-3097 (((-114) $ (-793)) NIL T ELT)) (-2155 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-3947 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4509)) ELT)) (-2713 (($) NIL T CONST)) (-4126 (((-3 (-560) "failed") $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-3 (-421 (-560)) "failed") $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1132)) ELT)) (-4046 (((-560) $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) ((|#2| $) 28 (|has| |#2| (-1132)) ELT)) 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2229 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . 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T) ((-571) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2229 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2229 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1247) . T) ((-1252) |has| |#1| (-939))) -((-2372 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-2446 ((|#1| $) 61 T ELT)) (-1802 ((|#1| $) 51 T ELT)) (-3855 (((-114) $ (-793)) 8 T ELT)) (-1799 (($) 7 T CONST)) (-2260 (($ $) 67 T ELT)) (-2313 (($ $) 55 T ELT)) (-4219 ((|#1| |#1| $) 53 T ELT)) (-3095 ((|#1| $) 52 T ELT)) (-1861 (((-663 |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-1788 (((-114) $ (-793)) 9 T ELT)) (-3284 (((-663 |#1|) $) 32 (|has| $ (-6 -4508)) ELT)) (-4143 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-1445 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4509)) ELT)) (-3654 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-4146 (((-114) $ (-793)) 10 T ELT)) (-3065 (((-793) $) 68 T ELT)) (-3409 (((-1189) $) 25 (|has| |#1| (-1132)) ELT)) (-3980 ((|#1| $) 46 T ELT)) (-3673 ((|#1| |#1| $) 59 T ELT)) (-3560 ((|#1| |#1| $) 58 T ELT)) (-3438 (($ |#1| $) 47 T ELT)) (-3958 (((-793) $) 62 T ELT)) (-3300 (((-1151) $) 24 (|has| |#1| (-1132)) ELT)) (-3458 ((|#1| $) 69 T ELT)) (-1944 ((|#1| $) 57 T ELT)) (-1579 ((|#1| $) 56 T ELT)) (-2817 ((|#1| $) 48 T ELT)) (-3554 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4508)) ELT)) (-2954 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-3792 (((-114) $ $) 14 T ELT)) (-3387 ((|#1| |#1| $) 65 T ELT)) (-2626 (((-114) $) 11 T ELT)) (-1457 (($) 12 T ELT)) (-2301 ((|#1| $) 66 T ELT)) (-4239 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-3352 (((-793) $) 50 T ELT)) (-3309 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2728 (($ $) 13 T ELT)) (-2489 (((-887) $) 20 (|has| |#1| (-632 (-887))) ELT)) (-3514 ((|#1| $) 60 T ELT)) (-4015 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-1466 (($ (-663 |#1|)) 49 T ELT)) (-4487 ((|#1| $) 70 T ELT)) (-3504 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4508)) ELT)) (-2416 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2387 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) +((-1378 (*1 *2 *3) (-12 (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-2890 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 *4)))) (-2654 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2654 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3296 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3018 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-4142 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3018 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-4142 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3187 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-114)))) (-1692 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-815)) (-4 *2 (-277 *4)))) (-3254 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-2907 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-1378 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-979 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1069 |t#2|) (-10 -8 (-15 -1378 ((-1 $ (-793)) |t#2|)) (-15 -2890 ((-663 |t#2|) $)) (-15 -2654 ((-793) $ |t#2|)) (-15 -2654 ((-793) $)) (-15 -3296 ((-793) $ |t#2|)) (-15 -3018 ((-663 (-793)) $)) (-15 -4142 ((-793) $)) (-15 -3018 ((-663 (-793)) $ |t#2|)) (-15 -4142 ((-793) $ |t#2|)) (-15 -3187 ((-114) $)) (-15 -1692 (|t#3| $)) (-15 -3254 ($ $)) (-15 -2907 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -1378 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2219 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . T) ((-175) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-633 (-915 (-391)))) (|has| |#3| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-633 (-915 (-560)))) (|has| |#3| (-633 (-915 (-560))))) ((-236 $) -2219 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2219 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2219 (|has| |#1| (-939)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2219 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2219 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1247) . T) ((-1252) |has| |#1| (-939))) +((-3749 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-4068 ((|#1| $) 61 T ELT)) (-3554 ((|#1| $) 51 T ELT)) (-3097 (((-114) $ (-793)) 8 T ELT)) (-2713 (($) 7 T CONST)) (-4137 (($ $) 67 T ELT)) (-4192 (($ $) 55 T ELT)) (-4144 ((|#1| |#1| $) 53 T ELT)) (-2041 ((|#1| $) 52 T ELT)) (-3058 (((-663 |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-2541 (((-114) $ (-793)) 9 T ELT)) (-2116 (((-663 |#1|) $) 32 (|has| $ (-6 -4508)) ELT)) (-2323 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2658 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4509)) ELT)) (-1782 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-1332 (((-114) $ (-793)) 10 T ELT)) (-4481 (((-793) $) 68 T ELT)) (-3718 (((-1189) $) 25 (|has| |#1| (-1132)) ELT)) (-3288 ((|#1| $) 46 T ELT)) (-4033 ((|#1| |#1| $) 59 T ELT)) (-2848 ((|#1| |#1| $) 58 T ELT)) (-3844 (($ |#1| $) 47 T ELT)) (-3870 (((-793) $) 62 T ELT)) (-1478 (((-1151) $) 24 (|has| |#1| (-1132)) ELT)) (-3127 ((|#1| $) 69 T ELT)) (-1790 ((|#1| $) 57 T ELT)) (-1773 ((|#1| $) 56 T ELT)) (-1735 ((|#1| $) 48 T ELT)) (-1575 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4508)) ELT)) (-4263 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-2315 (((-114) $ $) 14 T ELT)) (-4381 ((|#1| |#1| $) 65 T ELT)) (-4053 (((-114) $) 11 T ELT)) (-3152 (($) 12 T ELT)) (-2356 ((|#1| $) 66 T ELT)) (-4453 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-1643 (((-793) $) 50 T ELT)) (-1490 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-3970 (($ $) 13 T ELT)) (-3782 (((-887) $) 20 (|has| |#1| (-632 (-887))) ELT)) (-3277 ((|#1| $) 60 T ELT)) (-3460 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-1523 (($ (-663 |#1|)) 49 T ELT)) (-2753 ((|#1| $) 70 T ELT)) (-3646 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4508)) ELT)) (-2362 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-3764 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) (((-263 |#1|) (-142) (-1247)) (T -263)) -((-4239 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-4239 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1247)) (-4 *1 (-263 *3)))) (-3958 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1247)) (-5 *2 (-793)))) (-2446 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3514 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3673 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3560 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1944 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1579 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-2313 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247))))) -(-13 (-1152 |t#1|) (-1026 |t#1|) (-10 -8 (-15 -4239 ($)) (-15 -4239 ($ (-663 |t#1|))) (-15 -3958 ((-793) $)) (-15 -2446 (|t#1| $)) (-15 -3514 (|t#1| $)) (-15 -3673 (|t#1| |t#1| $)) (-15 -3560 (|t#1| |t#1| $)) (-15 -1944 (|t#1| $)) (-15 -1579 (|t#1| $)) (-15 -2313 ($ $)))) -(((-34) . 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|lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -3438 ($ (-2 (|:| -3865 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2098 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -1689 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2098 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| 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|notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3112 (-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 (-574)))) (-2988 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -1885 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -3112 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -3463 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity 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T) ((-466) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-571) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 #0#) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -2219 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-748) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-560))))) ((-236 $) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2229 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-560)))) ((-909 |#2|) |has| |#1| (-376)) ((-939) -12 (|has| |#1| (-376)) (|has| |#2| (-939))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) -12 (|has| |#1| (-376)) (|has| |#2| (-1182))) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1259 |#1|) . T) ((-1276 |#1| #0#) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2219 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2219 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2219 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2219 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2219 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-560)))) ((-909 |#2|) |has| |#1| (-376)) ((-939) -12 (|has| |#1| (-376)) (|has| |#2| (-939))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) -12 (|has| |#1| (-376)) (|has| |#2| (-1182))) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1259 |#1|) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2229 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2229 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2229 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2229 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) -12 (|has| (-1113) (-911 (-391))) (|has| |#1| (-911 (-391)))) ((-911 (-560)) -12 (|has| (-1113) (-911 (-560))) (|has| |#1| (-911 (-560)))) ((-979 |#1| #0# #2#) . T) ((-939) |has| |#1| (-939)) ((-950) |has| |#1| (-376)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2229 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2219 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2219 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2219 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2219 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) -12 (|has| (-1113) (-911 (-391))) (|has| |#1| (-911 (-391)))) ((-911 (-560)) -12 (|has| (-1113) (-911 (-560))) (|has| |#1| (-911 (-560)))) ((-979 |#1| #0# #2#) . T) ((-939) |has| |#1| (-939)) ((-950) |has| |#1| (-376)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2219 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . 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T) ((-662 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1069 |#2|) . T) ((-1082 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2229 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1276 |#1| #0#) . T) ((-1280 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2219 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 $ $) |has| (-421 (-560)) (-1143)) ((-302) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-376) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-571) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1069 |#2|) . T) ((-1082 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2219 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2219 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1276 |#1| #0#) . T) ((-1280 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2229 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2229 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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T) ((-1082 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2229 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2219 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2219 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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NIL NIL) (-1224 3109152 3115918 3115974 "TBAGG" 3116374 NIL TBAGG (NIL T T) -9 NIL 3116585 NIL) (-1223 3104036 3105710 3107464 "TBAGG-" 3107469 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103402 3103527 3103672 "TANEXP" 3103925 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102853 3103177 3103267 "TALGOP" 3103347 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3102247 3102364 3102502 "TABLEAU" 3102750 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095261 3102104 3102197 "TABLE" 3102202 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089791 3091089 3092337 "TABLBUMP" 3094047 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3089001 3089160 3089341 "SYSTEM" 3089632 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085406 3086159 3086942 "SYSSOLP" 3088252 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3085168 3085361 3085392 "SYSPTR" 3085397 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3084007 3084699 3084825 "SYSNNI" 3085011 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085103) (-1213 3083214 3083769 3083848 "SYSINT" 3083908 NIL SYSINT (NIL NIL) -8 NIL NIL 3083953) (-1212 3079312 3080492 3081202 "SYNTAX" 3082526 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076392 3077072 3077704 "SYMTAB" 3078702 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071491 3072543 3073526 "SYMS" 3075431 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068390 3070942 3071175 "SYMPOLY" 3071293 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067895 3067982 3068105 "SYMFUNC" 3068302 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063693 3065207 3066020 "SYMBOL" 3067104 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3057166 3058921 3060641 "SWITCH" 3061995 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049920 3056122 3056416 "SUTS" 3056930 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041398 3049302 3049566 "SUPXS" 3049714 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040545 3040684 3040901 "SUPFRACF" 3041266 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3040160 3040225 3040338 "SUP2" 3040480 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030683 3039778 3039904 "SUP" 3040069 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3029107 3029405 3029761 "SUMRF" 3030382 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028430 3028508 3028700 "SUMFS" 3029028 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010275 3027742 3027984 "SULS" 3028246 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009823 3010097 3010167 "SUCHTAST" 3010227 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3009064 3009348 3009488 "SUCH" 3009731 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002703 3003970 3004929 "SUBSPACE" 3008152 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3002123 3002223 3002387 "SUBRESP" 3002591 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2996134 2997416 2998563 "STTFNC" 3001023 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989328 2990799 2992110 "STTF" 2994870 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980445 2982510 2984304 "STTAYLOR" 2987569 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2973199 2980309 2980392 "STRTBL" 2980397 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967596 2972908 2973007 "STRING" 2973122 T STRING (NIL) -8 NIL NIL NIL) (-1188 2967100 2967183 2967327 "STREAM3" 2967513 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2966064 2966265 2966500 "STREAM2" 2966913 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965746 2965804 2965897 "STREAM1" 2966006 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957860 2963365 2963976 "STREAM" 2965170 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956852 2957057 2957288 "STINPROD" 2957676 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955967 2956341 2956489 "STEPAST" 2956726 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955463 2955715 2955745 "STEP" 2955825 T STEP (NIL) -9 NIL 2955903 NIL) (-1181 2948519 2955362 2955439 "STBL" 2955444 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2943069 2947682 2947725 "STAGG" 2947878 NIL STAGG (NIL T) -9 NIL 2947967 NIL) (-1179 2940621 2941373 2942245 "STAGG-" 2942250 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938593 2940391 2940483 "STACK" 2940564 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930600 2936734 2937190 "SREGSET" 2938223 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922947 2924394 2925907 "SRDCMPK" 2929206 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915247 2920306 2920336 "SRAGG" 2921639 T SRAGG (NIL) -9 NIL 2922247 NIL) (-1174 2914198 2914519 2914898 "SRAGG-" 2914903 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907782 2913145 2913566 "SQMATRIX" 2913824 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2901194 2904500 2905227 "SPLTREE" 2907127 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2897019 2897850 2898496 "SPLNODE" 2900620 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895994 2896299 2896329 "SPFCAT" 2896773 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894689 2894941 2895205 "SPECOUT" 2895752 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885335 2887653 2887683 "SPADXPT" 2892361 T SPADXPT (NIL) -9 NIL 2894527 NIL) (-1167 2885090 2885136 2885205 "SPADPRSR" 2885288 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882693 2885045 2885076 "SPADAST" 2885081 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874294 2876397 2876440 "SPACEC" 2880813 NIL SPACEC (NIL T) -9 NIL 2882629 NIL) (-1164 2872094 2874226 2874275 "SPACE3" 2874280 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870826 2871017 2871308 "SORTPAK" 2871899 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868888 2869221 2869633 "SOLVETRA" 2870490 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867926 2868160 2868421 "SOLVESER" 2868661 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2863158 2864118 2865113 "SOLVERAD" 2866978 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858883 2859582 2860311 "SOLVEFOR" 2862525 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852487 2858231 2858328 "SNTSCAT" 2858333 NIL SNTSCAT (NIL T T T T) -9 NIL 2858403 NIL) (-1157 2846031 2850810 2851201 "SMTS" 2852177 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839746 2845919 2845996 "SMP" 2846001 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837875 2838206 2838604 "SMITH" 2839443 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829400 2834454 2834557 "SMATCAT" 2835908 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836458 NIL) (-1153 2826172 2827163 2828341 "SMATCAT-" 2828346 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823641 2825380 2825423 "SKAGG" 2825684 NIL SKAGG (NIL T) -9 NIL 2825819 NIL) (-1151 2819131 2823110 2823294 "SINT" 2823446 T SINT (NIL) -8 NIL NIL 2823608) (-1150 2818897 2818941 2819007 "SIMPAN" 2819087 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817717 2817956 2818231 "SIGNRF" 2818656 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816532 2816701 2816985 "SIGNEF" 2817546 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815772 2816115 2816239 "SIGAST" 2816430 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814997 2815307 2815447 "SIG" 2815654 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812649 2813141 2813647 "SHP" 2814538 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2806022 2812550 2812626 "SHDP" 2812631 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805533 2805773 2805803 "SGROUP" 2805896 T SGROUP (NIL) -9 NIL 2805958 NIL) (-1142 2805385 2805417 2805490 "SGROUP-" 2805495 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2802104 2802874 2803597 "SGCF" 2804684 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795806 2801550 2801647 "SFRTCAT" 2801652 NIL SFRTCAT (NIL T T T T) -9 NIL 2801691 NIL) (-1139 2789125 2790245 2791381 "SFRGCD" 2794789 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2782143 2783324 2784510 "SFQCMPK" 2788058 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781745 2781852 2781963 "SFORT" 2782084 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780671 2781585 2781706 "SEXOF" 2781711 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776260 2777167 2777262 "SEXCAT" 2779884 NIL SEXCAT (NIL T T T T T) -9 NIL 2780444 NIL) (-1134 2775175 2776141 2776209 "SEX" 2776214 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773297 2773888 2774193 "SETMN" 2774916 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772827 2773015 2773045 "SETCAT" 2773162 T SETCAT (NIL) -9 NIL 2773247 NIL) (-1131 2772595 2772659 2772758 "SETCAT-" 2772763 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768698 2771056 2771099 "SETAGG" 2771969 NIL SETAGG (NIL T) -9 NIL 2772309 NIL) (-1129 2768120 2768272 2768509 "SETAGG-" 2768514 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764929 2768054 2768102 "SET" 2768107 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764312 2764625 2764726 "SEQAST" 2764850 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763439 2763805 2763866 "SEGXCAT" 2764152 NIL SEGXCAT (NIL T T) -9 NIL 2764272 NIL) (-1125 2762364 2762632 2762675 "SEGCAT" 2763197 NIL SEGCAT (NIL T) -9 NIL 2763418 NIL) (-1124 2761979 2762044 2762157 "SEGBIND2" 2762299 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760869 2761342 2761550 "SEGBIND" 2761806 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760388 2760670 2760747 "SEGAST" 2760814 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759597 2759733 2759937 "SEG2" 2760232 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758513 2759263 2759445 "SEG" 2759450 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757746 2758448 2758495 "SDVAR" 2758500 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2749097 2757516 2757646 "SDPOL" 2757651 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747666 2747956 2748275 "SCPKG" 2748812 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746788 2747002 2747194 "SCOPE" 2747496 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745984 2746142 2746321 "SCACHE" 2746643 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745568 2745802 2745832 "SASTCAT" 2745837 T SASTCAT (NIL) -9 NIL 2745850 NIL) (-1113 2744971 2745403 2745479 "SAOS" 2745514 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744530 2744571 2744744 "SAERFFC" 2744930 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2744117 2744158 2744317 "SAEFACT" 2744489 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2737144 2744014 2744094 "SAE" 2744099 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735447 2735779 2736180 "RURPK" 2736810 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2734024 2734390 2734695 "RULESET" 2735281 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733594 2733818 2733901 "RULECOLD" 2733976 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730709 2731347 2731805 "RULE" 2733275 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730493 2730527 2730598 "RTVALUE" 2730660 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729904 2730210 2730304 "RSTRCAST" 2730421 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724674 2725547 2726467 "RSETGCD" 2729103 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713238 2718982 2719079 "RSETCAT" 2723198 NIL RSETCAT (NIL T T T T) -9 NIL 2724295 NIL) (-1101 2711057 2711704 2712528 "RSETCAT-" 2712533 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703365 2704819 2706339 "RSDCMPK" 2709656 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701234 2701797 2701871 "RRCC" 2702957 NIL RRCC (NIL T T) -9 NIL 2703301 NIL) (-1098 2700555 2700759 2701038 "RRCC-" 2701043 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699938 2700251 2700352 "RPTAST" 2700476 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672317 2683050 2683117 "RPOLCAT" 2693783 NIL RPOLCAT (NIL T T T) -9 NIL 2696943 NIL) (-1095 2663287 2666155 2669277 "RPOLCAT-" 2669282 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653740 2661498 2661980 "ROUTINE" 2662827 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649789 2653366 2653506 "ROMAN" 2653622 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647901 2648649 2648909 "ROIRC" 2649594 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643614 2646390 2646420 "RNS" 2646724 T RNS (NIL) -9 NIL 2646998 NIL) (-1090 2642021 2642506 2643040 "RNS-" 2643115 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640982 2641386 2641588 "RNGBIND" 2641872 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640275 2640779 2640809 "RNG" 2640814 T RNG (NIL) -9 NIL 2640835 NIL) (-1087 2639570 2640048 2640091 "RMODULE" 2640096 NIL RMODULE (NIL T) -9 NIL 2640123 NIL) (-1086 2638394 2638500 2638836 "RMCAT2" 2639471 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634896 2637740 2638037 "RMATRIX" 2638156 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627395 2629983 2630098 "RMATCAT" 2633457 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634439 NIL) (-1083 2626734 2626917 2627224 "RMATCAT-" 2627229 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626307 2626521 2626564 "RLINSET" 2626626 NIL RLINSET (NIL T) -9 NIL 2626670 NIL) (-1081 2625868 2625949 2626077 "RINTERP" 2626226 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624792 2625466 2625496 "RING" 2625552 T RING (NIL) -9 NIL 2625644 NIL) (-1079 2624572 2624628 2624725 "RING-" 2624730 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623383 2623650 2623908 "RIDIST" 2624336 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2614008 2622851 2623057 "RGCHAIN" 2623231 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613266 2613750 2613791 "RGBCSPC" 2613849 NIL RGBCSPC (NIL T) -9 NIL 2613901 NIL) (-1075 2612332 2612791 2612832 "RGBCMDL" 2613064 NIL RGBCMDL (NIL T) -9 NIL 2613178 NIL) (-1074 2611972 2612041 2612144 "RFFACTOR" 2612263 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611691 2611732 2611829 "RFFACT" 2611931 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609742 2610172 2610554 "RFDIST" 2611331 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606682 2607350 2608020 "RF" 2609106 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2606129 2606227 2606390 "RETSOL" 2606584 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605747 2605845 2605888 "RETRACT" 2606021 NIL RETRACT (NIL T) -9 NIL 2606108 NIL) (-1068 2605590 2605621 2605708 "RETRACT-" 2605713 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2605138 2605412 2605482 "RETAST" 2605542 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597488 2604791 2604918 "RESULT" 2605033 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595923 2596757 2596956 "RESRING" 2597391 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595547 2595608 2595706 "RESLATC" 2595860 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595246 2595287 2595394 "REPSQ" 2595506 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594937 2594978 2595089 "REPDB" 2595205 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588769 2590226 2591449 "REP2" 2593749 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2585072 2585827 2586635 "REP1" 2587996 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582452 2583074 2583676 "REP" 2584492 T REP (NIL) -7 NIL NIL NIL) (-1058 2574460 2580593 2581049 "REGSET" 2582082 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2573169 2573608 2573858 "REF" 2574245 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572534 2572649 2572816 "REDORDER" 2573053 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567898 2571747 2571974 "RECLOS" 2572362 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566932 2567131 2567346 "REALSOLV" 2567705 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563379 2564217 2565101 "REAL0Q" 2566097 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558932 2559968 2561029 "REAL0" 2562360 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558766 2558819 2558849 "REAL" 2558854 T REAL (NIL) -9 NIL 2558889 NIL) (-1050 2558177 2558483 2558577 "RDUCEAST" 2558694 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557576 2557654 2557861 "RDIV" 2558099 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556626 2556818 2557031 "RDIST" 2557398 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555211 2555510 2555882 "RDETRS" 2556334 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2553005 2553477 2554015 "RDETR" 2554753 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551624 2551908 2552305 "RDEEFS" 2552721 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2550127 2550439 2550864 "RDEEF" 2551312 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543599 2547081 2547111 "RCFIELD" 2548406 T RCFIELD (NIL) -9 NIL 2549137 NIL) (-1042 2541555 2542167 2542863 "RCFIELD-" 2542938 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537607 2539628 2539671 "RCAGG" 2540755 NIL RCAGG (NIL T) -9 NIL 2541220 NIL) (-1040 2537217 2537329 2537492 "RCAGG-" 2537497 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536534 2536664 2536829 "RATRET" 2537101 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2536075 2536154 2536275 "RATFACT" 2536462 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535353 2535503 2535655 "RANDSRC" 2535945 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2535081 2535131 2535204 "RADUTIL" 2535302 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527205 2533912 2534223 "RADIX" 2534804 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516799 2527047 2527177 "RADFF" 2527182 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516428 2516521 2516551 "RADCAT" 2516711 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516198 2516258 2516358 "RADCAT-" 2516363 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2514109 2515968 2516060 "QUEUE" 2516141 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513734 2513783 2513914 "QUATCT2" 2514060 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2506105 2510157 2510199 "QUATCAT" 2510990 NIL QUATCAT (NIL T) -9 NIL 2511756 NIL) (-1028 2501986 2503281 2504671 "QUATCAT-" 2504767 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497825 2501919 2501967 "QUAT" 2501972 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2495081 2496873 2496916 "QUAGG" 2497297 NIL QUAGG (NIL T) -9 NIL 2497472 NIL) (-1025 2494629 2494903 2494973 "QQUTAST" 2495033 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493540 2494142 2494307 "QFORM" 2494510 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2493165 2493214 2493345 "QFCAT2" 2493491 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482841 2489012 2489054 "QFCAT" 2489722 NIL QFCAT (NIL T) -9 NIL 2490723 NIL) (-1021 2478156 2479609 2481203 "QFCAT-" 2481299 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477587 2477721 2477853 "QEQUAT" 2478046 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470605 2471786 2472972 "QCMPACK" 2476520 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469834 2470016 2470252 "QALGSET2" 2470423 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467284 2467820 2468250 "QALGSET" 2469489 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465951 2466193 2466512 "PWFFINTB" 2467057 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2464096 2464294 2464650 "PUSHVAR" 2465765 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459823 2461039 2461082 "PTRANFN" 2462993 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2458160 2458505 2458829 "PTPACK" 2459534 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457783 2457846 2457957 "PTFUNC2" 2458097 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451699 2456572 2456615 "PTCAT" 2456915 NIL PTCAT (NIL T) -9 NIL 2457068 NIL) (-1010 2451348 2451389 2451515 "PSQFR" 2451658 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449920 2450236 2450572 "PSEUDLIN" 2451046 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436440 2439015 2441341 "PSETPK" 2447680 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2429148 2432176 2432274 "PSETCAT" 2435315 NIL PSETCAT (NIL T T T T) -9 NIL 2436129 NIL) (-1006 2426873 2427615 2428439 "PSETCAT-" 2428444 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426186 2426381 2426411 "PSCURVE" 2426683 T PSCURVE (NIL) -9 NIL 2426850 NIL) (-1004 2421902 2423676 2423743 "PSCAT" 2424595 NIL PSCAT (NIL T T T) -9 NIL 2424835 NIL) (-1003 2420896 2421178 2421581 "PSCAT-" 2421586 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2419095 2419955 2420220 "PRTITION" 2420653 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418506 2418812 2418906 "PRTDAST" 2419023 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407350 2409772 2411962 "PRS" 2416368 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404970 2406672 2406712 "PRQAGG" 2406895 NIL PRQAGG (NIL T) -9 NIL 2406997 NIL) (-998 2404149 2404598 2404626 "PROPLOG" 2404765 T PROPLOG (NIL) -9 NIL 2404880 NIL) (-997 2403747 2403810 2403933 "PROPFUN2" 2404072 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2403044 2403183 2403355 "PROPFUN1" 2403608 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2401025 2401791 2402088 "PROPFRML" 2402780 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400470 2400601 2400729 "PROPERTY" 2400917 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394358 2398636 2399456 "PRODUCT" 2399696 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2394148 2394186 2394245 "PRINT" 2394319 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393464 2393605 2393757 "PRIMES" 2394028 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391511 2391930 2392396 "PRIMELT" 2393043 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391228 2391289 2391317 "PRIMCAT" 2391441 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390217 2390413 2390641 "PRIMARR2" 2391046 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385939 2390155 2390200 "PRIMARR" 2390205 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385576 2385638 2385749 "PREASSOC" 2385877 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382534 2385034 2385268 "PR" 2385387 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381985 2382142 2382170 "PPCURVE" 2382375 T PPCURVE (NIL) -9 NIL 2382511 NIL) (-983 2381532 2381780 2381863 "PORTNUM" 2381922 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378869 2379290 2379882 "POLYROOT" 2381113 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378246 2378310 2378544 "POLYLIFT" 2378805 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374467 2374970 2375599 "POLYCATQ" 2377791 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2360108 2366214 2366279 "POLYCAT" 2369793 NIL POLYCAT (NIL T T T) -9 NIL 2371671 NIL) (-978 2353227 2355419 2357803 "POLYCAT-" 2357808 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352808 2352882 2353002 "POLY2UP" 2353153 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352434 2352497 2352606 "POLY2" 2352745 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345642 2352038 2352198 "POLY" 2352307 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344303 2344566 2344842 "POLUTIL" 2345416 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342622 2342935 2343266 "POLTOPOL" 2344025 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337618 2342556 2342603 "POINT" 2342608 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335751 2336162 2336537 "PNTHEORY" 2337263 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334197 2334506 2334905 "PMTOOLS" 2335449 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333784 2333868 2333985 "PMSYM" 2334113 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333286 2333361 2333536 "PMQFCAT" 2333709 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332667 2332765 2332927 "PMPREDFS" 2333187 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2332010 2332132 2332288 "PMPRED" 2332544 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330664 2330882 2331260 "PMPLCAT" 2331772 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330190 2330275 2330427 "PMLSAGG" 2330579 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329657 2329739 2329921 "PMKERNEL" 2330108 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329268 2329349 2329462 "PMINS" 2329576 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328704 2328779 2328988 "PMFS" 2329193 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327920 2328050 2328255 "PMDOWN" 2328581 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2327169 2327303 2327466 "PMASSFS" 2327807 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326312 2326494 2326675 "PMASS" 2327008 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325961 2326035 2326129 "PLOTTOOL" 2326238 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321613 2322807 2323729 "PLOT3D" 2325059 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320501 2320702 2320937 "PLOT1" 2321417 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314922 2316312 2317460 "PLOT" 2319373 T PLOT (NIL) -8 NIL NIL NIL) (-953 2290097 2294988 2299839 "PLEQN" 2310188 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289784 2289837 2289940 "PINTERPA" 2290044 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2289090 2289224 2289404 "PINTERP" 2289649 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287175 2288348 2288376 "PID" 2288558 T PID (NIL) -9 NIL 2288692 NIL) (-949 2286920 2286963 2287038 "PICOERCE" 2287132 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2286016 2286684 2286771 "PI" 2286811 T PI (NIL) -8 NIL NIL 2286878) (-947 2285324 2285475 2285651 "PGROEB" 2285872 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280763 2281722 2282628 "PGE" 2284438 T PGE (NIL) -7 NIL NIL NIL) (-945 2278844 2279133 2279499 "PGCD" 2280480 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2278170 2278285 2278446 "PFRPAC" 2278728 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274421 2276718 2277071 "PFR" 2277849 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272774 2273054 2273379 "PFOTOOLS" 2274168 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271289 2271546 2271897 "PFOQ" 2272531 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269772 2270002 2270358 "PFO" 2271073 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266850 2268363 2268391 "PFECAT" 2268976 T PFECAT (NIL) -9 NIL 2269360 NIL) (-938 2266277 2266449 2266663 "PFECAT-" 2266668 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264850 2265132 2265433 "PFBRU" 2266026 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262680 2263068 2263500 "PFBR" 2264501 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258605 2262569 2262638 "PF" 2262643 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253659 2254812 2255682 "PERMGRP" 2257768 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251571 2252683 2252724 "PERMCAT" 2253124 NIL PERMCAT (NIL T) -9 NIL 2253422 NIL) (-932 2251218 2251265 2251389 "PERMAN" 2251524 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2247020 2248727 2249375 "PERM" 2250603 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244261 2246685 2246807 "PENDTREE" 2246931 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2243142 2243405 2243446 "PDSPC" 2243979 NIL PDSPC (NIL T) -9 NIL 2244224 NIL) (-928 2242197 2242463 2242825 "PDSPC-" 2242830 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240911 2241847 2241888 "PDRING" 2241893 NIL PDRING (NIL T) -9 NIL 2241921 NIL) (-926 2239654 2240416 2240470 "PDMOD" 2240475 NIL PDMOD (NIL T T) -9 NIL 2240579 NIL) (-925 2236821 2237647 2238315 "PDEPROB" 2239006 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234330 2234870 2235425 "PDEPACK" 2236286 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233218 2233432 2233683 "PDECOMP" 2234129 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230735 2231626 2231654 "PDECAT" 2232441 T PDECAT (NIL) -9 NIL 2233154 NIL) (-921 2230352 2230419 2230473 "PDDOM" 2230638 NIL PDDOM (NIL T T) -9 NIL 2230718 NIL) (-920 2230165 2230201 2230308 "PDDOM-" 2230313 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229910 2229949 2230039 "PCOMP" 2230126 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227950 2228711 2229008 "PBWLB" 2229639 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227576 2227639 2227748 "PATTERN2" 2227887 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225285 2225721 2226178 "PATTERN1" 2227165 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217464 2219358 2220696 "PATTERN" 2223968 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2217022 2217095 2217227 "PATRES2" 2217391 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214288 2214971 2215452 "PATRES" 2216587 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2212141 2212576 2212983 "PATMATCH" 2213955 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211595 2211846 2211887 "PATMAB" 2211994 NIL PATMAB (NIL T) -9 NIL 2212077 NIL) (-910 2210041 2210449 2210707 "PATLRES" 2211400 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209579 2209710 2209751 "PATAB" 2209756 NIL PATAB (NIL T) -9 NIL 2209928 NIL) (-908 2207719 2208156 2208579 "PARTPERM" 2209176 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207328 2207403 2207505 "PARSURF" 2207650 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206954 2207017 2207126 "PARSU2" 2207265 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206712 2206758 2206825 "PARSER" 2206907 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206321 2206396 2206498 "PARSCURV" 2206643 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205947 2206010 2206119 "PARSC2" 2206258 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205574 2205644 2205741 "PARPCURV" 2205883 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205200 2205263 2205372 "PARPC2" 2205511 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204189 2204573 2204755 "PARAMAST" 2205038 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203697 2203795 2203914 "PAN2EXPR" 2204090 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202390 2202818 2203046 "PALETTE" 2203489 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200735 2201395 2201755 "PAIR" 2202076 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193647 2199992 2200187 "PADICRC" 2200589 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185883 2192991 2193176 "PADICRAT" 2193494 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182673 2184543 2184583 "PADICCT" 2185164 NIL PADICCT (NIL NIL) -9 NIL 2185446 NIL) (-893 2180682 2182610 2182655 "PADIC" 2182660 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179627 2179839 2180107 "PADEPAC" 2180469 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178827 2178972 2179178 "PADE" 2179489 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2177060 2178035 2178315 "OWP" 2178631 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176505 2176766 2176863 "OVERSET" 2176983 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175425 2176110 2176282 "OVAR" 2176373 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163661 2166534 2168734 "OUTFORM" 2173245 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162943 2163258 2163385 "OUTBFILE" 2163554 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162220 2162415 2162443 "OUTBCON" 2162761 T OUTBCON (NIL) -9 NIL 2162927 NIL) (-884 2161803 2161933 2162090 "OUTBCON-" 2162095 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2161043 2161188 2161349 "OUT" 2161662 T OUT (NIL) -7 NIL NIL NIL) (-882 2160339 2160772 2160861 "OSI" 2160974 T OSI (NIL) -8 NIL NIL NIL) (-881 2159758 2160180 2160208 "OSGROUP" 2160213 T OSGROUP (NIL) -9 NIL 2160235 NIL) (-880 2158469 2158730 2159015 "ORTHPOL" 2159505 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155720 2158304 2158425 "OREUP" 2158430 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152823 2155411 2155538 "ORESUP" 2155662 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150323 2150851 2151412 "OREPCTO" 2152312 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143701 2146196 2146237 "OREPCAT" 2148585 NIL OREPCAT (NIL T) -9 NIL 2149689 NIL) (-875 2140674 2141630 2142688 "OREPCAT-" 2142693 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139866 2140144 2140172 "ORDTYPE" 2140481 T ORDTYPE (NIL) -9 NIL 2140644 NIL) (-873 2139167 2139383 2139638 "ORDTYPE-" 2139643 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138523 2138906 2139064 "ORDSTRCT" 2139069 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2138021 2138391 2138419 "ORDSET" 2138424 T ORDSET (NIL) -9 NIL 2138446 NIL) (-870 2136379 2137350 2137378 "ORDRING" 2137580 T ORDRING (NIL) -9 NIL 2137705 NIL) (-869 2136000 2136118 2136262 "ORDRING-" 2136267 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135251 2135816 2135844 "ORDMON" 2135849 T ORDMON (NIL) -9 NIL 2135870 NIL) (-867 2134395 2134560 2134755 "ORDFUNS" 2135100 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133610 2134125 2134153 "ORDFIN" 2134218 T ORDFIN (NIL) -9 NIL 2134292 NIL) (-865 2132864 2133003 2133189 "ORDCOMP2" 2133470 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129211 2131450 2131859 "ORDCOMP" 2132488 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125732 2126702 2127516 "OPTPROB" 2128417 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122474 2123173 2123877 "OPTPACK" 2125048 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2120087 2120913 2120941 "OPTCAT" 2121760 T OPTCAT (NIL) -9 NIL 2122410 NIL) (-860 2119405 2119764 2119869 "OPSIG" 2120002 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2119167 2119212 2119278 "OPQUERY" 2119359 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118473 2118753 2118794 "OPERCAT" 2119006 NIL OPERCAT (NIL T) -9 NIL 2119103 NIL) (-857 2118216 2118284 2118401 "OPERCAT-" 2118406 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2115125 2116527 2117031 "OP" 2117745 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114418 2114545 2114719 "ONECOMP2" 2114997 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2111031 2113215 2113584 "ONECOMP" 2114082 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110432 2110556 2110686 "OMSERVER" 2110921 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106946 2109872 2109912 "OMSAGG" 2109973 NIL OMSAGG (NIL T) -9 NIL 2110037 NIL) (-851 2105521 2105832 2106114 "OMPKG" 2106684 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103868 2105070 2105239 "OMLO" 2105402 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102804 2102975 2103195 "OMEXPR" 2103694 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101889 2102225 2102385 "OMERRK" 2102664 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2101126 2101435 2101571 "OMERR" 2101773 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100517 2100803 2100911 "OMENC" 2101038 T OMENC (NIL) -8 NIL NIL NIL) (-845 2094154 2095597 2096768 "OMDEV" 2099366 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093187 2093394 2093588 "OMCONN" 2093980 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092593 2092720 2092748 "OM" 2093047 T OM (NIL) -9 NIL NIL NIL) (-842 2090871 2092063 2092091 "OINTDOM" 2092096 T OINTDOM (NIL) -9 NIL 2092117 NIL) (-841 2087946 2089559 2089896 "OFMONOID" 2090566 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087180 2087883 2087928 "ODVAR" 2087933 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084317 2086925 2087080 "ODR" 2087085 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075722 2084093 2084219 "ODPOL" 2084224 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2069065 2075594 2075699 "ODP" 2075704 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067807 2068046 2068321 "ODETOOLS" 2068839 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064750 2065432 2066148 "ODESYS" 2067140 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059580 2060540 2061565 "ODERTRIC" 2063825 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2059000 2059088 2059282 "ODERED" 2059492 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055852 2056436 2057113 "ODERAT" 2058423 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052768 2053276 2053873 "ODEPRRIC" 2055381 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050663 2051307 2051793 "ODEPROB" 2052302 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2047129 2047668 2048315 "ODEPRIM" 2050142 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046372 2046480 2046740 "ODEPAL" 2047021 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042474 2043325 2044189 "ODEPACK" 2045528 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041517 2041642 2041864 "ODEINT" 2042363 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035582 2037043 2038490 "ODEIFTBL" 2040090 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030932 2031766 2032718 "ODEEF" 2034741 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030275 2030370 2030593 "ODECONST" 2030837 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028338 2029047 2029075 "ODECAT" 2029680 T ODECAT (NIL) -9 NIL 2030211 NIL) (-821 2027970 2028019 2028146 "OCTCT2" 2028289 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024463 2027675 2027797 "OCT" 2027880 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023686 2024256 2024284 "OCAMON" 2024289 T OCAMON (NIL) -9 NIL 2024310 NIL) (-818 2017950 2020729 2020769 "OC" 2021866 NIL OC (NIL T) -9 NIL 2022724 NIL) (-817 2014985 2015925 2016915 "OC-" 2017009 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014405 2014830 2014858 "OASGP" 2014863 T OASGP (NIL) -9 NIL 2014883 NIL) (-815 2013531 2014128 2014156 "OAMONS" 2014196 T OAMONS (NIL) -9 NIL 2014239 NIL) (-814 2012822 2013351 2013379 "OAMON" 2013384 T OAMON (NIL) -9 NIL 2013404 NIL) (-813 2011933 2012571 2012599 "OAGROUP" 2012604 T OAGROUP (NIL) -9 NIL 2012624 NIL) (-812 2011615 2011671 2011760 "NUMTUBE" 2011877 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2005134 2006706 2008242 "NUMQUAD" 2010099 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000814 2001848 2002883 "NUMODE" 2004119 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1998095 1999035 1999063 "NUMINT" 1999986 T NUMINT (NIL) -9 NIL 2000750 NIL) (-808 1997007 1997240 1997458 "NUMFMT" 1997897 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983190 1986311 1988843 "NUMERIC" 1994514 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976894 1982638 1982733 "NTSCAT" 1982738 NIL NTSCAT (NIL T T T T) -9 NIL 1982777 NIL) (-805 1976074 1976253 1976446 "NTPOLFN" 1976733 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975700 1975763 1975872 "NSUP2" 1976011 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962461 1972525 1973337 "NSUP" 1974921 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951297 1962235 1962368 "NSMP" 1962373 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949705 1950030 1950387 "NREP" 1950985 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948284 1948548 1948906 "NPCOEF" 1949448 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947332 1947465 1947681 "NORMRETR" 1948165 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945343 1945663 1946072 "NORMPK" 1947040 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1945022 1945056 1945180 "NORMMA" 1945309 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944805 1944840 1944909 "NONE1" 1944986 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944569 1944762 1944791 "NONE" 1944796 T NONE (NIL) -8 NIL NIL NIL) (-794 1944060 1944128 1944307 "NODE1" 1944501 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1942152 1943183 1943438 "NNI" 1943785 T NNI (NIL) -8 NIL NIL 1944020) (-792 1940548 1940885 1941249 "NLINSOL" 1941820 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936729 1937784 1938683 "NIPROB" 1939669 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935468 1935720 1936022 "NFINTBAS" 1936491 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934552 1935118 1935159 "NETCLT" 1935331 NIL NETCLT (NIL T) -9 NIL 1935413 NIL) (-788 1933224 1933491 1933772 "NCODIV" 1934320 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932980 1933023 1933098 "NCNTFRAC" 1933181 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1931136 1931524 1931944 "NCEP" 1932605 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929799 1930746 1930774 "NASRING" 1930884 T NASRING (NIL) -9 NIL 1930964 NIL) (-784 1929582 1929638 1929732 "NASRING-" 1929737 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928549 1929200 1929228 "NARNG" 1929345 T NARNG (NIL) -9 NIL 1929436 NIL) (-782 1928223 1928308 1928442 "NARNG-" 1928447 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1927060 1927309 1927544 "NAGSP" 1928008 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1918104 1920016 1921689 "NAGS" 1925407 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916628 1916960 1917291 "NAGF07" 1917793 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1911100 1912457 1913764 "NAGF04" 1915341 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903972 1905682 1907315 "NAGF02" 1909487 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1899136 1900296 1901413 "NAGF01" 1902875 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892716 1894330 1895915 "NAGE04" 1897571 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883777 1886006 1888136 "NAGE02" 1890606 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879670 1880677 1881641 "NAGE01" 1882833 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877447 1877999 1878557 "NAGD03" 1879132 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1869143 1871125 1873079 "NAGD02" 1875513 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862882 1864379 1865819 "NAGD01" 1867723 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1859019 1859913 1860750 "NAGC06" 1862065 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857466 1857816 1858172 "NAGC05" 1858683 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856830 1856961 1857105 "NAGC02" 1857342 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855631 1856358 1856398 "NAALG" 1856477 NIL NAALG (NIL T) -9 NIL 1856538 NIL) (-765 1855460 1855495 1855585 "NAALG-" 1855590 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849332 1850518 1851705 "MULTSQFR" 1854356 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848639 1848726 1848910 "MULTFACT" 1849244 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840777 1845222 1845275 "MTSCAT" 1846345 NIL MTSCAT (NIL T T) -9 NIL 1846861 NIL) (-761 1840483 1840543 1840635 "MTHING" 1840717 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840269 1840308 1840368 "MSYSCMD" 1840443 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1837014 1839830 1839871 "MSETAGG" 1839876 NIL MSETAGG (NIL T) -9 NIL 1839910 NIL) (-758 1832728 1835769 1836089 "MSET" 1836727 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828320 1830107 1830852 "MRING" 1832028 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827880 1827953 1828084 "MRF2" 1828247 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827492 1827533 1827677 "MRATFAC" 1827839 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1825062 1825399 1825830 "MPRFF" 1827197 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818389 1824916 1825013 "MPOLY" 1825018 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817873 1817914 1818122 "MPCPF" 1818348 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817381 1817430 1817614 "MPC3" 1817824 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816564 1816657 1816878 "MPC2" 1817296 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814841 1815202 1815592 "MONOTOOL" 1816224 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813986 1814369 1814397 "MONOID" 1814616 T MONOID (NIL) -9 NIL 1814763 NIL) (-747 1813502 1813651 1813832 "MONOID-" 1813837 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802454 1809322 1809381 "MONOGEN" 1810055 NIL MONOGEN (NIL T T) -9 NIL 1810511 NIL) (-745 1799504 1800407 1801407 "MONOGEN-" 1801526 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798221 1798769 1798797 "MONADWU" 1799189 T MONADWU (NIL) -9 NIL 1799427 NIL) (-743 1797551 1797752 1798000 "MONADWU-" 1798005 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796836 1797140 1797168 "MONAD" 1797375 T MONAD (NIL) -9 NIL 1797487 NIL) (-741 1796503 1796599 1796731 "MONAD-" 1796736 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794642 1795416 1795695 "MOEBIUS" 1796256 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793810 1794310 1794350 "MODULE" 1794355 NIL MODULE (NIL T) -9 NIL 1794394 NIL) (-738 1793348 1793474 1793664 "MODULE-" 1793669 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790878 1791712 1792039 "MODRING" 1793172 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787600 1788983 1789504 "MODOP" 1790407 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1786086 1786667 1786944 "MODMONOM" 1787463 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774826 1784377 1784791 "MODMON" 1785723 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771652 1773670 1773946 "MODFIELD" 1774701 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770563 1770933 1771123 "MMLFORM" 1771482 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1770083 1770132 1770311 "MMAP" 1770514 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767976 1768915 1768956 "MLO" 1769379 NIL MLO (NIL T) -9 NIL 1769621 NIL) (-729 1765324 1765858 1766460 "MLIFT" 1767457 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764703 1764799 1764953 "MKUCFUNC" 1765235 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764296 1764372 1764495 "MKRECORD" 1764626 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763319 1763505 1763733 "MKFUNC" 1764107 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762695 1762811 1762967 "MKFLCFN" 1763202 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761960 1762074 1762259 "MKBCFUNC" 1762588 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757943 1761514 1761650 "MINT" 1761844 T MINT (NIL) -8 NIL NIL NIL) (-722 1756725 1756998 1757275 "MHROWRED" 1757698 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751469 1755260 1755665 "MFLOAT" 1756340 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750814 1750902 1751073 "MFINFACT" 1751381 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1747093 1747977 1748861 "MESH" 1749950 T MESH (NIL) -7 NIL NIL NIL) (-718 1745447 1745795 1746148 "MDDFACT" 1746780 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741983 1744578 1744619 "MDAGG" 1744874 NIL MDAGG (NIL T) -9 NIL 1745017 NIL) (-716 1729685 1741276 1741483 "MCMPLX" 1741796 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728804 1728968 1729169 "MCDEN" 1729534 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726652 1726964 1727344 "MCALCFN" 1728534 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725529 1725817 1726050 "MAYBE" 1726458 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1723087 1723664 1724226 "MATSTOR" 1725000 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718509 1722459 1722707 "MATRIX" 1722872 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714209 1714982 1715718 "MATLIN" 1717866 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712785 1712956 1713289 "MATCAT2" 1714044 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1702124 1705842 1705919 "MATCAT" 1710951 NIL MATCAT (NIL T T T) -9 NIL 1712423 NIL) (-707 1698077 1699387 1700800 "MATCAT-" 1700805 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696153 1696513 1696897 "MAPPKG3" 1697752 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1695110 1695307 1695529 "MAPPKG2" 1695977 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693567 1693893 1694220 "MAPPKG1" 1694816 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692568 1692973 1693150 "MAPPAST" 1693410 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692173 1692237 1692360 "MAPHACK3" 1692504 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691753 1691826 1691940 "MAPHACK2" 1692105 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691179 1691294 1691436 "MAPHACK1" 1691644 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1689102 1689879 1690183 "MAGMA" 1690907 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688521 1688826 1688917 "MACROAST" 1689031 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684764 1686760 1687221 "M3D" 1688093 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678236 1683075 1683116 "LZSTAGG" 1683898 NIL LZSTAGG (NIL T) -9 NIL 1684193 NIL) (-695 1673918 1675367 1676824 "LZSTAGG-" 1676829 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670831 1671809 1672296 "LWORD" 1673463 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670353 1670635 1670710 "LSTAST" 1670776 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662281 1670124 1670258 "LSQM" 1670263 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661499 1661644 1661872 "LSPP" 1662136 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658236 1658952 1659682 "LSMP1" 1660801 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1656018 1656349 1656805 "LSMP" 1657925 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649146 1655108 1655149 "LSAGG" 1655211 NIL LSAGG (NIL T) -9 NIL 1655289 NIL) (-687 1645655 1646765 1647978 "LSAGG-" 1647983 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642950 1644799 1645048 "LPOLY" 1645450 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642526 1642617 1642740 "LPEFRAC" 1642859 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642209 1642288 1642316 "LOGIC" 1642427 T LOGIC (NIL) -9 NIL 1642509 NIL) (-683 1642065 1642094 1642165 "LOGIC-" 1642170 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641240 1641398 1641591 "LODOOPS" 1641921 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639764 1640013 1640366 "LODOF" 1640987 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635640 1638399 1638440 "LODOCAT" 1638878 NIL LODOCAT (NIL T) -9 NIL 1639089 NIL) (-679 1635355 1635431 1635558 "LODOCAT-" 1635563 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632341 1635196 1635314 "LODO2" 1635319 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629448 1632278 1632323 "LODO1" 1632328 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626543 1629364 1629430 "LODO" 1629435 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625412 1625589 1625894 "LODEEF" 1626366 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623589 1624506 1624759 "LO" 1625244 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618561 1621755 1621796 "LNAGG" 1622658 NIL LNAGG (NIL T) -9 NIL 1623093 NIL) (-672 1617654 1617922 1618264 "LNAGG-" 1618269 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613634 1614579 1615218 "LMOPS" 1617069 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612933 1613411 1613452 "LMODULE" 1613457 NIL LMODULE (NIL T) -9 NIL 1613483 NIL) (-669 1609888 1612578 1612701 "LMDICT" 1612843 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609464 1609678 1609719 "LLINSET" 1609780 NIL LLINSET (NIL T) -9 NIL 1609824 NIL) (-667 1609109 1609372 1609432 "LITERAL" 1609437 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608628 1608708 1608847 "LIST3" 1609029 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606726 1607074 1607473 "LIST2MAP" 1608275 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605715 1605911 1606139 "LIST2" 1606544 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598169 1604649 1604953 "LIST" 1605444 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597752 1597988 1598029 "LINSET" 1598034 NIL LINSET (NIL T) -9 NIL 1598068 NIL) (-661 1596566 1597260 1597427 "LINFORM" 1597637 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594865 1595593 1595634 "LINEXP" 1596124 NIL LINEXP (NIL T) -9 NIL 1596397 NIL) (-659 1593441 1594345 1594526 "LINELT" 1594736 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591998 1592278 1592589 "LINDEP" 1593193 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591134 1591730 1591840 "LINBASIS" 1591928 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587871 1588620 1589397 "LIMITRF" 1590389 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586156 1586470 1586879 "LIMITPS" 1587566 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584984 1585559 1585599 "LIECAT" 1585739 NIL LIECAT (NIL T) -9 NIL 1585890 NIL) (-653 1584819 1584852 1584940 "LIECAT-" 1584945 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578839 1584330 1584558 "LIE" 1584640 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1571024 1578379 1578535 "LIB" 1578703 T LIB (NIL) -8 NIL NIL NIL) (-650 1566593 1567542 1568477 "LGROBP" 1570141 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565217 1566125 1566153 "LFCAT" 1566360 T LFCAT (NIL) -9 NIL 1566499 NIL) (-648 1563155 1563489 1563839 "LF" 1564938 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1560015 1560687 1561375 "LEXTRIPK" 1562519 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556603 1557585 1558088 "LEXP" 1559595 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1556019 1556324 1556416 "LETAST" 1556531 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554405 1554730 1555131 "LEADCDET" 1555701 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553583 1553669 1553898 "LAZM3PK" 1554326 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1548094 1551660 1552198 "LAUPOL" 1553095 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547667 1547717 1547878 "LAPLACE" 1548044 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546515 1547231 1547272 "LALG" 1547334 NIL LALG (NIL T) -9 NIL 1547393 NIL) (-639 1546211 1546288 1546424 "LALG-" 1546429 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543948 1545312 1545563 "LA" 1546044 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543777 1543807 1543848 "KVTFROM" 1543910 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542534 1543144 1543329 "KTVLOGIC" 1543612 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542363 1542393 1542434 "KRCFROM" 1542496 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541255 1541454 1541753 "KOVACIC" 1542163 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1541084 1541114 1541155 "KONVERT" 1541217 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540913 1540943 1540984 "KOERCE" 1541046 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540397 1540490 1540622 "KERNEL2" 1540827 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1538084 1538990 1539367 "KERNEL" 1540053 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531555 1536561 1536615 "KDAGG" 1536992 NIL KDAGG (NIL T T) -9 NIL 1537198 NIL) (-628 1531066 1531208 1531413 "KDAGG-" 1531418 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523766 1530727 1530882 "KAFILE" 1530944 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523370 1523655 1523718 "JVMOP" 1523723 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1522106 1522610 1522859 "JVMMDACC" 1523141 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1521042 1521496 1521701 "JVMFDACC" 1521921 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519623 1520118 1520418 "JVMCSTTG" 1520762 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518759 1519163 1519324 "JVMCFACC" 1519482 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518437 1518676 1518725 "JVMBCODE" 1518730 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512456 1517948 1518176 "JORDAN" 1518258 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511769 1512105 1512226 "JOINAST" 1512355 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507804 1509946 1510000 "IXAGG" 1510929 NIL IXAGG (NIL T T) -9 NIL 1511388 NIL) (-617 1506657 1507029 1507448 "IXAGG-" 1507453 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501746 1506579 1506638 "IVECTOR" 1506643 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500471 1500749 1501015 "ITUPLE" 1501513 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498943 1499150 1499445 "ITRIGMNP" 1500293 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497670 1497892 1498175 "ITFUN3" 1498719 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497268 1497331 1497454 "ITFUN2" 1497593 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1496373 1496748 1496922 "ITFORM" 1497114 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494142 1495393 1495671 "ITAYLOR" 1496128 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482539 1488279 1489442 "ISUPS" 1493012 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481631 1481783 1482019 "ISUMP" 1482386 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476481 1481576 1481617 "ISTRING" 1481622 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475897 1476202 1476294 "ISAST" 1476409 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475094 1475188 1475404 "IRURPK" 1475811 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1474006 1474231 1474471 "IRSN" 1474874 T IRSN (NIL) -7 NIL NIL NIL) (-603 1472051 1472432 1472861 "IRRF2F" 1473644 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471792 1471836 1471912 "IRREDFFX" 1472007 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470365 1470666 1470965 "IROOT" 1471525 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469504 1469858 1470009 "IRFORM" 1470234 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468586 1468717 1468931 "IR2F" 1469387 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466175 1466694 1467260 "IR2" 1468064 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462615 1463859 1464551 "IR" 1465515 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462400 1462440 1462500 "IPRNTPK" 1462575 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458353 1462289 1462358 "IPF" 1462363 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456374 1458278 1458335 "IPADIC" 1458340 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455632 1455934 1456064 "IP4ADDR" 1456264 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454970 1455261 1455393 "IOMODE" 1455520 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453941 1454567 1454694 "IOBFILE" 1454863 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453351 1453845 1453873 "IOBCON" 1453878 T IOBCON (NIL) -9 NIL 1453899 NIL) (-589 1452856 1452920 1453103 "INVLAPLA" 1453287 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442426 1444858 1447244 "INTTR" 1450520 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438719 1439503 1440368 "INTTOOLS" 1441611 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438299 1438396 1438513 "INTSLPE" 1438622 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435766 1438222 1438281 "INTRVL" 1438286 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433344 1433880 1434455 "INTRF" 1435251 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432737 1432852 1432994 "INTRET" 1433242 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430710 1431123 1431593 "INTRAT" 1432345 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427955 1428556 1429175 "INTPM" 1430195 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424672 1425299 1426037 "INTPAF" 1427341 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419773 1420813 1421864 "INTPACK" 1423641 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1419019 1419177 1419385 "INTHERTR" 1419615 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418452 1418538 1418726 "INTHERAL" 1418933 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416220 1416741 1417198 "INTHEORY" 1418015 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407552 1409247 1411019 "INTG0" 1414572 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1388077 1392915 1397725 "INTFTBL" 1402762 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387302 1387464 1387637 "INTFACT" 1387936 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384699 1385175 1385732 "INTEF" 1386856 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382896 1383791 1383819 "INTDOM" 1384120 T INTDOM (NIL) -9 NIL 1384327 NIL) (-570 1382235 1382439 1382681 "INTDOM-" 1382686 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378103 1380524 1380578 "INTCAT" 1381377 NIL INTCAT (NIL T) -9 NIL 1381698 NIL) (-568 1377557 1377678 1377806 "INTBIT" 1377995 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376238 1376410 1376717 "INTALG" 1377402 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375715 1375811 1375968 "INTAF" 1376142 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368682 1375525 1375665 "INTABL" 1375670 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367923 1368485 1368550 "INT8" 1368584 T INT8 (NIL) -8 NIL NIL 1368629) (-563 1367163 1367725 1367790 "INT64" 1367824 T INT64 (NIL) -8 NIL NIL 1367869) (-562 1366403 1366965 1367030 "INT32" 1367064 T INT32 (NIL) -8 NIL NIL 1367109) (-561 1365643 1366205 1366270 "INT16" 1366304 T INT16 (NIL) -8 NIL NIL 1366349) (-560 1361831 1365440 1365549 "INT" 1365554 T INT (NIL) -8 NIL NIL NIL) (-559 1355926 1359379 1359407 "INS" 1360341 T INS (NIL) -9 NIL 1361006 NIL) (-558 1352980 1353937 1354911 "INS-" 1354984 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351737 1351982 1352280 "INPSIGN" 1352733 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350831 1350972 1351169 "INPRODPF" 1351617 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349701 1349842 1350079 "INPRODFF" 1350711 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348689 1348853 1349113 "INNMFACT" 1349537 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347868 1347983 1348171 "INMODGCD" 1348588 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346352 1346621 1346945 "INFSP" 1347613 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345512 1345653 1345836 "INFPROD0" 1346232 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345110 1345182 1345280 "INFORM1" 1345447 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341677 1343175 1343690 "INFORM" 1344603 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341182 1341289 1341403 "INFINITY" 1341583 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340256 1340902 1341003 "INETCLTS" 1341101 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338854 1339122 1339443 "INEP" 1340004 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337915 1338751 1338816 "INDE" 1338821 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337467 1337547 1337664 "INCRMAPS" 1337842 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336189 1336736 1336942 "INBFILE" 1337281 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331368 1332425 1333369 "INBFF" 1335277 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330222 1330545 1330573 "INBCON" 1331086 T INBCON (NIL) -9 NIL 1331352 NIL) (-540 1329432 1329697 1329973 "INBCON-" 1329978 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328851 1329156 1329247 "INAST" 1329361 T INAST (NIL) -8 NIL NIL NIL) (-538 1328218 1328530 1328636 "IMPTAST" 1328765 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324139 1328062 1328166 "IMATRIX" 1328171 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322831 1322970 1323286 "IMATQF" 1323995 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1321011 1321278 1321615 "IMATLIN" 1322587 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314926 1320935 1320993 "ILIST" 1320998 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312592 1314786 1314899 "IIARRAY2" 1314904 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307392 1312503 1312567 "IFF" 1312572 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306673 1307009 1307125 "IFAST" 1307296 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301185 1305965 1306153 "IFARRAY" 1306530 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300223 1301089 1301162 "IFAMON" 1301167 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299795 1299872 1299926 "IEVALAB" 1300133 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299458 1299538 1299698 "IEVALAB-" 1299703 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298522 1299347 1299422 "IDPOAMS" 1299427 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297655 1298411 1298486 "IDPOAM" 1298491 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1297036 1297570 1297632 "IDPO" 1297637 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295516 1296043 1296095 "IDPC" 1296607 NIL IDPC (NIL T T) -9 NIL 1296888 NIL) (-522 1294848 1295408 1295481 "IDPAM" 1295486 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1294063 1294740 1294813 "IDPAG" 1294818 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293607 1293869 1293959 "IDENT" 1293993 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289826 1290710 1291605 "IDECOMP" 1292764 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282461 1283749 1284796 "IDEAL" 1288862 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281603 1281733 1281933 "ICDEN" 1282345 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280578 1281083 1281230 "ICARD" 1281476 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278608 1278951 1279356 "IBPTOOLS" 1280255 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273723 1278228 1278341 "IBITS" 1278527 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270398 1271022 1271717 "IBATOOL" 1273140 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268159 1268639 1269172 "IBACHIN" 1269933 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265749 1268005 1268108 "IARRAY2" 1268113 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261462 1265675 1265732 "IARRAY1" 1265737 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254472 1259874 1260355 "IAN" 1261001 T IAN (NIL) -8 NIL NIL NIL) (-508 1253977 1254040 1254213 "IALGFACT" 1254409 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253469 1253618 1253646 "HYPCAT" 1253853 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252971 1253124 1253310 "HYPCAT-" 1253315 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252518 1252766 1252849 "HOSTNAME" 1252908 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252351 1252400 1252441 "HOMOTOP" 1252446 NIL HOMOTOP (NIL T) -9 NIL 1252479 NIL) (-503 1248784 1250283 1250324 "HOAGG" 1251305 NIL HOAGG (NIL T) -9 NIL 1252034 NIL) (-502 1247300 1247777 1248303 "HOAGG-" 1248308 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240336 1246893 1247043 "HEXADEC" 1247170 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1239048 1239306 1239569 "HEUGCD" 1240113 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237980 1238885 1239015 "HELLFDIV" 1239020 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235990 1237757 1237845 "HEAP" 1237924 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235187 1235542 1235676 "HEADAST" 1235876 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228574 1235102 1235164 "HDP" 1235169 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221586 1228209 1228361 "HDMP" 1228475 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220892 1221050 1221214 "HB" 1221442 T HB (NIL) -7 NIL NIL NIL) (-493 1213902 1220738 1220842 "HASHTBL" 1220847 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213318 1213623 1213715 "HASAST" 1213830 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210724 1212940 1213122 "HACKPI" 1213156 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205896 1210577 1210690 "GTSET" 1210695 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198935 1205774 1205872 "GSTBL" 1205877 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190684 1198100 1198356 "GSERIES" 1198735 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189715 1190228 1190256 "GROUP" 1190459 T GROUP (NIL) -9 NIL 1190593 NIL) (-486 1189039 1189240 1189491 "GROUP-" 1189496 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187388 1187727 1188114 "GROEBSOL" 1188716 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186216 1186576 1186627 "GRMOD" 1187156 NIL GRMOD (NIL T T) -9 NIL 1187324 NIL) (-483 1185972 1186020 1186148 "GRMOD-" 1186153 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181112 1182326 1183326 "GRIMAGE" 1184992 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179506 1179839 1180163 "GRDEF" 1180808 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178938 1179066 1179207 "GRAY" 1179385 T GRAY (NIL) -7 NIL NIL NIL) (-479 1178015 1178517 1178568 "GRALG" 1178721 NIL GRALG (NIL T T) -9 NIL 1178814 NIL) (-478 1177652 1177749 1177912 "GRALG-" 1177917 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174133 1177235 1177414 "GPOLSET" 1177558 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173481 1173544 1173802 "GOSPER" 1174070 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1169051 1169919 1170445 "GMODPOL" 1173180 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1168038 1168240 1168478 "GHENSEL" 1168863 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162110 1163037 1164057 "GENUPS" 1167122 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161801 1161858 1161947 "GENUFACT" 1162053 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161201 1161290 1161455 "GENPGCD" 1161719 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160669 1160710 1160923 "GENMFACT" 1161160 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159205 1159492 1159799 "GENEEZ" 1160412 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152377 1158816 1158978 "GDMP" 1159128 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141115 1146148 1147254 "GCNAALG" 1151360 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139242 1140290 1140318 "GCDDOM" 1140573 T GCDDOM (NIL) -9 NIL 1140730 NIL) (-465 1138682 1138839 1139054 "GCDDOM-" 1139059 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127154 1129628 1132020 "GBINTERN" 1136373 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124955 1125283 1125704 "GBF" 1126829 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123712 1123901 1124168 "GBEUCLID" 1124771 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122362 1122569 1122873 "GB" 1123491 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121693 1121836 1121985 "GAUSSFAC" 1122233 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1120014 1120362 1120676 "GALUTIL" 1121412 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118274 1118596 1118920 "GALPOLYU" 1119741 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115573 1115929 1116336 "GALFACTU" 1117971 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107187 1108878 1110486 "GALFACT" 1114005 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104473 1105233 1105261 "FVFUN" 1106417 T FVFUN (NIL) -9 NIL 1107137 NIL) (-454 1103703 1103921 1103949 "FVC" 1104240 T FVC (NIL) -9 NIL 1104423 NIL) (-453 1103304 1103528 1103596 "FUNDESC" 1103655 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102877 1103101 1103182 "FUNCTION" 1103256 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101554 1102178 1102381 "FTEM" 1102694 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099184 1099876 1100342 "FT" 1101108 T FT (NIL) -8 NIL NIL NIL) (-449 1097453 1097764 1098161 "FSUPFACT" 1098875 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095772 1096139 1096471 "FST" 1097141 T FST (NIL) -8 NIL NIL NIL) (-447 1094953 1095077 1095265 "FSRED" 1095654 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093642 1093908 1094255 "FSPRMELT" 1094668 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090852 1091386 1091872 "FSPECF" 1093205 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090374 1090434 1090604 "FSINT" 1090793 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088510 1089367 1089670 "FSERIES" 1090153 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087534 1087668 1087892 "FSCINT" 1088390 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086558 1086719 1086946 "FSAGG2" 1087387 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082422 1085502 1085543 "FSAGG" 1085913 NIL FSAGG (NIL T) -9 NIL 1086172 NIL) (-439 1080022 1080785 1081581 "FSAGG-" 1081676 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077682 1077980 1078528 "FS2UPS" 1079740 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076548 1076731 1077033 "FS2EXPXP" 1077507 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076176 1076225 1076354 "FS2" 1076499 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056400 1065950 1065991 "FS" 1069875 NIL FS (NIL T) -9 NIL 1072164 NIL) (-434 1044461 1048036 1052093 "FS-" 1052393 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043875 1044002 1044154 "FRUTIL" 1044341 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038386 1041564 1041604 "FRNAALG" 1042924 NIL FRNAALG (NIL T) -9 NIL 1043522 NIL) (-431 1033867 1035135 1036410 "FRNAALG-" 1037160 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033499 1033548 1033675 "FRNAAF2" 1033818 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031786 1032348 1032644 "FRMOD" 1033311 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030971 1031064 1031355 "FRIDEAL2" 1031693 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028576 1029346 1029664 "FRIDEAL" 1030762 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027667 1028123 1028164 "FRETRCT" 1028169 NIL FRETRCT (NIL T) -9 NIL 1028345 NIL) (-425 1026725 1027010 1027361 "FRETRCT-" 1027366 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023539 1025009 1025068 "FRAMALG" 1025950 NIL FRAMALG (NIL T T) -9 NIL 1026242 NIL) (-423 1021577 1022128 1022758 "FRAMALG-" 1022981 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021207 1021270 1021377 "FRAC2" 1021514 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014178 1020680 1020957 "FRAC" 1020962 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013808 1013871 1013978 "FR2" 1014115 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004725 1009303 1010661 "FR" 1012482 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998637 1002104 1002132 "FPS" 1003251 T FPS (NIL) -9 NIL 1003808 NIL) (-417 998062 998195 998359 "FPS-" 998505 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 995014 997019 997047 "FPC" 997272 T FPC (NIL) -9 NIL 997414 NIL) (-415 994795 994847 994944 "FPC-" 994949 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993553 994283 994324 "FPATMAB" 994329 NIL FPATMAB (NIL T) -9 NIL 994481 NIL) (-413 991696 992295 992642 "FPARFRAC" 993269 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986988 987588 988270 "FORTRAN" 991128 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984562 985226 985254 "FORTFN" 986314 T FORTFN (NIL) -9 NIL 986938 NIL) (-410 984314 984376 984404 "FORTCAT" 984463 T FORTCAT (NIL) -9 NIL 984525 NIL) (-409 982000 982530 983069 "FORT" 983795 T FORT (NIL) -7 NIL NIL NIL) (-408 981782 981818 981887 "FORMULA1" 981964 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979786 980398 980788 "FORMULA" 981412 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979303 979361 979534 "FORDER" 979728 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978363 978563 978756 "FOP" 979130 T FOP (NIL) -7 NIL NIL NIL) (-404 976776 977643 977817 "FNLA" 978245 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975395 975906 975934 "FNCAT" 976394 T FNCAT (NIL) -9 NIL 976654 NIL) (-402 974838 975354 975382 "FNAME" 975387 T FNAME (NIL) -8 NIL NIL NIL) (-401 973164 974337 974365 "FMTC" 974370 T FMTC (NIL) -9 NIL 974406 NIL) (-400 971713 973100 973146 "FMONOID" 973151 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968302 969668 969709 "FMONCAT" 970926 NIL FMONCAT (NIL T) -9 NIL 971531 NIL) (-398 965624 966372 966400 "FMFUN" 967544 T FMFUN (NIL) -9 NIL 968252 NIL) (-397 962497 963549 963603 "FMCAT" 964798 NIL FMCAT (NIL T T) -9 NIL 965293 NIL) (-396 961730 961947 961975 "FMC" 962265 T FMC (NIL) -9 NIL 962447 NIL) (-395 960398 961496 961596 "FM1" 961675 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959416 960140 960289 "FM" 960294 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957154 957606 958100 "FLOATRP" 958967 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954556 955092 955670 "FLOATCP" 956621 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947212 952285 952906 "FLOAT" 953955 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945730 946804 946845 "FLINEXP" 946850 NIL FLINEXP (NIL T) -9 NIL 946943 NIL) (-389 944860 945119 945447 "FLINEXP-" 945452 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943918 944080 944304 "FLASORT" 944712 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940836 941888 941940 "FLALG" 943167 NIL FLALG (NIL T T) -9 NIL 943634 NIL) (-386 939860 940021 940248 "FLAGG2" 940689 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933115 937269 937310 "FLAGG" 938572 NIL FLAGG (NIL T) -9 NIL 939224 NIL) (-384 931769 932180 932670 "FLAGG-" 932675 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928400 929614 929673 "FINRALG" 930801 NIL FINRALG (NIL T T) -9 NIL 931309 NIL) (-382 927524 927789 928128 "FINRALG-" 928133 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926830 927129 927157 "FINITE" 927353 T FINITE (NIL) -9 NIL 927460 NIL) (-380 918781 921360 921400 "FINAALG" 925067 NIL FINAALG (NIL T) -9 NIL 926520 NIL) (-379 913897 915163 916307 "FINAALG-" 917686 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912457 912879 912933 "FILECAT" 913617 NIL FILECAT (NIL T T) -9 NIL 913833 NIL) (-377 911735 912212 912315 "FILE" 912387 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909131 910965 910993 "FIELD" 911033 T FIELD (NIL) -9 NIL 911113 NIL) (-375 907673 908136 908647 "FIELD-" 908652 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905356 906308 906655 "FGROUP" 907359 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904428 904610 904830 "FGLMICPK" 905188 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899662 904353 904410 "FFX" 904415 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899257 899324 899459 "FFSLPE" 899595 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898755 898797 899006 "FFPOLY2" 899215 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894631 895527 896323 "FFPOLY" 897991 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889879 894550 894613 "FFP" 894618 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884389 889222 889412 "FFNBX" 889733 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878701 883524 883782 "FFNBP" 884243 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872718 877985 878196 "FFNB" 878534 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871538 871748 872063 "FFINTBAS" 872515 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867110 869785 869813 "FFIELDC" 870433 T FFIELDC (NIL) -9 NIL 870809 NIL) (-362 865688 866143 866640 "FFIELDC-" 866645 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865245 865303 865427 "FFHOM" 865630 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862904 863427 863944 "FFF" 864760 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857918 862646 862747 "FFCGX" 862847 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852936 857650 857757 "FFCGP" 857861 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847515 852663 852771 "FFCG" 852872 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846920 846969 847204 "FFCAT2" 847466 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825581 836652 836738 "FFCAT" 841903 NIL FFCAT (NIL T T T) -9 NIL 843354 NIL) (-354 820592 821826 823140 "FFCAT-" 824370 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815392 820503 820567 "FF" 820572 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 804045 808364 809584 "FEXPR" 814244 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802973 803442 803483 "FEVALAB" 803567 NIL FEVALAB (NIL T) -9 NIL 803828 NIL) (-350 802090 802342 802680 "FEVALAB-" 802685 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798952 799837 799952 "FDIVCAT" 801520 NIL FDIVCAT (NIL T T T T) -9 NIL 801957 NIL) (-348 798708 798741 798911 "FDIVCAT-" 798916 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797922 798015 798292 "FDIV2" 798615 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796332 797305 797508 "FDIV" 797821 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795240 795627 795829 "FCTRDATA" 796150 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793896 794185 794474 "FCPAK1" 794971 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792899 793396 793537 "FCOMP" 793787 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776213 780049 783587 "FC" 789381 T FC (NIL) -8 NIL NIL NIL) (-341 767902 772534 772574 "FAXF" 774376 NIL FAXF (NIL T) -9 NIL 775068 NIL) (-340 765023 765836 766661 "FAXF-" 767126 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759592 764399 764575 "FARRAY" 764880 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754151 756539 756592 "FAMR" 757615 NIL FAMR (NIL T T) -9 NIL 758075 NIL) (-337 752975 753343 753778 "FAMR-" 753783 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 752002 752897 752950 "FAMONOID" 752955 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749632 750484 750537 "FAMONC" 751478 NIL FAMONC (NIL T T) -9 NIL 751864 NIL) (-334 748106 749386 749523 "FAGROUP" 749528 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745859 746220 746623 "FACUTIL" 747787 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744946 745143 745365 "FACTFUNC" 745669 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736704 744249 744448 "EXPUPXS" 744802 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734157 734727 735313 "EXPRTUBE" 736138 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730368 731020 731750 "EXPRODE" 733496 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724802 725509 726315 "EXPR2UPS" 729666 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724428 724491 724600 "EXPR2" 724739 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708722 723077 723506 "EXPR" 724032 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699039 707873 708164 "EXPEXPAN" 708558 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698459 698763 698854 "EXITAST" 698968 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698223 698416 698445 "EXIT" 698450 T EXIT (NIL) -8 NIL NIL NIL) (-322 697844 697912 698025 "EVALCYC" 698155 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697361 697503 697544 "EVALAB" 697714 NIL EVALAB (NIL T) -9 NIL 697818 NIL) (-320 696818 696964 697185 "EVALAB-" 697190 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693926 695474 695502 "EUCDOM" 696057 T EUCDOM (NIL) -9 NIL 696407 NIL) (-318 692265 692773 693363 "EUCDOM-" 693368 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691891 691954 692063 "ESTOOLS2" 692202 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691636 691684 691764 "ESTOOLS1" 691843 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678953 681934 684684 "ESTOOLS" 688906 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678692 678730 678812 "ESCONT1" 678915 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 675000 675827 676607 "ESCONT" 677932 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674669 674725 674825 "ES2" 674944 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674293 674357 674466 "ES1" 674605 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667994 669924 669952 "ES" 672720 T ES (NIL) -9 NIL 674130 NIL) (-309 662671 664228 666045 "ES-" 666209 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661863 662016 662192 "ERROR" 662515 T ERROR (NIL) -7 NIL NIL NIL) (-307 654879 661722 661813 "EQTBL" 661818 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654505 654568 654677 "EQ2" 654816 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646764 649819 651268 "EQ" 653089 NIL -1484 (NIL T) -8 NIL NIL NIL) (-304 642007 643102 644195 "EP" 645703 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640547 640898 641204 "ENV" 641721 T ENV (NIL) -8 NIL NIL NIL) (-302 639507 640181 640209 "ENTIRER" 640214 T ENTIRER (NIL) -9 NIL 640260 NIL) (-301 635919 637689 638050 "EMR" 639315 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635023 635234 635288 "ELTAGG" 635668 NIL ELTAGG (NIL T T) -9 NIL 635879 NIL) (-299 634730 634804 634945 "ELTAGG-" 634950 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634488 634523 634577 "ELTAB" 634661 NIL ELTAB (NIL T T) -9 NIL 634713 NIL) (-297 633590 633760 633959 "ELFUTS" 634339 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633314 633388 633416 "ELEMFUN" 633521 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633178 633205 633273 "ELEMFUN-" 633278 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627589 631220 631261 "ELAGG" 632201 NIL ELAGG (NIL T) -9 NIL 632664 NIL) (-293 625766 626308 626971 "ELAGG-" 626976 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625048 625215 625371 "ELABOR" 625630 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623654 623988 624282 "ELABEXPR" 624774 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616166 618291 619120 "EFUPXS" 622929 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609292 611415 612226 "EFULS" 615441 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606729 607135 607607 "EFSTRUC" 608924 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596166 598086 599634 "EF" 605244 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595144 595651 595800 "EAB" 596037 T EAB (NIL) -8 NIL NIL NIL) (-285 594266 595103 595131 "E04UCFA" 595136 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593388 594225 594253 "E04NAFA" 594258 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592510 593347 593375 "E04MBFA" 593380 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591632 592469 592497 "E04JAFA" 592502 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590756 591591 591619 "E04GCFA" 591624 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589880 590715 590743 "E04FDFA" 590748 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 589002 589839 589867 "E04DGFA" 589872 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583079 584527 585891 "E04AGNT" 587658 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581699 582380 582420 "DVARCAT" 582761 NIL DVARCAT (NIL T) -9 NIL 582924 NIL) (-276 580849 581115 581429 "DVARCAT-" 581434 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572810 580648 580777 "DSMP" 580782 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571161 571952 571993 "DSEXT" 572356 NIL DSEXT (NIL T) -9 NIL 572650 NIL) (-273 569350 569874 570540 "DSEXT-" 570545 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569009 569074 569172 "DROPT1" 569285 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564028 565250 566387 "DROPT0" 567892 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558611 559973 561041 "DROPT" 562980 T DROPT (NIL) -8 NIL NIL NIL) (-269 556920 557281 557667 "DRAWPT" 558245 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556547 556606 556724 "DRAWHACK" 556861 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555248 555547 555838 "DRAWCX" 556276 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554757 554832 554983 "DRAWCURV" 555174 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545075 547187 549302 "DRAWCFUN" 552662 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539566 540585 541664 "DRAW" 544049 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536037 538231 538272 "DQAGG" 538901 NIL DQAGG (NIL T) -9 NIL 539175 NIL) (-262 522613 530248 530331 "DPOLCAT" 532183 NIL DPOLCAT (NIL T T T T) -9 NIL 532728 NIL) (-261 517132 518798 520756 "DPOLCAT-" 520761 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509989 516993 517091 "DPMO" 517096 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502743 509769 509936 "DPMM" 509941 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502265 502527 502616 "DOMTMPLT" 502674 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501614 502067 502147 "DOMCTOR" 502205 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500766 501094 501245 "DOMAIN" 501483 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493778 500401 500553 "DMP" 500667 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491555 492845 492886 "DMEXT" 492891 NIL DMEXT (NIL T) -9 NIL 493067 NIL) (-253 491149 491211 491355 "DLP" 491493 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484272 490476 490666 "DLIST" 490991 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480810 483097 483138 "DLAGG" 483688 NIL DLAGG (NIL T) -9 NIL 483918 NIL) (-250 479322 480136 480164 "DIVRING" 480256 T DIVRING (NIL) -9 NIL 480339 NIL) (-249 478505 478749 479049 "DIVRING-" 479054 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476547 476964 477370 "DISPLAY" 478119 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475377 475598 475863 "DIRPROD2" 476340 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468784 475291 475354 "DIRPROD" 475359 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456996 463495 463548 "DIRPCAT" 463806 NIL DIRPCAT (NIL NIL T) -9 NIL 464681 NIL) (-244 454196 454964 455845 "DIRPCAT-" 456182 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453477 453643 453829 "DIOSP" 454030 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449891 452361 452402 "DIOPS" 452836 NIL DIOPS (NIL T) -9 NIL 453065 NIL) (-241 449410 449554 449745 "DIOPS-" 449750 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448317 449089 449117 "DIFRING" 449122 T DIFRING (NIL) -9 NIL 449144 NIL) (-239 447965 448063 448091 "DIFFSPC" 448210 T DIFFSPC (NIL) -9 NIL 448285 NIL) (-238 447586 447688 447840 "DIFFSPC-" 447845 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446522 447120 447161 "DIFFMOD" 447166 NIL DIFFMOD (NIL T) -9 NIL 447264 NIL) (-236 446218 446275 446316 "DIFFDOM" 446437 NIL DIFFDOM (NIL T) -9 NIL 446505 NIL) (-235 446065 446095 446179 "DIFFDOM-" 446184 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443805 445269 445310 "DIFEXT" 445315 NIL DIFEXT (NIL T) -9 NIL 445468 NIL) (-233 440839 443309 443350 "DIAGG" 443355 NIL DIAGG (NIL T) -9 NIL 443375 NIL) (-232 440187 440380 440632 "DIAGG-" 440637 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435037 439146 439423 "DHMATRIX" 439956 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430505 431558 432568 "DFSFUN" 434047 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424739 429436 429748 "DFLOAT" 430213 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422978 423283 423672 "DFINTTLS" 424447 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419797 420999 421399 "DERHAM" 422644 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417333 419572 419661 "DEQUEUE" 419741 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416575 416720 416903 "DEGRED" 417195 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412981 413750 414596 "DEFINTRF" 415803 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410518 411005 411597 "DEFINTEF" 412500 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409802 410138 410253 "DEFAST" 410423 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402838 409395 409545 "DECIMAL" 409672 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400296 400808 401314 "DDFACT" 402382 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399886 399935 400086 "DBLRESP" 400247 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399087 399656 399747 "DBASIS" 399835 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396871 397317 397678 "DBASE" 398853 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396059 396351 396497 "DATAARY" 396770 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395117 396018 396046 "D03FAFA" 396051 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394176 395076 395104 "D03EEFA" 395109 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392102 392592 393081 "D03AGNT" 393707 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391343 392061 392089 "D02EJFA" 392094 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390584 391302 391330 "D02CJFA" 391335 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389825 390543 390571 "D02BHFA" 390576 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389066 389784 389812 "D02BBFA" 389817 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382197 383852 385458 "D02AGNT" 387480 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379947 380488 381034 "D01WGTS" 381671 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378954 379906 379934 "D01TRNS" 379939 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377962 378913 378941 "D01GBFA" 378946 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376970 377921 377949 "D01FCFA" 377954 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375978 376929 376957 "D01ASFA" 376962 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374986 375937 375965 "D01AQFA" 375970 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373994 374945 374973 "D01APFA" 374978 T D01APFA (NIL) -8 NIL NIL NIL) (-200 373002 373953 373981 "D01ANFA" 373986 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 372010 372961 372989 "D01AMFA" 372994 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 371018 371969 371997 "D01ALFA" 372002 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 370026 370977 371005 "D01AKFA" 371010 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 369034 369985 370013 "D01AJFA" 370018 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362257 363882 365443 "D01AGNT" 367493 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361576 361722 361874 "CYCLOTOM" 362125 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358231 359024 359751 "CYCLES" 360869 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357531 357677 357848 "CVMP" 358092 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355318 355630 355999 "CTRIGMNP" 357259 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354791 355049 355150 "CTORKIND" 355237 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353996 354384 354412 "CTORCAT" 354594 T CTORCAT (NIL) -9 NIL 354707 NIL) (-188 353570 353705 353864 "CTORCAT-" 353869 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352984 353244 353352 "CTORCALL" 353494 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352342 352778 352851 "CTOR" 352931 T CTOR (NIL) -8 NIL NIL NIL) (-185 351698 351815 351968 "CSTTOOLS" 352239 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347395 348154 348912 "CRFP" 351010 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346810 347116 347208 "CRCEAST" 347323 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345833 346042 346270 "CRAPACK" 346614 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345213 345318 345522 "CPMATCH" 345709 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344932 344966 345072 "CPIMA" 345179 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341190 341952 342671 "COORDSYS" 344267 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340578 340723 340865 "CONTOUR" 341068 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336043 338581 339073 "CONTFRAC" 340118 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335917 335944 335972 "CONDUIT" 336009 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334871 335545 335573 "COMRING" 335578 T COMRING (NIL) -9 NIL 335630 NIL) (-174 333853 334229 334413 "COMPPROP" 334707 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333508 333549 333677 "COMPLPAT" 333812 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333138 333201 333308 "COMPLEX2" 333445 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321521 332947 333056 "COMPLEX" 333061 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320842 320981 321141 "COMPILER" 321381 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320554 320595 320693 "COMPFACT" 320801 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301927 314258 314298 "COMPCAT" 315302 NIL COMPCAT (NIL T) -9 NIL 316650 NIL) (-167 290815 294366 297993 "COMPCAT-" 298349 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290538 290572 290675 "COMMUPC" 290781 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290326 290366 290425 "COMMONOP" 290499 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289848 290130 290205 "COMMAAST" 290271 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289355 289599 289686 "COMM" 289781 T COMM (NIL) -8 NIL NIL NIL) (-162 288550 288798 288826 "COMBOPC" 289164 T COMBOPC (NIL) -9 NIL 289339 NIL) (-161 287404 287656 287898 "COMBINAT" 288340 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283747 284435 285062 "COMBF" 286826 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282409 282863 283098 "COLOR" 283532 T COLOR (NIL) -8 NIL NIL NIL) (-158 281825 282130 282222 "COLONAST" 282337 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281459 281512 281637 "CMPLXRT" 281772 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280847 281159 281258 "CLLCTAST" 281380 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276306 277377 278457 "CLIP" 279787 T CLIP (NIL) -7 NIL NIL NIL) (-154 274479 275407 275647 "CLIF" 276133 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270461 272597 272638 "CLAGG" 273567 NIL CLAGG (NIL T) -9 NIL 274103 NIL) (-152 268805 269340 269923 "CLAGG-" 269928 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268343 268434 268574 "CINTSLPE" 268714 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265808 266315 266863 "CHVAR" 267871 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264848 265522 265550 "CHARZ" 265555 T CHARZ (NIL) -9 NIL 265570 NIL) (-148 264596 264642 264720 "CHARPOL" 264802 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263514 264227 264255 "CHARNZ" 264302 T CHARNZ (NIL) -9 NIL 264358 NIL) (-146 260458 261568 262097 "CHAR" 263005 T CHAR (NIL) -8 NIL NIL NIL) (-145 260166 260245 260273 "CFCAT" 260384 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259389 259518 259701 "CDEN" 260050 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254986 258542 258822 "CCLASS" 259129 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254207 254394 254571 "CATEGORY" 254829 T -10 (NIL) -8 NIL NIL NIL) (-141 253702 254126 254174 "CATCTOR" 254179 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253093 253405 253503 "CATAST" 253624 T CATAST (NIL) -8 NIL NIL NIL) (-139 252509 252814 252906 "CASEAST" 253021 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251605 251765 251986 "CARTEN2" 252356 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246503 247762 248506 "CARTEN" 250917 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244633 245653 245910 "CARD" 246266 T CARD (NIL) -8 NIL NIL NIL) (-135 244155 244437 244512 "CAPSLAST" 244578 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243597 243853 243881 "CACHSET" 244013 T CACHSET (NIL) -9 NIL 244091 NIL) (-133 242987 243375 243403 "CABMON" 243453 T CABMON (NIL) -9 NIL 243509 NIL) (-132 242424 242691 242801 "BYTEORD" 242897 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237351 241929 242101 "BYTEBUF" 242272 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236109 236866 237015 "BYTE" 237178 T BYTE (NIL) -8 NIL NIL 237307) (-129 233371 235801 235908 "BTREE" 236035 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230573 233019 233141 "BTOURN" 233281 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227680 230015 230056 "BTCAT" 230124 NIL BTCAT (NIL T) -9 NIL 230201 NIL) (-126 227329 227427 227576 "BTCAT-" 227581 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222218 226575 226603 "BTAGG" 226717 T BTAGG (NIL) -9 NIL 226827 NIL) (-124 221672 221833 222039 "BTAGG-" 222044 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218408 220950 221165 "BSTREE" 221489 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217516 217672 217856 "BRILL" 218264 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213911 216214 216255 "BRAGG" 216904 NIL BRAGG (NIL T) -9 NIL 217162 NIL) (-120 212344 212846 213401 "BRAGG-" 213406 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204580 211688 211873 "BPADICRT" 212191 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202589 204517 204562 "BPADIC" 204567 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202281 202317 202431 "BOUNDZRO" 202553 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 200008 200466 200941 "BOP1" 201839 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194990 196434 197346 "BOP" 199116 T BOP (NIL) -8 NIL NIL NIL) (-114 193655 194578 194720 "BOOLEAN" 194868 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193248 193405 193433 "BOOLE" 193544 T BOOLE (NIL) -9 NIL 193625 NIL) (-112 193116 193143 193209 "BOOLE-" 193214 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192285 192785 192839 "BMODULE" 192844 NIL BMODULE (NIL T T) -9 NIL 192909 NIL) (-110 187606 192083 192156 "BITS" 192232 T BITS (NIL) -8 NIL NIL NIL) (-109 187003 187146 187286 "BINDING" 187486 T BINDING (NIL) -8 NIL NIL NIL) (-108 180042 186598 186747 "BINARY" 186874 T BINARY (NIL) -8 NIL NIL NIL) (-107 177649 179269 179310 "BGAGG" 179570 NIL BGAGG (NIL T) -9 NIL 179707 NIL) (-106 177474 177512 177603 "BGAGG-" 177608 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176497 176858 177063 "BFUNCT" 177289 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175167 175365 175653 "BEZOUT" 176321 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171365 174019 174349 "BBTREE" 174870 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170948 171044 171072 "BASTYPE" 171249 T BASTYPE (NIL) -9 NIL 171348 NIL) (-101 170606 170705 170840 "BASTYPE-" 170845 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170028 170116 170268 "BALFACT" 170517 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168764 169443 169629 "AUTOMOR" 169873 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168490 168495 168521 "ATTREG" 168526 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166652 167187 167539 "ATTRBUT" 168156 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166206 166480 166546 "ATTRAST" 166604 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165706 165855 165881 "ATRIG" 166082 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165503 165556 165643 "ATRIG-" 165648 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165086 165320 165346 "ASTCAT" 165351 T ASTCAT (NIL) -9 NIL 165381 NIL) (-92 164795 164872 164991 "ASTCAT-" 164996 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162769 164571 164659 "ASTACK" 164738 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161258 161571 161936 "ASSOCEQ" 162451 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160182 160917 161041 "ASP9" 161165 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158942 159787 159929 "ASP80" 160071 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158669 158890 158929 "ASP8" 158934 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157515 158346 158464 "ASP78" 158582 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156376 157195 157312 "ASP77" 157429 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155180 156014 156145 "ASP74" 156276 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153972 154815 154947 "ASP73" 155079 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152762 153607 153739 "ASP7" 153871 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151758 152588 152688 "ASP6" 152693 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150597 151435 151553 "ASP55" 151671 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149438 150271 150390 "ASP50" 150509 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148418 149139 149249 "ASP49" 149359 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147094 147957 148125 "ASP42" 148307 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145763 146627 146797 "ASP41" 146981 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144743 145464 145574 "ASP4" 145684 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143585 144420 144538 "ASP35" 144656 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143314 143533 143572 "ASP34" 143577 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143033 143118 143194 "ASP33" 143269 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141819 142668 142800 "ASP31" 142932 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141548 141767 141806 "ASP30" 141811 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141265 141352 141428 "ASP29" 141503 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140994 141213 141252 "ASP28" 141257 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140723 140942 140981 "ASP27" 140986 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139699 140421 140532 "ASP24" 140643 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138668 139501 139613 "ASP20" 139618 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137503 138342 138461 "ASP19" 138580 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137222 137307 137383 "ASP12" 137458 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135966 136821 136965 "ASP10" 137109 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134946 135667 135777 "ASP1" 135887 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132558 134790 134881 "ARRAY2" 134886 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131572 131763 131984 "ARRAY12" 132381 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126932 131220 131334 "ARRAY1" 131489 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120977 123134 123209 "ARR2CAT" 125839 NIL ARR2CAT (NIL T T T) -9 NIL 126597 NIL) (-56 118267 119155 120109 "ARR2CAT-" 120114 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117518 117894 118019 "ARITY" 118160 T ARITY (NIL) -8 NIL NIL NIL) (-54 116276 116446 116745 "APPRULE" 117354 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115921 115975 116094 "APPLYORE" 116222 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115175 115322 115479 "ANY1" 115795 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114475 114768 114888 "ANY" 115073 T ANY (NIL) -8 NIL NIL NIL) (-50 111801 112912 113239 "ANTISYM" 114199 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111245 111508 111604 "ANON" 111723 T ANON (NIL) -8 NIL NIL NIL) (-48 104401 109784 110238 "AN" 110809 T AN (NIL) -8 NIL NIL NIL) (-47 100057 101673 101724 "AMR" 102472 NIL AMR (NIL T T) -9 NIL 103072 NIL) (-46 99109 99390 99753 "AMR-" 99758 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82578 99026 99087 "ALIST" 99092 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78875 82172 82341 "ALGSC" 82496 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75325 75985 76592 "ALGPKG" 78315 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74590 74703 74887 "ALGMFACT" 75211 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70573 71204 71798 "ALGMANIP" 74174 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59912 70199 70349 "ALGFF" 70506 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59084 59239 59418 "ALGFACT" 59770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57873 58611 58649 "ALGEBRA" 58654 NIL ALGEBRA (NIL T) -9 NIL 58695 NIL) (-37 57573 57650 57782 "ALGEBRA-" 57787 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38527 55410 55462 "ALAGG" 55598 NIL ALAGG (NIL T T) -9 NIL 55759 NIL) (-35 38027 38176 38202 "AHYP" 38403 T AHYP (NIL) -9 NIL NIL NIL) (-34 36912 37206 37232 "AGG" 37731 T AGG (NIL) -9 NIL 38010 NIL) (-33 36310 36508 36722 "AGG-" 36727 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34070 34539 34944 "AF" 35952 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33490 33795 33885 "ADDAST" 33998 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32722 33017 33173 "ACPLOT" 33352 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20273 29654 29692 "ACFS" 30299 NIL ACFS (NIL T) -9 NIL 30538 NIL) (-28 18180 18790 19552 "ACFS-" 19557 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16213 16239 "ACF" 17118 T ACF (NIL) -9 NIL 17531 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3473039 3473044 3473049 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3473024 3473029 3473034 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3473009 3473014 3473019 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472994 3472999 3473004 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471980 3472869 3472946 "ZMOD" 3472951 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3471016 3471198 3471421 "ZLINDEP" 3471812 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3460178 3462084 3464056 "ZDSOLVE" 3469146 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459412 3459565 3459754 "YSTREAM" 3460024 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458772 3459081 3459196 "YDIAGRAM" 3459319 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3456220 3458073 3458277 "XRPOLY" 3458615 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452487 3454091 3454666 "XPR" 3455692 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449818 3451494 3451549 "XPOLYC" 3451837 NIL XPOLYC (NIL T T) -9 NIL 3451950 NIL) (-1319 3447213 3449149 3449353 "XPOLY" 3449649 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3443159 3445730 3446118 "XPBWPOLY" 3446871 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3438051 3439630 3439685 "XFALG" 3441857 NIL XFALG (NIL T T) -9 NIL 3442646 NIL) (-1316 3433314 3436027 3436069 "XF" 3436690 NIL XF (NIL T) -9 NIL 3437090 NIL) (-1315 3432911 3433023 3433192 "XF-" 3433197 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3432026 3432148 3432353 "XEXPPKG" 3432803 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429767 3431876 3431972 "XDPOLY" 3431977 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428422 3429160 3429203 "XALG" 3429208 NIL XALG (NIL T) -9 NIL 3429319 NIL) (-1311 3421332 3426399 3426893 "WUTSET" 3428014 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419434 3420384 3420707 "WP" 3421143 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418982 3419256 3419326 "WHILEAST" 3419386 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418394 3418699 3418793 "WHEREAST" 3418910 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3417268 3417478 3417773 "WFFINTBS" 3418191 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3415136 3415599 3416061 "WEIER" 3416840 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3414060 3414618 3414660 "VSPACE" 3414796 NIL VSPACE (NIL T) -9 NIL 3414870 NIL) (-1304 3413892 3413925 3414016 "VSPACE-" 3414021 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413689 3413743 3413811 "VOID" 3413846 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409957 3410752 3411489 "VIEWDEF" 3412974 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398901 3401505 3403678 "VIEW3D" 3407806 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390918 3392812 3394391 "VIEW2D" 3397344 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3389018 3389413 3389819 "VIEW" 3390534 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387571 3387854 3388172 "VECTOR2" 3388748 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382477 3387341 3387433 "VECTOR" 3387514 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375422 3380181 3380224 "VECTCAT" 3381219 NIL VECTCAT (NIL T) -9 NIL 3381806 NIL) (-1295 3374364 3374690 3375080 "VECTCAT-" 3375085 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373770 3374015 3374135 "VARIABLE" 3374279 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373703 3373708 3373738 "UTYPE" 3373743 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372511 3372687 3372949 "UTSODETL" 3373529 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369903 3370411 3370935 "UTSODE" 3372052 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359906 3365836 3365879 "UTSCAT" 3366991 NIL UTSCAT (NIL T) -9 NIL 3367749 NIL) (-1289 3357032 3357976 3358965 "UTSCAT-" 3358970 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356653 3356702 3356835 "UTS2" 3356983 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347963 3354414 3354894 "UTS" 3356231 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341830 3344773 3344816 "URAGG" 3346886 NIL URAGG (NIL T) -9 NIL 3347609 NIL) (-1285 3338553 3339632 3340755 "URAGG-" 3340760 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333922 3337188 3337653 "UPXSSING" 3338217 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326337 3333826 3333898 "UPXSCONS" 3333903 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3315081 3322539 3322601 "UPXSCCA" 3323175 NIL UPXSCCA (NIL T T) -9 NIL 3323408 NIL) (-1281 3314701 3314804 3314978 "UPXSCCA-" 3314983 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303345 3310528 3310571 "UPXSCAT" 3311219 NIL UPXSCAT (NIL T) -9 NIL 3311828 NIL) (-1279 3302769 3302854 3303033 "UPXS2" 3303260 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3294247 3302151 3302415 "UPXS" 3302563 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292883 3293154 3293505 "UPSQFREE" 3293990 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285707 3289149 3289204 "UPSCAT" 3290284 NIL UPSCAT (NIL T T) -9 NIL 3291050 NIL) (-1275 3284863 3285118 3285445 "UPSCAT-" 3285450 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284484 3284533 3284666 "UPOLYC2" 3284814 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268611 3277611 3277654 "UPOLYC" 3279755 NIL UPOLYC (NIL T) -9 NIL 3280976 NIL) (-1272 3259459 3262365 3265512 "UPOLYC-" 3265517 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258780 3258905 3259069 "UPMP" 3259348 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258327 3258414 3258553 "UPDIVP" 3258693 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256865 3257144 3257460 "UPDECOMP" 3258076 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3256078 3256208 3256394 "UPCDEN" 3256749 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255591 3255666 3255815 "UP2" 3256003 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3246166 3255274 3255403 "UP" 3255510 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245371 3245508 3245713 "UNISEG2" 3246009 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243724 3244575 3244852 "UNISEG" 3245129 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242766 3242964 3243190 "UNIFACT" 3243540 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229476 3242670 3242742 "ULSCONS" 3242747 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3209272 3222556 3222618 "ULSCCAT" 3223256 NIL ULSCCAT (NIL T T) -9 NIL 3223545 NIL) (-1260 3208268 3208567 3208955 "ULSCCAT-" 3208960 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196709 3203814 3203857 "ULSCAT" 3204720 NIL ULSCAT (NIL T) -9 NIL 3205451 NIL) (-1258 3196133 3196218 3196397 "ULS2" 3196624 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177943 3195445 3195687 "ULS" 3195949 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176862 3177562 3177676 "UINT8" 3177787 T UINT8 (NIL) -8 NIL NIL 3177879) (-1255 3175780 3176480 3176594 "UINT64" 3176705 T UINT64 (NIL) -8 NIL NIL 3176797) (-1254 3174698 3175398 3175512 "UINT32" 3175623 T UINT32 (NIL) -8 NIL NIL 3175715) (-1253 3173616 3174316 3174430 "UINT16" 3174541 T UINT16 (NIL) -8 NIL NIL 3174633) (-1252 3171695 3172862 3172892 "UFD" 3173104 T UFD (NIL) -9 NIL 3173218 NIL) (-1251 3171477 3171535 3171630 "UFD-" 3171635 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170535 3170742 3170958 "UDVO" 3171283 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168301 3168760 3169231 "UDPO" 3170099 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3168013 3168256 3168287 "TYPEAST" 3168292 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167946 3167951 3167981 "TYPE" 3167986 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166899 3167119 3167359 "TWOFACT" 3167740 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165874 3166308 3166543 "TUPLE" 3166699 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163511 3164084 3164623 "TUBETOOL" 3165357 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162317 3162558 3162800 "TUBE" 3163304 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150452 3155074 3155171 "TSETCAT" 3160440 NIL TSETCAT (NIL T T T T) -9 NIL 3161972 NIL) (-1241 3144920 3146784 3148675 "TSETCAT-" 3148680 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3139099 3143892 3144175 "TS" 3144672 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133572 3134585 3135514 "TRMANIP" 3138235 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3133001 3133076 3133239 "TRIMAT" 3133504 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130813 3131104 3131461 "TRIGMNIP" 3132750 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130297 3130446 3130476 "TRIGCAT" 3130689 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129942 3130045 3130186 "TRIGCAT-" 3130191 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126556 3128800 3129081 "TREE" 3129696 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125662 3126358 3126388 "TRANFUN" 3126423 T TRANFUN (NIL) -9 NIL 3126489 NIL) (-1232 3124881 3125132 3125412 "TRANFUN-" 3125417 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124679 3124717 3124778 "TOPSP" 3124842 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3124009 3124142 3124296 "TOOLSIGN" 3124560 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122523 3123186 3123425 "TEXTFILE" 3123792 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122298 3122335 3122407 "TEX1" 3122486 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3120102 3120751 3121180 "TEX" 3121891 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119738 3119813 3119903 "TEMUTL" 3120034 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117832 3118172 3118497 "TBCMPPK" 3119461 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3109152 3115918 3115974 "TBAGG" 3116374 NIL TBAGG (NIL T T) -9 NIL 3116585 NIL) (-1223 3104036 3105710 3107464 "TBAGG-" 3107469 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103402 3103527 3103672 "TANEXP" 3103925 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102853 3103177 3103267 "TALGOP" 3103347 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3102247 3102364 3102502 "TABLEAU" 3102750 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095261 3102104 3102197 "TABLE" 3102202 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089791 3091089 3092337 "TABLBUMP" 3094047 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3089001 3089160 3089341 "SYSTEM" 3089632 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085406 3086159 3086942 "SYSSOLP" 3088252 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3085168 3085361 3085392 "SYSPTR" 3085397 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3084007 3084699 3084825 "SYSNNI" 3085011 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085103) (-1213 3083214 3083769 3083848 "SYSINT" 3083908 NIL SYSINT (NIL NIL) -8 NIL NIL 3083953) (-1212 3079312 3080492 3081202 "SYNTAX" 3082526 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076392 3077072 3077704 "SYMTAB" 3078702 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071491 3072543 3073526 "SYMS" 3075431 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068390 3070942 3071175 "SYMPOLY" 3071293 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067895 3067982 3068105 "SYMFUNC" 3068302 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063693 3065207 3066020 "SYMBOL" 3067104 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3057166 3058921 3060641 "SWITCH" 3061995 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049920 3056122 3056416 "SUTS" 3056930 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041398 3049302 3049566 "SUPXS" 3049714 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040545 3040684 3040901 "SUPFRACF" 3041266 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3040160 3040225 3040338 "SUP2" 3040480 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030683 3039778 3039904 "SUP" 3040069 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3029107 3029405 3029761 "SUMRF" 3030382 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028430 3028508 3028700 "SUMFS" 3029028 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010275 3027742 3027984 "SULS" 3028246 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009823 3010097 3010167 "SUCHTAST" 3010227 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3009064 3009348 3009488 "SUCH" 3009731 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002703 3003970 3004929 "SUBSPACE" 3008152 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3002123 3002223 3002387 "SUBRESP" 3002591 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2996134 2997416 2998563 "STTFNC" 3001023 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989328 2990799 2992110 "STTF" 2994870 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980445 2982510 2984304 "STTAYLOR" 2987569 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2973199 2980309 2980392 "STRTBL" 2980397 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967596 2972908 2973007 "STRING" 2973122 T STRING (NIL) -8 NIL NIL NIL) (-1188 2967100 2967183 2967327 "STREAM3" 2967513 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2966064 2966265 2966500 "STREAM2" 2966913 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965746 2965804 2965897 "STREAM1" 2966006 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957860 2963365 2963976 "STREAM" 2965170 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956852 2957057 2957288 "STINPROD" 2957676 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955967 2956341 2956489 "STEPAST" 2956726 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955463 2955715 2955745 "STEP" 2955825 T STEP (NIL) -9 NIL 2955903 NIL) (-1181 2948519 2955362 2955439 "STBL" 2955444 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2943069 2947682 2947725 "STAGG" 2947878 NIL STAGG (NIL T) -9 NIL 2947967 NIL) (-1179 2940621 2941373 2942245 "STAGG-" 2942250 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938593 2940391 2940483 "STACK" 2940564 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930600 2936734 2937190 "SREGSET" 2938223 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922947 2924394 2925907 "SRDCMPK" 2929206 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915247 2920306 2920336 "SRAGG" 2921639 T SRAGG (NIL) -9 NIL 2922247 NIL) (-1174 2914198 2914519 2914898 "SRAGG-" 2914903 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907782 2913145 2913566 "SQMATRIX" 2913824 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2901194 2904500 2905227 "SPLTREE" 2907127 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2897019 2897850 2898496 "SPLNODE" 2900620 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895994 2896299 2896329 "SPFCAT" 2896773 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894689 2894941 2895205 "SPECOUT" 2895752 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885335 2887653 2887683 "SPADXPT" 2892361 T SPADXPT (NIL) -9 NIL 2894527 NIL) (-1167 2885090 2885136 2885205 "SPADPRSR" 2885288 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882693 2885045 2885076 "SPADAST" 2885081 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874294 2876397 2876440 "SPACEC" 2880813 NIL SPACEC (NIL T) -9 NIL 2882629 NIL) (-1164 2872094 2874226 2874275 "SPACE3" 2874280 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870826 2871017 2871308 "SORTPAK" 2871899 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868888 2869221 2869633 "SOLVETRA" 2870490 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867926 2868160 2868421 "SOLVESER" 2868661 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2863158 2864118 2865113 "SOLVERAD" 2866978 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858883 2859582 2860311 "SOLVEFOR" 2862525 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852487 2858231 2858328 "SNTSCAT" 2858333 NIL SNTSCAT (NIL T T T T) -9 NIL 2858403 NIL) (-1157 2846031 2850810 2851201 "SMTS" 2852177 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839746 2845919 2845996 "SMP" 2846001 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837875 2838206 2838604 "SMITH" 2839443 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829400 2834454 2834557 "SMATCAT" 2835908 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836458 NIL) (-1153 2826172 2827163 2828341 "SMATCAT-" 2828346 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823641 2825380 2825423 "SKAGG" 2825684 NIL SKAGG (NIL T) -9 NIL 2825819 NIL) (-1151 2819131 2823110 2823294 "SINT" 2823446 T SINT (NIL) -8 NIL NIL 2823608) (-1150 2818897 2818941 2819007 "SIMPAN" 2819087 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817717 2817956 2818231 "SIGNRF" 2818656 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816532 2816701 2816985 "SIGNEF" 2817546 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815772 2816115 2816239 "SIGAST" 2816430 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814997 2815307 2815447 "SIG" 2815654 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812649 2813141 2813647 "SHP" 2814538 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2806022 2812550 2812626 "SHDP" 2812631 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805533 2805773 2805803 "SGROUP" 2805896 T SGROUP (NIL) -9 NIL 2805958 NIL) (-1142 2805385 2805417 2805490 "SGROUP-" 2805495 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2802104 2802874 2803597 "SGCF" 2804684 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795806 2801550 2801647 "SFRTCAT" 2801652 NIL SFRTCAT (NIL T T T T) -9 NIL 2801691 NIL) (-1139 2789125 2790245 2791381 "SFRGCD" 2794789 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2782143 2783324 2784510 "SFQCMPK" 2788058 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781745 2781852 2781963 "SFORT" 2782084 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780671 2781585 2781706 "SEXOF" 2781711 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776260 2777167 2777262 "SEXCAT" 2779884 NIL SEXCAT (NIL T T T T T) -9 NIL 2780444 NIL) (-1134 2775175 2776141 2776209 "SEX" 2776214 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773297 2773888 2774193 "SETMN" 2774916 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772827 2773015 2773045 "SETCAT" 2773162 T SETCAT (NIL) -9 NIL 2773247 NIL) (-1131 2772595 2772659 2772758 "SETCAT-" 2772763 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768698 2771056 2771099 "SETAGG" 2771969 NIL SETAGG (NIL T) -9 NIL 2772309 NIL) (-1129 2768120 2768272 2768509 "SETAGG-" 2768514 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764929 2768054 2768102 "SET" 2768107 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764312 2764625 2764726 "SEQAST" 2764850 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763439 2763805 2763866 "SEGXCAT" 2764152 NIL SEGXCAT (NIL T T) -9 NIL 2764272 NIL) (-1125 2762364 2762632 2762675 "SEGCAT" 2763197 NIL SEGCAT (NIL T) -9 NIL 2763418 NIL) (-1124 2761979 2762044 2762157 "SEGBIND2" 2762299 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760869 2761342 2761550 "SEGBIND" 2761806 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760388 2760670 2760747 "SEGAST" 2760814 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759597 2759733 2759937 "SEG2" 2760232 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758513 2759263 2759445 "SEG" 2759450 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757746 2758448 2758495 "SDVAR" 2758500 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2749097 2757516 2757646 "SDPOL" 2757651 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747666 2747956 2748275 "SCPKG" 2748812 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746788 2747002 2747194 "SCOPE" 2747496 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745984 2746142 2746321 "SCACHE" 2746643 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745568 2745802 2745832 "SASTCAT" 2745837 T SASTCAT (NIL) -9 NIL 2745850 NIL) (-1113 2744971 2745403 2745479 "SAOS" 2745514 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744530 2744571 2744744 "SAERFFC" 2744930 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2744117 2744158 2744317 "SAEFACT" 2744489 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2737144 2744014 2744094 "SAE" 2744099 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735447 2735779 2736180 "RURPK" 2736810 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2734024 2734390 2734695 "RULESET" 2735281 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733594 2733818 2733901 "RULECOLD" 2733976 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730709 2731347 2731805 "RULE" 2733275 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730493 2730527 2730598 "RTVALUE" 2730660 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729904 2730210 2730304 "RSTRCAST" 2730421 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724674 2725547 2726467 "RSETGCD" 2729103 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713238 2718982 2719079 "RSETCAT" 2723198 NIL RSETCAT (NIL T T T T) -9 NIL 2724295 NIL) (-1101 2711057 2711704 2712528 "RSETCAT-" 2712533 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703365 2704819 2706339 "RSDCMPK" 2709656 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701234 2701797 2701871 "RRCC" 2702957 NIL RRCC (NIL T T) -9 NIL 2703301 NIL) (-1098 2700555 2700759 2701038 "RRCC-" 2701043 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699938 2700251 2700352 "RPTAST" 2700476 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672317 2683050 2683117 "RPOLCAT" 2693783 NIL RPOLCAT (NIL T T T) -9 NIL 2696943 NIL) (-1095 2663287 2666155 2669277 "RPOLCAT-" 2669282 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653740 2661498 2661980 "ROUTINE" 2662827 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649789 2653366 2653506 "ROMAN" 2653622 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647901 2648649 2648909 "ROIRC" 2649594 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643614 2646390 2646420 "RNS" 2646724 T RNS (NIL) -9 NIL 2646998 NIL) (-1090 2642021 2642506 2643040 "RNS-" 2643115 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640982 2641386 2641588 "RNGBIND" 2641872 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640275 2640779 2640809 "RNG" 2640814 T RNG (NIL) -9 NIL 2640835 NIL) (-1087 2639570 2640048 2640091 "RMODULE" 2640096 NIL RMODULE (NIL T) -9 NIL 2640123 NIL) (-1086 2638394 2638500 2638836 "RMCAT2" 2639471 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634896 2637740 2638037 "RMATRIX" 2638156 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627395 2629983 2630098 "RMATCAT" 2633457 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634439 NIL) (-1083 2626734 2626917 2627224 "RMATCAT-" 2627229 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626307 2626521 2626564 "RLINSET" 2626626 NIL RLINSET (NIL T) -9 NIL 2626670 NIL) (-1081 2625868 2625949 2626077 "RINTERP" 2626226 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624792 2625466 2625496 "RING" 2625552 T RING (NIL) -9 NIL 2625644 NIL) (-1079 2624572 2624628 2624725 "RING-" 2624730 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623383 2623650 2623908 "RIDIST" 2624336 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2614008 2622851 2623057 "RGCHAIN" 2623231 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613266 2613750 2613791 "RGBCSPC" 2613849 NIL RGBCSPC (NIL T) -9 NIL 2613901 NIL) (-1075 2612332 2612791 2612832 "RGBCMDL" 2613064 NIL RGBCMDL (NIL T) -9 NIL 2613178 NIL) (-1074 2611972 2612041 2612144 "RFFACTOR" 2612263 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611691 2611732 2611829 "RFFACT" 2611931 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609742 2610172 2610554 "RFDIST" 2611331 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606682 2607350 2608020 "RF" 2609106 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2606129 2606227 2606390 "RETSOL" 2606584 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605747 2605845 2605888 "RETRACT" 2606021 NIL RETRACT (NIL T) -9 NIL 2606108 NIL) (-1068 2605590 2605621 2605708 "RETRACT-" 2605713 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2605138 2605412 2605482 "RETAST" 2605542 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597488 2604791 2604918 "RESULT" 2605033 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595923 2596757 2596956 "RESRING" 2597391 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595547 2595608 2595706 "RESLATC" 2595860 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595246 2595287 2595394 "REPSQ" 2595506 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594937 2594978 2595089 "REPDB" 2595205 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588769 2590226 2591449 "REP2" 2593749 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2585072 2585827 2586635 "REP1" 2587996 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582452 2583074 2583676 "REP" 2584492 T REP (NIL) -7 NIL NIL NIL) (-1058 2574460 2580593 2581049 "REGSET" 2582082 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2573169 2573608 2573858 "REF" 2574245 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572534 2572649 2572816 "REDORDER" 2573053 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567898 2571747 2571974 "RECLOS" 2572362 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566932 2567131 2567346 "REALSOLV" 2567705 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563379 2564217 2565101 "REAL0Q" 2566097 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558932 2559968 2561029 "REAL0" 2562360 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558766 2558819 2558849 "REAL" 2558854 T REAL (NIL) -9 NIL 2558889 NIL) (-1050 2558177 2558483 2558577 "RDUCEAST" 2558694 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557576 2557654 2557861 "RDIV" 2558099 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556626 2556818 2557031 "RDIST" 2557398 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555211 2555510 2555882 "RDETRS" 2556334 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2553005 2553477 2554015 "RDETR" 2554753 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551624 2551908 2552305 "RDEEFS" 2552721 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2550127 2550439 2550864 "RDEEF" 2551312 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543599 2547081 2547111 "RCFIELD" 2548406 T RCFIELD (NIL) -9 NIL 2549137 NIL) (-1042 2541555 2542167 2542863 "RCFIELD-" 2542938 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537607 2539628 2539671 "RCAGG" 2540755 NIL RCAGG (NIL T) -9 NIL 2541220 NIL) (-1040 2537217 2537329 2537492 "RCAGG-" 2537497 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536534 2536664 2536829 "RATRET" 2537101 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2536075 2536154 2536275 "RATFACT" 2536462 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535353 2535503 2535655 "RANDSRC" 2535945 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2535081 2535131 2535204 "RADUTIL" 2535302 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527205 2533912 2534223 "RADIX" 2534804 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516799 2527047 2527177 "RADFF" 2527182 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516428 2516521 2516551 "RADCAT" 2516711 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516198 2516258 2516358 "RADCAT-" 2516363 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2514109 2515968 2516060 "QUEUE" 2516141 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513734 2513783 2513914 "QUATCT2" 2514060 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2506105 2510157 2510199 "QUATCAT" 2510990 NIL QUATCAT (NIL T) -9 NIL 2511756 NIL) (-1028 2501986 2503281 2504671 "QUATCAT-" 2504767 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497825 2501919 2501967 "QUAT" 2501972 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2495081 2496873 2496916 "QUAGG" 2497297 NIL QUAGG (NIL T) -9 NIL 2497472 NIL) (-1025 2494629 2494903 2494973 "QQUTAST" 2495033 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493540 2494142 2494307 "QFORM" 2494510 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2493165 2493214 2493345 "QFCAT2" 2493491 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482841 2489012 2489054 "QFCAT" 2489722 NIL QFCAT (NIL T) -9 NIL 2490723 NIL) (-1021 2478156 2479609 2481203 "QFCAT-" 2481299 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477587 2477721 2477853 "QEQUAT" 2478046 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470605 2471786 2472972 "QCMPACK" 2476520 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469834 2470016 2470252 "QALGSET2" 2470423 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467284 2467820 2468250 "QALGSET" 2469489 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465951 2466193 2466512 "PWFFINTB" 2467057 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2464096 2464294 2464650 "PUSHVAR" 2465765 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459823 2461039 2461082 "PTRANFN" 2462993 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2458160 2458505 2458829 "PTPACK" 2459534 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457783 2457846 2457957 "PTFUNC2" 2458097 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451699 2456572 2456615 "PTCAT" 2456915 NIL PTCAT (NIL T) -9 NIL 2457068 NIL) (-1010 2451348 2451389 2451515 "PSQFR" 2451658 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449920 2450236 2450572 "PSEUDLIN" 2451046 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436440 2439015 2441341 "PSETPK" 2447680 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2429148 2432176 2432274 "PSETCAT" 2435315 NIL PSETCAT (NIL T T T T) -9 NIL 2436129 NIL) (-1006 2426873 2427615 2428439 "PSETCAT-" 2428444 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426186 2426381 2426411 "PSCURVE" 2426683 T PSCURVE (NIL) -9 NIL 2426850 NIL) (-1004 2421902 2423676 2423743 "PSCAT" 2424595 NIL PSCAT (NIL T T T) -9 NIL 2424835 NIL) (-1003 2420896 2421178 2421581 "PSCAT-" 2421586 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2419095 2419955 2420220 "PRTITION" 2420653 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418506 2418812 2418906 "PRTDAST" 2419023 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407350 2409772 2411962 "PRS" 2416368 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404970 2406672 2406712 "PRQAGG" 2406895 NIL PRQAGG (NIL T) -9 NIL 2406997 NIL) (-998 2404149 2404598 2404626 "PROPLOG" 2404765 T PROPLOG (NIL) -9 NIL 2404880 NIL) (-997 2403747 2403810 2403933 "PROPFUN2" 2404072 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2403044 2403183 2403355 "PROPFUN1" 2403608 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2401025 2401791 2402088 "PROPFRML" 2402780 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400470 2400601 2400729 "PROPERTY" 2400917 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394358 2398636 2399456 "PRODUCT" 2399696 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2394148 2394186 2394245 "PRINT" 2394319 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393464 2393605 2393757 "PRIMES" 2394028 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391511 2391930 2392396 "PRIMELT" 2393043 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391228 2391289 2391317 "PRIMCAT" 2391441 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390217 2390413 2390641 "PRIMARR2" 2391046 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385939 2390155 2390200 "PRIMARR" 2390205 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385576 2385638 2385749 "PREASSOC" 2385877 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382534 2385034 2385268 "PR" 2385387 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381985 2382142 2382170 "PPCURVE" 2382375 T PPCURVE (NIL) -9 NIL 2382511 NIL) (-983 2381532 2381780 2381863 "PORTNUM" 2381922 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378869 2379290 2379882 "POLYROOT" 2381113 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378246 2378310 2378544 "POLYLIFT" 2378805 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374467 2374970 2375599 "POLYCATQ" 2377791 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2360108 2366214 2366279 "POLYCAT" 2369793 NIL POLYCAT (NIL T T T) -9 NIL 2371671 NIL) (-978 2353227 2355419 2357803 "POLYCAT-" 2357808 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352808 2352882 2353002 "POLY2UP" 2353153 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352434 2352497 2352606 "POLY2" 2352745 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345642 2352038 2352198 "POLY" 2352307 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344303 2344566 2344842 "POLUTIL" 2345416 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342622 2342935 2343266 "POLTOPOL" 2344025 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337618 2342556 2342603 "POINT" 2342608 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335751 2336162 2336537 "PNTHEORY" 2337263 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334197 2334506 2334905 "PMTOOLS" 2335449 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333784 2333868 2333985 "PMSYM" 2334113 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333286 2333361 2333536 "PMQFCAT" 2333709 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332667 2332765 2332927 "PMPREDFS" 2333187 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2332010 2332132 2332288 "PMPRED" 2332544 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330664 2330882 2331260 "PMPLCAT" 2331772 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330190 2330275 2330427 "PMLSAGG" 2330579 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329657 2329739 2329921 "PMKERNEL" 2330108 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329268 2329349 2329462 "PMINS" 2329576 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328704 2328779 2328988 "PMFS" 2329193 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327920 2328050 2328255 "PMDOWN" 2328581 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2327169 2327303 2327466 "PMASSFS" 2327807 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326312 2326494 2326675 "PMASS" 2327008 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325961 2326035 2326129 "PLOTTOOL" 2326238 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321613 2322807 2323729 "PLOT3D" 2325059 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320501 2320702 2320937 "PLOT1" 2321417 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314922 2316312 2317460 "PLOT" 2319373 T PLOT (NIL) -8 NIL NIL NIL) (-953 2290097 2294988 2299839 "PLEQN" 2310188 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289784 2289837 2289940 "PINTERPA" 2290044 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2289090 2289224 2289404 "PINTERP" 2289649 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287175 2288348 2288376 "PID" 2288558 T PID (NIL) -9 NIL 2288692 NIL) (-949 2286920 2286963 2287038 "PICOERCE" 2287132 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2286016 2286684 2286771 "PI" 2286811 T PI (NIL) -8 NIL NIL 2286878) (-947 2285324 2285475 2285651 "PGROEB" 2285872 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280763 2281722 2282628 "PGE" 2284438 T PGE (NIL) -7 NIL NIL NIL) (-945 2278844 2279133 2279499 "PGCD" 2280480 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2278170 2278285 2278446 "PFRPAC" 2278728 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274421 2276718 2277071 "PFR" 2277849 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272774 2273054 2273379 "PFOTOOLS" 2274168 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271289 2271546 2271897 "PFOQ" 2272531 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269772 2270002 2270358 "PFO" 2271073 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266850 2268363 2268391 "PFECAT" 2268976 T PFECAT (NIL) -9 NIL 2269360 NIL) (-938 2266277 2266449 2266663 "PFECAT-" 2266668 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264850 2265132 2265433 "PFBRU" 2266026 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262680 2263068 2263500 "PFBR" 2264501 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258605 2262569 2262638 "PF" 2262643 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253659 2254812 2255682 "PERMGRP" 2257768 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251571 2252683 2252724 "PERMCAT" 2253124 NIL PERMCAT (NIL T) -9 NIL 2253422 NIL) (-932 2251218 2251265 2251389 "PERMAN" 2251524 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2247020 2248727 2249375 "PERM" 2250603 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244261 2246685 2246807 "PENDTREE" 2246931 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2243142 2243405 2243446 "PDSPC" 2243979 NIL PDSPC (NIL T) -9 NIL 2244224 NIL) (-928 2242197 2242463 2242825 "PDSPC-" 2242830 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240911 2241847 2241888 "PDRING" 2241893 NIL PDRING (NIL T) -9 NIL 2241921 NIL) (-926 2239654 2240416 2240470 "PDMOD" 2240475 NIL PDMOD (NIL T T) -9 NIL 2240579 NIL) (-925 2236821 2237647 2238315 "PDEPROB" 2239006 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234330 2234870 2235425 "PDEPACK" 2236286 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233218 2233432 2233683 "PDECOMP" 2234129 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230735 2231626 2231654 "PDECAT" 2232441 T PDECAT (NIL) -9 NIL 2233154 NIL) (-921 2230352 2230419 2230473 "PDDOM" 2230638 NIL PDDOM (NIL T T) -9 NIL 2230718 NIL) (-920 2230165 2230201 2230308 "PDDOM-" 2230313 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229910 2229949 2230039 "PCOMP" 2230126 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227950 2228711 2229008 "PBWLB" 2229639 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227576 2227639 2227748 "PATTERN2" 2227887 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225285 2225721 2226178 "PATTERN1" 2227165 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217464 2219358 2220696 "PATTERN" 2223968 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2217022 2217095 2217227 "PATRES2" 2217391 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214288 2214971 2215452 "PATRES" 2216587 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2212141 2212576 2212983 "PATMATCH" 2213955 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211595 2211846 2211887 "PATMAB" 2211994 NIL PATMAB (NIL T) -9 NIL 2212077 NIL) (-910 2210041 2210449 2210707 "PATLRES" 2211400 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209579 2209710 2209751 "PATAB" 2209756 NIL PATAB (NIL T) -9 NIL 2209928 NIL) (-908 2207719 2208156 2208579 "PARTPERM" 2209176 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207328 2207403 2207505 "PARSURF" 2207650 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206954 2207017 2207126 "PARSU2" 2207265 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206712 2206758 2206825 "PARSER" 2206907 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206321 2206396 2206498 "PARSCURV" 2206643 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205947 2206010 2206119 "PARSC2" 2206258 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205574 2205644 2205741 "PARPCURV" 2205883 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205200 2205263 2205372 "PARPC2" 2205511 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204189 2204573 2204755 "PARAMAST" 2205038 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203697 2203795 2203914 "PAN2EXPR" 2204090 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202390 2202818 2203046 "PALETTE" 2203489 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200735 2201395 2201755 "PAIR" 2202076 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193647 2199992 2200187 "PADICRC" 2200589 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185883 2192991 2193176 "PADICRAT" 2193494 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182673 2184543 2184583 "PADICCT" 2185164 NIL PADICCT (NIL NIL) -9 NIL 2185446 NIL) (-893 2180682 2182610 2182655 "PADIC" 2182660 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179627 2179839 2180107 "PADEPAC" 2180469 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178827 2178972 2179178 "PADE" 2179489 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2177060 2178035 2178315 "OWP" 2178631 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176505 2176766 2176863 "OVERSET" 2176983 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175425 2176110 2176282 "OVAR" 2176373 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163661 2166534 2168734 "OUTFORM" 2173245 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162943 2163258 2163385 "OUTBFILE" 2163554 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162220 2162415 2162443 "OUTBCON" 2162761 T OUTBCON (NIL) -9 NIL 2162927 NIL) (-884 2161803 2161933 2162090 "OUTBCON-" 2162095 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2161043 2161188 2161349 "OUT" 2161662 T OUT (NIL) -7 NIL NIL NIL) (-882 2160339 2160772 2160861 "OSI" 2160974 T OSI (NIL) -8 NIL NIL NIL) (-881 2159758 2160180 2160208 "OSGROUP" 2160213 T OSGROUP (NIL) -9 NIL 2160235 NIL) (-880 2158469 2158730 2159015 "ORTHPOL" 2159505 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155720 2158304 2158425 "OREUP" 2158430 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152823 2155411 2155538 "ORESUP" 2155662 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150323 2150851 2151412 "OREPCTO" 2152312 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143701 2146196 2146237 "OREPCAT" 2148585 NIL OREPCAT (NIL T) -9 NIL 2149689 NIL) (-875 2140674 2141630 2142688 "OREPCAT-" 2142693 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139866 2140144 2140172 "ORDTYPE" 2140481 T ORDTYPE (NIL) -9 NIL 2140644 NIL) (-873 2139167 2139383 2139638 "ORDTYPE-" 2139643 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138523 2138906 2139064 "ORDSTRCT" 2139069 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2138021 2138391 2138419 "ORDSET" 2138424 T ORDSET (NIL) -9 NIL 2138446 NIL) (-870 2136379 2137350 2137378 "ORDRING" 2137580 T ORDRING (NIL) -9 NIL 2137705 NIL) (-869 2136000 2136118 2136262 "ORDRING-" 2136267 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135251 2135816 2135844 "ORDMON" 2135849 T ORDMON (NIL) -9 NIL 2135870 NIL) (-867 2134395 2134560 2134755 "ORDFUNS" 2135100 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133610 2134125 2134153 "ORDFIN" 2134218 T ORDFIN (NIL) -9 NIL 2134292 NIL) (-865 2132864 2133003 2133189 "ORDCOMP2" 2133470 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129211 2131450 2131859 "ORDCOMP" 2132488 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125732 2126702 2127516 "OPTPROB" 2128417 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122474 2123173 2123877 "OPTPACK" 2125048 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2120087 2120913 2120941 "OPTCAT" 2121760 T OPTCAT (NIL) -9 NIL 2122410 NIL) (-860 2119405 2119764 2119869 "OPSIG" 2120002 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2119167 2119212 2119278 "OPQUERY" 2119359 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118473 2118753 2118794 "OPERCAT" 2119006 NIL OPERCAT (NIL T) -9 NIL 2119103 NIL) (-857 2118216 2118284 2118401 "OPERCAT-" 2118406 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2115125 2116527 2117031 "OP" 2117745 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114418 2114545 2114719 "ONECOMP2" 2114997 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2111031 2113215 2113584 "ONECOMP" 2114082 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110432 2110556 2110686 "OMSERVER" 2110921 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106946 2109872 2109912 "OMSAGG" 2109973 NIL OMSAGG (NIL T) -9 NIL 2110037 NIL) (-851 2105521 2105832 2106114 "OMPKG" 2106684 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103868 2105070 2105239 "OMLO" 2105402 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102804 2102975 2103195 "OMEXPR" 2103694 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101889 2102225 2102385 "OMERRK" 2102664 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2101126 2101435 2101571 "OMERR" 2101773 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100517 2100803 2100911 "OMENC" 2101038 T OMENC (NIL) -8 NIL NIL NIL) (-845 2094154 2095597 2096768 "OMDEV" 2099366 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093187 2093394 2093588 "OMCONN" 2093980 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092593 2092720 2092748 "OM" 2093047 T OM (NIL) -9 NIL NIL NIL) (-842 2090871 2092063 2092091 "OINTDOM" 2092096 T OINTDOM (NIL) -9 NIL 2092117 NIL) (-841 2087946 2089559 2089896 "OFMONOID" 2090566 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087180 2087883 2087928 "ODVAR" 2087933 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084317 2086925 2087080 "ODR" 2087085 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075722 2084093 2084219 "ODPOL" 2084224 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2069065 2075594 2075699 "ODP" 2075704 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067807 2068046 2068321 "ODETOOLS" 2068839 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064750 2065432 2066148 "ODESYS" 2067140 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059580 2060540 2061565 "ODERTRIC" 2063825 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2059000 2059088 2059282 "ODERED" 2059492 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055852 2056436 2057113 "ODERAT" 2058423 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052768 2053276 2053873 "ODEPRRIC" 2055381 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050663 2051307 2051793 "ODEPROB" 2052302 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2047129 2047668 2048315 "ODEPRIM" 2050142 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046372 2046480 2046740 "ODEPAL" 2047021 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042474 2043325 2044189 "ODEPACK" 2045528 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041517 2041642 2041864 "ODEINT" 2042363 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035582 2037043 2038490 "ODEIFTBL" 2040090 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030932 2031766 2032718 "ODEEF" 2034741 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030275 2030370 2030593 "ODECONST" 2030837 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028338 2029047 2029075 "ODECAT" 2029680 T ODECAT (NIL) -9 NIL 2030211 NIL) (-821 2027970 2028019 2028146 "OCTCT2" 2028289 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024463 2027675 2027797 "OCT" 2027880 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023686 2024256 2024284 "OCAMON" 2024289 T OCAMON (NIL) -9 NIL 2024310 NIL) (-818 2017950 2020729 2020769 "OC" 2021866 NIL OC (NIL T) -9 NIL 2022724 NIL) (-817 2014985 2015925 2016915 "OC-" 2017009 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014405 2014830 2014858 "OASGP" 2014863 T OASGP (NIL) -9 NIL 2014883 NIL) (-815 2013531 2014128 2014156 "OAMONS" 2014196 T OAMONS (NIL) -9 NIL 2014239 NIL) (-814 2012822 2013351 2013379 "OAMON" 2013384 T OAMON (NIL) -9 NIL 2013404 NIL) (-813 2011933 2012571 2012599 "OAGROUP" 2012604 T OAGROUP (NIL) -9 NIL 2012624 NIL) (-812 2011615 2011671 2011760 "NUMTUBE" 2011877 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2005134 2006706 2008242 "NUMQUAD" 2010099 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000814 2001848 2002883 "NUMODE" 2004119 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1998095 1999035 1999063 "NUMINT" 1999986 T NUMINT (NIL) -9 NIL 2000750 NIL) (-808 1997007 1997240 1997458 "NUMFMT" 1997897 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983190 1986311 1988843 "NUMERIC" 1994514 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976894 1982638 1982733 "NTSCAT" 1982738 NIL NTSCAT (NIL T T T T) -9 NIL 1982777 NIL) (-805 1976074 1976253 1976446 "NTPOLFN" 1976733 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975700 1975763 1975872 "NSUP2" 1976011 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962461 1972525 1973337 "NSUP" 1974921 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951297 1962235 1962368 "NSMP" 1962373 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949705 1950030 1950387 "NREP" 1950985 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948284 1948548 1948906 "NPCOEF" 1949448 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947332 1947465 1947681 "NORMRETR" 1948165 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945343 1945663 1946072 "NORMPK" 1947040 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1945022 1945056 1945180 "NORMMA" 1945309 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944805 1944840 1944909 "NONE1" 1944986 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944569 1944762 1944791 "NONE" 1944796 T NONE (NIL) -8 NIL NIL NIL) (-794 1944060 1944128 1944307 "NODE1" 1944501 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1942152 1943183 1943438 "NNI" 1943785 T NNI (NIL) -8 NIL NIL 1944020) (-792 1940548 1940885 1941249 "NLINSOL" 1941820 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936729 1937784 1938683 "NIPROB" 1939669 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935468 1935720 1936022 "NFINTBAS" 1936491 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934552 1935118 1935159 "NETCLT" 1935331 NIL NETCLT (NIL T) -9 NIL 1935413 NIL) (-788 1933224 1933491 1933772 "NCODIV" 1934320 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932980 1933023 1933098 "NCNTFRAC" 1933181 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1931136 1931524 1931944 "NCEP" 1932605 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929799 1930746 1930774 "NASRING" 1930884 T NASRING (NIL) -9 NIL 1930964 NIL) (-784 1929582 1929638 1929732 "NASRING-" 1929737 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928549 1929200 1929228 "NARNG" 1929345 T NARNG (NIL) -9 NIL 1929436 NIL) (-782 1928223 1928308 1928442 "NARNG-" 1928447 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1927060 1927309 1927544 "NAGSP" 1928008 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1918104 1920016 1921689 "NAGS" 1925407 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916628 1916960 1917291 "NAGF07" 1917793 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1911100 1912457 1913764 "NAGF04" 1915341 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903972 1905682 1907315 "NAGF02" 1909487 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1899136 1900296 1901413 "NAGF01" 1902875 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892716 1894330 1895915 "NAGE04" 1897571 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883777 1886006 1888136 "NAGE02" 1890606 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879670 1880677 1881641 "NAGE01" 1882833 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877447 1877999 1878557 "NAGD03" 1879132 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1869143 1871125 1873079 "NAGD02" 1875513 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862882 1864379 1865819 "NAGD01" 1867723 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1859019 1859913 1860750 "NAGC06" 1862065 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857466 1857816 1858172 "NAGC05" 1858683 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856830 1856961 1857105 "NAGC02" 1857342 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855631 1856358 1856398 "NAALG" 1856477 NIL NAALG (NIL T) -9 NIL 1856538 NIL) (-765 1855460 1855495 1855585 "NAALG-" 1855590 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849332 1850518 1851705 "MULTSQFR" 1854356 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848639 1848726 1848910 "MULTFACT" 1849244 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840777 1845222 1845275 "MTSCAT" 1846345 NIL MTSCAT (NIL T T) -9 NIL 1846861 NIL) (-761 1840483 1840543 1840635 "MTHING" 1840717 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840269 1840308 1840368 "MSYSCMD" 1840443 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1837014 1839830 1839871 "MSETAGG" 1839876 NIL MSETAGG (NIL T) -9 NIL 1839910 NIL) (-758 1832728 1835769 1836089 "MSET" 1836727 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828320 1830107 1830852 "MRING" 1832028 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827880 1827953 1828084 "MRF2" 1828247 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827492 1827533 1827677 "MRATFAC" 1827839 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1825062 1825399 1825830 "MPRFF" 1827197 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818389 1824916 1825013 "MPOLY" 1825018 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817873 1817914 1818122 "MPCPF" 1818348 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817381 1817430 1817614 "MPC3" 1817824 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816564 1816657 1816878 "MPC2" 1817296 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814841 1815202 1815592 "MONOTOOL" 1816224 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813986 1814369 1814397 "MONOID" 1814616 T MONOID (NIL) -9 NIL 1814763 NIL) (-747 1813502 1813651 1813832 "MONOID-" 1813837 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802454 1809322 1809381 "MONOGEN" 1810055 NIL MONOGEN (NIL T T) -9 NIL 1810511 NIL) (-745 1799504 1800407 1801407 "MONOGEN-" 1801526 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798221 1798769 1798797 "MONADWU" 1799189 T MONADWU (NIL) -9 NIL 1799427 NIL) (-743 1797551 1797752 1798000 "MONADWU-" 1798005 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796836 1797140 1797168 "MONAD" 1797375 T MONAD (NIL) -9 NIL 1797487 NIL) (-741 1796503 1796599 1796731 "MONAD-" 1796736 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794642 1795416 1795695 "MOEBIUS" 1796256 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793810 1794310 1794350 "MODULE" 1794355 NIL MODULE (NIL T) -9 NIL 1794394 NIL) (-738 1793348 1793474 1793664 "MODULE-" 1793669 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790878 1791712 1792039 "MODRING" 1793172 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787600 1788983 1789504 "MODOP" 1790407 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1786086 1786667 1786944 "MODMONOM" 1787463 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774826 1784377 1784791 "MODMON" 1785723 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771652 1773670 1773946 "MODFIELD" 1774701 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770563 1770933 1771123 "MMLFORM" 1771482 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1770083 1770132 1770311 "MMAP" 1770514 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767976 1768915 1768956 "MLO" 1769379 NIL MLO (NIL T) -9 NIL 1769621 NIL) (-729 1765324 1765858 1766460 "MLIFT" 1767457 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764703 1764799 1764953 "MKUCFUNC" 1765235 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764296 1764372 1764495 "MKRECORD" 1764626 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763319 1763505 1763733 "MKFUNC" 1764107 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762695 1762811 1762967 "MKFLCFN" 1763202 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761960 1762074 1762259 "MKBCFUNC" 1762588 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757943 1761514 1761650 "MINT" 1761844 T MINT (NIL) -8 NIL NIL NIL) (-722 1756725 1756998 1757275 "MHROWRED" 1757698 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751469 1755260 1755665 "MFLOAT" 1756340 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750814 1750902 1751073 "MFINFACT" 1751381 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1747093 1747977 1748861 "MESH" 1749950 T MESH (NIL) -7 NIL NIL NIL) (-718 1745447 1745795 1746148 "MDDFACT" 1746780 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741983 1744578 1744619 "MDAGG" 1744874 NIL MDAGG (NIL T) -9 NIL 1745017 NIL) (-716 1729685 1741276 1741483 "MCMPLX" 1741796 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728804 1728968 1729169 "MCDEN" 1729534 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726652 1726964 1727344 "MCALCFN" 1728534 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725529 1725817 1726050 "MAYBE" 1726458 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1723087 1723664 1724226 "MATSTOR" 1725000 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718509 1722459 1722707 "MATRIX" 1722872 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714209 1714982 1715718 "MATLIN" 1717866 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712785 1712956 1713289 "MATCAT2" 1714044 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1702124 1705842 1705919 "MATCAT" 1710951 NIL MATCAT (NIL T T T) -9 NIL 1712423 NIL) (-707 1698077 1699387 1700800 "MATCAT-" 1700805 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696153 1696513 1696897 "MAPPKG3" 1697752 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1695110 1695307 1695529 "MAPPKG2" 1695977 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693567 1693893 1694220 "MAPPKG1" 1694816 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692568 1692973 1693150 "MAPPAST" 1693410 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692173 1692237 1692360 "MAPHACK3" 1692504 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691753 1691826 1691940 "MAPHACK2" 1692105 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691179 1691294 1691436 "MAPHACK1" 1691644 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1689102 1689879 1690183 "MAGMA" 1690907 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688521 1688826 1688917 "MACROAST" 1689031 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684764 1686760 1687221 "M3D" 1688093 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678236 1683075 1683116 "LZSTAGG" 1683898 NIL LZSTAGG (NIL T) -9 NIL 1684193 NIL) (-695 1673918 1675367 1676824 "LZSTAGG-" 1676829 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670831 1671809 1672296 "LWORD" 1673463 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670353 1670635 1670710 "LSTAST" 1670776 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662281 1670124 1670258 "LSQM" 1670263 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661499 1661644 1661872 "LSPP" 1662136 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658236 1658952 1659682 "LSMP1" 1660801 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1656018 1656349 1656805 "LSMP" 1657925 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649146 1655108 1655149 "LSAGG" 1655211 NIL LSAGG (NIL T) -9 NIL 1655289 NIL) (-687 1645655 1646765 1647978 "LSAGG-" 1647983 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642950 1644799 1645048 "LPOLY" 1645450 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642526 1642617 1642740 "LPEFRAC" 1642859 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642209 1642288 1642316 "LOGIC" 1642427 T LOGIC (NIL) -9 NIL 1642509 NIL) (-683 1642065 1642094 1642165 "LOGIC-" 1642170 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641240 1641398 1641591 "LODOOPS" 1641921 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639764 1640013 1640366 "LODOF" 1640987 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635640 1638399 1638440 "LODOCAT" 1638878 NIL LODOCAT (NIL T) -9 NIL 1639089 NIL) (-679 1635355 1635431 1635558 "LODOCAT-" 1635563 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632341 1635196 1635314 "LODO2" 1635319 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629448 1632278 1632323 "LODO1" 1632328 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626543 1629364 1629430 "LODO" 1629435 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625412 1625589 1625894 "LODEEF" 1626366 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623589 1624506 1624759 "LO" 1625244 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618561 1621755 1621796 "LNAGG" 1622658 NIL LNAGG (NIL T) -9 NIL 1623093 NIL) (-672 1617654 1617922 1618264 "LNAGG-" 1618269 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613634 1614579 1615218 "LMOPS" 1617069 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612933 1613411 1613452 "LMODULE" 1613457 NIL LMODULE (NIL T) -9 NIL 1613483 NIL) (-669 1609888 1612578 1612701 "LMDICT" 1612843 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609464 1609678 1609719 "LLINSET" 1609780 NIL LLINSET (NIL T) -9 NIL 1609824 NIL) (-667 1609109 1609372 1609432 "LITERAL" 1609437 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608628 1608708 1608847 "LIST3" 1609029 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606726 1607074 1607473 "LIST2MAP" 1608275 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605715 1605911 1606139 "LIST2" 1606544 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598169 1604649 1604953 "LIST" 1605444 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597752 1597988 1598029 "LINSET" 1598034 NIL LINSET (NIL T) -9 NIL 1598068 NIL) (-661 1596566 1597260 1597427 "LINFORM" 1597637 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594865 1595593 1595634 "LINEXP" 1596124 NIL LINEXP (NIL T) -9 NIL 1596397 NIL) (-659 1593441 1594345 1594526 "LINELT" 1594736 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591998 1592278 1592589 "LINDEP" 1593193 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591134 1591730 1591840 "LINBASIS" 1591928 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587871 1588620 1589397 "LIMITRF" 1590389 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586156 1586470 1586879 "LIMITPS" 1587566 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584984 1585559 1585599 "LIECAT" 1585739 NIL LIECAT (NIL T) -9 NIL 1585890 NIL) (-653 1584819 1584852 1584940 "LIECAT-" 1584945 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578839 1584330 1584558 "LIE" 1584640 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1571024 1578379 1578535 "LIB" 1578703 T LIB (NIL) -8 NIL NIL NIL) (-650 1566593 1567542 1568477 "LGROBP" 1570141 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565217 1566125 1566153 "LFCAT" 1566360 T LFCAT (NIL) -9 NIL 1566499 NIL) (-648 1563155 1563489 1563839 "LF" 1564938 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1560015 1560687 1561375 "LEXTRIPK" 1562519 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556603 1557585 1558088 "LEXP" 1559595 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1556019 1556324 1556416 "LETAST" 1556531 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554405 1554730 1555131 "LEADCDET" 1555701 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553583 1553669 1553898 "LAZM3PK" 1554326 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1548094 1551660 1552198 "LAUPOL" 1553095 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547667 1547717 1547878 "LAPLACE" 1548044 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546515 1547231 1547272 "LALG" 1547334 NIL LALG (NIL T) -9 NIL 1547393 NIL) (-639 1546211 1546288 1546424 "LALG-" 1546429 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543948 1545312 1545563 "LA" 1546044 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543777 1543807 1543848 "KVTFROM" 1543910 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542534 1543144 1543329 "KTVLOGIC" 1543612 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542363 1542393 1542434 "KRCFROM" 1542496 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541255 1541454 1541753 "KOVACIC" 1542163 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1541084 1541114 1541155 "KONVERT" 1541217 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540913 1540943 1540984 "KOERCE" 1541046 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540397 1540490 1540622 "KERNEL2" 1540827 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1538084 1538990 1539367 "KERNEL" 1540053 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531555 1536561 1536615 "KDAGG" 1536992 NIL KDAGG (NIL T T) -9 NIL 1537198 NIL) (-628 1531066 1531208 1531413 "KDAGG-" 1531418 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523766 1530727 1530882 "KAFILE" 1530944 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523370 1523655 1523718 "JVMOP" 1523723 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1522106 1522610 1522859 "JVMMDACC" 1523141 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1521042 1521496 1521701 "JVMFDACC" 1521921 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519623 1520118 1520418 "JVMCSTTG" 1520762 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518759 1519163 1519324 "JVMCFACC" 1519482 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518437 1518676 1518725 "JVMBCODE" 1518730 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512456 1517948 1518176 "JORDAN" 1518258 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511769 1512105 1512226 "JOINAST" 1512355 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507804 1509946 1510000 "IXAGG" 1510929 NIL IXAGG (NIL T T) -9 NIL 1511388 NIL) (-617 1506657 1507029 1507448 "IXAGG-" 1507453 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501746 1506579 1506638 "IVECTOR" 1506643 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500471 1500749 1501015 "ITUPLE" 1501513 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498943 1499150 1499445 "ITRIGMNP" 1500293 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497670 1497892 1498175 "ITFUN3" 1498719 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497268 1497331 1497454 "ITFUN2" 1497593 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1496373 1496748 1496922 "ITFORM" 1497114 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494142 1495393 1495671 "ITAYLOR" 1496128 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482539 1488279 1489442 "ISUPS" 1493012 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481631 1481783 1482019 "ISUMP" 1482386 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476481 1481576 1481617 "ISTRING" 1481622 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475897 1476202 1476294 "ISAST" 1476409 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475094 1475188 1475404 "IRURPK" 1475811 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1474006 1474231 1474471 "IRSN" 1474874 T IRSN (NIL) -7 NIL NIL NIL) (-603 1472051 1472432 1472861 "IRRF2F" 1473644 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471792 1471836 1471912 "IRREDFFX" 1472007 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470365 1470666 1470965 "IROOT" 1471525 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469504 1469858 1470009 "IRFORM" 1470234 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468586 1468717 1468931 "IR2F" 1469387 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466175 1466694 1467260 "IR2" 1468064 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462615 1463859 1464551 "IR" 1465515 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462400 1462440 1462500 "IPRNTPK" 1462575 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458353 1462289 1462358 "IPF" 1462363 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456374 1458278 1458335 "IPADIC" 1458340 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455632 1455934 1456064 "IP4ADDR" 1456264 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454970 1455261 1455393 "IOMODE" 1455520 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453941 1454567 1454694 "IOBFILE" 1454863 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453351 1453845 1453873 "IOBCON" 1453878 T IOBCON (NIL) -9 NIL 1453899 NIL) (-589 1452856 1452920 1453103 "INVLAPLA" 1453287 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442426 1444858 1447244 "INTTR" 1450520 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438719 1439503 1440368 "INTTOOLS" 1441611 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438299 1438396 1438513 "INTSLPE" 1438622 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435766 1438222 1438281 "INTRVL" 1438286 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433344 1433880 1434455 "INTRF" 1435251 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432737 1432852 1432994 "INTRET" 1433242 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430710 1431123 1431593 "INTRAT" 1432345 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427955 1428556 1429175 "INTPM" 1430195 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424672 1425299 1426037 "INTPAF" 1427341 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419773 1420813 1421864 "INTPACK" 1423641 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1419019 1419177 1419385 "INTHERTR" 1419615 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418452 1418538 1418726 "INTHERAL" 1418933 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416220 1416741 1417198 "INTHEORY" 1418015 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407552 1409247 1411019 "INTG0" 1414572 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1388077 1392915 1397725 "INTFTBL" 1402762 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387302 1387464 1387637 "INTFACT" 1387936 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384699 1385175 1385732 "INTEF" 1386856 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382896 1383791 1383819 "INTDOM" 1384120 T INTDOM (NIL) -9 NIL 1384327 NIL) (-570 1382235 1382439 1382681 "INTDOM-" 1382686 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378103 1380524 1380578 "INTCAT" 1381377 NIL INTCAT (NIL T) -9 NIL 1381698 NIL) (-568 1377557 1377678 1377806 "INTBIT" 1377995 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376238 1376410 1376717 "INTALG" 1377402 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375715 1375811 1375968 "INTAF" 1376142 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368682 1375525 1375665 "INTABL" 1375670 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367923 1368485 1368550 "INT8" 1368584 T INT8 (NIL) -8 NIL NIL 1368629) (-563 1367163 1367725 1367790 "INT64" 1367824 T INT64 (NIL) -8 NIL NIL 1367869) (-562 1366403 1366965 1367030 "INT32" 1367064 T INT32 (NIL) -8 NIL NIL 1367109) (-561 1365643 1366205 1366270 "INT16" 1366304 T INT16 (NIL) -8 NIL NIL 1366349) (-560 1361831 1365440 1365549 "INT" 1365554 T INT (NIL) -8 NIL NIL NIL) (-559 1355926 1359379 1359407 "INS" 1360341 T INS (NIL) -9 NIL 1361006 NIL) (-558 1352980 1353937 1354911 "INS-" 1354984 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351737 1351982 1352280 "INPSIGN" 1352733 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350831 1350972 1351169 "INPRODPF" 1351617 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349701 1349842 1350079 "INPRODFF" 1350711 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348689 1348853 1349113 "INNMFACT" 1349537 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347868 1347983 1348171 "INMODGCD" 1348588 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346352 1346621 1346945 "INFSP" 1347613 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345512 1345653 1345836 "INFPROD0" 1346232 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345110 1345182 1345280 "INFORM1" 1345447 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341677 1343175 1343690 "INFORM" 1344603 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341182 1341289 1341403 "INFINITY" 1341583 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340256 1340902 1341003 "INETCLTS" 1341101 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338854 1339122 1339443 "INEP" 1340004 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337915 1338751 1338816 "INDE" 1338821 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337467 1337547 1337664 "INCRMAPS" 1337842 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336189 1336736 1336942 "INBFILE" 1337281 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331368 1332425 1333369 "INBFF" 1335277 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330222 1330545 1330573 "INBCON" 1331086 T INBCON (NIL) -9 NIL 1331352 NIL) (-540 1329432 1329697 1329973 "INBCON-" 1329978 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328851 1329156 1329247 "INAST" 1329361 T INAST (NIL) -8 NIL NIL NIL) (-538 1328218 1328530 1328636 "IMPTAST" 1328765 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324139 1328062 1328166 "IMATRIX" 1328171 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322831 1322970 1323286 "IMATQF" 1323995 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1321011 1321278 1321615 "IMATLIN" 1322587 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314926 1320935 1320993 "ILIST" 1320998 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312592 1314786 1314899 "IIARRAY2" 1314904 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307392 1312503 1312567 "IFF" 1312572 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306673 1307009 1307125 "IFAST" 1307296 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301185 1305965 1306153 "IFARRAY" 1306530 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300223 1301089 1301162 "IFAMON" 1301167 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299795 1299872 1299926 "IEVALAB" 1300133 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299458 1299538 1299698 "IEVALAB-" 1299703 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298522 1299347 1299422 "IDPOAMS" 1299427 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297655 1298411 1298486 "IDPOAM" 1298491 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1297036 1297570 1297632 "IDPO" 1297637 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295516 1296043 1296095 "IDPC" 1296607 NIL IDPC (NIL T T) -9 NIL 1296888 NIL) (-522 1294848 1295408 1295481 "IDPAM" 1295486 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1294063 1294740 1294813 "IDPAG" 1294818 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293607 1293869 1293959 "IDENT" 1293993 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289826 1290710 1291605 "IDECOMP" 1292764 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282461 1283749 1284796 "IDEAL" 1288862 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281603 1281733 1281933 "ICDEN" 1282345 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280578 1281083 1281230 "ICARD" 1281476 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278608 1278951 1279356 "IBPTOOLS" 1280255 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273723 1278228 1278341 "IBITS" 1278527 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270398 1271022 1271717 "IBATOOL" 1273140 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268159 1268639 1269172 "IBACHIN" 1269933 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265749 1268005 1268108 "IARRAY2" 1268113 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261462 1265675 1265732 "IARRAY1" 1265737 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254472 1259874 1260355 "IAN" 1261001 T IAN (NIL) -8 NIL NIL NIL) (-508 1253977 1254040 1254213 "IALGFACT" 1254409 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253469 1253618 1253646 "HYPCAT" 1253853 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252971 1253124 1253310 "HYPCAT-" 1253315 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252518 1252766 1252849 "HOSTNAME" 1252908 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252351 1252400 1252441 "HOMOTOP" 1252446 NIL HOMOTOP (NIL T) -9 NIL 1252479 NIL) (-503 1248784 1250283 1250324 "HOAGG" 1251305 NIL HOAGG (NIL T) -9 NIL 1252034 NIL) (-502 1247300 1247777 1248303 "HOAGG-" 1248308 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240336 1246893 1247043 "HEXADEC" 1247170 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1239048 1239306 1239569 "HEUGCD" 1240113 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237980 1238885 1239015 "HELLFDIV" 1239020 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235990 1237757 1237845 "HEAP" 1237924 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235187 1235542 1235676 "HEADAST" 1235876 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228574 1235102 1235164 "HDP" 1235169 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221586 1228209 1228361 "HDMP" 1228475 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220892 1221050 1221214 "HB" 1221442 T HB (NIL) -7 NIL NIL NIL) (-493 1213902 1220738 1220842 "HASHTBL" 1220847 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213318 1213623 1213715 "HASAST" 1213830 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210724 1212940 1213122 "HACKPI" 1213156 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205896 1210577 1210690 "GTSET" 1210695 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198935 1205774 1205872 "GSTBL" 1205877 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190684 1198100 1198356 "GSERIES" 1198735 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189715 1190228 1190256 "GROUP" 1190459 T GROUP (NIL) -9 NIL 1190593 NIL) (-486 1189039 1189240 1189491 "GROUP-" 1189496 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187388 1187727 1188114 "GROEBSOL" 1188716 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186216 1186576 1186627 "GRMOD" 1187156 NIL GRMOD (NIL T T) -9 NIL 1187324 NIL) (-483 1185972 1186020 1186148 "GRMOD-" 1186153 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181112 1182326 1183326 "GRIMAGE" 1184992 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179506 1179839 1180163 "GRDEF" 1180808 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178938 1179066 1179207 "GRAY" 1179385 T GRAY (NIL) -7 NIL NIL NIL) (-479 1178015 1178517 1178568 "GRALG" 1178721 NIL GRALG (NIL T T) -9 NIL 1178814 NIL) (-478 1177652 1177749 1177912 "GRALG-" 1177917 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174133 1177235 1177414 "GPOLSET" 1177558 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173481 1173544 1173802 "GOSPER" 1174070 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1169051 1169919 1170445 "GMODPOL" 1173180 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1168038 1168240 1168478 "GHENSEL" 1168863 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162110 1163037 1164057 "GENUPS" 1167122 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161801 1161858 1161947 "GENUFACT" 1162053 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161201 1161290 1161455 "GENPGCD" 1161719 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160669 1160710 1160923 "GENMFACT" 1161160 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159205 1159492 1159799 "GENEEZ" 1160412 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152377 1158816 1158978 "GDMP" 1159128 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141115 1146148 1147254 "GCNAALG" 1151360 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139242 1140290 1140318 "GCDDOM" 1140573 T GCDDOM (NIL) -9 NIL 1140730 NIL) (-465 1138682 1138839 1139054 "GCDDOM-" 1139059 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127154 1129628 1132020 "GBINTERN" 1136373 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124955 1125283 1125704 "GBF" 1126829 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123712 1123901 1124168 "GBEUCLID" 1124771 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122362 1122569 1122873 "GB" 1123491 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121693 1121836 1121985 "GAUSSFAC" 1122233 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1120014 1120362 1120676 "GALUTIL" 1121412 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118274 1118596 1118920 "GALPOLYU" 1119741 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115573 1115929 1116336 "GALFACTU" 1117971 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107187 1108878 1110486 "GALFACT" 1114005 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104473 1105233 1105261 "FVFUN" 1106417 T FVFUN (NIL) -9 NIL 1107137 NIL) (-454 1103703 1103921 1103949 "FVC" 1104240 T FVC (NIL) -9 NIL 1104423 NIL) (-453 1103304 1103528 1103596 "FUNDESC" 1103655 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102877 1103101 1103182 "FUNCTION" 1103256 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101554 1102178 1102381 "FTEM" 1102694 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099184 1099876 1100342 "FT" 1101108 T FT (NIL) -8 NIL NIL NIL) (-449 1097453 1097764 1098161 "FSUPFACT" 1098875 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095772 1096139 1096471 "FST" 1097141 T FST (NIL) -8 NIL NIL NIL) (-447 1094953 1095077 1095265 "FSRED" 1095654 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093642 1093908 1094255 "FSPRMELT" 1094668 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090852 1091386 1091872 "FSPECF" 1093205 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090374 1090434 1090604 "FSINT" 1090793 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088510 1089367 1089670 "FSERIES" 1090153 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087534 1087668 1087892 "FSCINT" 1088390 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086558 1086719 1086946 "FSAGG2" 1087387 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082422 1085502 1085543 "FSAGG" 1085913 NIL FSAGG (NIL T) -9 NIL 1086172 NIL) (-439 1080022 1080785 1081581 "FSAGG-" 1081676 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077682 1077980 1078528 "FS2UPS" 1079740 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076548 1076731 1077033 "FS2EXPXP" 1077507 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076176 1076225 1076354 "FS2" 1076499 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056400 1065950 1065991 "FS" 1069875 NIL FS (NIL T) -9 NIL 1072164 NIL) (-434 1044461 1048036 1052093 "FS-" 1052393 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043875 1044002 1044154 "FRUTIL" 1044341 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038386 1041564 1041604 "FRNAALG" 1042924 NIL FRNAALG (NIL T) -9 NIL 1043522 NIL) (-431 1033867 1035135 1036410 "FRNAALG-" 1037160 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033499 1033548 1033675 "FRNAAF2" 1033818 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031786 1032348 1032644 "FRMOD" 1033311 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030971 1031064 1031355 "FRIDEAL2" 1031693 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028576 1029346 1029664 "FRIDEAL" 1030762 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027667 1028123 1028164 "FRETRCT" 1028169 NIL FRETRCT (NIL T) -9 NIL 1028345 NIL) (-425 1026725 1027010 1027361 "FRETRCT-" 1027366 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023539 1025009 1025068 "FRAMALG" 1025950 NIL FRAMALG (NIL T T) -9 NIL 1026242 NIL) (-423 1021577 1022128 1022758 "FRAMALG-" 1022981 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021207 1021270 1021377 "FRAC2" 1021514 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014178 1020680 1020957 "FRAC" 1020962 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013808 1013871 1013978 "FR2" 1014115 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004725 1009303 1010661 "FR" 1012482 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998637 1002104 1002132 "FPS" 1003251 T FPS (NIL) -9 NIL 1003808 NIL) (-417 998062 998195 998359 "FPS-" 998505 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 995014 997019 997047 "FPC" 997272 T FPC (NIL) -9 NIL 997414 NIL) (-415 994795 994847 994944 "FPC-" 994949 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993553 994283 994324 "FPATMAB" 994329 NIL FPATMAB (NIL T) -9 NIL 994481 NIL) (-413 991696 992295 992642 "FPARFRAC" 993269 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986988 987588 988270 "FORTRAN" 991128 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984562 985226 985254 "FORTFN" 986314 T FORTFN (NIL) -9 NIL 986938 NIL) (-410 984314 984376 984404 "FORTCAT" 984463 T FORTCAT (NIL) -9 NIL 984525 NIL) (-409 982000 982530 983069 "FORT" 983795 T FORT (NIL) -7 NIL NIL NIL) (-408 981782 981818 981887 "FORMULA1" 981964 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979786 980398 980788 "FORMULA" 981412 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979303 979361 979534 "FORDER" 979728 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978363 978563 978756 "FOP" 979130 T FOP (NIL) -7 NIL NIL NIL) (-404 976776 977643 977817 "FNLA" 978245 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975395 975906 975934 "FNCAT" 976394 T FNCAT (NIL) -9 NIL 976654 NIL) (-402 974838 975354 975382 "FNAME" 975387 T FNAME (NIL) -8 NIL NIL NIL) (-401 973164 974337 974365 "FMTC" 974370 T FMTC (NIL) -9 NIL 974406 NIL) (-400 971713 973100 973146 "FMONOID" 973151 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968302 969668 969709 "FMONCAT" 970926 NIL FMONCAT (NIL T) -9 NIL 971531 NIL) (-398 965624 966372 966400 "FMFUN" 967544 T FMFUN (NIL) -9 NIL 968252 NIL) (-397 962497 963549 963603 "FMCAT" 964798 NIL FMCAT (NIL T T) -9 NIL 965293 NIL) (-396 961730 961947 961975 "FMC" 962265 T FMC (NIL) -9 NIL 962447 NIL) (-395 960398 961496 961596 "FM1" 961675 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959416 960140 960289 "FM" 960294 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957154 957606 958100 "FLOATRP" 958967 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954556 955092 955670 "FLOATCP" 956621 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947212 952285 952906 "FLOAT" 953955 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945730 946804 946845 "FLINEXP" 946850 NIL FLINEXP (NIL T) -9 NIL 946943 NIL) (-389 944860 945119 945447 "FLINEXP-" 945452 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943918 944080 944304 "FLASORT" 944712 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940836 941888 941940 "FLALG" 943167 NIL FLALG (NIL T T) -9 NIL 943634 NIL) (-386 939860 940021 940248 "FLAGG2" 940689 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933115 937269 937310 "FLAGG" 938572 NIL FLAGG (NIL T) -9 NIL 939224 NIL) (-384 931769 932180 932670 "FLAGG-" 932675 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928400 929614 929673 "FINRALG" 930801 NIL FINRALG (NIL T T) -9 NIL 931309 NIL) (-382 927524 927789 928128 "FINRALG-" 928133 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926830 927129 927157 "FINITE" 927353 T FINITE (NIL) -9 NIL 927460 NIL) (-380 918781 921360 921400 "FINAALG" 925067 NIL FINAALG (NIL T) -9 NIL 926520 NIL) (-379 913897 915163 916307 "FINAALG-" 917686 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912457 912879 912933 "FILECAT" 913617 NIL FILECAT (NIL T T) -9 NIL 913833 NIL) (-377 911735 912212 912315 "FILE" 912387 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909131 910965 910993 "FIELD" 911033 T FIELD (NIL) -9 NIL 911113 NIL) (-375 907673 908136 908647 "FIELD-" 908652 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905356 906308 906655 "FGROUP" 907359 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904428 904610 904830 "FGLMICPK" 905188 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899662 904353 904410 "FFX" 904415 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899257 899324 899459 "FFSLPE" 899595 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898755 898797 899006 "FFPOLY2" 899215 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894631 895527 896323 "FFPOLY" 897991 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889879 894550 894613 "FFP" 894618 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884389 889222 889412 "FFNBX" 889733 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878701 883524 883782 "FFNBP" 884243 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872718 877985 878196 "FFNB" 878534 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871538 871748 872063 "FFINTBAS" 872515 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867110 869785 869813 "FFIELDC" 870433 T FFIELDC (NIL) -9 NIL 870809 NIL) (-362 865688 866143 866640 "FFIELDC-" 866645 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865245 865303 865427 "FFHOM" 865630 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862904 863427 863944 "FFF" 864760 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857918 862646 862747 "FFCGX" 862847 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852936 857650 857757 "FFCGP" 857861 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847515 852663 852771 "FFCG" 852872 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846920 846969 847204 "FFCAT2" 847466 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825581 836652 836738 "FFCAT" 841903 NIL FFCAT (NIL T T T) -9 NIL 843354 NIL) (-354 820592 821826 823140 "FFCAT-" 824370 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815392 820503 820567 "FF" 820572 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 804045 808364 809584 "FEXPR" 814244 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802973 803442 803483 "FEVALAB" 803567 NIL FEVALAB (NIL T) -9 NIL 803828 NIL) (-350 802090 802342 802680 "FEVALAB-" 802685 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798952 799837 799952 "FDIVCAT" 801520 NIL FDIVCAT (NIL T T T T) -9 NIL 801957 NIL) (-348 798708 798741 798911 "FDIVCAT-" 798916 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797922 798015 798292 "FDIV2" 798615 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796332 797305 797508 "FDIV" 797821 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795240 795627 795829 "FCTRDATA" 796150 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793896 794185 794474 "FCPAK1" 794971 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792899 793396 793537 "FCOMP" 793787 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776213 780049 783587 "FC" 789381 T FC (NIL) -8 NIL NIL NIL) (-341 767902 772534 772574 "FAXF" 774376 NIL FAXF (NIL T) -9 NIL 775068 NIL) (-340 765023 765836 766661 "FAXF-" 767126 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759592 764399 764575 "FARRAY" 764880 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754151 756539 756592 "FAMR" 757615 NIL FAMR (NIL T T) -9 NIL 758075 NIL) (-337 752975 753343 753778 "FAMR-" 753783 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 752002 752897 752950 "FAMONOID" 752955 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749632 750484 750537 "FAMONC" 751478 NIL FAMONC (NIL T T) -9 NIL 751864 NIL) (-334 748106 749386 749523 "FAGROUP" 749528 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745859 746220 746623 "FACUTIL" 747787 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744946 745143 745365 "FACTFUNC" 745669 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736704 744249 744448 "EXPUPXS" 744802 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734157 734727 735313 "EXPRTUBE" 736138 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730368 731020 731750 "EXPRODE" 733496 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724802 725509 726315 "EXPR2UPS" 729666 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724428 724491 724600 "EXPR2" 724739 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708722 723077 723506 "EXPR" 724032 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699039 707873 708164 "EXPEXPAN" 708558 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698459 698763 698854 "EXITAST" 698968 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698223 698416 698445 "EXIT" 698450 T EXIT (NIL) -8 NIL NIL NIL) (-322 697844 697912 698025 "EVALCYC" 698155 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697361 697503 697544 "EVALAB" 697714 NIL EVALAB (NIL T) -9 NIL 697818 NIL) (-320 696818 696964 697185 "EVALAB-" 697190 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693926 695474 695502 "EUCDOM" 696057 T EUCDOM (NIL) -9 NIL 696407 NIL) (-318 692265 692773 693363 "EUCDOM-" 693368 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691891 691954 692063 "ESTOOLS2" 692202 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691636 691684 691764 "ESTOOLS1" 691843 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678953 681934 684684 "ESTOOLS" 688906 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678692 678730 678812 "ESCONT1" 678915 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 675000 675827 676607 "ESCONT" 677932 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674669 674725 674825 "ES2" 674944 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674293 674357 674466 "ES1" 674605 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667994 669924 669952 "ES" 672720 T ES (NIL) -9 NIL 674130 NIL) (-309 662671 664228 666045 "ES-" 666209 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661863 662016 662192 "ERROR" 662515 T ERROR (NIL) -7 NIL NIL NIL) (-307 654879 661722 661813 "EQTBL" 661818 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654505 654568 654677 "EQ2" 654816 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646764 649819 651268 "EQ" 653089 NIL -1545 (NIL T) -8 NIL NIL NIL) (-304 642007 643102 644195 "EP" 645703 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640547 640898 641204 "ENV" 641721 T ENV (NIL) -8 NIL NIL NIL) (-302 639507 640181 640209 "ENTIRER" 640214 T ENTIRER (NIL) -9 NIL 640260 NIL) (-301 635919 637689 638050 "EMR" 639315 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635023 635234 635288 "ELTAGG" 635668 NIL ELTAGG (NIL T T) -9 NIL 635879 NIL) (-299 634730 634804 634945 "ELTAGG-" 634950 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634488 634523 634577 "ELTAB" 634661 NIL ELTAB (NIL T T) -9 NIL 634713 NIL) (-297 633590 633760 633959 "ELFUTS" 634339 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633314 633388 633416 "ELEMFUN" 633521 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633178 633205 633273 "ELEMFUN-" 633278 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627589 631220 631261 "ELAGG" 632201 NIL ELAGG (NIL T) -9 NIL 632664 NIL) (-293 625766 626308 626971 "ELAGG-" 626976 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625048 625215 625371 "ELABOR" 625630 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623654 623988 624282 "ELABEXPR" 624774 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616166 618291 619120 "EFUPXS" 622929 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609292 611415 612226 "EFULS" 615441 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606729 607135 607607 "EFSTRUC" 608924 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596166 598086 599634 "EF" 605244 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595144 595651 595800 "EAB" 596037 T EAB (NIL) -8 NIL NIL NIL) (-285 594266 595103 595131 "E04UCFA" 595136 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593388 594225 594253 "E04NAFA" 594258 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592510 593347 593375 "E04MBFA" 593380 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591632 592469 592497 "E04JAFA" 592502 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590756 591591 591619 "E04GCFA" 591624 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589880 590715 590743 "E04FDFA" 590748 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 589002 589839 589867 "E04DGFA" 589872 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583079 584527 585891 "E04AGNT" 587658 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581699 582380 582420 "DVARCAT" 582761 NIL DVARCAT (NIL T) -9 NIL 582924 NIL) (-276 580849 581115 581429 "DVARCAT-" 581434 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572810 580648 580777 "DSMP" 580782 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571161 571952 571993 "DSEXT" 572356 NIL DSEXT (NIL T) -9 NIL 572650 NIL) (-273 569350 569874 570540 "DSEXT-" 570545 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569009 569074 569172 "DROPT1" 569285 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564028 565250 566387 "DROPT0" 567892 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558611 559973 561041 "DROPT" 562980 T DROPT (NIL) -8 NIL NIL NIL) (-269 556920 557281 557667 "DRAWPT" 558245 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556547 556606 556724 "DRAWHACK" 556861 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555248 555547 555838 "DRAWCX" 556276 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554757 554832 554983 "DRAWCURV" 555174 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545075 547187 549302 "DRAWCFUN" 552662 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539566 540585 541664 "DRAW" 544049 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536037 538231 538272 "DQAGG" 538901 NIL DQAGG (NIL T) -9 NIL 539175 NIL) (-262 522613 530248 530331 "DPOLCAT" 532183 NIL DPOLCAT (NIL T T T T) -9 NIL 532728 NIL) (-261 517132 518798 520756 "DPOLCAT-" 520761 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509989 516993 517091 "DPMO" 517096 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502743 509769 509936 "DPMM" 509941 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502265 502527 502616 "DOMTMPLT" 502674 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501614 502067 502147 "DOMCTOR" 502205 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500766 501094 501245 "DOMAIN" 501483 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493778 500401 500553 "DMP" 500667 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491555 492845 492886 "DMEXT" 492891 NIL DMEXT (NIL T) -9 NIL 493067 NIL) (-253 491149 491211 491355 "DLP" 491493 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484272 490476 490666 "DLIST" 490991 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480810 483097 483138 "DLAGG" 483688 NIL DLAGG (NIL T) -9 NIL 483918 NIL) (-250 479322 480136 480164 "DIVRING" 480256 T DIVRING (NIL) -9 NIL 480339 NIL) (-249 478505 478749 479049 "DIVRING-" 479054 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476547 476964 477370 "DISPLAY" 478119 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475377 475598 475863 "DIRPROD2" 476340 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468784 475291 475354 "DIRPROD" 475359 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456996 463495 463548 "DIRPCAT" 463806 NIL DIRPCAT (NIL NIL T) -9 NIL 464681 NIL) (-244 454196 454964 455845 "DIRPCAT-" 456182 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453477 453643 453829 "DIOSP" 454030 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449891 452361 452402 "DIOPS" 452836 NIL DIOPS (NIL T) -9 NIL 453065 NIL) (-241 449410 449554 449745 "DIOPS-" 449750 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448317 449089 449117 "DIFRING" 449122 T DIFRING (NIL) -9 NIL 449144 NIL) (-239 447965 448063 448091 "DIFFSPC" 448210 T DIFFSPC (NIL) -9 NIL 448285 NIL) (-238 447586 447688 447840 "DIFFSPC-" 447845 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446522 447120 447161 "DIFFMOD" 447166 NIL DIFFMOD (NIL T) -9 NIL 447264 NIL) (-236 446218 446275 446316 "DIFFDOM" 446437 NIL DIFFDOM (NIL T) -9 NIL 446505 NIL) (-235 446065 446095 446179 "DIFFDOM-" 446184 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443805 445269 445310 "DIFEXT" 445315 NIL DIFEXT (NIL T) -9 NIL 445468 NIL) (-233 440839 443309 443350 "DIAGG" 443355 NIL DIAGG (NIL T) -9 NIL 443375 NIL) (-232 440187 440380 440632 "DIAGG-" 440637 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435037 439146 439423 "DHMATRIX" 439956 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430505 431558 432568 "DFSFUN" 434047 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424739 429436 429748 "DFLOAT" 430213 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422978 423283 423672 "DFINTTLS" 424447 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419797 420999 421399 "DERHAM" 422644 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417333 419572 419661 "DEQUEUE" 419741 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416575 416720 416903 "DEGRED" 417195 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412981 413750 414596 "DEFINTRF" 415803 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410518 411005 411597 "DEFINTEF" 412500 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409802 410138 410253 "DEFAST" 410423 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402838 409395 409545 "DECIMAL" 409672 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400296 400808 401314 "DDFACT" 402382 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399886 399935 400086 "DBLRESP" 400247 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399087 399656 399747 "DBASIS" 399835 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396871 397317 397678 "DBASE" 398853 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396059 396351 396497 "DATAARY" 396770 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395117 396018 396046 "D03FAFA" 396051 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394176 395076 395104 "D03EEFA" 395109 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392102 392592 393081 "D03AGNT" 393707 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391343 392061 392089 "D02EJFA" 392094 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390584 391302 391330 "D02CJFA" 391335 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389825 390543 390571 "D02BHFA" 390576 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389066 389784 389812 "D02BBFA" 389817 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382197 383852 385458 "D02AGNT" 387480 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379947 380488 381034 "D01WGTS" 381671 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378954 379906 379934 "D01TRNS" 379939 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377962 378913 378941 "D01GBFA" 378946 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376970 377921 377949 "D01FCFA" 377954 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375978 376929 376957 "D01ASFA" 376962 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374986 375937 375965 "D01AQFA" 375970 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373994 374945 374973 "D01APFA" 374978 T D01APFA (NIL) -8 NIL NIL NIL) (-200 373002 373953 373981 "D01ANFA" 373986 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 372010 372961 372989 "D01AMFA" 372994 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 371018 371969 371997 "D01ALFA" 372002 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 370026 370977 371005 "D01AKFA" 371010 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 369034 369985 370013 "D01AJFA" 370018 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362257 363882 365443 "D01AGNT" 367493 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361576 361722 361874 "CYCLOTOM" 362125 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358231 359024 359751 "CYCLES" 360869 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357531 357677 357848 "CVMP" 358092 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355318 355630 355999 "CTRIGMNP" 357259 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354791 355049 355150 "CTORKIND" 355237 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353996 354384 354412 "CTORCAT" 354594 T CTORCAT (NIL) -9 NIL 354707 NIL) (-188 353570 353705 353864 "CTORCAT-" 353869 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352984 353244 353352 "CTORCALL" 353494 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352342 352778 352851 "CTOR" 352931 T CTOR (NIL) -8 NIL NIL NIL) (-185 351698 351815 351968 "CSTTOOLS" 352239 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347395 348154 348912 "CRFP" 351010 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346810 347116 347208 "CRCEAST" 347323 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345833 346042 346270 "CRAPACK" 346614 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345213 345318 345522 "CPMATCH" 345709 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344932 344966 345072 "CPIMA" 345179 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341190 341952 342671 "COORDSYS" 344267 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340578 340723 340865 "CONTOUR" 341068 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336043 338581 339073 "CONTFRAC" 340118 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335917 335944 335972 "CONDUIT" 336009 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334871 335545 335573 "COMRING" 335578 T COMRING (NIL) -9 NIL 335630 NIL) (-174 333853 334229 334413 "COMPPROP" 334707 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333508 333549 333677 "COMPLPAT" 333812 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333138 333201 333308 "COMPLEX2" 333445 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321521 332947 333056 "COMPLEX" 333061 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320842 320981 321141 "COMPILER" 321381 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320554 320595 320693 "COMPFACT" 320801 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301927 314258 314298 "COMPCAT" 315302 NIL COMPCAT (NIL T) -9 NIL 316650 NIL) (-167 290815 294366 297993 "COMPCAT-" 298349 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290538 290572 290675 "COMMUPC" 290781 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290326 290366 290425 "COMMONOP" 290499 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289848 290130 290205 "COMMAAST" 290271 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289355 289599 289686 "COMM" 289781 T COMM (NIL) -8 NIL NIL NIL) (-162 288550 288798 288826 "COMBOPC" 289164 T COMBOPC (NIL) -9 NIL 289339 NIL) (-161 287404 287656 287898 "COMBINAT" 288340 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283747 284435 285062 "COMBF" 286826 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282409 282863 283098 "COLOR" 283532 T COLOR (NIL) -8 NIL NIL NIL) (-158 281825 282130 282222 "COLONAST" 282337 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281459 281512 281637 "CMPLXRT" 281772 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280847 281159 281258 "CLLCTAST" 281380 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276306 277377 278457 "CLIP" 279787 T CLIP (NIL) -7 NIL NIL NIL) (-154 274479 275407 275647 "CLIF" 276133 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270461 272597 272638 "CLAGG" 273567 NIL CLAGG (NIL 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(-75 144743 145464 145574 "ASP4" 145684 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143585 144420 144538 "ASP35" 144656 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143314 143533 143572 "ASP34" 143577 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143033 143118 143194 "ASP33" 143269 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141819 142668 142800 "ASP31" 142932 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141548 141767 141806 "ASP30" 141811 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141265 141352 141428 "ASP29" 141503 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140994 141213 141252 "ASP28" 141257 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140723 140942 140981 "ASP27" 140986 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139699 140421 140532 "ASP24" 140643 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138668 139501 139613 "ASP20" 139618 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137503 138342 138461 "ASP19" 138580 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137222 137307 137383 "ASP12" 137458 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) 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NIL) (-36 38527 55410 55462 "ALAGG" 55598 NIL ALAGG (NIL T T) -9 NIL 55759 NIL) (-35 38027 38176 38202 "AHYP" 38403 T AHYP (NIL) -9 NIL NIL NIL) (-34 36912 37206 37232 "AGG" 37731 T AGG (NIL) -9 NIL 38010 NIL) (-33 36310 36508 36722 "AGG-" 36727 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34070 34539 34944 "AF" 35952 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33490 33795 33885 "ADDAST" 33998 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32722 33017 33173 "ACPLOT" 33352 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20273 29654 29692 "ACFS" 30299 NIL ACFS (NIL T) -9 NIL 30538 NIL) (-28 18180 18790 19552 "ACFS-" 19557 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16213 16239 "ACF" 17118 T ACF (NIL) -9 NIL 17531 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
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*1 (-803 *2)) (-4 *2 (-571)) (-4 *2 (-1080)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-1000 *3 *2)) (-4 *2 (-1273 *3)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) + (-4 *4 (-871)) (-4 *2 (-571)))) + ((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *3 (-1096 *4 *5 *6)) + (-5 *2 (-663 (-2 (|:| |val| *3) (|:| -2307 *1)))) + (-4 *1 (-1102 *4 *5 *6 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-560))) (-5 *1 (-1078))))) (((*1 *2) (-12 (-5 *2 (-987 (-1151))) (-5 *1 (-357 *3 *4)) (-14 *3 (-948)) (-14 *4 (-948)))) @@ -8705,8 +9686,85 @@ ((*1 *2) (-12 (-5 *2 (-987 (-1151))) (-5 *1 (-359 *3 *4)) (-4 *3 (-363)) (-14 *4 (-948))))) -(((*1 *1) (-5 *1 (-1116)))) -(((*1 *1 *2) (-12 (-5 *2 (-187 (-257))) (-5 *1 (-256))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1207)) (-5 *1 (-1094))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-972 *3) (-972 *3))) (-5 *1 (-179 *3)) + (-4 *3 (-13 (-376) (-1233) (-1033)))))) +(((*1 *2 *3 *3 *3 *3 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+ (|partial| -12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-114)) + (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-114)) + (-5 *1 (-1138 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-571)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3361 *4))) + (-5 *1 (-1000 *4 *3)) (-4 *3 (-1273 *4))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-663 *4)) (-4 *4 (-376)) (-4 *2 (-1273 *4)) + (-5 *1 (-952 *4 *2))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1066)) (-5 *1 (-780))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1132)) (-4 *6 (-1132)) + (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-706 *4 *5 *6)) (-4 *4 (-1132))))) +(((*1 *2 *2) (-12 (-5 *2 (-948)) (-5 *1 (-369 *3)) (-4 *3 (-363))))) +(((*1 *2 *3) + (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1273 (-560)))))) +(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-391)) (-5 *1 (-97)))) + ((*1 *2 *3 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-391)) (-5 *1 (-97))))) +(((*1 *2 *1) (-12 (-5 *2 (-1134)) (-5 *1 (-1211))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) + (|:| -3112 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (-5 *2 + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-195))))) +(((*1 *2 *2) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-571)) + (-4 *4 (-815)) (-4 *5 (-871)) (-5 *1 (-1008 *3 *4 *5 *6))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-803 *2)) (-4 *2 (-1080))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1 (-114) *7 (-663 *7))) (-4 *1 (-1242 *4 *5 *6 *7)) + (-4 *4 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(-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) + (|:| |xpnt| (-560)))) + (-4 *4 (-13 (-1273 *3) (-571) (-10 -8 (-15 -3040 ($ $ $))))) + (-4 *3 (-571)) (-5 *1 (-1277 *3 *4))))) +(((*1 *2 *2) (-12 (-5 *1 (-991 *2)) (-4 *2 (-559))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1201 *1)) (-5 *3 (-1207)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-1201 *1)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-975 *1)) (-4 *1 (-27)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1207)) (-4 *1 (-29 *3)) (-4 *3 (-571)))) + ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-571))))) +(((*1 *1 *2 *2) + (-12 + (-5 *2 + (-3 (|:| I (-326 (-560))) (|:| -4340 (-326 (-391))) + (|:| CF (-326 (-171 (-391)))) (|:| |switch| (-1206)))) + (-5 *1 (-1206))))) +(((*1 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) + ((*1 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230)))) + ((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-445 *3 *2)) (-4 *2 (-435 *3)))) + ((*1 *1 *1) (-4 *1 (-1170)))) +(((*1 *1 *1) (-5 *1 (-1094)))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-319) 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(-5 *2 (-793)) (-4 *3 (-1080)) (-4 *1 (-708 *3 *4 *5)) + (-4 *4 (-385 *3)) (-4 *5 (-385 *3)))) + ((*1 *1 *2) + (-12 (-4 *2 (-1080)) (-4 *1 (-1154 *3 *2 *4 *5)) (-4 *4 (-245 *3 *2)) + (-4 *5 (-245 *3 *2))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -3985 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -1355 (-663 (-229))))) (-5 *2 (-663 (-1207))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1201 *7)) (-4 *7 (-979 *6 *4 *5)) (-4 *4 (-815)) @@ -9390,7 +10530,7 @@ (-5 *1 (-980 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -2489 ($ *7)) (-15 -2198 (*7 $)) (-15 -2214 (*7 $))))))) + (-10 -8 (-15 -3782 ($ *7)) (-15 -3668 (*7 $)) (-15 -3678 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1004 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-814)) (-4 *5 (-871)) (-5 *2 (-663 *5)))) @@ -9400,49 +10540,57 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-975 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1207))) (-5 *1 (-1071 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 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*8)) (-15 -3668 (*8 $)) (-15 -3678 (*8 $)))))))) +(((*1 *2 *2 *3 *4) + (-12 (-5 *3 (-663 (-630 *6))) (-5 *4 (-1207)) (-5 *2 (-630 *6)) + (-4 *6 (-435 *5)) (-4 *5 (-1132)) (-5 *1 (-587 *5 *6))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-270))) (-5 *1 (-1300)))) + ((*1 *2 *1) (-12 (-5 *2 (-663 (-270))) (-5 *1 (-1300)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-270))) (-5 *1 (-1301)))) + ((*1 *2 *1) (-12 (-5 *2 (-663 (-270))) (-5 *1 (-1301))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-543))))) +(((*1 *2 *3) + (-12 (-5 *3 (-560)) (-4 *4 (-1273 (-421 *3))) (-5 *2 (-948)) + (-5 *1 (-942 *4 *5)) (-4 *5 (-1273 (-421 *4)))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814)))) ((*1 *1 *2 *3) @@ -9535,10 +10656,10 @@ (-4 *2 (-376)) (-14 *5 (-1024 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-735 *5 *6 *7)) (-4 *5 (-871)) - (-4 *6 (-245 (-2387 *4) (-793))) + (-4 *6 (-245 (-3764 *4) (-793))) (-14 *7 - (-1 (-114) (-2 (|:| -4012 *5) (|:| -1553 *6)) - (-2 (|:| -4012 *5) (|:| -1553 *6)))) + (-1 (-114) (-2 (|:| -2028 *5) (|:| -4035 *6)) + (-2 (|:| -2028 *5) (|:| -4035 *6)))) (-14 *4 (-663 (-1207))) (-4 *2 (-175)) (-5 *1 (-475 *4 *2 *5 *6 *7 *8)) (-4 *8 (-979 *2 *6 (-888 *4))))) ((*1 *1 *2 *3) @@ -9568,590 +10689,389 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-1004 *4 *3 *2)) (-4 *4 (-1080)) (-4 *3 (-814)) (-4 *2 (-871))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-376)) (-5 *1 (-1056 *3 *2)) (-4 *2 (-680 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-376)) (-5 *2 (-2 (|:| -1540 *3) (|:| -3136 (-663 *5)))) - (-5 *1 (-1056 *5 *3)) (-5 *4 (-663 *5)) (-4 *3 (-680 *5))))) -(((*1 *2 *3 *3 *3) - (|partial| -12 (-4 *4 (-13 (-376) (-149) (-1069 (-560)))) - (-4 *5 (-1273 *4)) (-5 *2 (-663 (-421 *5))) (-5 *1 (-1047 *4 *5)) - (-5 *3 (-421 *5))))) -(((*1 *1 *1 *1) (-5 *1 (-887)))) -(((*1 *2 *1) - (-12 (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-385 *3)) - (-4 *5 (-385 *3)) (-5 *2 (-663 (-663 *3))))) - ((*1 *2 *1) - (-12 (-4 *1 (-1084 *3 *4 *5 *6 *7)) (-4 *5 (-1080)) - (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 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+ ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-793)) (-5 *2 (-1303)) (-5 *1 (-1301))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-663 (-48))) (-5 *2 (-419 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1273 (-48))))) @@ -10413,8 +11361,8 @@ (-12 (-4 *4 (-13 (-871) - (-10 -8 (-15 -2154 ((-1207) $)) - (-15 -1706 ((-3 $ "failed") (-1207)))))) + (-10 -8 (-15 -1808 ((-1207) $)) + (-15 -3514 ((-3 $ "failed") (-1207)))))) (-4 *5 (-815)) (-4 *7 (-571)) (-5 *2 (-419 *3)) (-5 *1 (-470 *4 *5 *6 *7 *3)) (-4 *6 (-571)) (-4 *3 (-979 *7 *5 *4)))) @@ -10463,13 +11411,13 @@ (-12 (-4 *4 (-815)) (-4 *5 (-13 (-871) - (-10 -8 (-15 -2154 ((-1207) $)) - (-15 -1706 ((-3 $ "failed") (-1207)))))) + (-10 -8 (-15 -1808 ((-1207) $)) + (-15 -3514 ((-3 $ "failed") (-1207)))))) (-4 *6 (-319)) (-5 *2 (-419 *3)) (-5 *1 (-752 *4 *5 *6 *3)) (-4 *3 (-979 (-975 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-815)) - (-4 *5 (-13 (-871) (-10 -8 (-15 -2154 ((-1207) $))))) (-4 *6 (-571)) + (-4 *5 (-13 (-871) (-10 -8 (-15 -1808 ((-1207) $))))) (-4 *6 (-571)) (-5 *2 (-419 *3)) (-5 *1 (-754 *4 *5 *6 *3)) (-4 *3 (-979 (-421 (-975 *6)) *4 *5)))) ((*1 *2 *3) @@ -10505,277 +11453,117 @@ ((*1 *2 *1) (-12 (-5 *2 (-419 *1)) (-4 *1 (-1252)))) ((*1 *2 *3) (-12 (-5 *2 (-419 *3)) (-5 *1 (-1263 *3)) (-4 *3 (-1273 (-560)))))) -(((*1 *1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-342))))) -(((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1301)))) - ((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1301))))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-1248))) (-5 *1 (-703)))) - ((*1 *2 *1) (-12 (-5 *2 (-663 (-1212))) (-5 *1 (-1146))))) -(((*1 *2 *2) - (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1273 (-560)))))) -(((*1 *2) - (-12 (-4 *2 (-13 (-435 *3) (-1033))) (-5 *1 (-287 *3 *2)) - (-4 *3 (-571))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *1)) (-4 *1 (-466)))) - ((*1 *1 *1 *1) (-4 *1 (-466)))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-115)))) - ((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-115)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) - (-4 *5 (-277 *3)) (-4 *6 (-815)) 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|continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3112 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1066)) (-5 *1 (-315))))) +(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *3 *3 *5 *6 *3 *6 *6 *5 *6 *6 *6 *6 + *5 *3 *3 *3 *3 *3 *6 *6 *6 *3 *3 *3 *3 *3 *7 *4 *4 *4 *4 *3 *8 + *9) + (-12 (-5 *4 (-711 (-229))) (-5 *5 (-114)) (-5 *6 (-229)) + (-5 *7 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\ No newline at end of file |