diff options
Diffstat (limited to 'src/share/algebra')
| -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 | 1315 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9060 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 26194 |
5 files changed, 19389 insertions, 19390 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 4fe747fa..f00b171a 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294960 . 3486916218) +(2294960 . 3486967787) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1995) +(-32 R -2022) ((|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 -1060) (QUOTE (-576))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1995 UP UPUP -1648) +(-40 -2022 UP UPUP -2948) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4459 |has| (-419 |#2|) (-374)) (-4464 |has| (-419 |#2|) (-374)) (-4458 |has| (-419 |#2|) (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2748 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2748 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2748 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2748 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2748 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -652) (QUOTE (-576)))) (-2748 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -1995) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2802 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2802 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2802 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-41 R -2022) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|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."))) ((-4466 . T) (-4467 . T)) -((-2748 (-12 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) +((-2802 (-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1995) +(-54 |Base| R -2022) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2634) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2676) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2634) +(-62 -2676) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2634) +(-63 -2676) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2634) +(-64 -2676) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2634) +(-65 -2676) ((|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 -2634) +(-66 -2676) ((|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 -2634) +(-67 -2676) ((|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 -2634) +(-68 -2676) ((|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 -2634) +(-69 -2676) ((|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 -2634) +(-70 -2676) ((|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 -2634) +(-71 -2676) ((|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 -2634) +(-72 -2676) ((|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 -2634) +(-73 -2676) ((|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 -2634) +(-74 -2676) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2634) +(-77 -2676) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2634) +(-78 -2676) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2634) +(-79 -2676) ((|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 -2634) +(-80 -2676) ((|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 -2634) +(-81 -2676) ((|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 -2634) +(-82 -2676) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2634) +(-83 -2676) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2634) +(-84 -2676) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2634) +(-85 -2676) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2634) +(-86 -2676) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2634) +(-87 -2676) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2634) +(-88 -2676) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2634) +(-89 -2676) ((|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}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|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 \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|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."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2748 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) +((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) (-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 \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1995 UP) +(-116 -2022 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 @@ -403,7 +403,7 @@ NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-929))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1044))) (|HasCategory| (-117 |#1|) (QUOTE (-833))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-2748 (|HasCategory| (-117 |#1|) (QUOTE (-833))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1174))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1198)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-929)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-929))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1044))) (|HasCategory| (-117 |#1|) (QUOTE (-833))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-2802 (|HasCategory| (-117 |#1|) (QUOTE (-833))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1174))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1198)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-929)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -419,7 +419,7 @@ NIL (-122 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"))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -439,15 +439,15 @@ NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-128 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."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|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 \\spad{`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."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2748 (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-130) (QUOTE (-862))) (-2748 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-2802 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2802 (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-130) (QUOTE (-862))) (-2802 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -472,11 +472,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4468 "*") . T)) NIL -(-136 |minix| -2703 S T$) +(-136 |minix| -2755 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2703 R) +(-137 |minix| -2755 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -499,7 +499,7 @@ NIL (-142) ((|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}."))) ((-4466 . T) (-4456 . T) (-4467 . T)) -((-2748 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-2802 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-143 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}\\spad{'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}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4463 . T)) NIL -(-149 -1995 UP UPUP) +(-149 -2022 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -1995) +(-159 R -2022) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasCategory| |#2| (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasAttribute| |#2| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) (-167 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})"))) -((-4459 -2748 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4465 |has| |#1| (-6 -4465)) (-4143 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4459 -2802 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4465 |has| |#1| (-6 -4465)) (-4155 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-168 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}."))) -((-4459 -2748 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4465 |has| |#1| (-6 -4465)) (-4143 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2748 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-929))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-929))))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2748 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4465)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-360))))) +((-4459 -2802 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4465 |has| |#1| (-6 -4465)) (-4155 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2802 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-929))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-929))))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4465)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-360))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1995) +(-190 R -2022) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1995 UP UPUP R) +(-217 -2022 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -1995 FP) +(-218 -2022 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|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."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2748 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) +((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1995) +(-221 R -2022) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-225 |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}."))) ((-4463 . T)) NIL -(-226 R -1995) +(-226 R -2022) ((|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 (-227) ((|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}."))) -((-4130 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-228) ((|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)}.}"))) @@ -847,7 +847,7 @@ NIL (-229 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}"))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-230 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 @@ -896,22 +896,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-242 S -2703 R) +(-242 S -2755 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 (-374))) (|HasCategory| |#3| (QUOTE (-806))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4463)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-739))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1071))) (|HasCategory| |#3| (QUOTE (-1122)))) -(-243 -2703 R) +(-243 -2755 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"))) ((-4460 |has| |#2| (-1071)) (-4461 |has| |#2| (-1071)) (-4463 |has| |#2| (-6 -4463)) (-4466 . T)) NIL -(-244 -2703 A B) +(-244 -2755 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 -(-245 -2703 R) +(-245 -2755 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."))) ((-4460 |has| |#2| (-1071)) (-4461 |has| |#2| (-1071)) (-4463 |has| |#2| (-6 -4463)) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-806))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -931,7 +931,7 @@ NIL (-250 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}"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-251 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -943,7 +943,7 @@ NIL (-253 |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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (-2748 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2748 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-929))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) (-254) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|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 \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -1023,7 +1023,7 @@ NIL (-273 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"))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . 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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 @@ -1068,11 +1068,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-285 R -1995) +(-285 R -2022) ((|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 -(-286 R -1995) +(-286 R -2022) ((|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 @@ -1124,7 +1124,7 @@ 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 -(-299 S R |Mod| -2444 -1661 |exactQuo|) +(-299 S R |Mod| -2921 -3073 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL @@ -1146,21 +1146,21 @@ NIL NIL (-304 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4466 . T) (-4467 . 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Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-307 -1995 S) +(-307 -2022 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 -(-308 E -1995) +(-308 E -2022) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1208,7 +1208,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-320 -1995) +(-320 -2022) ((|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 @@ -1223,7 +1223,7 @@ NIL (-323 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))}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . 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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 @@ -1234,9 +1234,9 @@ NIL NIL (-326 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4463 -2748 (-12 (|has| |#1| (-568)) (-2748 (|has| |#1| (-1071)) (|has| |#1| (-485)))) (|has| |#1| (-1071)) (|has| |#1| (-485))) (-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) ((-4468 "*") |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-568)) (-4458 |has| |#1| (-568))) -((-2748 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) 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(QUOTE -652) (QUOTE (-576)))))) (-2802 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1134)))) (-2802 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))))) (-2802 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1071)))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1134))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1071))) (|HasCategory| $ (LIST (QUOTE -1060) (QUOTE (-576))))) +(-327 R -2022) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1247,7 +1247,7 @@ NIL (-329 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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2748 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2320) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) (-330 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1279,12 +1279,12 @@ NIL (-337 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."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -1995) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -2022) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-379)))) -(-339 -1995) +(-339 -2022) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL @@ -1308,15 +1308,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-345 S -1995 UP UPUP R) +(-345 S -2022 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-346 -1995 UP UPUP R) +(-346 -2022 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-347 -1995 UP UPUP R) +(-347 -2022 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1336,26 +1336,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-352 S -1995 UP UPUP) +(-352 S -2022 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -1995 UP UPUP) +(-353 -2022 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4459 |has| (-419 |#2|) (-374)) (-4464 |has| (-419 |#2|) (-374)) (-4458 |has| (-419 |#2|) (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-354 |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."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) +((-2802 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1372,31 +1372,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL -(-361 R UP -1995) +(-361 R UP -2022) ((|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 (-362 |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."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) +((-2802 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) (-363 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 |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}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) +((-2802 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) (-366 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -1995 GF) +((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -2022 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1404,14 +1404,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-369 -1995 FP FPP) +(-369 -2022 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-370 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-371 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1490,7 +1490,7 @@ NIL NIL (-390) ((|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}."))) -((-4449 . T) (-4457 . T) (-4130 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4449 . T) (-4457 . T) (-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-391 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1544,7 +1544,7 @@ 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 -(-404 -1995 UP UPUP R) +(-404 -2022 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 @@ -1568,11 +1568,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-410 -2634 |returnType| -1383 |symbols|) +(-410 -2676 |returnType| -1373 |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 -(-411 -1995 UP) +(-411 -2022 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 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1594,7 +1594,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#1| (QUOTE -4457))) (-416) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-4130 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-417 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."))) @@ -1607,7 +1607,7 @@ NIL (-419 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4453 -12 (|has| |#1| (-6 -4464)) (|has| |#1| (-464)) (|has| |#1| (-6 -4453))) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-862)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841))))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4464)) (|HasAttribute| |#1| (QUOTE -4453)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-862)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841))))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4464)) (|HasAttribute| |#1| (QUOTE -4453)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-420 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1628,11 +1628,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -1995 UP A) +(-425 R -2022 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4463 . T)) NIL -(-426 R -1995 UP A |ibasis|) +(-426 R -2022 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 -1060) (|devaluate| |#2|)))) @@ -1651,7 +1651,7 @@ NIL (-430 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1243))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1243)))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1243))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1243)))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-431 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1680,7 +1680,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4466 . T) (-4456 . T) (-4467 . T)) NIL -(-438 R -1995) +(-438 R -2022) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1688,7 +1688,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4453 -12 (|has| |#1| (-6 -4453)) (|has| |#2| (-6 -4453))) (-4460 . T) (-4461 . T) (-4463 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4453)) (|HasAttribute| |#2| (QUOTE -4453)))) -(-440 R -1995) +(-440 R -2022) ((|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 @@ -1698,17 +1698,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1134))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-442 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4463 -2748 (|has| |#1| (-1071)) (|has| |#1| (-485))) (-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) ((-4468 "*") |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-568)) (-4458 |has| |#1| (-568))) +((-4463 -2802 (|has| |#1| (-1071)) (|has| |#1| (-485))) (-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) ((-4468 "*") |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-568)) (-4458 |has| |#1| (-568))) NIL -(-443 R -1995) +(-443 R -2022) ((|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 -(-444 R -1995) +(-444 R -2022) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-445 R -1995) +(-445 R -2022) ((|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 @@ -1716,7 +1716,7 @@ 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 -(-447 R -1995 UP) +(-447 R -2022 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 -1060) (QUOTE (-48))))) @@ -1748,7 +1748,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-455 R UP -1995) +(-455 R UP -2022) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1795,7 +1795,7 @@ NIL (-466 |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"))) (((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . 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A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1860,7 +1860,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -1995 R) +(-483 |lv| -2022 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 @@ -1875,11 +1875,11 @@ NIL (-486 |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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . 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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)}"))) ((-4467 . T) (-4466 . T)) @@ -1895,7 +1895,7 @@ NIL (-491 |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."))) ((-4466 . T) (-4467 . 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1903,11 +1903,11 @@ NIL (-493 |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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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1915,8 +1915,8 @@ NIL (-496 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -1995 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-497 -2022 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1927,7 +1927,7 @@ NIL (-499) ((|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."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . 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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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,7 +1952,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -1995 UP |AlExt| |AlPol|) +(-506 -2022 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1963,16 +1963,16 @@ NIL (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-509 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 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 -(-511 R UP -1995) +(-511 R UP -2022) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1992,7 +1992,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-516 -1995 |Expon| |VarSet| |DPoly|) +(-516 -2022 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1198))))) @@ -2043,7 +2043,7 @@ NIL (-528 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-529) ((|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 @@ -2051,15 +2051,15 @@ NIL (-530 |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}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((-2748 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) +((-2802 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) (-531 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-532 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."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-533 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2071,7 +2071,7 @@ NIL (-535 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."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|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 @@ -2104,7 +2104,7 @@ 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| (-784) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-1122))))) -(-544 K -1995 |Par|) +(-544 K -2022 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2128,7 +2128,7 @@ 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 -(-550 K -1995 |Par|) +(-550 K -2022 |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 @@ -2179,12 +2179,12 @@ NIL (-562 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) -(-563 R -1995) +((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) +(-563 R -2022) ((|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 -(-564 R0 -1995 UP UPUP R) +(-564 R0 -2022 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 @@ -2194,7 +2194,7 @@ NIL NIL (-566 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-4130 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4144 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-567 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."))) @@ -2204,7 +2204,7 @@ 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."))) ((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL -(-569 R -1995) +(-569 R -2022) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2216,7 +2216,7 @@ 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 -(-572 R -1995 L) +(-572 R -2022 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -669) (|devaluate| |#2|)))) @@ -2224,11 +2224,11 @@ 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 -(-574 -1995 UP UPUP R) +(-574 -2022 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 -(-575 -1995 UP) +(-575 -2022 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 @@ -2240,15 +2240,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-578 R -1995 L) +(-578 R -2022 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -669) (|devaluate| |#2|)))) -(-579 R -1995) +(-579 R -2022) ((|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 -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -1995 UP) +(-580 -2022 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2256,27 +2256,27 @@ 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 -(-582 -1995) +(-582 -2022) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-583 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."))) -((-4130 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4144 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-584) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-585 R -1995) +(-585 R -2022) ((|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 -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -1995 UP) +(-586 -2022 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 -(-587 R -1995) +(-587 R -2022) ((|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 @@ -2308,11 +2308,11 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-595 R -1995) +(-595 R -2022) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-596 E -1995) +(-596 E -2022) ((|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 @@ -2320,7 +2320,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-598 -1995) +(-598 -2022) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4461 . T) (-4460 . T)) ((|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-1198))))) @@ -2351,7 +2351,7 @@ NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2748 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-145) (QUOTE (-862))) (-2748 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-2802 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2802 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-145) (QUOTE (-862))) (-2802 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-606 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 @@ -2359,7 +2359,7 @@ NIL (-607 |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}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) (-608 |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.}"))) (((-4468 "*") |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) @@ -2376,7 +2376,7 @@ 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 -(-612 R -1995 FG) +(-612 R -2022 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2387,7 +2387,7 @@ NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-615 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2406,12 +2406,12 @@ NIL NIL (-619 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4463 -2748 (-2675 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4461 . T) (-4460 . T)) -((-2748 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4463 -2802 (-2724 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4461 . T) (-4460 . T)) +((-2802 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |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."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102)))) (-621 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 @@ -2436,7 +2436,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -1995 UP) +(-627 -2022 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4460 . T) (-4461 . T) (-4463 . T)) ((|HasCategory| |#1| (QUOTE (-861)))) -(-634 R -1995) +(-634 R -2022) ((|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 @@ -2496,18 +2496,18 @@ 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 -(-642 R -1995) +(-642 R -2022) ((|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 -(-643 |lv| -1995) +(-643 |lv| -2022) ((|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 (-644) ((|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."))) ((-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1180) (QUOTE (-862))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122)))) +((-12 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1180) (QUOTE (-862))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (QUOTE (-1122)))) (-645 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2518,8 +2518,8 @@ NIL NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4463 -2748 (-2675 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4461 . T) (-4460 . T)) -((-2748 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4463 -2802 (-2724 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4461 . T) (-4460 . T)) +((-2802 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2531,7 +2531,7 @@ NIL (-650 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2665 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) +((-2712 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) (-651 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|) (|List| (|OrderedVariableList| |#2|))) "\\spad{linearElement([x1,..,xn],[b1,..,bn]) constructs a linear element with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{b1},{}...\\spad{bn}."))) ((-4461 . T) (-4460 . T)) @@ -2559,7 +2559,7 @@ NIL (-657 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."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-658 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2571,7 +2571,7 @@ NIL (-660 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-661 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2588,7 +2588,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-665 R -1995 L) +(-665 R -2022 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 @@ -2608,11 +2608,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4460 . T) (-4461 . T) (-4463 . T)) NIL -(-670 -1995 UP) +(-670 -2022 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)))) -(-671 A -3307) +(-671 A -1411) ((|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}}"))) ((-4460 . T) (-4461 . T) (-4463 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) @@ -2648,11 +2648,11 @@ 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}."))) ((-4467 . T) (-4466 . T)) NIL -(-680 -1995) +(-680 -2022) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-681 -1995 |Row| |Col| M) +(-681 -2022 |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 @@ -2663,7 +2663,7 @@ NIL (-683 |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."))) ((-4463 . T) (-4466 . T) (-4460 . T) (-4461 . T)) -((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2748 (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2802 (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-684) ((|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 @@ -2683,7 +2683,7 @@ NIL (-688 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 -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-689) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2739,7 +2739,7 @@ NIL (-702 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."))) ((-4466 . T) (-4467 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-703 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2748,7 +2748,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-705 S -1995 FLAF FLAS) +(-705 S -2022 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2758,8 +2758,8 @@ NIL NIL (-707) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4459 . T) (-4464 |has| (-712) (-374)) (-4458 |has| (-712) (-374)) (-4143 . 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As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4467 . T)) @@ -2772,13 +2772,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) 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(|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 (-712) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) 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T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) +((-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-713 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."))) @@ -2804,7 +2804,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-726 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) (-4463 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-728 R |Mod| -2444 -1661 |exactQuo|) +(-728 R |Mod| -2921 -3073 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4463 . T)) NIL @@ -2852,7 +2852,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4461 . T) (-4460 . T)) NIL -(-731 -1995) +(-731 -2022) ((|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]]}."))) ((-4463 . T)) NIL @@ -2888,7 +2888,7 @@ 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 -(-740 -1995 UP) +(-740 -2022 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 @@ -2907,7 +2907,7 @@ NIL (-744 |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."))) (((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (-2748 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2748 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-929))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) (-745 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 @@ -3040,11 +3040,11 @@ 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 -(-778 -1995) +(-778 -2022) ((|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 -(-779 P -1995) +(-779 P -2022) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3052,7 +3052,7 @@ NIL NIL NIL NIL -(-781 UP -1995) +(-781 UP -2022) ((|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 @@ -3068,7 +3068,7 @@ 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."))) (((-4468 "*") . T)) NIL -(-785 R -1995) +(-785 R -2022) ((|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 @@ -3088,7 +3088,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-790 -1995 |ExtF| |SUEx| |ExtP| |n|) +(-790 -2022 |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 @@ -3103,7 +3103,7 @@ NIL (-793 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . 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(-576))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-1198)))) (-2712 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-576))))) (-2712 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-1198)))) (-2712 (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-576))))))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-794 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3111,7 +3111,7 @@ NIL (-795 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-796 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3172,23 +3172,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4460 . T) (-4461 . T) (-4463 . T)) NIL -(-811 -2748 R OS S) +(-811 -2802 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-812 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2748 (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2748 (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2802 (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (-813) ((|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 -(-814 R -1995 L) +(-814 R -2022 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-815 R -1995) +(-815 R -2022) ((|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 @@ -3196,7 +3196,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-817 R -1995) +(-817 R -2022) ((|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 @@ -3204,11 +3204,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-819 -1995 UP UPUP R) +(-819 -2022 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 -(-820 -1995 UP L LQ) +(-820 -2022 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3216,38 +3216,38 @@ 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 -(-822 -1995 UP L LQ) +(-822 -2022 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-823 -1995 UP) +(-823 -2022 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-824 -1995 L UP A LO) +(-824 -2022 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 -(-825 -1995 UP) +(-825 -2022 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-826 -1995 LO) +(-826 -2022 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 -(-827 -1995 LODO) +(-827 -2022 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-828 -2703 S |f|) +(-828 -2755 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4460 |has| |#2| (-1071)) (-4461 |has| |#2| (-1071)) (-4463 |has| |#2| (-6 -4463)) (-4466 . 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T)) -((|HasCategory| |#1| (QUOTE (-929))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-831 (-1198)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-830 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4468 "*") |has| |#2| (-374)) (-4459 |has| |#2| (-374)) (-4464 |has| |#2| (-374)) (-4458 |has| |#2| (-374)) (-4463 . T) (-4461 . T) (-4460 . T)) @@ -3315,7 +3315,7 @@ NIL (-846 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."))) ((-4463 |has| |#1| (-861))) -((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-21))) (-2748 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2748 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-21))) (-2802 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-847 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3355,12 +3355,12 @@ NIL (-856 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4463 |has| |#1| (-861))) -((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-21))) (-2748 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2748 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-21))) (-2802 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-857) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-858 -2703 S) +(-858 -2755 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 @@ -3404,11 +3404,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) -(-869 R |sigma| -4256) +(-869 R |sigma| -4262) ((|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."))) ((-4460 . T) (-4461 . T) (-4463 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) -(-870 |x| R |sigma| -4256) +(-870 |x| R |sigma| -4262) ((|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}."))) ((-4460 . T) (-4461 . T) (-4463 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) @@ -3475,15 +3475,15 @@ NIL (-886 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-885 |#1|) (QUOTE (-929))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-148))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-885 |#1|) (QUOTE (-1044))) (|HasCategory| (-885 |#1|) (QUOTE (-833))) (|HasCategory| (-885 |#1|) (QUOTE (-862))) (-2748 (|HasCategory| (-885 |#1|) (QUOTE (-833))) (|HasCategory| (-885 |#1|) (QUOTE (-862)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (QUOTE (-1174))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (QUOTE (-237))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (QUOTE (-238))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -526) (QUOTE (-1198)) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -885) (|devaluate| |#1|)) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (QUOTE (-317))) (|HasCategory| (-885 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-929)))) (|HasCategory| (-885 |#1|) (QUOTE (-146))))) +((|HasCategory| (-885 |#1|) (QUOTE (-929))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-148))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-885 |#1|) (QUOTE (-1044))) (|HasCategory| (-885 |#1|) (QUOTE (-833))) (|HasCategory| (-885 |#1|) (QUOTE (-862))) (-2802 (|HasCategory| (-885 |#1|) (QUOTE (-833))) (|HasCategory| (-885 |#1|) (QUOTE (-862)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (QUOTE (-1174))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (QUOTE (-237))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (QUOTE (-238))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -526) (QUOTE (-1198)) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -885) (|devaluate| |#1|)) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (QUOTE (-317))) (|HasCategory| (-885 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-929)))) (|HasCategory| (-885 |#1|) (QUOTE (-146))))) (-887 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862))) (-2748 (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1174))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862))) (-2802 (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1174))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) (-888 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))))) (-889) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3543,7 +3543,7 @@ NIL (-903 |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 (-2665 (|HasCategory| |#2| (QUOTE (-1071)))) (-2665 (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))))) (-12 (|HasCategory| |#2| (QUOTE (-1071))) (-2665 (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198))))) +((-12 (-2712 (|HasCategory| |#2| (QUOTE (-1071)))) (-2712 (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))))) (-12 (|HasCategory| |#2| (QUOTE (-1071))) (-2712 (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198))))) (-904 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3552,7 +3552,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-906 R -2066) +(-906 R -2097) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3584,7 +3584,7 @@ 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 -(-914 UP -1995) +(-914 UP -2022) ((|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 @@ -3615,7 +3615,7 @@ NIL (-921 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-922 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3631,7 +3631,7 @@ NIL (-925 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."))) ((-4463 . T)) -((-2748 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) +((-2802 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (-926 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3652,7 +3652,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-931 R0 -1995 UP UPUP R) +(-931 R0 -2022 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 @@ -3680,7 +3680,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-938 -1995) +(-938 -2022) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3696,11 +3696,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4468 "*") . T)) NIL -(-942 -1995 P) +(-942 -2022 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-943 |xx| -1995) +(-943 |xx| -2022) ((|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 @@ -3724,7 +3724,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-949 R -1995) +(-949 R -2022) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3736,7 +3736,7 @@ 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 -(-952 S R -1995) +(-952 S R -2022) ((|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 @@ -3756,11 +3756,11 @@ 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 -902) (|devaluate| |#1|)))) -(-957 R -1995 -2066) +(-957 R -2022 -2097) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-958 -2066) +(-958 -2097) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3783,7 +3783,7 @@ NIL (-963 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-964 |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 @@ -3808,7 +3808,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) NIL -(-970 E V R P -1995) +(-970 E V R P -2022) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3819,8 +3819,8 @@ NIL (-972 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}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-973 E V R P -1995) +((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-973 E V R P -2022) ((|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 (-464)))) @@ -3843,12 +3843,12 @@ NIL (-978 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-979) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-980 -1995) +(-980 -2022) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3863,11 +3863,11 @@ NIL (-983 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}"))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4464))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4464))) (-984 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"))) ((-4463 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-806)))) (-12 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(|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-806)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-806))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-806))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-739))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-739)))) (-12 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-806))))) (-12 (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-739)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-985) ((|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 \\spad{`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 @@ -3956,7 +3956,7 @@ 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 -(-1007 K R UP -1995) +(-1007 K R UP -2022) ((|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 @@ -4015,11 +4015,11 @@ NIL (-1021 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.}"))) ((-4459 |has| |#1| (-300)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-557)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-557)))) (-1022 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}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1023 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4028,14 +4028,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1025 -1995 UP UPUP |radicnd| |n|) +(-1025 -2022 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4459 |has| (-419 |#2|) (-374)) (-4464 |has| (-419 |#2|) (-374)) (-4458 |has| (-419 |#2|) (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2748 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2748 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2748 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2748 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2748 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -652) (QUOTE (-576)))) (-2748 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2802 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2802 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2802 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (-1026 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2748 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) +((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) (-1027) ((|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 @@ -4068,19 +4068,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4459 . T) (-4464 . T) (-4458 . T) (-4461 . T) (-4460 . T) ((-4468 "*") . T) (-4463 . T)) NIL -(-1035 R -1995) +(-1035 R -2022) ((|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 -(-1036 R -1995) +(-1036 R -2022) ((|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 -(-1037 -1995 UP) +(-1037 -2022 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 -(-1038 -1995 UP) +(-1038 -2022 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 @@ -4115,8 +4115,8 @@ NIL (-1046 |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"))) ((-4459 . T) (-4464 . T) (-4458 . T) (-4461 . T) (-4460 . T) ((-4468 "*") . T) (-4463 . T)) -((-2748 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (QUOTE (-576))))) -(-1047 -1995 L) +((-2802 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (QUOTE (-576))))) +(-1047 -2022 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 @@ -4152,14 +4152,14 @@ 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 -(-1056 -1995 |Expon| |VarSet| |FPol| |LFPol|) +(-1056 -2022 |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"))) (((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL (-1057) ((|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.}"))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (QUOTE (-1198))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1122))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1198))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102)))) (-1058) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4216,7 +4216,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4463 . T)) NIL -(-1072 |xx| -1995) +(-1072 |xx| -2022) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4235,7 +4235,7 @@ NIL (-1076 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4466 . T) (-4461 . T) (-4460 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2748 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-877))))) +((|HasCategory| |#3| (QUOTE (-174))) (-2802 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-877))))) (-1077 |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 @@ -4271,7 +4271,7 @@ NIL (-1085) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (QUOTE (-1198))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1122))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1198))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102)))) (-1086 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4320,11 +4320,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1098 |Base| R -1995) +(-1098 |Base| R -2022) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1099 |Base| R -1995) +(-1099 |Base| R -2022) ((|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 @@ -4339,7 +4339,7 @@ NIL (-1102 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."))) ((-4459 |has| |#1| (-374)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (-1103 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4367,7 +4367,7 @@ NIL (-1109 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"))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1110 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4427,7 +4427,7 @@ NIL (-1124 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)}}"))) ((-4466 . T) (-4456 . T) (-4467 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1125 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL @@ -4471,7 +4471,7 @@ NIL (-1135 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4460 |has| |#3| (-1071)) (-4461 |has| |#3| (-1071)) (-4463 |has| |#3| (-6 -4463)) (-4466 . 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(-576))))) (-12 (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1071))) (|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-862))) (-12 (|HasCategory| |#3| (QUOTE (-1071))) (|HasCategory| |#3| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1071)))) (-12 (|HasCategory| |#3| (QUOTE (-1071))) (|HasCategory| |#3| (LIST (QUOTE -920) (QUOTE (-1198))))) (-2802 (|HasCategory| |#3| (QUOTE (-1071))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-576)))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1122)))) (|HasAttribute| |#3| (QUOTE -4463)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1071)))) (-12 (|HasCategory| |#3| (QUOTE (-1071))) (|HasCategory| |#3| (LIST (QUOTE -918) (QUOTE (-1198))))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (-1136 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4480,7 +4480,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1138 R -1995) +(-1138 R -2022) ((|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 @@ -4519,16 +4519,16 @@ NIL (-1147 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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2748 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1148 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1149 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}"))) ((-4467 . T) (-4466 . T)) NIL -(-1150 UP -1995) +(-1150 UP -2022) ((|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 @@ -4583,11 +4583,11 @@ NIL (-1163 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1162) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122))) (-2748 (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122)))) (-2748 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1162) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122))))) (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1162) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122))) (-2802 (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122)))) (-2802 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1162) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122))))) (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-102)))) (-1164 |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}."))) ((-4463 . T) (-4455 |has| |#2| (-6 (-4468 "*"))) (-4466 . T) (-4460 . T) (-4461 . T)) -((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2748 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-374))) (-2748 (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-374))) (-2802 (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1165 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4607,7 +4607,7 @@ NIL (-1169 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1170 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 @@ -4619,7 +4619,7 @@ NIL (-1172 |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."))) ((-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122)))) +((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122)))) (-1173) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4647,15 +4647,15 @@ NIL (-1179 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) ((-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1180) ((|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"))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2748 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-145) (QUOTE (-862))) (-2748 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-2802 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2802 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-145) (QUOTE (-862))) (-2802 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-1181 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#1|)))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#1|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102)))) (-1182 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4686,9 +4686,9 @@ NIL NIL (-1189 |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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\\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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2748 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2320) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) (-1196 |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}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|)))) (|HasCategory| (-784) (QUOTE (-1134))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2320) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|)))) (|HasCategory| (-784) (QUOTE (-1134))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) (-1197) ((|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 @@ -4731,7 +4731,7 @@ NIL (-1200 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2748 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-993) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4464))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-993) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4464))) (-1201) ((|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 @@ -4775,7 +4775,7 @@ NIL (-1211 |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}"))) ((-4466 . T) (-4467 . T)) -((-12 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4286) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2748 (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) (-1212 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4831,7 +4831,7 @@ NIL (-1225 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4467 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1226 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4840,7 +4840,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1228 R -1995) +(-1228 R -2022) ((|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 @@ -4848,7 +4848,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1230 R -1995) +(-1230 R -2022) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -902) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -902) (|devaluate| |#1|))))) @@ -4863,7 +4863,7 @@ NIL (-1233 |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}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4461 . T) (-4460 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1234 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4876,7 +4876,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) -(-1237 -1995) +(-1237 -2022) ((|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.")) 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|#3|) (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1281 |#1| |#2| |#3|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1281 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1281 |#1| |#2| |#3|) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1281 |#1| |#2| |#3|) (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-374)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1281 |#1| |#2| |#3|) (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1281 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1254 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 @@ -4979,7 +4979,7 @@ NIL (-1262 |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}"))) (((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4462 |has| |#2| (-374)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4995,7 +4995,7 @@ NIL (-1266 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|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 -918) (QUOTE (-1198)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1134))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3515) (LIST (|devaluate| |#2|) (QUOTE (-1198)))))) +((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1134))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3501) (LIST (|devaluate| |#2|) (QUOTE (-1198)))))) (-1267 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) @@ -5023,15 +5023,15 @@ NIL (-1273 |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)}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2748 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2320) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-1274 |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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2748 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2748 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2320) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) (-1275 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))}."))) (((-4468 "*") |has| (-1274 |#2| |#3| |#4|) (-174)) (-4459 |has| (-1274 |#2| |#3| |#4|) (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-174))) (-2748 (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-568)))) +((|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-174))) (-2802 (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-568)))) (-1276 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5047,7 +5047,7 @@ NIL (-1279 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-576)))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasSignature| |#2| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2320) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1198))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasSignature| |#2| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4190) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1198))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) (-1280 |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."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) @@ -5055,12 +5055,12 @@ NIL (-1281 |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}."))) (((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2748 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|)))) (|HasCategory| (-784) (QUOTE (-1134))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasSignature| |#1| (LIST (QUOTE -3515) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasCategory| |#1| (QUOTE (-374))) (-2748 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2320) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -1998) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|)))) (|HasCategory| (-784) (QUOTE (-1134))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) (-1282 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1283 -1995 UP L UTS) +(-1283 -2022 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 (-568)))) @@ -5087,7 +5087,7 @@ NIL (-1289 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."))) ((-4467 . T) (-4466 . T)) -((-2748 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2748 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2748 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2748 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1290) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5120,7 +5120,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1298 K R UP -1995) +(-1298 K R UP -2022) ((|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 @@ -5156,11 +5156,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4459 |has| |#2| (-6 -4459)) (-4461 . T) (-4460 . T) (-4463 . T)) NIL -(-1307 S -1995) +(-1307 S -2022) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1308 -1995) +(-1308 -2022) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 5db33608..7f7190d7 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205224 . 3486916226) -(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((#0=(-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) #0#) |has| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4286 |#1|) (|:| -4440 |#2|))))) -((((-576)) . T) (($) -2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T)) +(205224 . 3486967795) +(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((#0=(-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) #0#) |has| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))))) +((((-576)) . T) (($) -2802 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-576)) . T)) -((($ $) -2748 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576))))) +((($ $) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-576)) |has| |#1| (-652 (-576))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) . T)) -((($) -2748 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) +((($) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) (|has| |#1| (-929)) ((((-877)) . T)) ((((-877)) . T)) @@ -22,23 +22,23 @@ ((((-548)) . T) (((-1180)) . T) (((-227)) . T) (((-390)) . T) (((-908 (-390))) . T)) (((|#1|) . T)) ((((-227)) . T) (((-877)) . T)) -(-2748 (|has| |#2| (-806)) (|has| |#2| (-862))) -(-2748 (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) +(-2802 (|has| |#2| (-806)) (|has| |#2| (-862))) +(-2802 (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-861))) -((($ $) . T) ((#0=(-419 (-576)) #0#) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1| |#1|) . 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T)) @@ -51,14 +51,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1203)) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-1060 (-576))) (((-419 (-576))) |has| |#1| (-1060 (-419 (-576))))) -(-2748 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) -(((|#2| (-494 (-3437 |#1|) (-784))) . T)) -((((-1198)) -2748 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) +(-2802 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(((|#2| (-494 (-3440 |#1|) (-784))) . T)) +((((-1198)) -2802 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) (((|#1| (-543 (-1198))) . T)) ((((-1180)) . T) (((-978 (-130))) . T) (((-877)) . T)) ((((-877)) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((#0=(-885 |#1|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (|has| |#4| (-379)) (|has| |#3| (-379)) @@ -74,14 +74,14 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-568)) -((((-576)) . T) (((-419 (-576))) -2748 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1060 (-419 (-576))))) ((|#2|) . T) (($) -2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) (((-879 |#1|)) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) -((((-2 (|:| -3146 |#1|) (|:| -2128 |#2|))) . T)) +((((-576)) . T) (((-419 (-576))) -2802 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1060 (-419 (-576))))) ((|#2|) . T) (($) -2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) (((-879 |#1|)) . T)) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) +((((-2 (|:| -3178 |#1|) (|:| -1801 |#2|))) . T)) ((($) . T)) ((((-877)) |has| |#1| (-625 (-877))) ((|#1|) . T)) -((((-576)) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T) (($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (((-1198)) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) +((((-576)) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T) (($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (((-1198)) . T)) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) ((((-548)) |has| |#1| (-626 (-548)))) ((((-1198)) . T)) (((|#1|) . T)) @@ -102,12 +102,12 @@ ((((-877)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2748 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) +(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . 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T) (($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) +(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . T) (($ $) -2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) ((($ $) . T)) ((($) . T)) ((((-576)) . T) (($) . T) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) @@ -131,30 +131,30 @@ (|has| |#1| (-379)) (((|#1|) . T)) ((((-877)) . T)) -((((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1281 |#1| |#2| |#3|)) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) +((((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1281 |#1| |#2| |#3|)) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) -(((|#1|) . 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T)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) (|has| |#1| (-1122)) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) (|has| |#1| (-1122)) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) (|has| |#1| (-861)) (((|#1| |#1|) . T)) ((($) . T) (((-419 (-576))) . T)) @@ -169,12 +169,12 @@ (|has| |#3| (-806)) (|has| |#3| (-806)) (((|#1| |#2|) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1203)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) (((-1198) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1198) |#2|)))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) ((((-576)) . T) (((-419 (-576))) . T)) (((|#1| (-1198) (-1110 (-1198)) (-543 (-1110 (-1198)))) . T)) ((((-576) |#1|) . T)) @@ -194,29 +194,29 @@ ((((-1180) |#1|) . T)) ((((-1256 (-576)) $) . T) (((-576) (-130)) . T)) (((|#1|) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) (((|#3| (-784)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) ((($) . T) (((-419 (-576))) . T)) ((($) . T)) ((($) . 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T)) ((((-419 (-576))) . T) (($) . T)) @@ -227,7 +227,7 @@ (((|#1|) . T)) (|has| |#2| (-374)) ((((-1256 (-576)) $) . T) (((-576) |#1|) . T)) -((($) -2748 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) +((($) -2802 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) (((|#1| |#2|) . T)) ((((-877)) . T)) @@ -240,13 +240,13 @@ ((((-877)) . T)) ((((-877)) . T)) (((|#1| |#1|) . T)) -(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . T) (($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) -((($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . 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T) (($) -2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) +((($) -2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +(((|#2|) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071))) (($) |has| |#2| (-1071)) (((-576)) -12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071)))) ((((-877)) . T)) ((((-877)) . T)) ((((-877)) . T)) @@ -257,10 +257,10 @@ ((((-171 (-227))) |has| |#1| (-1044)) (((-171 (-390))) |has| |#1| (-1044)) (((-548)) |has| |#1| (-626 (-548))) (((-1194 |#1|)) . T) (((-908 (-576))) |has| |#1| (-626 (-908 (-576)))) (((-908 (-390))) |has| |#1| (-626 (-908 (-390))))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (((|#1|) . 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T)) -((((-2 (|:| -3146 |#1|) (|:| -2128 |#2|))) . T) (((-877)) . T)) +((((-2 (|:| -3178 |#1|) (|:| -1801 |#2|))) . T) (((-877)) . T)) ((((-548)) |has| |#1| (-626 (-548))) (((-908 (-390))) |has| |#1| (-626 (-908 (-390)))) (((-908 (-576))) |has| |#1| (-626 (-908 (-576))))) -(((|#4|) -2748 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1071)))) -(((|#3|) -2748 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071)))) -((((-2 (|:| -3146 |#1|) (|:| -2128 |#2|))) . T)) +(((|#4|) -2802 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1071)))) +(((|#3|) -2802 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071)))) +((((-2 (|:| -3178 |#1|) (|:| -1801 |#2|))) . T)) ((((-877)) . T)) ((((-877)) . T)) ((((-548)) . T) (((-576)) . T) (((-908 (-576))) . T) (((-390)) . T) (((-227)) . T)) @@ -325,15 +325,15 @@ (((|#1|) . T) (((-576)) |has| |#1| (-1060 (-576))) (((-419 (-576))) |has| |#1| (-1060 (-419 (-576))))) ((($) . 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T)) @@ -348,15 +348,15 @@ (|has| |#1| (-1122)) ((((-930 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) ((((-548)) |has| |#1| (-626 (-548)))) ((((-877)) . T) (((-1203)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) ((((-1203)) . 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T)) (((|#1| (-993)) . T)) ((((-576)) . T) ((|#2|) . T)) @@ -368,7 +368,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1174)) -((((-2 (|:| -4286 (-1180)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4291 (-1180)) (|:| -4440 |#1|))) . T)) (|has| (-1275 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1275 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -380,28 +380,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-576)) |has| |#2| (-652 (-576)))) -((((-1147 |#1| (-1198))) . T) (((-576)) . T) (((-831 (-1198))) . T) (($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) (((-1198)) . T)) +((((-1147 |#1| (-1198))) . T) (((-576)) . T) (((-831 (-1198))) . T) (($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) (((-1198)) . 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T)) -((($) -2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-877)) . T)) ((((-877)) . T)) (|has| (-1274 |#2| |#3| |#4|) (-148)) @@ -412,18 +412,18 @@ ((((-877)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071))) (((|#1|) . T)) ((($) . T)) ((((-576) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-861))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-861))) ((((-877)) |has| |#1| (-1122))) -((($) -2748 (|has| |#1| (-238)) (|has| |#1| (-237)))) -(-2748 (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071)) (|has| |#1| (-1134))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) +((($) -2802 (|has| |#1| (-238)) (|has| |#1| (-237)))) +(-2802 (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071)) (|has| |#1| (-1134))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-930 |#1|)) . T)) ((((-419 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-576) |#1|))) @@ -434,7 +434,7 @@ ((((-877)) . T)) ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) (|has| |#1| (-374)) -(-2748 (-12 (|has| (-1281 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) +(-2802 (-12 (|has| (-1281 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-784) |#1|))) @@ -448,23 +448,23 @@ ((((-1256 (-576)) $) . T) (((-576) |#1|) . T)) ((((-877)) . T)) (((|#2|) . T)) -(-2748 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568)) (((-576)) . T)) (|has| |#2| (-806)) (|has| |#2| (-806)) -((((-1281 |#1| |#2| |#3|)) . 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T)) -((($ (-1198)) -2748 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) +((($ (-1198)) -2802 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) (((#0=(-712) (-1194 #0#)) . T)) ((((-593 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((((-419 (-576))) . T) (($) . T)) @@ -472,18 +472,18 @@ ((((-877)) . T) (((-1289 |#3|)) . T)) ((((-593 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((($) . T) (((-419 (-576))) . T)) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2748 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2802 (|has| |#1| (-174)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) . T)) ((((-877)) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((($) . 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T) (($) -2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374)))) (((|#3|) |has| |#3| (-1071))) -((($) -2748 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2802 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) (|has| (-1116 |#1|) (-1122)) (((|#2| (-832 |#1|)) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T)) @@ -491,20 +491,20 @@ (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) . 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T)) -((($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-419 $) (-419 $)) |has| |#1| (-568)) (($ $) . T) ((|#1| |#1|) . T)) -((($) -2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((#0=(-1104) |#2|) . T) ((#0# $) . T) (($ $) . T)) ((((-877)) . T)) ((((-930 |#1|)) . T)) @@ -513,22 +513,22 @@ ((((-245 |#1| |#2|) |#2|) . T)) ((((-877)) . T)) (((|#3|) |has| |#3| (-1122)) (((-576)) -12 (|has| |#3| (-1060 (-576))) (|has| |#3| (-1122))) (((-419 (-576))) -12 (|has| |#3| (-1060 (-419 (-576)))) (|has| |#3| (-1122)))) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#1|) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) ((((-548)) |has| |#1| (-626 (-548)))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -4286 (-1198)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4291 (-1198)) (|:| -4440 (-52)))) . T)) (|has| |#1| (-374)) ((((-1203)) . T)) (((|#1|) . T)) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-861))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-861))) ((($) . T)) ((((-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) (|has| |#2| (-833)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-861)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-543 |#3|)) . T)) ((((-877)) . T)) @@ -537,15 +537,15 @@ (|has| |#1| (-379)) ((((-419 (-576))) . T)) (((|#1|) . T)) -(-2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((((-419 (-576))) . T)) ((((-1180) |#1|) . T)) (|has| |#1| (-379)) ((((-576)) . T)) ((((-576)) . T)) (((|#1|) . T) (((-576)) . T)) -(-2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) ((((-877)) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) ((((-1198)) -12 (|has| |#1| (-374)) (|has| |#1| (-918 (-1198))))) @@ -559,12 +559,12 @@ ((((-576) |#3|) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-652 (-576)))) (|has| |#2| (-1071)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) -(-2748 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) +(-2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((((-877)) . T)) ((((-1275 |#1| |#2| |#3| |#4|)) . T)) ((((-419 (-576))) . T) (((-576)) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) @@ -573,9 +573,9 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((((-576)) . T)) ((((-576)) . T)) -((($) . T) (((-576)) . 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T)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) . T)) @@ -938,7 +938,7 @@ ((((-657 |#1|)) . T)) ((((-877)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) (((|#2|) |has| |#2| (-319 |#2|))) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -949,14 +949,14 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) (|has| |#2| (-379)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-862)) (|has| |#1| (-1122))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . 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T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) -((($) . T) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T) (((-576)) |has| |#1| (-652 (-576)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((($) . T) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T) (((-576)) |has| |#1| (-652 (-576)))) ((((-877)) . T)) ((((-1196 |#1| |#2| |#3|) $) -12 (|has| (-1196 |#1| |#2| |#3|) (-296 (-1196 |#1| |#2| |#3|) (-1196 |#1| |#2| |#3|))) (|has| |#1| (-374))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . T) (((-419 (-576)) |#1|) . T)) @@ -977,7 +977,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-576)) . T) (($) . T)) -((($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((($) . T) (((-576)) . T) ((|#2|) . T)) ((((-576)) . T) (($) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) ((((-419 (-576))) . T) (((-576)) . T)) @@ -986,29 +986,29 @@ (((|#1|) . T)) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1071))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1071))) ((((-112)) . T)) ((((-548)) |has| |#1| (-626 (-548))) (((-227)) . #0=(|has| |#1| (-1044))) (((-390)) . #0#)) ((((-877)) . T)) (((|#1|) . 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T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) (((|#1| (-993)) . T)) (((|#1| |#1|) . T)) ((($) . T)) @@ -1037,23 +1037,23 @@ (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) -(-2748 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-739)) (|has| |#2| (-739)))) +(-2802 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-739)) (|has| |#2| (-739)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-576)) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) ((((-877)) . T)) -(-2748 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2802 (|has| |#1| (-238)) (|has| |#1| (-237))) (|has| |#1| (-360)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-419 (-576))) . T)) -((($) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) (|has| |#1| (-841)) ((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) (((-576)) |has| |#1| (-1060 (-576))) ((|#1|) . T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) (((|#1| $) |has| |#1| (-296 |#1| |#1|))) ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568))) @@ -1061,8 +1061,8 @@ (((|#4|) |has| |#4| (-1122))) (((|#3|) |has| |#3| (-1122))) (|has| |#3| (-379)) -((($) |has| |#1| (-568)) ((|#1|) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) (((-576)) . 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T)) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1071))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1071))) (((|#1|) |has| |#1| (-174))) (|has| $ (-148)) (|has| $ (-148)) ((((-1203)) . T)) (((|#1|) |has| |#1| (-174))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) ((((-877)) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1071)) (|has| |#1| (-1134))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1071)) (|has| |#1| (-1134))) ((($ $) |has| |#1| (-296 $ $)) ((|#1| $) |has| |#1| (-296 |#1| |#1|))) (((|#1| (-419 (-576))) . T)) (((|#1|) . T)) @@ -1112,8 +1112,8 @@ (((|#1|) . T)) ((((-1198)) . T)) (|has| |#1| (-568)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-568)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -1125,7 +1125,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-148)) -(((|#2| (-245 (-3437 |#1|) (-784)) (-879 |#1|)) . T)) +(((|#2| (-245 (-3440 |#1|) (-784)) (-879 |#1|)) . T)) (((|#1| (-543 |#3|) |#3|) . T)) (|has| |#1| (-146)) (((#0=(-419 (-576)) #0#) |has| |#2| (-374)) (($ $) . T)) @@ -1139,12 +1139,12 @@ (|has| |#1| (-146)) ((((-419 (-576))) |has| |#2| (-374)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) -(-2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) -(-2748 (|has| |#1| (-360)) (|has| |#1| (-379))) +(-2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#1| (-360)) (|has| |#1| (-379))) ((((-1164 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) -(((|#2|) . T) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (|has| |#3| (-806)) (|has| |#3| (-806)) ((((-877)) . T)) @@ -1172,18 +1172,18 @@ ((((-877)) . T)) ((((-877)) . T)) (((|#1| |#2|) . T)) -((((-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198)))) (((-1104)) . T)) +((((-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198)))) (((-1104)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-624 $)) . T)) (((|#1| (-419 (-576))) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) ((($ (-1285 |#2|)) . T) (($ (-1198)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-918 (-1198))))) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) -((((-576)) -2748 (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122))) (|has| |#2| (-1071))) ((|#2|) |has| |#2| (-1122)) (((-419 (-576))) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122)))) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) +((((-576)) -2802 (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122))) (|has| |#2| (-1071))) ((|#2|) |has| |#2| (-1122)) (((-419 (-576))) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122)))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) @@ -1191,15 +1191,15 @@ ((((-877)) . T)) ((((-877)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4286 |#1|) (|:| -4440 |#2|))))) -(((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) (((-2 (|:| -4286 (-1180)) (|:| -4440 |#1|))) |has| (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|)) (-319 (-2 (|:| -4286 (-1180)) (|:| -4440 |#1|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))))) +(((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) (((-2 (|:| -4291 (-1180)) (|:| -4440 |#1|))) |has| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (-319 (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|))))) ((((-877)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-576)) |has| |#2| (-652 (-576)))) ((((-1198) (-52)) . T)) -((((-1198)) -2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198))))) +((((-1198)) -2802 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-879 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-841)) @@ -1207,10 +1207,10 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T)) ((((-576)) . T) (($) . T) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (|has| (-1116 |#1|) (-1122)) -(((|#2| |#2|) -2748 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071)))) -(((|#2|) -2748 (|has| |#2| (-174)) (|has| |#2| (-374)))) -((((-576) (-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2748 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071)))) +(((|#2| |#2|) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071)))) +(((|#2|) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)))) +((((-576) (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071)))) ((((-576)) . T)) ((((-1203)) . T)) ((((-784)) . T)) @@ -1229,34 +1229,34 @@ (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) ((($) . T) (((-419 (-576))) . T)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-568))) ((((-1203)) . T)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((((-576)) . T)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-568))) (|has| |#1| (-146)) ((((-576)) . 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T)) -((($) -2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) -((($) -2748 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) +((($) -2802 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2802 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) ((((-576) |#2|) . T)) -((($ (-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) +((($ (-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-379)) @@ -1275,43 +1275,43 @@ ((((-877)) . 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T)) (((|#1|) |has| |#1| (-319 |#1|))) @@ -1321,21 +1321,21 @@ (|has| |#1| (-379)) ((((-1198) $) |has| |#1| (-526 (-1198) $)) (($ $) |has| |#1| (-319 $)) ((|#1| |#1|) |has| |#1| (-319 |#1|)) (((-1198) |#1|) |has| |#1| (-526 (-1198) |#1|))) ((((-1198)) |has| |#1| (-918 (-1198)))) -(-2748 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2802 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-400) |#1|) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) (((|#2|) . T) (((-877)) . T)) ((((-877)) . T)) (((|#2|) . T)) ((((-930 |#1|)) . T)) ((((-877)) . T) (((-1203)) . T)) ((((-1203)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) @@ -1344,7 +1344,7 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) (((|#1| |#1|) . T)) (((#0=(-885 |#1|)) |has| #0# (-319 #0#))) -((((-576)) . T) (($) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T)) +((((-576)) . T) (($) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-806)) (|has| |#2| (-806)) @@ -1353,7 +1353,7 @@ (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) (|has| |#2| (-1071)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1224)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) @@ -1367,7 +1367,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-419 (-576)) #0#) . T)) (|has| |#1| (-374)) ((((-576)) . T) (((-419 (-576))) . T) (($) . 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T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) +((($) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) ((((-576)) |has| #0=(-419 |#2|) (-652 (-576))) ((#0#) . T)) ((($) . T) (((-576)) . T)) ((((-576) (-145)) . T)) -((((-576) (-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T) ((|#1| |#2|) . T)) +((((-576) (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T) ((|#1| |#2|) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) ((((-877)) . T)) ((((-930 |#1|)) . T)) (|has| |#1| (-374)) @@ -1415,11 +1415,11 @@ (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-861)) -((($) -2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . 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T)) -(((|#2|) -2748 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071)))) +(((|#2|) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071)))) (|has| $ (-148)) ((((-419 |#2|)) . T)) ((((-419 (-576))) |has| #0=(-419 |#2|) (-1060 (-419 (-576)))) (((-576)) |has| #0# (-1060 (-576))) ((#0#) . T)) @@ -1562,11 +1562,11 @@ (|has| |#2| (-148)) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) (((|#1|) . T)) (|has| |#2| (-238)) @@ -1603,9 +1603,9 @@ ((((-877)) . T)) ((((-877)) . T)) ((((-1021 |#1|)) . T) ((|#1|) . T)) -((((-1198)) -2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198)))) (((-831 (-1198))) . 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T)) (|has| |#2| (-148)) (|has| |#1| (-485)) -(-2748 (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071))) +(-2802 (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071))) (|has| |#1| (-374)) ((((-877)) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -1761,8 +1761,8 @@ (|has| |#1| (-861)) ((((-877)) . T)) (((|#2|) . T)) -((((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2748 (|has| |#1| (-374)) (|has| |#1| (-568))) (((-1281 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2748 (|has| |#1| (-374)) (|has| |#1| (-568)))) +((((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2802 (|has| |#1| (-374)) (|has| |#1| (-568))) (((-1281 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2802 (|has| |#1| (-374)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) . T) (((-576)) . T) (((-832 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1771,8 +1771,8 @@ ((((-930 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((((-877)) . T)) ((((-877)) . T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) -(((|#2| (-494 (-3437 |#1|) (-784)) (-879 |#1|)) . T)) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(((|#2| (-494 (-3440 |#1|) (-784)) (-879 |#1|)) . T)) ((((-419 (-576))) . #0=(|has| |#2| (-374))) (($) . #0#)) (((|#1| (-543 (-1198)) (-1198)) . T)) (((|#1|) . T)) @@ -1793,19 +1793,19 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -4286 (-1180)) (|:| -4440 |#1|))) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4291 (-1180)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -4286 (-1198)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4291 (-1198)) (|:| -4440 (-52)))) . T)) ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) ((((-1198) (-52)) . 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T) (((-576)) |has| |#1| (-1060 (-576))) (((-419 (-576))) |has| |#1| (-1060 (-419 (-576))))) (|has| |#1| (-862)) (|has| |#1| (-862)) @@ -1826,15 +1826,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1122)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1122)))) -(((|#3|) -2748 (|has| |#3| (-174)) (|has| |#3| (-374)))) -((($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -(-2748 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-929))) -((($) -2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . 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T)) @@ -1843,7 +1843,7 @@ (|has| |#1| (-833)) (|has| |#1| (-833)) (((|#1|) . T)) -(-2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-861)) (|has| |#1| (-861)) (|has| |#1| (-861)) @@ -1852,14 +1852,14 @@ ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) ((((-1198)) |has| |#1| (-918 (-1198))) (((-1104)) . T)) (((|#1|) . T)) (|has| |#1| (-861)) -(((#0=(-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) #0#) |has| (-2 (|:| -4286 (-1180)) (|:| -4440 (-52))) (-319 (-2 (|:| -4286 (-1180)) (|:| -4440 (-52)))))) +(((#0=(-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) #0#) |has| (-2 (|:| -4291 (-1180)) (|:| -4440 (-52))) (-319 (-2 (|:| -4291 (-1180)) (|:| -4440 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (|has| |#1| (-1122)) ((((-877)) . T) (((-1203)) . T)) @@ -1883,14 +1883,14 @@ (((|#1| (-784) (-1104)) . T)) (((|#3|) . T)) ((((-145)) . T)) -((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) (((-576)) -2748 (|has| |#1| (-861)) (|has| |#1| (-1060 (-576)))) ((|#1|) . T)) +((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) (((-576)) -2802 (|has| |#1| (-861)) (|has| |#1| (-1060 (-576)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-145)) . 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T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1909,31 +1909,31 @@ ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568))) (((|#2|) . T)) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2748 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2802 (|has| |#1| (-174)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) . T)) ((($) |has| |#1| (-861))) ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) (|has| |#1| (-929)) ((((-1198)) . T)) ((((-877)) . T)) -((($) -2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1281 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) . 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T)) ((($) |has| |#1| (-238))) @@ -2234,12 +2234,12 @@ (|has| |#1| (-146)) ((($) |has| |#1| (-568)) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#1|) |has| |#1| (-174))) -((($) -2748 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-576)) . T) ((|#1|) . T) (($) . T) (((-419 (-576))) . T) (((-1198)) |has| |#1| (-1060 (-1198)))) (((|#1| |#2|) . T)) -((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) (((-576)) -2748 (|has| |#1| (-861)) (|has| |#1| (-1060 (-576)))) ((|#1|) . T)) -(-2748 (-12 (|has| |#4| (-238)) (|has| |#4| (-1071))) (-12 (|has| |#4| (-237)) (|has| |#4| (-1071)))) -(-2748 (-12 (|has| |#3| (-238)) (|has| |#3| (-1071))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1071)))) +((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) (((-576)) -2802 (|has| |#1| (-861)) (|has| |#1| (-1060 (-576)))) ((|#1|) . T)) +(-2802 (-12 (|has| |#4| (-238)) (|has| |#4| (-1071))) (-12 (|has| |#4| (-237)) (|has| |#4| (-1071)))) +(-2802 (-12 (|has| |#3| (-238)) (|has| |#3| (-1071))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1071)))) ((((-145)) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2250,13 +2250,13 @@ ((((-877)) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) ((($) . T) (((-576)) |has| |#1| (-652 (-576))) ((|#1|) . 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T) (($ (-1198)) -12 (|has| |#1| (-15 * (|#1| (-784) |#1|))) (|has| |#1| (-918 (-1198))))) (|has| |#1| (-929)) @@ -2264,7 +2264,7 @@ (((|#2|) |has| |#2| (-1071))) (|has| |#1| (-374)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4286 |#1|) (|:| -4440 |#2|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))))) (((|#1|) |has| |#1| (-174))) ((($ (-879 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2275,7 +2275,7 @@ (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-657 $)) . T) (((-1180)) . T) (((-1198)) . T) (((-576)) . T) (((-227)) . T) (((-877)) . T)) -((((-576)) -2748 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071))) ((|#3|) -2748 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-739)) (|has| |#3| (-1071))) (($) |has| |#3| (-1071))) +((((-576)) -2802 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071))) ((|#3|) -2802 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-739)) (|has| |#3| (-1071))) (($) |has| |#3| (-1071))) ((((-419 (-576))) . T) (((-576)) . T) (((-624 $)) . T)) (((|#1|) . T)) ((((-877)) . T)) @@ -2290,7 +2290,7 @@ (((|#1| (-419 (-576)) (-1104)) . T)) (((|#1| (-784) (-1104)) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-576)) -2748 (|has| (-419 (-576)) (-1060 (-576))) (|has| |#1| (-1060 (-576)))) (((-419 (-576))) . T)) +(((|#1|) . T) (((-576)) -2802 (|has| (-419 (-576)) (-1060 (-576))) (|has| |#1| (-1060 (-576)))) (((-419 (-576))) . T)) (((|#1| (-614 |#1| |#3|) (-614 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2310,37 +2310,37 @@ ((((-712)) . T)) ((((-712)) . T)) (((|#2|) |has| |#2| (-174))) -(-2748 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2802 (|has| |#1| (-238)) (|has| |#1| (-237))) ((((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1060 (-419 (-576))))) -((((-112)) |has| |#1| (-1122)) (((-877)) -2748 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071)) (|has| |#1| (-1134)) (|has| |#1| (-1122)))) +((((-112)) |has| |#1| (-1122)) (((-877)) -2802 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071)) (|has| |#1| (-1134)) (|has| |#1| (-1122)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . 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T) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) ((((-576) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4286 |#1|) (|:| -4440 |#2|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))))) ((((-390)) . T)) ((((-712)) . T)) ((((-419 (-576))) . #0=(|has| |#2| (-374))) (($) . #0#)) (((|#1|) |has| |#1| (-174))) ((((-419 (-972 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) -(-2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1071))) @@ -2352,7 +2352,7 @@ ((((-1198)) |has| |#2| (-918 (-1198)))) (|has| |#1| (-862)) ((((-877)) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (|has| |#1| (-804)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-485)) @@ -2360,8 +2360,8 @@ (|has| |#1| (-379)) (|has| |#1| (-379)) (|has| |#1| (-374)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1071)) (|has| |#1| (-1134))) -((($) -2748 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1071)) (|has| |#1| (-1134))) +((($) -2802 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-360)) @@ -2372,7 +2372,7 @@ (|has| |#1| (-38 (-419 (-576)))) (((|#2|) . T) (((-877)) . T)) (((|#2|) . T) (((-877)) . T)) -((($ (-1198)) -2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198))))) +((($ (-1198)) -2802 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198))))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2383,18 +2383,18 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-862)) -((((-2 (|:| -4286 (-1180)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4291 (-1180)) (|:| -4440 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4286 |#1|) (|:| -4440 |#2|)))) ((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122)))) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)))) ((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122)))) (((|#2|) . 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T)) @@ -2632,13 +2632,13 @@ ((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((|#1|) . T) (((-576)) . T)) (|has| |#2| (-146)) (|has| |#2| (-148)) -(-2748 (|has| |#2| (-833)) (|has| |#2| (-862))) +(-2802 (|has| |#2| (-833)) (|has| |#2| (-862))) ((((-930 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) ((((-576)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-576)) . T)) (((|#2|) . T)) -((((-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) +((((-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-374))) ((((-419 |#2|)) . T)) @@ -2647,10 +2647,10 @@ ((((-877)) . T)) ((((-877)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) -(((|#1|) -2748 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2802 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) @@ -2660,14 +2660,14 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-374))) -((($) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) (((|#2|) . T)) ((((-419 (-576))) . T) (((-712)) . T) (($) . T)) -((($) . T) (((-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) -(-2748 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2802 (|has| |#1| (-238)) (|has| |#1| (-237))) (((#0=(-793 |#1| (-879 |#2|)) #0#) |has| (-793 |#1| (-879 |#2|)) (-319 (-793 |#1| (-879 |#2|))))) -((($) -2748 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2802 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T) (($) . T)) ((((-879 |#1|)) . T)) (((|#2|) |has| |#2| (-174))) @@ -2676,7 +2676,7 @@ ((((-1198)) |has| |#1| (-918 (-1198))) (((-1104)) . T)) ((((-1198)) |has| |#1| (-918 (-1198))) (((-1110 (-1198))) . T)) (((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122)))) -((($ (-1198)) -2748 (-12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071))) (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071))))) +((($ (-1198)) -2802 (-12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071))) (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071))))) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2685,13 +2685,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . 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T)) -(-2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1274 |#2| |#3| |#4|)) . T) (((-419 (-576))) |has| #0# (-38 (-419 (-576))))) ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) -(-2748 (-12 (|has| |#1| (-317)) (|has| |#1| (-929))) (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071))) +(-2802 (-12 (|has| |#1| (-317)) (|has| |#1| (-929))) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071))) ((((-576)) |has| |#1| (-652 (-576))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-877)) . T)) @@ -2821,7 +2821,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . 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T) (((-576)) . T)) -((((-2 (|:| -4286 (-1180)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4291 (-1180)) (|:| -4440 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) ((((-877)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1|) . T)) -(-2748 (|has| |#1| (-300)) (|has| |#1| (-374))) +(-2802 (|has| |#1| (-300)) (|has| |#1| (-374))) ((((-145)) . T)) ((((-576)) |has| #0=(-419 |#2|) (-652 (-576))) ((#0#) . T) (((-419 (-576))) . T) (($) . T)) (|has| |#1| (-861)) @@ -2869,7 +2869,7 @@ ((((-877)) . T)) ((((-877)) . T)) ((((-189)) . T) (((-877)) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-877)) . T)) ((((-877)) . T)) @@ -2886,8 +2886,8 @@ (|has| |#1| (-862)) ((((-877)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-2 (|:| -4286 (-1180)) (|:| -4440 |#1|))) . T)) -((($) -2748 (-12 (|has| (-1196 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1196 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) +((((-2 (|:| -4291 (-1180)) (|:| -4440 |#1|))) . T)) +((($) -2802 (-12 (|has| (-1196 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1196 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) ((((-877)) . T)) (((|#2|) |has| |#2| (-374))) ((((-877)) . T)) @@ -2902,19 +2902,19 @@ (|has| |#3| (-1071)) (|has| |#1| (-1122)) ((((-1198) (-52)) . T)) -(-2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-576)) . T)) (((|#1|) . T)) @@ -2926,12 +2926,12 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (|has| |#1| (-833)) (((#0=(-930 |#1|) #0#) . T) (($ $) . T) ((#1=(-419 (-576)) #1#) . T)) ((((-419 |#2|)) . T)) (|has| |#1| (-861)) -((((-1225 |#1|)) . T) (((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-1225 |#1|)) . T) (((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) (((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) . T) ((#1=(-576) #1#) . T) (($ $) . T)) ((((-930 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-1071)) (((-576)) -12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071)))) @@ -2948,35 +2948,35 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . 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T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) (((#0=(-419 (-576)) #0#) . T) ((#1=(-712) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) |has| |#1| (-374))) ((((-877)) . T)) (|has| |#1| (-1122)) (((|#1|) . T)) -(((|#1|) -2748 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) -(((|#1|) -2748 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) +(((|#1|) -2802 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) +(((|#1|) -2802 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) (((|#2|) . T)) ((((-419 (-576))) . T) (((-712)) . T) (($) . T)) ((((-591)) . T)) (((|#3| |#3|) . T)) -((($ (-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) +((($ (-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) (|has| |#1| (-862)) (|has| |#2| (-238)) ((((-879 |#1|)) . T)) @@ -2997,10 +2997,10 @@ (|has| |#1| (-1122)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2748 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2802 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T)) (((|#2|) . T) (((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((|#1|) . T) (($) . T) (((-576)) . T)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (((|#2|) . T) (((-576)) |has| |#2| (-652 (-576)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3043,7 +3043,7 @@ (|has| |#2| (-1044)) ((($) . T)) (|has| |#1| (-929)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3053,32 +3053,32 @@ (|has| |#1| (-374)) ((((-930 |#1|)) . T)) ((($) . T) (((-576)) . T) ((|#1|) . T) (((-419 (-576))) . 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T)) -(-2748 (-12 (|has| |#3| (-238)) (|has| |#3| (-1071))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1071)))) +(-2802 (-12 (|has| |#3| (-238)) (|has| |#3| (-1071))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1071)))) ((($) . T) (((-419 (-576))) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T) (((-624 $)) . T)) ((((-576)) . T) (($) . T)) ((((-576)) . T) (($) . T)) ((((-784) |#1|) . T)) -(((|#2| (-245 (-3437 |#1|) (-784))) . T)) +(((|#2| (-245 (-3440 |#1|) (-784))) . T)) (((|#1| (-543 |#3|)) . T)) ((((-419 (-576))) . T)) -(-2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((((-1180)) . T) (((-877)) . T)) -(((#0=(-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) #0#) |has| (-2 (|:| -4286 (-1198)) (|:| -4440 (-52))) (-319 (-2 (|:| -4286 (-1198)) (|:| -4440 (-52)))))) +(((#0=(-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) #0#) |has| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (-319 (-2 (|:| -4291 (-1198)) (|:| -4440 (-52)))))) ((((-1180)) . T)) (|has| |#1| (-929)) (|has| |#2| (-374)) (((|#1|) . T) (($) . T) (((-576)) . T)) -(-2748 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) +(-2802 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-877)) . T)) (((|#1|) . T)) @@ -3095,11 +3095,11 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (-12 (|has| |#1| (-557)) (|has| |#1| (-841))) ((((-877)) . T)) -((((-1198)) -2748 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))))) +((((-1198)) -2802 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))))) (|has| |#1| (-374)) ((((-1198)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-918 (-1198))))) (|has| |#1| (-374)) @@ -3112,13 +3112,13 @@ ((((-576) |#1|) . T)) ((((-1198)) |has| |#1| (-918 (-1198)))) (((|#1|) . T)) -(-2748 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2802 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#2|) |has| |#1| (-374))) (((|#2|) |has| |#1| (-374))) -(-2748 (|has| |#4| (-806)) (|has| |#4| (-862))) -(-2748 (|has| |#3| (-806)) (|has| |#3| (-862))) +(-2802 (|has| |#4| (-806)) (|has| |#4| (-862))) +(-2802 (|has| |#3| (-806)) (|has| |#3| (-862))) ((((-576)) . T) (($) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) @@ -3153,32 +3153,32 @@ ((((-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-902 (-390)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-902 (-576))))) (((|#1|) . T)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) (((|#3|) . 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T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (|has| |#1| (-38 (-419 (-576)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-419 (-576)))) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-379))) ((($) . T)) (|has| |#1| (-148)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) ((($) . T)) ((((-593 |#1|)) . T)) @@ -3194,7 +3194,7 @@ ((((-419 (-576))) |has| |#2| (-1060 (-576))) (((-576)) |has| |#2| (-1060 (-576))) (((-1198)) |has| |#2| (-1060 (-1198))) ((|#2|) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2748 (|has| |#1| (-146)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-360))) (|has| |#1| (-148)) ((((-877)) . T)) ((($) . T)) @@ -3214,15 +3214,15 @@ ((((-419 |#2|)) . T)) ((((-877)) . T)) (((|#1|) . T)) -((((-1198)) -2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198))))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +((((-1198)) -2802 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198))))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) (|has| |#1| (-804)) (|has| |#1| (-804)) ((((-877)) . T)) ((((-930 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-877)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3231,7 +3231,7 @@ ((((-1275 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568)) (((-419 (-576))) |has| |#1| (-568))) ((((-877)) . T)) -(-2748 (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1071)))) +(-2802 (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1071)))) ((((-877)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3244,10 +3244,10 @@ ((((-877)) . T)) (((|#2|) . T)) ((((-576)) . T)) -((((-1198)) -2748 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) +((((-1198)) -2802 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) ((((-877)) . T)) ((((-576)) . T)) -(-2748 (|has| |#2| (-806)) (|has| |#2| (-862))) +(-2802 (|has| |#2| (-806)) (|has| |#2| (-862))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-877)) . T)) ((((-877)) . T)) @@ -3259,10 +3259,10 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (|has| |#1| (-374)) (|has| |#1| (-374)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) ((((-576) $) . T) (((-657 (-576)) $) . T)) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071)) (|has| |#1| (-1134)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-739)) (|has| |#1| (-918 (-1198))) (|has| |#1| (-1071)) (|has| |#1| (-1134)) (|has| |#1| (-1122))) (|has| |#1| (-1174)) ((((-930 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((($) . T)) @@ -3272,20 +3272,20 @@ (((#0=(-117 |#1|) $) |has| #0# (-296 #0# #0#))) (((|#1|) |has| |#1| (-174))) ((((-326 |#1|)) . T) (((-576)) . T)) -(-2748 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2802 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) ((((-877)) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-877)) . T)) -((((-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) +((((-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) (((|#1|) |has| |#1| (-319 |#1|))) ((((-576) |#1|) . T) (((-1256 (-576)) $) . T)) (((|#1| |#2|) . T)) ((((-1198) |#1|) . T)) -(((|#1|) -2748 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2802 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . T)) ((($ (-1198)) . T)) -(((|#1|) -2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1071)))) +(((|#1|) -2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1071)))) ((((-576)) . T) (((-419 (-576))) . T)) (((|#1|) . T)) (|has| |#1| (-568)) @@ -3294,15 +3294,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-568)) ((($) . T)) (|has| |#1| (-1122)) ((((-793 |#1| (-879 |#2|))) |has| (-793 |#1| (-879 |#2|)) (-319 (-793 |#1| (-879 |#2|))))) -(-2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3311,17 +3311,17 @@ (((|#1| (-784)) . T)) (|has| |#1| (-238)) (((|#1| (-543 (-1110 (-1198)))) . T)) -((($) -2748 (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))))) +((($) -2802 (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))))) ((((-593 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) -((((-2 (|:| -4286 (-1180)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4291 (-1180)) (|:| -4440 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-576)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (|has| |#2| (-374)) ((((-877)) . T)) ((((-877)) . T)) -(-2748 (|has| |#3| (-806)) (|has| |#3| (-862))) +(-2802 (|has| |#3| (-806)) (|has| |#3| (-862))) ((((-877)) . T)) ((((-1142)) . T) (((-877)) . T)) ((((-548)) . T) (((-877)) . T)) @@ -3332,14 +3332,14 @@ ((((-576)) . T)) (((|#3|) . T)) ((((-877)) . T)) -(-2748 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) -((((-576)) . 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T) (($) -2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) (((-879 |#1|)) . T)) +((((-1147 |#1| |#2|)) . T) ((|#2|) . T) (($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) (((-576)) . T)) +((((-1194 |#1|)) . T) (((-576)) . T) (($) -2802 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) (((-1104)) . T) ((|#1|) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576)))))) +(-2802 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1071))) (((#0=(-593 |#1|) #0#) . T) (($ $) . T) ((#1=(-419 (-576)) #1#) . T)) ((($ $) . T) ((#0=(-419 (-576)) #0#) . T)) -((((-1147 |#1| (-1198))) . T) (((-576)) . T) (((-1110 (-1198))) . T) (($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) (((-1198)) . T)) +((((-1147 |#1| (-1198))) . T) (((-576)) . T) (((-1110 (-1198))) . T) (($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576))))) (((-1198)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1| (-1289 |#1|) (-1289 |#1|)) . T)) ((((-593 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) @@ -3354,7 +3354,7 @@ ((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((|#1|) . T) (((-576)) . T)) (((|#1|) . T)) ((((-877)) . T)) -(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2748 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) +(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2802 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-304 |#3|)) . T)) (((|#1|) . T)) @@ -3363,30 +3363,30 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) -((($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2802 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2802 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) (((|#2|) . 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T)) -(-2748 (|has| |#2| (-806)) (|has| |#2| (-862))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#2| (-806)) (|has| |#2| (-862))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) ((((-1198)) . T) ((|#1|) . T)) @@ -3398,15 +3398,15 @@ (((#0=(-419 (-576)) #0#) . T)) ((((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174))) -(-2748 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071))) +(-2802 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1071))) (((|#1|) . T)) (((|#1|) . T)) -(-2748 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) +(-2802 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) (((|#1|) . T)) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) ((((-548)) . T)) ((((-877)) . T)) -((($) -2748 (-12 (|has| |#3| (-238)) (|has| |#3| (-1071))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1071))))) +((($) -2802 (-12 (|has| |#3| (-238)) (|has| |#3| (-1071))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1071))))) (|has| |#1| (-862)) ((((-877)) . T)) ((((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) @@ -3422,21 +3422,21 @@ ((($ $) . T) ((#0=(-419 (-576)) #0#) . T)) ((((-1198)) |has| |#1| (-918 (-1198)))) ((((-930 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) -((($) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) -(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . T) (($ $) -2748 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((($) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) +(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . 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T) (((-576)) |has| |#2| (-1060 (-576))) (((-419 (-576))) |has| |#2| (-1060 (-419 (-576))))) ((((-1104)) . T) ((|#2|) . T) (((-576)) |has| |#2| (-1060 (-576))) (((-419 (-576))) |has| |#2| (-1060 (-419 (-576))))) (((|#1|) . T)) @@ -3455,11 +3455,11 @@ ((($) |has| |#1| (-379))) (|has| |#2| (-833)) (|has| |#2| (-833)) -((((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2|) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) +((((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2|) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) ((($ (-1198)) |has| |#1| (-918 (-1198)))) (((|#1|) . T) (((-576)) |has| |#1| (-1060 (-576))) (((-419 (-576))) |has| |#1| (-1060 (-419 (-576))))) -((($) -2748 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360)))) -(((|#1|) . T) (((-419 (-576))) -2748 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) +((($) -2802 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360)))) +(((|#1|) . T) (((-419 (-576))) -2802 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) ((((-576)) |has| |#1| (-902 (-576))) (((-390)) |has| |#1| (-902 (-390)))) (((|#1|) . T)) @@ -3474,7 +3474,7 @@ (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1122)))) -(((|#2|) -2748 (|has| |#2| (-6 (-4468 "*"))) (|has| |#2| (-174)))) +(((|#2|) -2802 (|has| |#2| (-6 (-4468 "*"))) (|has| |#2| (-174)))) (((|#2|) . T)) (|has| |#1| (-374)) (((|#2|) . T)) @@ -3488,12 +3488,12 @@ (((|#2| (-784)) . T)) ((((-1198)) . T)) ((((-885 |#1|)) . T)) -(-2748 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071))) -(-2748 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-806)) (|has| |#3| (-1071))) +(-2802 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071))) +(-2802 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-806)) (|has| |#3| (-1071))) ((((-877)) . T)) (((|#1|) . T)) -(-2748 (|has| |#2| (-806)) (|has| |#2| (-862))) -(-2748 (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) +(-2802 (|has| |#2| (-806)) (|has| |#2| (-862))) +(-2802 (-12 (|has| |#1| (-806)) (|has| |#2| (-806))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) ((((-885 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-379)) @@ -3511,7 +3511,7 @@ (((|#1|) . T)) ((((-877)) . T)) ((($) . T) ((|#2|) . T) (((-419 (-576))) . T) (((-576)) |has| |#2| (-652 (-576)))) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) @@ -3520,7 +3520,7 @@ (((|#1|) . T)) ((((-877)) . T)) (|has| |#2| (-929)) -((((-2 (|:| -4286 (-1198)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4291 (-1198)) (|:| -4440 (-52)))) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-908 (-390))) |has| |#2| (-626 (-908 (-390)))) (((-908 (-576))) |has| |#2| (-626 (-908 (-576))))) ((((-877)) . T)) ((((-877)) . T)) @@ -3531,7 +3531,7 @@ ((((-1194 |#1|)) . T) (((-877)) . T)) ((((-877)) . T)) ((((-419 (-576))) |has| |#2| (-1060 (-419 (-576)))) (((-576)) |has| |#2| (-1060 (-576))) ((|#2|) . T) (((-879 |#1|)) . T)) -((((-1198)) -2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198)))) (((-1104)) . T)) +((((-1198)) -2802 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198)))) (((-1104)) . T)) ((((-117 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((((-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) (((-576)) |has| |#1| (-1060 (-576))) ((|#1|) . T) (((-1198)) . T)) ((((-877)) . T)) @@ -3550,10 +3550,10 @@ ((((-657 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) ((($) . T) (((-576)) . T) (((-1275 |#1| |#2| |#3| |#4|)) . T) (((-419 (-576))) . 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T)) @@ -3568,16 +3568,16 @@ ((((-419 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-877)) . T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) -(((|#2| (-494 (-3437 |#1|) (-784))) . T)) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(((|#2| (-494 (-3440 |#1|) (-784))) . T)) ((((-576) |#1|) . T)) ((((-1180)) . T) (((-877)) . T)) (((|#2| |#2|) . T)) (((|#1| (-543 (-1198))) . T)) -(-2748 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) +(-2802 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) ((((-576)) . T)) (((|#2|) . T)) -((($) -2748 (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))))) +((($) -2802 (-12 (|has| |#2| (-238)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))))) (((|#2|) . T)) ((((-1198)) |has| |#1| (-918 (-1198))) (((-1104)) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-652 (-576)))) @@ -3586,9 +3586,9 @@ ((($) . T) (((-419 (-576))) . T)) ((($) . T)) ((($) . T)) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) (((|#1|) . T)) -((($) -2748 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-877)) . T)) ((((-145)) . T)) (((|#1|) . T) (((-419 (-576))) . T)) @@ -3597,7 +3597,7 @@ ((((-877)) . T)) (((|#1|) . T)) (|has| |#1| (-1174)) -((($ (-1198)) -2748 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) +((($ (-1198)) -2802 (|has| (-419 |#2|) (-918 (-1198))) (|has| (-419 |#2|) (-920 (-1198))))) (((|#1|) . T)) (((|#1| (-543 (-879 |#2|)) (-879 |#2|) (-793 |#1| (-879 |#2|))) . T)) ((((-419 $) (-419 $)) |has| |#1| (-568)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3622,44 +3622,44 @@ (|has| |#1| (-1122)) (|has| |#1| (-1122)) (|has| |#2| (-374)) -(((|#1|) . T) (($) -2748 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) +(((|#1|) . T) (($) -2802 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) (|has| |#1| (-374)) (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576)))) -((($) -2748 (|has| |#2| (-238)) (|has| |#2| (-237)))) +((($) -2802 (|has| |#2| (-238)) (|has| |#2| (-237)))) ((((-576)) . T)) (|has| |#1| (-1122)) -((($ (-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) +((($ (-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) ((((-1198)) -12 (|has| |#4| (-918 (-1198))) (|has| |#4| (-1071)))) ((((-1198)) -12 (|has| |#3| (-918 (-1198))) (|has| |#3| (-1071)))) (((|#1|) . T)) (|has| |#1| (-238)) -(((|#2| (-245 (-3437 |#1|) (-784))) . T)) +(((|#2| (-245 (-3440 |#1|) (-784))) . 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T)) (((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-419 (-576))) . T) (($) . T)) @@ -3862,7 +3862,7 @@ ((((-877)) . T)) ((((-877)) . T)) ((((-877)) . T)) -(-2748 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2802 (|has| |#1| (-238)) (|has| |#1| (-237))) (((|#1|) . T) (((-877)) . T) (((-1203)) . T)) ((((-1203)) . T)) ((((-877)) . T)) @@ -3871,23 +3871,23 @@ ((($) . T) (((-576)) . T) (((-117 |#1|)) . T) (((-419 (-576))) . T)) ((((-879 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T) (((-576)) |has| |#2| (-652 (-576)))) ((($) . T) (((-576)) . T)) (((|#1| (-543 (-879 |#2|)) (-879 |#2|) (-793 |#1| (-879 |#2|))) . T)) -((($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-1126)) . T)) ((((-877)) . T)) ((((-1203)) . T) (((-877)) . T)) ((((-1203)) . T) (((-877)) . T)) ((((-1203)) . T)) ((((-1203)) . T)) -((($) -2748 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-652 (-576)))) ((($) . T) (((-576)) . T)) (|has| |#2| (-929)) -((($) -2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#1| |#2| (-245 |#1| |#2|) (-245 |#1| |#2|)) . T)) ((((-877)) . T)) (((|#1|) . T)) @@ -3902,9 +3902,9 @@ (((|#1| |#1|) |has| |#1| (-174))) ((((-712)) . T)) ((((-712)) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) ((((-1203)) . T)) -(-2748 (|has| |#2| (-806)) (|has| |#2| (-862))) +(-2802 (|has| |#2| (-806)) (|has| |#2| (-862))) (((|#1|) |has| |#1| (-174))) ((((-1203)) . T)) (((|#1| |#1|) . T)) @@ -3917,19 +3917,19 @@ (((|#1| (-576)) . T)) (((|#1|) . T)) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) -((($ (-1198)) -2748 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198)))) (($ (-1104)) . T)) +((($ (-1198)) -2802 (|has| |#1| (-918 (-1198))) (|has| |#1| (-920 (-1198)))) (($ (-1104)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1203)) . T)) ((((-1203)) . T)) ((((-1203)) . T)) ((((-1203)) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1203)) . T)) ((((-1203)) . T)) (|has| |#1| (-374)) (|has| |#1| (-374)) -(-2748 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-174)) (|has| |#1| (-568))) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1| (-784)) . T)) @@ -3937,24 +3937,24 @@ (((|#1| (-543 |#2|) |#2|) . T)) ((((-576) |#1|) . T)) ((((-576) |#1|) . T)) -(-2748 (|has| |#1| (-102)) (|has| |#1| (-1122))) -(-2748 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237))) +(-2802 (|has| |#1| (-102)) (|has| |#1| (-1122))) +(-2802 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237))) ((((-576) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-908 (-390))) . T) (((-908 (-576))) . T) (((-1198)) . T) (((-548)) . T)) -(-2748 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) -(-2748 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-806)) (|has| |#2| (-806)))) +(-2802 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-806)) (|has| |#2| (-1071))) +(-2802 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-806)) (|has| |#2| (-806)))) ((((-877)) . T)) ((((-576)) . T)) ((((-576)) . T)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1198)) -12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071)))) (|has| |#2| (-1071)) -(-2748 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-739)) (|has| |#2| (-739)))) +(-2802 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-739)) (|has| |#2| (-739)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-374)) @@ -3987,7 +3987,7 @@ (((|#1| |#2|) . T)) ((((-576)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-576)) . T)) -(-2748 (|has| |#1| (-360)) (|has| |#1| (-379))) +(-2802 (|has| |#1| (-360)) (|has| |#1| (-379))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-419 (-576))) . T) (($) . T) (((-576)) . T)) @@ -3996,11 +3996,11 @@ ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-652 (-576)))) ((($) . T) (((-576)) |has| |#1| (-652 (-576))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) |has| |#2| (-1122)) (((-576)) -12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122))) (((-419 (-576))) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122)))) -(-2748 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2802 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) (((|#1|) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-862)) (|has| |#1| (-1122)))) ((((-576) $) . T) (((-657 (-576)) $) . T)) ((($) . T) (((-419 (-576))) . T)) (|has| |#1| (-929)) @@ -4012,14 +4012,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-576)) . T)) ((((-1203)) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-861))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-861))) (((|#2|) . T)) -(-2748 (|has| |#1| (-21)) (|has| |#1| (-861))) +(-2802 (|has| |#1| (-21)) (|has| |#1| (-861))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-877)) -2748 (-12 (|has| |#1| (-625 (-877))) (|has| |#2| (-625 (-877)))) (-12 (|has| |#1| (-1122)) (|has| |#2| (-1122))))) +((((-877)) -2802 (-12 (|has| |#1| (-625 (-877))) (|has| |#2| (-625 (-877)))) (-12 (|has| |#1| (-1122)) (|has| |#2| (-1122))))) ((((-419 |#2|) |#3|) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -4028,7 +4028,7 @@ ((($) . T) (((-576)) . T)) (|has| (-419 |#2|) (-148)) (|has| (-419 |#2|) (-146)) -(-2748 (|has| |#3| (-806)) (|has| |#3| (-862))) +(-2802 (|has| |#3| (-806)) (|has| |#3| (-862))) ((($) . T)) ((((-712)) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) @@ -4044,7 +4044,7 @@ ((((-1203)) . T)) ((((-576)) . T)) (((|#2|) . T)) -((((-1198)) -2748 (-12 (|has| (-1196 |#1| |#2| |#3|) (-918 (-1198))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198)))))) +((((-1198)) -2802 (-12 (|has| (-1196 |#1| |#2| |#3|) (-918 (-1198))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198)))))) ((((-1198)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-918 (-1198))))) ((((-1198)) -12 (|has| |#1| (-15 * (|#1| (-784) |#1|))) (|has| |#1| (-918 (-1198))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4060,11 +4060,11 @@ ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1162 |#1| |#2|)) . T)) ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) -(((|#2|) . T) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) -((((-2 (|:| -4286 (-1198)) (|:| -4440 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 (-1198)) (|:| -4440 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1044)) -(((|#2|) . T) (((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) ((($) . T)) ((((-877)) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-908 (-576))) |has| |#2| (-626 (-908 (-576)))) (((-908 (-390))) |has| |#2| (-626 (-908 (-390)))) (((-390)) . #0=(|has| |#2| (-1044))) (((-227)) . #0#)) @@ -4073,7 +4073,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-1198)) -2748 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) +((((-1198)) -2802 (|has| |#2| (-918 (-1198))) (|has| |#2| (-920 (-1198))))) ((((-877)) . T)) (((|#2|) . T)) ((((-877)) . T)) @@ -4083,15 +4083,15 @@ ((((-1196 |#1| |#2| |#3|)) . T)) ((((-1196 |#1| |#2| |#3|)) . T) (((-1189 |#1| |#2| |#3|)) . T)) ((((-877)) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) ((((-576) |#1|) . T)) ((((-1196 |#1| |#2| |#3|)) |has| |#1| (-374))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-374)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2748 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1071))) (($) |has| |#4| (-1071)) (((-576)) -12 (|has| |#4| (-652 (-576))) (|has| |#4| (-1071)))) -(((|#2|) . T) ((|#3|) -2748 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071))) (($) |has| |#3| (-1071)) (((-576)) -12 (|has| |#3| (-652 (-576))) (|has| |#3| (-1071)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2802 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1071))) (($) |has| |#4| (-1071)) (((-576)) -12 (|has| |#4| (-652 (-576))) (|has| |#4| (-1071)))) +(((|#2|) . T) ((|#3|) -2802 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1071))) (($) |has| |#3| (-1071)) (((-576)) -12 (|has| |#3| (-652 (-576))) (|has| |#3| (-1071)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -4105,7 +4105,7 @@ ((((-189)) . T) (((-877)) . T)) ((((-877)) . T)) (((|#1|) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) ((((-130)) . T) (((-877)) . T)) ((((-576) |#1|) . T) (((-1256 (-576)) $) . T)) ((((-877)) . T)) @@ -4115,14 +4115,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . T) (((-419 (-576)) |#1|) . T)) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-929))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-929))) ((($ (-1198)) |has| |#1| (-1071))) -(-2748 (|has| |#1| (-862)) (|has| |#1| (-1122))) +(-2802 (|has| |#1| (-862)) (|has| |#1| (-1122))) ((((-877)) . T)) ((((-877)) . T)) ((((-877)) . T)) (((|#1| (-543 |#2|)) . T)) -((((-2 (|:| -4286 (-1198)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4291 (-1198)) (|:| -4440 (-52)))) . T)) ((((-576) (-130)) . T)) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) @@ -4137,8 +4137,8 @@ ((((-1203)) . T)) ((((-877)) . T) (((-1203)) . T)) ((((-877)) . T) (((-1203)) . T)) -(-2748 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) -(-2748 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) +(-2802 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) +(-2802 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-929))) ((($) . T)) (((|#2| (-543 (-879 |#1|))) . T)) ((((-1203)) . T)) @@ -4153,7 +4153,7 @@ ((((-1203)) . T)) ((((-877)) . T) (((-1203)) . T)) ((((-1203)) . T)) -((((-877)) -2748 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) +((((-877)) -2802 (|has| |#1| (-625 (-877))) (|has| |#1| (-1122)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1180) |#1|) . T)) @@ -4161,7 +4161,7 @@ ((((-419 |#2|)) . T)) (|has| |#1| (-568)) (|has| |#1| (-568)) -((((-2 (|:| -4286 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4291 |#1|) (|:| -4440 |#2|))) . T)) (((|#2| (-784)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-419 (-576))) . T)) @@ -4171,14 +4171,14 @@ ((((-576)) . T) (($) . T)) (((|#2| $) |has| |#2| (-296 |#2| |#2|))) (((|#1| (-657 |#1|)) |has| |#1| (-861))) -(-2748 (|has| |#1| (-238)) (|has| |#1| (-360))) -(-2748 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-238)) (|has| |#1| (-360))) +(-2802 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1285 |#1|)) . T) (((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1060 (-419 (-576))))) (|has| |#1| (-1122)) (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) -((((-1285 |#1|)) . T) (((-576)) . T) (($) -2748 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) (((-1104)) . T) ((|#2|) . T) (((-419 (-576))) -2748 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1060 (-419 (-576)))))) -((((-1021 |#1|)) . T) ((|#1|) . T) (((-576)) -2748 (|has| (-1021 |#1|) (-1060 (-576))) (|has| |#1| (-1060 (-576)))) (((-419 (-576))) -2748 (|has| (-1021 |#1|) (-1060 (-419 (-576)))) (|has| |#1| (-1060 (-419 (-576)))))) +((((-1285 |#1|)) . T) (((-576)) . 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-1080) T) ((-299 . -1134) T) ((-490 . -93) T) ((-419 . -237) 190584) ((-366 . -625) 190566) ((-363 . -625) 190548) ((-355 . -625) 190530) ((-273 . -626) 190278) ((-273 . -625) 190260) ((-253 . -625) 190242) ((-253 . -626) 190103) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1163 . -625) 190085) ((-1142 . -653) 190072) ((-1142 . -1073) 190059) ((-832 . -739) T) ((-832 . -872) T) ((-614 . -298) 190036) ((-593 . -730) 190001) ((-491 . -626) NIL) ((-491 . -625) 189983) ((-530 . -730) 189928) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-930 . -625) 189910) ((-930 . -626) 189892) ((-398 . -739) T) ((-887 . -1078) 189844) ((-887 . -111) 189782) ((-727 . -1071) T) ((-725 . -1265) 189766) ((-707 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 189698) ((-390 . -808) T) ((-169 . -1239) T) ((-225 . -1122) T) ((-390 . -805) T) ((-59 . -626) 189659) ((-227 . -807) T) ((-227 . -804) T) ((-59 . -625) 189571) ((-227 . -739) T) 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-300) 187283) ((-1208 . -1239) T) ((-1205 . -379) T) ((-1204 . -379) T) ((-1168 . -152) 187267) ((-1142 . -102) T) ((-1140 . -1122) T) ((-1102 . -23) T) ((-1102 . -1134) T) ((-1097 . -102) T) ((-1079 . -625) 187234) ((-1025 . -421) 187206) ((-947 . -975) T) ((-750 . -319) 187144) ((-75 . -1239) T) ((-677 . -393) 187116) ((-171 . -929) 187069) ((-30 . -975) T) ((-112 . -857) T) ((-1 . -625) 187051) ((-1021 . -912) 186972) ((-129 . -664) 186954) ((-50 . -632) 186938) ((-707 . -659) 186873) ((-607 . -918) 186786) ((-450 . -102) T) ((-129 . -384) 186768) ((-142 . -319) NIL) ((-887 . -1071) T) ((-846 . -862) 186747) ((-81 . -1239) T) ((-724 . -300) T) ((-40 . -1080) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 186729) ((-171 . -661) 186603) ((-519 . -625) 186585) ((-362 . -148) 186567) ((-362 . -146) T) ((-370 . -1134) T) ((-364 . -1134) T) ((-356 . -1134) T) ((-1026 . -317) T) ((-934 . -317) T) ((-887 . -248) T) ((-108 . -1134) T) ((-887 . -238) 186546) ((-1273 . -111) 186367) 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-113) T) ((-354 . -1122) T) ((-323 . -1174) NIL) ((-299 . -132) T) ((-406 . -1122) T) ((-885 . -1080) T) ((-707 . -381) 184492) ((-365 . -659) 184422) ((-225 . -632) 184399) ((-337 . -296) 184351) ((-486 . -111) 184172) ((-1273 . -1071) T) ((-1252 . -1071) T) ((-829 . -388) 184156) ((-837 . -1239) T) ((-171 . -739) T) ((-1304 . -1239) T) ((-667 . -102) T) ((-1273 . -248) 184135) ((-1273 . -238) 184087) ((-1252 . -238) 183992) ((-1252 . -248) 183971) ((-1025 . -414) NIL) ((-683 . -652) 183919) ((-326 . -38) 183829) ((-323 . -38) 183758) ((-69 . -625) 183740) ((-329 . -505) 183706) ((-48 . -659) 183656) ((-1211 . -298) 183635) ((-1247 . -862) T) ((-1135 . -1134) 183613) ((-83 . -1239) T) ((-61 . -625) 183595) ((-879 . -865) T) ((-491 . -298) 183574) ((-1304 . -1060) 183551) ((-1186 . -1122) T) ((-1135 . -23) 183403) ((-829 . -918) 183339) ((-1262 . -739) T) ((-1124 . -1239) T) ((-486 . -628) 183165) ((-362 . -237) T) ((-1109 . -300) 183096) ((-986 . -1122) T) ((-909 . -102) T) ((-795 . -300) 183007) ((-337 . -19) 182991) ((-59 . -298) 182968) ((-793 . -300) 182899) ((-870 . -739) T) ((-118 . -861) NIL) ((-528 . -298) 182876) ((-337 . -616) 182853) ((-508 . -298) 182830) ((-466 . -300) 182761) ((-1057 . -319) 182612) ((-891 . -502) 182593) ((-891 . -625) 182559) ((-694 . -502) 182540) ((-583 . -739) T) ((-689 . -502) 182521) ((-694 . -625) 182471) ((-689 . -625) 182437) ((-675 . -625) 182419) ((-490 . -502) 182400) ((-490 . -625) 182366) ((-250 . -626) 182327) ((-250 . -502) 182304) ((-139 . -502) 182285) ((-138 . -502) 182266) ((-134 . -502) 182247) ((-250 . -625) 182139) ((-215 . -102) T) ((-139 . -625) 182105) ((-138 . -625) 182071) ((-134 . -625) 182037) ((-1169 . -34) T) ((-963 . -1239) T) ((-354 . -730) 181982) ((-683 . -25) T) ((-683 . -21) T) ((-1198 . -628) 181963) ((-341 . -1239) T) ((-486 . -1071) T) ((-647 . -429) 181928) ((-619 . -429) 181893) ((-1142 . -1174) T) ((-1274 . -317) 181872) ((-725 . -1073) 181695) ((-593 . -300) T) ((-530 . -300) T) ((-1253 . -317) 181674) ((-486 . -238) 181626) ((-486 . -248) 181605) ((-451 . -1239) T) ((-725 . -653) 181434) ((-1253 . -1044) NIL) ((-1102 . -132) T) ((-887 . -808) 181413) ((-145 . -102) T) ((-40 . -1122) T) ((-887 . -805) 181392) ((-657 . -1032) 181376) ((-592 . -1080) T) ((-576 . -1080) T) ((-507 . -1080) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 181360) ((-323 . -412) 181321) ((-364 . -132) T) ((-356 . -132) T) ((-1203 . -1122) T) ((-1142 . -38) 181308) ((-1116 . -625) 181275) ((-108 . -132) T) ((-974 . -1122) T) ((-941 . -1122) T) ((-784 . -1122) T) ((-685 . -1122) T) ((-714 . -148) T) ((-117 . -148) T) ((-1311 . -21) T) ((-1311 . -25) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-677 . -1078) 181259) ((-543 . -862) T) ((-512 . -862) T) ((-376 . -1239) T) ((-366 . -1078) 181211) ((-363 . -1078) 181163) ((-355 . -1078) 181115) ((-258 . -1239) T) ((-257 . -1239) T) ((-273 . -1078) 180958) ((-253 . -1078) 180801) ((-677 . -111) 180780) ((-830 . -1243) 180759) ((-559 . -857) T) 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-234) 176926) ((-1233 . -1024) 176892) ((-1195 . -940) 176871) ((-1189 . -940) 176850) ((-1189 . -833) NIL) ((-1021 . -1073) 176746) ((-987 . -1239) T) ((-930 . -248) T) ((-830 . -374) 176725) ((-396 . -23) T) ((-128 . -1122) 176703) ((-122 . -1122) 176681) ((-930 . -238) T) ((-129 . -34) T) ((-390 . -661) 176646) ((-1021 . -653) 176594) ((-885 . -730) 176581) ((-1318 . -659) 176553) ((-1068 . -152) 176518) ((-1015 . -1239) T) ((-877 . -1239) T) ((-40 . -174) T) ((-707 . -423) 176500) ((-725 . -319) 176487) ((-849 . -661) 176447) ((-840 . -661) 176421) ((-329 . -25) T) ((-329 . -21) T) ((-671 . -296) 176400) ((-592 . -1122) T) ((-576 . -1122) T) ((-507 . -1122) T) ((-1194 . -1239) T) ((-250 . -298) 176377) ((-1147 . -1239) T) ((-869 . -1239) T) ((-323 . -272) 176338) ((-323 . -232) 176299) ((-1244 . -865) T) ((-1194 . -902) NIL) ((-55 . -1122) T) ((-1147 . -902) 176158) ((-130 . -862) T) ((-1194 . -1060) 176038) ((-1147 . -1060) 175921) ((-185 . -625) 175903) ((-869 . -1060) 175799) 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174059) ((-651 . -661) 174043) ((-219 . -1243) T) ((-419 . -912) 173964) ((-227 . -1060) 173924) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 173905) ((-370 . -25) T) ((-326 . -659) 173560) ((-323 . -659) 173474) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 173420) ((-250 . -628) 173397) ((-139 . -628) 173378) ((-138 . -628) 173359) ((-134 . -628) 173340) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1080) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1084 . -1239) T) ((-972 . -1239) T) ((-726 . -1239) T) ((-671 . -625) 173322) ((-493 . -1239) T) ((-750 . -749) 173306) ((-347 . -625) 173288) ((-68 . -394) T) ((-68 . -407) T) ((-1124 . -107) 173272) ((-1084 . -902) 173254) ((-972 . -902) 173179) ((-666 . -1134) T) ((-635 . -730) 173166) ((-493 . -902) NIL) ((-1168 . -102) T) ((-1116 . -630) 173150) ((-1084 . -1060) 173132) ((-97 . -625) 173114) ((-489 . -148) T) ((-972 . -1060) 172994) ((-118 . -730) 172939) ((-725 . -920) 172846) ((-666 . -23) T) ((-493 . -1060) 172722) ((-1109 . -626) NIL) ((-1109 . -625) 172704) ((-795 . -626) NIL) ((-795 . -625) 172665) ((-793 . -626) 172299) ((-793 . -625) 172213) ((-1135 . -652) 172119) ((-812 . -865) 172098) ((-473 . -625) 172080) ((-466 . -625) 172062) ((-466 . -626) 171923) ((-1057 . -231) 171869) ((-887 . -929) 171848) ((-127 . -34) T) ((-830 . -132) T) ((-662 . -625) 171830) ((-590 . -102) T) ((-366 . -1308) 171814) ((-363 . -1308) 171798) ((-355 . -1308) 171782) ((-122 . -526) 171715) ((-128 . -526) 171648) ((-523 . -805) T) ((-523 . -808) T) ((-522 . -807) T) ((-103 . -319) 171586) ((-224 . -102) 171536) ((-712 . -174) T) ((-707 . -1122) T) ((-887 . -661) 171452) ((-65 . -395) T) ((-284 . -625) 171434) ((-65 . -407) T) ((-972 . -388) 171418) ((-885 . -300) T) ((-50 . -625) 171400) ((-1021 . -38) 171348) ((-1142 . -659) 171320) ((-593 . -625) 171302) ((-493 . -388) 171286) ((-593 . -626) 171268) ((-530 . -625) 171250) ((-930 . -1308) 171237) ((-886 . -1239) T) ((-714 . -464) T) ((-507 . -526) 171203) ((-1300 . -1239) T) ((-1299 . -1239) T) ((-499 . -374) T) ((-366 . -379) 171182) ((-363 . -379) 171161) ((-355 . -379) 171140) ((-727 . -739) T) ((-219 . -374) T) ((-117 . -464) T) ((-1312 . -1303) 171124) ((-886 . -900) 171101) ((-886 . -902) NIL) ((-984 . -862) 171000) ((-828 . -862) 170951) ((-1246 . -102) T) ((-667 . -669) 170935) ((-1225 . -34) T) ((-173 . -625) 170917) ((-1135 . -25) 170750) ((-1135 . -21) 170661) ((-886 . -1060) 170638) ((-972 . -918) 170619) ((-1262 . -47) 170596) ((-930 . -379) T) ((-605 . -865) T) ((-59 . -664) 170580) ((-528 . -664) 170564) ((-493 . -918) 170541) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -664) 170525) ((-59 . -384) 170509) ((-635 . -174) T) ((-528 . -384) 170493) ((-508 . -384) 170477) ((-558 . -1239) T) ((-840 . -721) 170461) ((-1194 . -317) 170440) ((-1200 . -132) T) ((-1164 . -1073) 170424) ((-118 . -174) T) ((-1164 . -653) 170356) ((-1168 . -319) 170294) ((-171 . -1239) T) ((-1301 . -132) T) ((-1274 . -940) 170273) ((-1253 . -940) 170252) ((-1253 . -833) NIL) ((-881 . -1073) 170222) ((-647 . -757) 170206) ((-619 . -757) 170190) ((-1252 . -929) 170143) ((-1046 . -1122) T) ((-925 . -1134) T) ((-881 . -653) 170113) ((-707 . -730) 170063) ((-916 . -1239) T) ((-886 . -388) 170040) ((-886 . -349) 170017) ((-854 . -1239) T) ((-821 . -1239) T) ((-171 . -900) 170001) ((-171 . -902) 169926) ((-782 . -1239) T) ((-690 . -1239) T) ((-1289 . -526) 169859) ((-1273 . -661) 169756) ((-1102 . -234) 169629) ((-499 . -1134) T) ((-365 . -1122) T) ((-219 . -1134) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1060) 169525) ((-304 . -912) 169482) ((-329 . -862) T) ((-1252 . -661) 169290) ((-887 . -807) 169269) ((-887 . -804) 169248) ((-887 . -739) T) ((-499 . -23) T) ((-370 . -234) 169221) ((-364 . -234) 169194) ((-356 . -234) 169167) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 169105) ((-86 . -407) T) ((-225 . -625) 169087) ((-108 . -234) 169074) ((-219 . -23) T) ((-1313 . -1306) 169053) ((-690 . -1060) 169037) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1262 . -1239) T) ((-137 . -482) 168992) ((-870 . -1239) T) ((-667 . -659) 168951) ((-48 . -1122) T) ((-725 . -272) 168935) ((-725 . -232) 168919) ((-886 . -918) NIL) ((-583 . -1239) T) ((-1262 . -902) NIL) ((-905 . -102) T) ((-901 . -102) T) ((-400 . -1122) T) ((-171 . -388) 168903) ((-171 . -349) 168887) ((-1262 . -1060) 168767) ((-870 . -1060) 168663) ((-1164 . -102) T) ((-1021 . -920) 168586) ((-675 . -805) 168565) ((-666 . -132) T) ((-675 . -808) 168544) ((-118 . -526) 168452) ((-583 . -1060) 168434) ((-304 . -1296) 168404) ((-1189 . -865) NIL) ((-881 . -102) T) ((-983 . -568) 168383) ((-1233 . -1078) 168266) ((-1025 . -1073) 168211) ((-494 . -652) 168117) ((-924 . -1122) T) ((-1046 . -730) 168054) ((-724 . -1078) 168019) ((-1025 . -653) 167964) ((-629 . -102) T) ((-614 . -34) T) ((-1169 . -1239) T) ((-1233 . -111) 167833) ((-486 . -661) 167730) ((-365 . -730) 167675) ((-171 . -918) 167634) ((-712 . -300) T) ((-707 . -174) T) ((-724 . -111) 167590) ((-1318 . -1080) T) ((-1262 . -388) 167574) ((-430 . -1243) 167552) ((-1140 . -625) 167534) ((-323 . -861) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1252 . -804) 167487) ((-1252 . -807) 167440) ((-1273 . -739) T) ((-1252 . -739) T) ((-48 . -730) 167405) ((-227 . -1044) T) ((-1275 . -423) 167371) ((-1262 . -918) 167314) ((-362 . -1296) 167291) ((-1233 . -628) 167173) ((-731 . -739) T) ((-343 . -625) 167155) ((-532 . -865) 167134) ((-1135 . -234) 167025) ((-112 . -625) 167007) ((-112 . -626) 166989) ((-731 . -485) T) ((-724 . -628) 166939) ((-1312 . -1073) 166923) ((-494 . -25) 166756) ((-128 . -501) 166740) ((-122 . -501) 166724) ((-494 . -21) 166635) ((-1312 . -653) 166605) ((-635 . -300) T) ((-598 . -1078) 166580) ((-449 . -1122) T) ((-1084 . -317) T) ((-118 . -300) T) ((-1126 . -102) T) ((-1025 . -102) T) ((-598 . -111) 166548) ((-1233 . -1071) T) ((-1164 . -319) 166486) ((-1084 . -1044) T) ((-1076 . -25) T) 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-929) 165735) ((-253 . -929) 165714) ((-795 . -1078) 165537) ((-793 . -1078) 165380) ((-620 . -1239) T) ((-1186 . -625) 165362) ((-1109 . -111) 165191) ((-1068 . -102) T) ((-487 . -1239) T) ((-473 . -1078) 165162) ((-466 . -1078) 165005) ((-677 . -661) 164989) ((-886 . -317) T) ((-795 . -111) 164798) ((-793 . -111) 164627) ((-366 . -661) 164579) ((-363 . -661) 164531) ((-355 . -661) 164483) ((-273 . -661) 164372) ((-253 . -661) 164261) ((-1180 . -862) T) ((-1110 . -1060) 164245) ((-1098 . -1060) 164222) ((-1026 . -865) T) ((-1022 . -34) T) ((-473 . -111) 164183) ((-466 . -111) 164012) ((-993 . -865) T) ((-986 . -625) 163994) ((-983 . -1134) T) ((-978 . -1239) T) ((-127 . -1032) 163978) ((-863 . -1239) T) ((-886 . -1044) NIL) ((-748 . -1134) T) ((-728 . -1134) T) ((-671 . -628) 163896) ((-1289 . -501) 163880) ((-1206 . -1239) T) ((-1205 . -1239) T) ((-1164 . -38) 163840) ((-983 . -23) T) ((-930 . -661) 163805) ((-880 . -1122) T) ((-856 . -102) T) ((-830 . -21) T) ((-647 . -1073) 163789) 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-234) 161222) ((-50 . -1071) T) ((-1196 . -568) 161201) ((-1195 . -1243) 161180) ((-1195 . -568) 161131) ((-1189 . -1243) 161110) ((-1189 . -568) 161061) ((-1046 . -300) T) ((-593 . -1071) T) ((-530 . -1071) T) ((-1025 . -38) 161006) ((-372 . -1060) 160990) ((-332 . -1060) 160974) ((-1021 . -659) 160897) ((-390 . -902) 160879) ((-849 . -1239) T) ((-840 . -1239) T) ((-838 . -1239) T) ((-812 . -1134) T) ((-930 . -739) T) ((-593 . -248) T) ((-593 . -238) T) ((-530 . -238) T) ((-530 . -248) T) ((-1148 . -568) 160858) ((-365 . -300) T) ((-660 . -708) 160842) ((-390 . -1060) 160802) ((-304 . -1073) 160723) ((-350 . -912) 160702) ((-1142 . -1080) T) ((-103 . -126) 160686) ((-304 . -653) 160628) ((-812 . -23) T) ((-1311 . -1306) 160604) ((-1309 . -1306) 160583) ((-1289 . -296) 160535) ((-419 . -319) 160500) ((-1275 . -1122) T) ((-1164 . -920) 160423) ((-885 . -625) 160405) ((-849 . -1060) 160374) ((-205 . -800) T) ((-204 . -800) T) ((-203 . -800) T) ((-202 . -800) T) ((-201 . -800) T) ((-200 . -800) T) ((-199 . -800) T) ((-198 . -800) T) ((-197 . -800) T) ((-196 . -800) T) ((-559 . -625) 160356) ((-507 . -1024) T) ((-283 . -852) T) ((-282 . -852) T) ((-281 . -852) T) ((-280 . -852) T) ((-48 . -300) T) ((-279 . -852) T) ((-278 . -852) T) ((-277 . -852) T) ((-195 . -800) T) ((-624 . -862) T) ((-667 . -423) 160340) ((-683 . -237) 160291) ((-225 . -628) 160253) ((-110 . -862) T) ((-666 . -21) T) ((-666 . -25) T) ((-1312 . -38) 160223) ((-118 . -296) 160174) ((-1289 . -19) 160158) ((-1253 . -865) NIL) ((-1289 . -616) 160135) ((-1302 . -1122) T) ((-362 . -1073) 160080) ((-1099 . -1122) T) ((-1009 . -1122) T) ((-983 . -132) T) ((-830 . -234) 160067) ((-750 . -1122) T) ((-362 . -653) 160012) ((-748 . -132) T) ((-728 . -132) T) ((-523 . -806) T) ((-523 . -807) T) ((-465 . -132) T) ((-419 . -1174) 159990) ((-225 . -1071) T) ((-304 . -102) 159772) ((-142 . -1122) T) ((-712 . -1024) T) ((-1127 . -296) 159728) ((-91 . -1239) T) ((-128 . -625) 159660) ((-122 . -625) 159592) ((-1318 . -174) T) ((-1195 . -374) 159571) ((-1189 . -374) 159550) ((-326 . -1122) T) ((-430 . -132) T) ((-323 . -1122) T) ((-419 . -38) 159502) ((-1155 . -102) T) ((-1275 . -730) 159394) ((-1157 . -1284) T) ((-1118 . -1239) T) ((-1112 . -1239) T) ((-667 . -1080) T) ((-1095 . -1239) T) ((-1088 . -1239) T) ((-1058 . -1239) T) ((-1041 . -1239) T) ((-329 . -146) 159373) ((-329 . -148) 159352) ((-140 . -1122) T) ((-137 . -1122) T) ((-115 . -1122) T) ((-873 . -102) T) ((-638 . -1239) T) ((-495 . -1239) T) ((-592 . -625) 159334) ((-576 . -626) 159233) ((-576 . -625) 159215) ((-507 . -625) 159197) ((-507 . -626) 159142) ((-497 . -23) T) ((-220 . -1239) T) ((-494 . -862) 159093) ((-499 . -652) 159075) ((-985 . -625) 159057) ((-1025 . -920) 158966) ((-219 . -652) 158948) ((-227 . -416) T) ((-675 . -661) 158932) ((-55 . -625) 158914) ((-1194 . -940) 158893) ((-744 . -1134) T) ((-527 . -1239) T) ((-522 . -1239) T) ((-520 . -1239) T) ((-362 . -102) T) ((-1238 . -1105) T) ((-1142 . -857) T) ((-831 . -862) T) 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-174) T) ((-1212 . -625) 158104) ((-250 . -34) T) ((-354 . -628) 158034) ((-406 . -628) 158016) ((-946 . -996) T) ((-1225 . -1239) T) ((-675 . -804) 157995) ((-675 . -807) 157974) ((-410 . -407) T) ((-535 . -102) 157924) ((-1245 . -1239) T) ((-1057 . -1122) T) ((-419 . -920) 157847) ((-224 . -1017) 157831) ((-851 . -1239) T) ((-516 . -102) T) ((-635 . -625) 157813) ((-45 . -862) NIL) ((-635 . -626) 157790) ((-1057 . -622) 157765) ((-921 . -526) 157698) ((-329 . -237) 157650) ((-354 . -1071) T) ((-118 . -626) NIL) ((-118 . -625) 157632) ((-887 . -1239) T) ((-683 . -429) 157616) ((-683 . -1145) 157561) ((-512 . -152) 157543) ((-354 . -238) T) ((-354 . -248) T) ((-40 . -1078) 157488) ((-887 . -900) 157472) ((-887 . -902) 157397) ((-725 . -1080) T) ((-707 . -1024) NIL) ((-1273 . -47) 157367) ((-1252 . -47) 157344) ((-1163 . -1032) 157315) ((-1142 . -730) 157302) ((-3 . |UnionCategory|) T) ((-1127 . -625) 157284) ((-1102 . -148) 157263) ((-1102 . -146) 157214) ((-1026 . -374) T) ((-986 . -628) 157198) ((-227 . -940) T) ((-40 . -111) 157127) ((-887 . -1060) 156991) ((-1025 . -232) 156968) ((-1025 . -272) 156945) ((-714 . -1073) 156932) ((-934 . -374) T) ((-714 . -653) 156919) ((-329 . -1227) 156885) ((-390 . -317) T) ((-329 . -1224) 156851) ((-326 . -174) 156830) ((-323 . -174) T) ((-620 . -1215) 156806) ((-593 . -1308) 156793) ((-530 . -1308) 156770) ((-117 . -1073) 156757) ((-370 . -148) 156736) ((-370 . -146) 156687) ((-364 . -148) 156666) ((-364 . -146) 156617) ((-356 . -148) 156596) ((-117 . -653) 156583) ((-356 . -146) 156534) ((-329 . -35) 156500) ((-487 . -1215) 156479) ((0 . |EnumerationCategory|) T) ((-329 . -95) 156445) ((-390 . -1044) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -240) 156395) ((-667 . -1122) T) ((-620 . -107) 156342) ((-497 . -132) T) ((-487 . -107) 156292) ((-245 . -1134) 156270) ((-31 . -1239) T) ((-887 . -388) 156254) ((-887 . -349) 156238) ((-245 . -23) 156090) ((-40 . -628) 156020) ((-1302 . -526) 155953) ((-1084 . -940) T) ((-1084 . -833) T) ((-593 . -379) T) ((-530 . -379) T) ((-1281 . -568) 155932) ((-1274 . -1243) 155911) ((-1274 . -568) 155862) ((-1273 . -1239) T) ((-1253 . -1243) 155841) ((-362 . -1174) T) ((-337 . -34) T) ((-44 . -429) 155825) ((-1203 . -628) 155761) ((-888 . -1239) T) ((-402 . -757) 155745) ((-1253 . -568) 155696) ((-1252 . -1239) T) ((-1164 . -659) 155655) ((-744 . -132) T) ((-685 . -628) 155639) ((-1252 . -902) 155512) ((-1252 . -900) 155482) ((-1196 . -132) T) ((-1195 . -132) T) ((-1189 . -132) T) ((-1148 . -132) T) ((-321 . -1105) T) ((-1046 . -1024) T) ((-750 . -526) 155415) ((-1026 . -23) T) ((-1026 . -1134) T) ((-909 . -1122) T) ((-145 . -857) T) ((-1025 . -360) NIL) ((-704 . -625) 155397) ((-963 . -865) 155376) ((-535 . -319) 155314) ((-993 . -23) T) ((-142 . -526) NIL) ((-881 . -659) 155259) ((-934 . -1134) T) ((-934 . -23) T) ((-887 . -918) 155218) ((-362 . -38) 155183) ((-885 . -1078) 155170) ((-341 . -865) T) ((-82 . -625) 155152) ((-40 . -1071) T) ((-885 . -111) 155137) 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-501) 152804) ((-48 . -625) 152786) ((-48 . -626) 152731) ((-245 . -132) 152602) ((-1312 . -659) 152561) ((-1262 . -940) 152540) ((-829 . -1243) 152519) ((-400 . -502) 152500) ((-1057 . -526) 152344) ((-400 . -625) 152310) ((-829 . -568) 152241) ((-598 . -661) 152216) ((-273 . -47) 152188) ((-253 . -47) 152145) ((-543 . -521) 152122) ((-592 . -628) 152094) ((-576 . -628) 152066) ((-507 . -628) 151999) ((-1096 . -1239) T) ((-1022 . -1239) T) ((-1281 . -23) T) ((-1281 . -1134) T) ((-1274 . -1134) T) ((-1274 . -23) T) ((-1253 . -1134) T) ((-712 . -1078) 151964) ((-1253 . -23) T) ((-1233 . -739) T) ((-1142 . -300) T) ((-1135 . -237) 151861) ((-1026 . -132) T) ((-1025 . -381) 151833) ((-112 . -379) T) ((-486 . -918) 151739) ((-993 . -132) T) ((-924 . -625) 151721) ((-55 . -628) 151703) ((-91 . -107) 151687) ((-934 . -132) T) ((-925 . -862) 151638) ((-714 . -1174) T) ((-712 . -111) 151594) ((-856 . -659) 151511) ((-608 . -1134) T) ((-607 . -1134) T) ((-725 . -730) 151340) ((-724 . -739) T) 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. -568) T) ((-972 . -568) 142148) ((-1194 . -23) T) ((-1173 . -1105) T) ((-1147 . -23) T) ((-869 . -23) T) ((-493 . -568) 142079) ((-1164 . -730) 142011) ((-683 . -1073) 141995) ((-1168 . -526) 141928) ((-683 . -653) 141912) ((-1057 . -626) NIL) ((-1057 . -625) 141894) ((-96 . -1105) T) ((-1318 . -1078) 141881) ((-881 . -730) 141851) ((-1318 . -111) 141836) ((-1233 . -47) 141805) ((-1189 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1126 . -1122) T) ((-1025 . -1122) T) ((-62 . -625) 141787) ((-1102 . -912) 141656) ((-1046 . -805) T) ((-1046 . -808) T) ((-1281 . -25) T) ((-1281 . -21) T) ((-1274 . -21) T) ((-1274 . -25) T) ((-885 . -661) 141643) ((-1253 . -21) T) ((-1253 . -25) T) ((-1049 . -152) 141627) ((-1026 . -234) 141614) ((-887 . -833) 141593) ((-887 . -940) T) ((-725 . -296) 141520) ((-608 . -21) T) ((-350 . -659) 141479) ((-108 . -912) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -659) 141396) ((-40 . -739) T) ((-224 . -526) 141329) ((-607 . -25) T) ((-488 . -152) 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119186) ((-1253 . -35) 119152) ((-1252 . -1134) T) ((-605 . -152) 119134) ((-1102 . -360) 119113) ((-176 . -300) T) ((-118 . -388) 119090) ((-118 . -349) 119067) ((-171 . -234) 118992) ((-885 . -317) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-326 . -739) 118841) ((-323 . -739) T) ((-651 . -132) T) ((-486 . -374) 118820) ((-370 . -360) 118799) ((-364 . -360) 118778) ((-356 . -360) 118757) ((-326 . -485) 118736) ((-1273 . -23) T) ((-1252 . -23) T) ((-731 . -1134) T) ((-727 . -132) T) ((-666 . -102) T) ((-489 . -730) 118701) ((-675 . -865) 118680) ((-45 . -292) 118630) ((-105 . -1122) T) ((-68 . -625) 118612) ((-250 . -865) 118591) ((-992 . -102) T) ((-879 . -102) T) ((-635 . -918) 118550) ((-1313 . -1122) T) ((-392 . -1122) T) ((-1262 . -234) 118537) ((-1238 . -1122) T) ((-82 . -1239) T) ((-1135 . -272) 118506) ((-1084 . -862) T) ((-118 . -918) NIL) ((-795 . -940) 118485) ((-726 . -862) T) ((-543 . -1122) T) ((-512 . -1122) T) ((-366 . -1243) T) ((-363 . -1243) T) ((-355 . -1243) T) 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. -21) T) ((-519 . -25) T) ((-1189 . -38) 98848) ((-350 . -1071) T) ((-145 . -1239) T) ((-1102 . -174) T) ((-176 . -1071) T) ((-1148 . -38) 98745) ((-725 . -47) 98722) ((-370 . -174) T) ((-364 . -174) T) ((-531 . -57) 98696) ((-509 . -57) 98646) ((-362 . -1308) 98623) ((-227 . -464) T) ((-329 . -300) 98574) ((-356 . -174) T) ((-176 . -248) T) ((-1252 . -862) 98473) ((-108 . -174) T) ((-887 . -1014) 98457) ((-671 . -1134) T) ((-593 . -374) T) ((-593 . -339) 98444) ((-530 . -339) 98421) ((-530 . -374) T) ((-326 . -317) 98400) ((-323 . -317) T) ((-614 . -862) 98379) ((-1135 . -730) 98321) ((-532 . -292) 98305) ((-671 . -23) T) ((-430 . -232) 98289) ((-430 . -272) 98273) ((-323 . -1044) NIL) ((-347 . -23) T) ((-103 . -1032) 98257) ((-45 . -36) 98236) ((-624 . -1122) T) ((-362 . -379) T) ((-536 . -102) T) ((-507 . -27) T) ((-245 . -319) 98174) ((-1109 . -1134) T) ((-1312 . -661) 98148) ((-795 . -1134) T) ((-793 . -1134) T) ((-1200 . -423) 98132) ((-466 . -1134) T) ((-1084 . -464) T) ((-1173 . -1122) T) ((-972 . -464) 98083) ((-1137 . -1105) T) ((-110 . -1122) T) ((-1109 . -23) T) ((-1181 . -526) 97866) ((-830 . -1080) T) ((-795 . -23) T) ((-793 . -23) T) ((-493 . -464) 97817) ((-473 . -23) T) ((-392 . -393) 97796) ((-366 . -234) 97769) ((-363 . -234) 97742) ((-355 . -234) 97715) ((-466 . -23) T) ((-273 . -234) 97660) ((-258 . -912) 97527) ((-257 . -912) 97394) ((-96 . -1122) T) ((-725 . -1239) T) ((-683 . -296) 97371) ((-496 . -526) 97304) ((-1281 . -1073) 97187) ((-1281 . -653) 97084) ((-1274 . -653) 96925) ((-1274 . -1073) 96760) ((-1253 . -653) 96556) ((-1253 . -1073) 96346) ((-299 . -300) T) ((-1104 . -625) 96328) ((-559 . -865) T) ((-1104 . -626) 96309) ((-419 . -929) 96288) ((-1233 . -132) T) ((-50 . -1134) T) ((-1189 . -412) 96240) ((-1046 . -940) T) ((-1025 . -739) T) ((-856 . -661) 96213) ((-725 . -902) NIL) ((-608 . -1073) 96173) ((-593 . -1134) T) ((-530 . -1134) T) ((-607 . -1073) 96056) ((-1179 . -34) T) ((-1026 . -319) NIL) ((-828 . -501) 96040) ((-608 . 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81255) ((-356 . -625) 81237) ((-66 . -408) T) ((-66 . -407) T) ((-108 . -626) 81167) ((-108 . -625) 81109) ((-213 . -913) T) ((-978 . -152) 81093) ((-784 . -132) T) ((-683 . -628) 81011) ((-135 . -739) T) ((-117 . -739) T) ((-1273 . -35) 80977) ((-1076 . -501) 80961) ((-592 . -23) T) ((-576 . -23) T) ((-507 . -23) T) ((-1252 . -95) 80927) ((-1252 . -35) 80893) ((-1194 . -102) T) ((-1147 . -102) T) ((-869 . -102) T) ((-229 . -501) 80877) ((-1311 . -111) 80856) ((-1309 . -111) 80835) ((-44 . -1078) 80819) ((-1312 . -1239) T) ((-1311 . -628) 80765) ((-1311 . -1071) T) ((-1309 . -628) 80694) ((-1309 . -1071) T) ((-1262 . -1265) 80678) ((-870 . -867) 80662) ((-1200 . -300) 80641) ((-1126 . -1239) T) ((-110 . -296) 80591) ((-1025 . -1239) T) ((-129 . -152) 80573) ((-1164 . -918) 80532) ((-44 . -111) 80511) ((-1244 . -1122) T) ((-1203 . -1284) T) ((-1189 . -861) NIL) ((-1188 . -502) 80492) ((-683 . -1071) T) ((-1188 . -625) 80458) ((-1180 . -625) 80440) ((-486 . -237) 80392) ((-1085 . -622) 80367) ((-1016 . -502) 80348) ((-74 . -453) T) ((-74 . -407) T) ((-1085 . -1122) T) ((-153 . -1078) 80332) ((-1016 . -625) 80298) ((-683 . -238) 80277) ((-583 . -566) 80261) ((-366 . -148) 80240) ((-366 . -146) 80191) ((-363 . -148) 80170) ((-363 . -146) 80121) ((-355 . -148) 80100) ((-355 . -146) 80051) ((-273 . -146) 80030) ((-273 . -148) 80009) ((-253 . -148) 79988) ((-118 . -374) T) ((-253 . -146) 79967) ((-1180 . -626) NIL) ((-153 . -111) 79946) ((-1025 . -1060) 79834) ((-1179 . -1239) T) ((-707 . -1243) T) ((-812 . -1080) T) ((-712 . -1134) T) ((-1025 . -388) 79811) ((-518 . -1239) T) ((-514 . -1239) T) ((-930 . -146) T) ((-930 . -148) 79793) ((-885 . -132) T) ((-828 . -1078) 79714) ((-712 . -23) T) ((-707 . -568) T) ((-227 . -1073) 79679) ((-660 . -625) 79611) ((-660 . -626) 79572) ((-644 . -626) NIL) ((-644 . -625) 79554) ((-499 . -174) T) ((-227 . -653) 79519) ((-219 . -174) T) ((-225 . -21) T) ((-225 . -25) T) ((-486 . -1227) 79485) ((-486 . -1224) 79451) ((-283 . -625) 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78188) ((-1157 . -1122) T) ((-972 . -1073) 78031) ((-1147 . -319) 78018) ((-1118 . -1105) T) ((-635 . -1134) T) ((-1084 . -653) 78005) ((-1112 . -1105) T) ((-972 . -653) 77854) ((-1109 . -234) 77799) ((-493 . -1073) 77642) ((-1095 . -1105) T) ((-1088 . -1105) T) ((-1058 . -1105) T) ((-1041 . -1105) T) ((-118 . -1134) T) ((-493 . -653) 77491) ((-795 . -234) 77478) ((-832 . -102) T) ((-638 . -1105) T) ((-635 . -23) T) ((-1172 . -526) 77270) ((-495 . -1105) T) ((-983 . -1122) T) ((-398 . -102) T) ((-334 . -102) T) ((-220 . -1105) T) ((-856 . -1239) T) ((-153 . -1071) T) ((-744 . -423) 77254) ((-118 . -23) T) ((-1025 . -918) 77206) ((-748 . -1122) T) ((-728 . -1122) T) ((-1281 . -659) 77116) ((-1274 . -659) 76998) ((-465 . -1122) T) ((-419 . -1239) T) ((-326 . -442) 76982) ((-604 . -93) T) ((-1049 . -626) 76943) ((-270 . -1239) T) ((-1046 . -1243) T) ((-227 . -102) T) ((-1049 . -625) 76905) ((-829 . -272) 76889) ((-829 . -232) 76873) ((-828 . -628) 76671) ((-1253 . -659) 76508) ((-1046 . 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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 ec825864..8a7823a2 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3486916216) +(30 . 3486967785) (4469 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,663 +488,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |sup| |unmakeSUP| |meatAxe| |mainValue| |setRow!| - |arg2| |alphabetic?| |exp1| |string| |finite?| |getStream| - |listYoungTableaus| |localAbs| |f02abf| |shanksDiscLogAlgorithm| - |host| |cAcosh| |e04naf| |leftLcm| |rightFactorCandidate| |say| |bits| - |putProperties| |packageCall| |clipWithRanges| |notelem| |dflist| - |lazyVariations| |conditions| |solid?| |iisech| |odd?| |setTex!| - |prefixRagits| |lllip| |monicRightFactorIfCan| |zeroDimPrime?| - |augment| |exprHasLogarithmicWeights| |simplify| |title| |ignore?| - |match| |expIfCan| |string?| |empty?| |reset| |jacobi| |unaryFunction| - |s21bbf| |predicates| |integer?| |unitVector| |setEmpty!| - |usingTable?| |binarySearchTree| |complexEigenvalues| |upperCase?| - |purelyTranscendental?| |internalSubQuasiComponent?| |arguments| - |integralAtInfinity?| |s17aff| |pointColorPalette| |write| - |transcendent?| |outputSpacing| |inc| |f04asf| |linearPolynomials| - |replaceKthElement| |compdegd| |hostPlatform| |e| |qfactor| |save| - |processTemplate| |viewPosDefault| |subQuasiComponent?| - |expandTrigProducts| |e01saf| |resetNew| GF2FG |OMputEndApp| - |genericPosition| |nothing| |digits| |child| |OMunhandledSymbol| - |sequences| |power!| |simplifyExp| |modularGcdPrimitive| - |genericLeftMinimalPolynomial| |internalSubPolSet?| |anfactor| - |mkAnswer| |functionIsContinuousAtEndPoints| |redPol| |lfextendedint| - |expandPower| |numberOfDivisors| |top| |doublyTransitive?| |failed?| - |mvar| |operation| |qqq| |semiIndiceSubResultantEuclidean| - |removeRedundantFactorsInContents| |associative?| |s17dcf| - |mainCoefficients| |continue| |nextPrime| |lazyIntegrate| |setvalue!| - |unexpand| |goodPoint| |acschIfCan| |OMputError| |geometric| - |primitivePart| |sn| |build| |parts| |pointLists| |superHeight| - |dimension| |OMParseError?| |stoseInternalLastSubResultant| |primes| - |inverse| |extend| |assign| ** |palgRDE| |hash| |e01sef| - |complexNumericIfCan| |clipParametric| |coordinate| |discriminant| - |topFortranOutputStack| |polyRDE| |rootProduct| |count| |qroot| - |traverse| |parametersOf| |sizePascalTriangle| |pointPlot| - |reducedQPowers| |torsionIfCan| |primPartElseUnitCanonical!| - |branchPointAtInfinity?| |c05adf| |expenseOfEvaluation| - |nativeModuleExtension| |radicalEigenvectors| - |numberOfComputedEntries| |routines| |viewWriteDefault| - |extendedResultant| |useSingleFactorBound?| |rur| |rotatey| - |clipPointsDefault| |constant| |quasiComponent| |outputFixed| - |rewriteIdealWithRemainder| |fill!| |leftZero| |rowEchelonLocal| - |karatsubaDivide| |PDESolve| |points| |sumOfKthPowerDivisors| - |factors| |qualifier| |mantissa| |binaryTournament| |cAtan| - |removeRoughlyRedundantFactorsInPol| |tube| |cAcos| |e01daf| - |rightExtendedGcd| |yellow| |realRoots| |mkcomm| |curryLeft| - |skewSFunction| |iiabs| |deepestInitial| |vectorise| |readInt32!| - |coercePreimagesImages| |lprop| |testDim| |gcdPrimitive| - |leftAlternative?| |purelyAlgebraicLeadingMonomial?| - |normalizedAssociate| |rotate!| |rischDEsys| |rationalPower| - |invmultisect| |edf2fi| |explicitlyFinite?| |f02bbf| - |prepareSubResAlgo| |hclf| |connectTo| |semiLastSubResultantEuclidean| - |unrankImproperPartitions1| |highCommonTerms| |numerators| |permanent| - |ldf2lst| |ptFunc| |linearMatrix| |leftTraceMatrix| |c06frf| - |insertTop!| |showAllElements| |solveLinear| |complementaryBasis| - |maximumExponent| |lighting| |isNot| |mapExpon| |iiacsc| |complete| - |e02akf| |extensionDegree| |mdeg| |universe| |makeTerm| - |primlimintfrac| |checkPrecision| |getGoodPrime| |returnTypeOf| - |stripCommentsAndBlanks| |RittWuCompare| |check| |legendre| - |chebyshevU| |diagonals| |e02bdf| |oddInfiniteProduct| |laplace| - |s14baf| |mathieu11| |zeroSetSplit| |bat| |constantCoefficientRicDE| - |tRange| |leader| |listexp| |regularRepresentation| |inHallBasis?| - |categories| |conjugate| |isPower| |selectSumOfSquaresRoutines| - |numer| |sparsityIF| |listBranches| |retractIfCan| |crushedSet| - |getMeasure| |areEquivalent?| |lazyResidueClass| |blankSeparate| - |partialFraction| |complement| |OMputEndObject| |denom| |singular?| - |hasSolution?| |appendPoint| |totalfract| |f01maf| |acothIfCan| |call| - |difference| |setScreenResolution| |column| |identity| FG2F - |factorFraction| |symmetric?| |repeating| |exponents| |argumentListOf| - |removeDuplicates| |cyclicSubmodule| |pi| |ReduceOrder| - |basisOfLeftAnnihilator| |nilFactor| |leftExtendedGcd| |orbits| - |monomialIntegrate| |setfirst!| |sizeMultiplication| |merge!| - |infinity| |f01rcf| |f2st| |debug3D| |bag| |concat| |lifting1| |step| - |explicitlyEmpty?| |rischDE| |iiacos| |interpolate| |ridHack1| - |tryFunctionalDecomposition| |pushdown| |e04dgf| |modulus| - |findConstructor| |isOr| |OMencodingUnknown| |pr2dmp| |eulerPhi| - |xCoord| |getOrder| |nthFactor| |roughBasicSet| |rightGcd| |tanIfCan| - |mightHaveRoots| |merge| |kernel| |compiledFunction| |s19aaf| - |removeZeroes| |f01qcf| |createRandomElement| |decomposeFunc| - |connect| |OMbindTCP| |cos2sec| |list| |ptree| |cycleRagits| - |OMencodingSGML| |hdmpToDmp| |fortranDoubleComplex| |lhs| |init| - |kmax| |plus!| |printingInfo?| |writeByte!| |largest| |draw| - |midpoints| |clearCache| |setStatus| |algebraicOf| |cAcsch| |rhs| - |matrixDimensions| |iiacoth| |explicitEntries?| |tubePlot| - |countRealRoots| |subscript| |sort!| |removeRedundantFactors| - |weakBiRank| |intcompBasis| |inf| |relativeApprox| |monicRightDivide| - |subNode?| |readInt16!| |OMputApp| |latex| |subMatrix| |currentEnv| - |writeInt8!| |ideal| |OMUnknownCD?| |UP2ifCan| |conjugates| |mesh?| - |basisOfLeftNucloid| |deriv| |toseInvertible?| - |leftCharacteristicPolynomial| |subNodeOf?| |clearTheSymbolTable| - |createNormalPoly| |resize| |makeObject| |mapUp!| |euler| |zCoord| - |domainTemplate| |ord| |groebner?| |extendedIntegrate| |safeFloor| - |deepCopy| |coef| |univariateSolve| |mkIntegral| - |noncommutativeJordanAlgebra?| |showAll?| |inverseIntegralMatrix| - |qelt| |totalLex| |leaf?| |symFunc| |newSubProgram| |directory| - |imagI| |OMgetInteger| |redpps| |untab| |rootsOf| |qsetelt| |top!| - |simplifyPower| |overset?| |besselK| |infiniteProduct| |rationalIfCan| - |selectNonFiniteRoutines| |powmod| |df2ef| |genus| |xRange| |delay| - |mainSquareFreePart| |generalSqFr| |numericalOptimization| - |selectOptimizationRoutines| |completeHermite| |nextSublist| - |balancedBinaryTree| |kind| |f01ref| |derivative| |systemSizeIF| - |resultantnaif| |yRange| |middle| |expintfldpoly| |restorePrecision| - |bubbleSort!| |op| |evaluate| |minPoints3D| |OMUnknownSymbol?| |more?| - |quoted?| |zRange| |kernels| |lieAdmissible?| |box| |readByte!| - |rightMult| |round| |unary?| |oblateSpheroidal| |seriesToOutputForm| - |getGraph| |map!| |fortranTypeOf| |symmetricSquare| |trapezoidalo| - |operator| |upperCase| |nextPartition| |rangeIsFinite| |constant?| - |lazyPseudoRemainder| |normalForm| |qsetelt!| |optional?| SEGMENT - |iicos| |expenseOfEvaluationIF| |removeZero| |perfectNthPower?| - |fortranInteger| |copyInto!| |jokerMode| |setProperty| |OMgetString| - |leftRankPolynomial| |compBound| |expextendedint| |univariate| - |leftFactor| |mapBivariate| |gcdPolynomial| |quoByVar| |over| - |clikeUniv| |sort| |maxIndex| |iiacsch| |rewriteSetWithReduction| - |fmecg| |capacity| |compactFraction| |setPosition| |hitherPlane| - |qPot| |rational| |dec| |nextsubResultant2| |relationsIdeal| - |leftQuotient| |s17agf| |listConjugateBases| |union| |slash| - |viewThetaDefault| |splitLinear| |arity| |cardinality| - |symmetricDifference| |factor| |overbar| |lowerCase| - |resetAttributeButtons| |rarrow| |leftDiscriminant| |equiv| - |definingInequation| |acsch| |LagrangeInterpolation| |sqrt| - |makeResult| |scalarMatrix| |palgRDE0| |birth| |twoFactor| - |showClipRegion| |extractSplittingLeaf| |argscript| |comp| |random| - |beauzamyBound| |safetyMargin| |readUInt8!| |real| |f02aaf| - |functionIsFracPolynomial?| |linearElement| |divisor| |ip4Address| - |dimensionsOf| |chiSquare1| |romberg| |imag| |asimpson| |OMsend| F2FG - |properties| |noKaratsuba| |isOp| |nthRootIfCan| - |wordsForStrongGenerators| |changeMeasure| |copy| |polar| |pushucoef| - |directProduct| |closedCurve?| |numericalIntegration| |super| |droot| - |setLegalFortranSourceExtensions| |contractSolve| |translate| |irCtor| - |commutator| |exponential| |rootOf| |tubePointsDefault| |s18def| - |eigenMatrix| |rootSplit| |sdf2lst| |part?| |remove!| |gethi| - |pushuconst| |brace| |nlde| |module| |bottom!| |setFormula!| - |flagFactor| |factorSquareFreeByRecursion| |showScalarValues| |mulmod| - |rotate| |destruct| |imagi| |sturmVariationsOf| |approxSqrt| |d01ajf| - |cschIfCan| |realZeros| |binomial| |iiGamma| |fortranLiteralLine| - |zag| |patternVariable| |match?| |erf| |coefChoose| - |removeRoughlyRedundantFactorsInPols| |light| |uniform| - |localIntegralBasis| |autoCoerce| |coerceL| |e01baf| |nextItem| - |permutations| |nullary| |generic?| |setAdaptive| |quadraticForm| - |cycleEntry| |palgLODE0| |OMsupportsCD?| |linear?| |brillhartTrials| - |prolateSpheroidal| |univcase| |mathieu24| |printStats!| - |createLowComplexityNormalBasis| |expand| |rationalPoint?| |iCompose| - |monomial| |totolex| |dilog| |rightRank| |roughBase?| - |reduceByQuasiMonic| |complexRoots| |subPolSet?| |repSq| |filterWhile| - |divisors| |maxint| |multivariate| |OMputEndBind| |close| |sin| - |copies| |modularFactor| |rightUnits| |leftReducedSystem| |contains?| - F |style| |filterUntil| |variables| |reverseLex| |iterationVar| - |numberOfFractionalTerms| |cos| |edf2efi| |OMgetApp| - |definingPolynomial| |shuffle| |select| |patternMatch| - |primPartElseUnitCanonical| |tanQ| |display| |tan| |eof?| |stFunc1| - |mapMatrixIfCan| |e04mbf| |clearTable!| |lexTriangular| |symbolTable| - |stoseInvertibleSet| |tubeRadiusDefault| |ramifiedAtInfinity?| |cot| - |primintegrate| |divideIfCan| |bezoutResultant| |queue| |real?| - |ratPoly| |scanOneDimSubspaces| |uniform01| |wreath| |sec| |external?| - |minPoints| |imagj| |status| |collectQuasiMonic| |att2Result| - |pushFortranOutputStack| |e02dcf| |csc| |moebiusMu| |zero?| |cAsec| - |axes| |controlPanel| |popFortranOutputStack| |mapUnivariateIfCan| - |drawToScale| |optpair| |debug| |taylor| |pseudoQuotient| |asin| - |predicate| |cLog| |elements| |generalizedContinuumHypothesisAssumed?| - |tubeRadius| |tryFunctionalDecomposition?| |mainMonomial| - |outputAsFortran| |factorials| |symmetricGroup| D |laurent| - |leadingExponent| |input| |acos| |edf2ef| |isOpen?| |acosIfCan| - |internalLastSubResultant| |sin2csc| |pair?| |iidsum| |enterInCache| - |puiseux| |library| |fixedDivisor| |atan| |constantOperator| - |normalElement| EQ |makeCos| |curveColorPalette| |poisson| |lllp| - |acot| |insertRoot!| |mergeDifference| |subresultantSequence| - |karatsubaOnce| |janko2| |solve1| |getSyntaxFormsFromFile| |inv| - |pdf2df| |asec| |OMgetEndAtp| |orthonormalBasis| |lazyPseudoDivide| - |shiftRight| |messagePrint| |integerIfCan| |lazyPquo| |ground?| - |overlabel| |acsc| |replace| |zeroSetSplitIntoTriangularSystems| - |removeSuperfluousCases| |mainExpression| |leftNorm| - |leftScalarTimes!| |subResultantsChain| |ground| |set| |sinh| - |bfEntry| |integral?| |zeroVector| |solveRetract| - |stoseSquareFreePart| |relerror| |abs| |exponent| |leadingMonomial| - |sylvesterSequence| |cosh| |resultantEuclideannaif| |leftFactorIfCan| - |binaryTree| |OMputFloat| |double| |algebraic?| |OMgetFloat| |randomR| - |ceiling| |leadingCoefficient| |generalInfiniteProduct| |tanh| - |rotatex| |OMgetBVar| |readable?| |abelianGroup| |size| - |noLinearFactor?| |algintegrate| |writeBytes!| |endOfFile?| - |primitiveMonomials| |parameters| |coth| |boundOfCauchy| - |makingStats?| |leftDivide| |deepestTail| |rootRadius| |parent| - |edf2df| |getPickedPoints| |print| |reductum| |sech| |startPolynomial| - |complexForm| |groebnerFactorize| |primitivePart!| |extendedEuclidean| - |dualSignature| |mapDown!| |fixedPoint| |resolve| |subset?| |csch| - |groebgen| |subCase?| |OMReadError?| |halfExtendedSubResultantGcd2| - |insertionSort!| |OMgetAttr| |extract!| |f04qaf| |rquo| |has?| |asinh| - |mapdiv| |true| |sylvesterMatrix| |quotient| |category| |charpol| - |outputMeasure| |vector| |primextendedint| |OMgetEndObject| - |curveColor| |cAsinh| |domain| |monomialIntPoly| |antisymmetric?| - |choosemon| |companionBlocks| |optional| |evenlambert| |recolor| - |differentiate| |setMinPoints| |karatsuba| |truncate| |externalList| - |package| |splitConstant| |complexElementary| |minimumExponent| RF2UTS - |iicsch| |declare!| |viewWriteAvailable| |nand| |matrixConcat3D| - |OMopenString| |insert| |e02ajf| |lex| |f02akf| |radicalEigenvalues| - |signAround| |f04adf| |zeroDim?| |revert| |pureLex| |show| - |nonLinearPart| |fortranComplex| |OMputBVar| |weierstrass| |OMreadStr| - |lazyEvaluate| |c06gcf| |quotedOperators| |search| |OMputEndBVar| - |rightRegularRepresentation| |f01qdf| |integralRepresents| |max| - |trivialIdeal?| |node| |semiResultantReduitEuclidean| |OMgetObject| - |closeComponent| |clearDenominator| |trace| - |semiResultantEuclideannaif| |nextLatticePermutation| - |rightTraceMatrix| |viewport2D| |s15adf| |componentUpperBound| |plot| - |addPointLast| |iiatan| |tableForDiscreteLogarithm| |collect| - |imports| |generalTwoFactor| |yCoordinates| |f04jgf| |f02awf| - |OMputAttr| |setClipValue| |stop| |contract| |leadingCoefficientRicDE| - |monomials| |bivariatePolynomials| |numberOfCycles| |OMputObject| - |prinshINFO| |multiple?| |rCoord| |elaborate| |cycleElt| |weighted| - |root?| |decimal| |segment| |Lazard| |getProperty| |bat1| - |quasiMonicPolynomials| |formula| |flatten| |differentialVariables| - |c02aff| |whitePoint| |bounds| |parseString| |genericRightNorm| - |isMult| |infRittWu?| |irForm| |firstSubsetGray| |LiePolyIfCan| - |mapExponents| |s19adf| |hue| |lyndon?| |semicolonSeparate| - |quasiMonic?| |c06gqf| |isQuotient| |space| |monomRDEsys| |cAcot| - |baseRDE| |integrate| |var1StepsDefault| |transform| |s17def| - |inverseColeman| |newReduc| |mkPrim| |lookup| |firstNumer| - |rootKerSimp| |algebraicVariables| |subresultantVector| |readLine!| - |sumOfDivisors| |nrows| |comparison| |removeSquaresIfCan| |calcRanges| - |medialSet| |variationOfParameters| |createLowComplexityTable| - |extractTop!| |squareMatrix| |monomial?| |ncols| |unknownEndian| - |leviCivitaSymbol| |repeatUntilLoop| |rightNorm| |bivariateSLPEBR| - |setImagSteps| |FormatRoman| |ode1| |expintegrate| |lfunc| - |selectIntegrationRoutines| |groebner| |perspective| |symbolTableOf| - |seriesSolve| |monicDivide| |unitCanonical| |extendedSubResultantGcd| - |height| |units| |log10| |solveLinearPolynomialEquationByFractions| - |selectsecond| |rootPoly| |euclideanNormalForm| |argumentList!| - |equation| |every?| |vconcat| |algebraicCoefficients?| |composite| - |bitand| |s15aef| |aCubic| |hspace| |roman| |laguerreL| - |genericRightMinimalPolynomial| |OMclose| |printInfo!| |extractIndex| - |outerProduct| |bitior| |ScanFloatIgnoreSpacesIfCan| |setTopPredicate| - |rationalPoints| |setOrder| |radicalRoots| |Is| |readBytes!| - |inGroundField?| |pascalTriangle| |leaves| |ellipticCylindrical| - |writeLine!| |PollardSmallFactor| |elRow2!| |HermiteIntegrate| - |var2StepsDefault| |dequeue| |limitPlus| |makeGraphImage| |coerceP| - |rightRankPolynomial| |cSec| |expint| |cyclic| 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|evaluateInverse| |cyclicEntries| |besselJ| |dmp2rfi| |integers| - |exists?| |discreteLog| |stopTableInvSet!| |setAdaptive3D| - |coefficient| |adaptive?| |alternating| |tanintegrate| |mainVariable| - |doubleComplex?| |dioSolve| |genericLeftTraceForm| - |halfExtendedResultant2| |cscIfCan| |iidprod| Y |exponentialOrder| - |psolve| |returnType!| |littleEndian| |linearAssociatedOrder| |sample| - |label| |disjunction| |lowerCase!| |numFunEvals3D| |cCsch| |iiacot| - |makeViewport2D| |characteristicSet| |computeCycleEntry| - |semiResultantEuclidean2| |constantToUnaryFunction| |d02bbf| - |swapColumns!| |setLabelValue| |testModulus| |e01bhf| |pmintegrate| - |trailingCoefficient| |pow| |palginfieldint| |shiftLeft| |s18adf| - |createThreeSpace| |copy!| |laguerre| |commutativeEquality| |leftOne| - |result| |printHeader| |brillhartIrreducible?| |open?| |f02ajf| - |fortranLiteral| |separant| |swapRows!| |coerceS| |totalDifferential| - |gcdcofact| |setMaxPoints| |collectUnder| |factorSquareFree| - 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|dim| |case| |inRadical?| - |asinhIfCan| |zoom| |assert| |deleteProperty!| |partialDenominators| - |readUInt16!| |port| |prevPrime| |sec2cos| |pattern| |Zero| |inR?| - |stiffnessAndStabilityFactor| |palgint0| |univariate?| - |associatedSystem| |d01bbf| |hypergeometric0F1| |substitute| |One| - |basicSet| |front| |deref| |tab1| |prinpolINFO| |matrixGcd| |t| - |kroneckerDelta| |shufflein| |cAtanh| |shift| NOT |setProperties| - |identitySquareMatrix| |youngDiagram| |output| |factorByRecursion| - |identification| |asechIfCan| |LyndonWordsList1| |bracket| |multiset| - OR |cAcoth| |hMonic| |addMatchRestricted| |concat!| |palgintegrate| - |nodes| |asinIfCan| |subspace| |message| |graphCurves| AND |nary?| - |putProperty| |dominantTerm| |symmetricPower| |collectUpper| |iitan| - |whatInfinity| |ffactor| |numericIfCan| |cCsc| |LazardQuotient2| - |countRealRootsMultiple| |nil?| |virtualDegree| |mirror| - |divisorCascade| |readInt8!| |lifting| |linearlyDependentOverZ?| - |unitNormalize| |elt| 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|dimensions| <= |infLex?| - |limit| |axesColorDefault| |arbitrary| |target| |flexible?| - |linkToFortran| |cycleLength| |fracPart| |OMputInteger| - |roughEqualIdeals?| |applyRules| >= |shellSort| |Hausdorff| - |asecIfCan| |tex| |complexIntegrate| |directSum| |leastMonomial| - |belong?| |hostByteOrder| |characteristicPolynomial| |expr| |iisinh| - |elRow1!| |f01qef| |chineseRemainder| |leftMinimalPolynomial| - |doubleFloatFormat| |outputAsScript| |consnewpol| |normal| - |diagonalMatrix| |central?| |balancedFactorisation| |cyclotomic| - |pmComplexintegrate| |convergents| |eigenvector| |rowEch| - |safeCeiling| |linear| |clearFortranOutputStack| |iiacosh| + - |hyperelliptic| |approxNthRoot| |c06ebf| |type| |corrPoly| - |numberOfMonomials| |modularGcd| |addiag| |getCode| - |lazyPseudoQuotient| - |float| |elColumn2!| |polygamma| LODO2FUN - |increase| |toScale| |semiDiscriminantEuclidean| |upperCase!| - |polynomial| |nullSpace| |variable| |basisOfCommutingElements| / - |raisePolynomial| |permutationGroup| |isTimes| |critT| |e04ucf| - |leftTrace| |divideIfCan!| |linearDependence| |iterators| - |splitDenominator| |thetaCoord| |viewpoint| |cdr| |dictionary| - |entry?| |traceMatrix| |c06fpf| |maxdeg| |monicDecomposeIfCan| - |component| |hasPredicate?| |arrayStack| |selectFiniteRoutines| - |cfirst| |associatorDependence| |startTableInvSet!| - |createMultiplicationMatrix| |euclideanGroebner| - |cyclotomicFactorization| |roughSubIdeal?| |varselect| |cap| |atoms| - |groebSolve| |computePowers| |id| |slex| |f07adf| |printStatement| - |recur| |conditionP| |value| |fillPascalTriangle| |polCase| - |frobenius| |length| |symbol| |padecf| |coerceImages| |lo| |internal?| - |leftUnit| |resultantReduitEuclidean| |yCoord| |measure2Result| - |figureUnits| |generalizedInverse| |scripts| |expression| |sinhcosh| - |KrullNumber| |mapSolve| |mapmult| |bezoutMatrix| |complexLimit| - |scripted?| |basisOfLeftNucleus| |innerSolve| |distance| |integer| - |power| |factorial| |OMgetAtp| |errorKind| GE - |generalizedContinuumHypothesisAssumed| |iiperm| |cyclicCopy| |weight| - |e02bef| |lowerPolynomial| |heap| |e02aef| |isAbsolutelyIrreducible?| - GT |radicalEigenvector| |internalAugment| |nthCoef| - |possiblyNewVariety?| |getExplanations| |basisOfCenter| |repeating?| - |randomLC| |polynomialZeros| LE |drawComplexVectorField| - |factorsOfCyclicGroupSize| |explogs2trigs| |numberOfIrreduciblePoly| - |readUInt32!| |deepExpand| |isPlus| |imagJ| |car| LT |s17ahf| - |evenInfiniteProduct| |s18dcf| |leadingIdeal| |pdct| |depth| |inspect| - |coshIfCan| |hconcat| |jordanAdmissible?| |lieAlgebra?| |nthExponent| - |rational?| |eigenvectors| |setelt!| |socf2socdf| |curve?| - |expressIdealMember| |numberOfOperations| |makeEq| |s17dlf| - |OMputBind| |positiveRemainder| |numberOfChildren| |critB| |setUnion| - |selectOrPolynomials| |bandedJacobian| |airyBi| |pointSizeDefault| - |logGamma| |lflimitedint| |inputOutputBinaryFile| |cubic| |keys| - |rightRemainder| |baseRDEsys| |leftRegularRepresentation| - |characteristicSerie| |changeThreshhold| |definingEquations| - |removeSinhSq| |tanhIfCan| |graphs| |bigEndian| |index| |irVar| - |perfectSquare?| |randnum| |complexEigenvectors| |sqfrFactor| - |plenaryPower| |sinhIfCan| |numeric| |pole?| |lastSubResultant| - |leftRecip| |nullary?| |s17aef| |OMserve| |genericLeftNorm| |radical| - |divergence| |bumptab| |explimitedint| |hasHi| |fprindINFO| - |linearlyDependent?| |exptMod| |c06ecf| |iiasin| |Nul| |quotientByP| - |trapezoidal| |pair| |diagonalProduct| |escape| |tree| |open| - |rangePascalTriangle| |listOfMonoms| |vark| |validExponential| - |s17dhf| |bright| |approximants| |e02ddf| |squareFreePart| |d01gaf| - |sturmSequence| |vertConcat| |setMinPoints3D| |duplicates| - |binomThmExpt| |lazyIrreducibleFactors| - |removeSuperfluousQuasiComponents| |mpsode| |viewDefaults| |spherical| - |iiasec| |rationalApproximation| |FormatArabic| |leadingIndex| - |mapCoef| |eval| |initTable!| |tanNa| |iFTable| |outputBinaryFile| 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|ipow| |cyclicParents| |exprToUPS| |d03eef| |rem| |errorInfo| - |myDegree| |OMopenFile| |makeVariable| |findCycle| |mainMonomials| - |modifyPoint| |minIndex| |iisqrt2| |rk4qc| |quickSort| - |probablyZeroDim?| |cartesian| |quo| |clearTheIFTable| - |rewriteSetByReducingWithParticularGenerators| |primintfldpoly| - |stoseInvertibleSetsqfreg| |setClosed| |varList| |meshFun2Var| - |setDifference| |maxPoints3D| |shiftRoots| |compose| |outputList| - |normalizeIfCan| |rightLcm| |iipow| |d01amf| |environment| - |wordInGenerators| |lcm| |principalIdeal| |normInvertible?| - |tanh2trigh| |computeInt| |increment| |overlap| |delete| |div| - |refine| |viewDeltaYDefault| |OMgetEndAttr| |cotIfCan| |qinterval| - |retractable?| |isExpt| |isAtom| |exactQuotient!| |f02bjf| |postfix| - |fullPartialFraction| |exquo| |headAst| |s21bdf| |generateIrredPoly| - |atanhIfCan| |charthRoot| |intersect| |principalAncestors| |zerosOf| - |getMultiplicationTable| |append| |nor| |denominators| |unitNormal| ~= - 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|irreducibleFactors| |polygon?| |cycleTail| - |monom| |lift| |leftRank| |powern| |getConstant| |positiveSolve| - |nullity| |lastSubResultantElseSplit| |powerSum| |swap| - |halfExtendedResultant1| |c02agf| |listRepresentation| |property| - |loadNativeModule| |omError| |reduce| |algebraicDecompose| |point| - |polyPart| |unparse| |screenResolution3D| |makeprod| |position!| - |coth2tanh| |f01mcf| |supRittWu?| |stopTable!| - |nextNormalPrimitivePoly| |genericLeftTrace| |getButtonValue| |c06gbf| - |parametric?| |acscIfCan| |const| |laurentRep| |option?| |variable?| - |lfinfieldint| |coleman| |f07fef| |surface| |leadingTerm| |acoshIfCan| - |s14abf| |OMgetBind| |antiCommutative?| |e04ycf| |supersub| |minPoly| - |series| |dimensionOfIrreducibleRepresentation| |rroot| |palgint| - |intensity| |measure| |selectfirst| |LazardQuotient| |stFuncN| |shade| - |comment| |log| |permutationRepresentation| |createIrreduciblePoly| - |mathieu22| |phiCoord| |viewDeltaXDefault| |center| |push| - |tubePoints| |fortranReal| |OMputEndAtp| |denomLODE| |setelt| |hex| - |bitTruth| |e02gaf| |rotatez| |list?| |computeCycleLength| |select!| - |singRicDE| |numberOfComponents| |polygon| |removeCosSq| - |structuralConstants| |currentSubProgram| |algDsolve| |scale| - |checkForZero| |solveid| |f2df| |direction| |symmetricProduct| |min| - |autoReduced?| |makeUnit| |dihedralGroup| |sumOfSquares| - |setMaxPoints3D| |logpart| |redmat| |irreducibleRepresentation| - |selectPDERoutines| |infieldIntegrate| |normalise| |clearTheFTable| - |normalDeriv| |OMlistCDs| |factorOfDegree| |cross| |realElementary| - |airyAi| |functorData| |s17adf| |idealiser| |f07fdf| |inverseLaplace| - |meshPar1Var| |showTheSymbolTable| |rspace| |shape| |jacobian| - |closedCurve| |startTableGcd!| |besselI| |makeCrit| |atanIfCan| - |d02gbf| |realEigenvectors| |d02kef| |partitions| |ratDenom| |tanSum| - |ef2edf| |components| |minPol| |byte| |categoryMode| |laplacian| - |bernoulli| |setLength!| |OMgetEndApp| |e04gcf| |getMatch| |badValues| - |realSolve| |zero| |alphanumeric| |parabolicCylindrical| |reverse| - |e02zaf| |e04fdf| |s19abf| |weights| |curryRight| |normFactors| - |hasoln| |presub| |patternMatchTimes| |coordinates| |eq?| - |getZechTable| |li| |positive?| |henselFact| |An| |startStats!| - |branchPoint?| |s01eaf| |paren| |extractProperty| |And| |multisect| - |basisOfRightNucloid| |decrease| |enumerate| |chvar| |unknown| - |completeEval| |d02bhf| |viewPhiDefault| |factorPolynomial| |Or| - |stosePrepareSubResAlgo| |presuper| |physicalLength| |sech2cosh| - |taylorIfCan| |unitsColorDefault| |LyndonWordsList| |c05nbf| |pastel| - |trim| |Not| |nthFractionalTerm| |radix| |Aleph| |alternative?| - |characteristic| |invertibleElseSplit?| |d03edf| |cyclicEqual?| - |digit| |physicalLength!| |fractRagits| |scopes| |innerint| - |exprToGenUPS| |members| |nthRoot| |irDef| |nextColeman| |write!| - |int| |pToHdmp| |read!| |resetBadValues| |complexZeros| |mapGen| - |rubiksGroup| |chiSquare| |cSech| |norm| |limitedIntegrate| |epilogue| - |aromberg| |imagk| |singularitiesOf| |c06fuf| |partialQuotients| - |e01sbf| |nonSingularModel| |voidMode| |d02gaf| |graeffe| |s18aff| - |purelyAlgebraic?| |lazyPrem| |incrementKthElement| - |fortranCarriageReturn| |null?| |taylorQuoByVar| |powers| |diag| - |iicoth| |trigs| |initiallyReduced?| |factor1| |OMputAtp| |test| - |jordanAlgebra?| |hermiteH| |scan| |moebius| |remove| |iExquo| - |f02agf| |exportedOperators| |linearAssociatedExp| |f02aef| - |univariatePolynomialsGcds| |idealiserMatrix| |s17acf| |mindegTerm| - |var1Steps| |nextIrreduciblePoly| |e01sff| |integralMatrixAtInfinity| - |d01aqf| |doubleRank| |determinant| |radPoly| |ParCondList| - |multiplyExponents| |last| |sign| |extendIfCan| |subResultantGcd| - |sorted?| |logical?| |commonDenominator| UP2UTS |integralBasis| - |assoc| |fintegrate| |elementary| |trigs2explogs| - |absolutelyIrreducible?| |critMonD1| |range| - |removeIrreducibleRedundantFactors| |internalInfRittWu?| |Beta| - |condition| |tower| |bringDown| |deleteRoutine!| |mainVariables| - |SturmHabichtMultiple| |gramschmidt| |getOperator| |operators| - |limitedint| |close!| |remainder| |zeroMatrix| |infieldint| - |subTriSet?| |precision| |quatern| |minimize| |infinityNorm| |prefix| - |setColumn!| |iicsc| |mat| |setref| |product| |iisin| |besselY| - |generalLambert| |setPredicates| |recip| |cylindrical| |e02baf| - |trueEqual| |elaboration| |factorsOfDegree| |dAndcExp| - |nextPrimitivePoly| |divide| |obj| |parabolic| |s20adf| |eq| - |polyRicDE| |putGraph| |Ei| |solveInField| |perfectNthRoot| - |coefficients| |eisensteinIrreducible?| |low| |cache| |iter| |exprex| - |nextsousResultant2| |one?| |integralLastSubResultant| - |complexNumeric| |OMconnInDevice| |fractRadix| |constantIfCan| - |d01gbf| |optAttributes| |invertible?| |cyclePartition| |compound?| - |c06eaf| |stoseInvertible?| |sqfree| |monomRDE| |prime?| - |pseudoDivide| |drawStyle| |s21bcf| |oddlambert| |sin?| |f02axf| - |polarCoordinates| |updatF| |f02wef| |OMwrite| |setPoly| |hermite| - |reduceBasisAtInfinity| |crest| |invertibleSet| |transcendenceDegree| - |separateDegrees| |primlimitedint| |nextNormalPoly| |redPo| - |rightQuotient| |graphStates| |useEisensteinCriterion| - |removeRoughlyRedundantFactorsInContents| |splitNodeOf!| |lowerBound| - |imagK| |quadratic?| |sequence| |createNormalElement| |llprop| - |aspFilename| |pseudoRemainder| |subst| |e02bbf| |smith| - |genericRightTrace| |changeWeightLevel| |numberOfNormalPoly| |cCos| - |LiePoly| |isList| |drawComplex| |wholeRagits| |factorGroebnerBasis| - |mappingAst| |exp| |rowEchLocal| |oddintegers| |f04axf| |innerSolve1| - |d01fcf| |substring?| |stFunc2| |character?| |dmpToHdmp| |bytes| - |selectMultiDimensionalRoutines| |scalarTypeOf| |csch2sinh| - |radicalSolve| |map| |reverse!| |iitanh| |getOperands| |rootBound| - |minRowIndex| |interReduce| |branchIfCan| |algSplitSimple| |Si| - |squareFreeFactors| |table| |generator| |linearPart| |df2mf| - |mainDefiningPolynomial| |suffix?| |zeroDimPrimary?| |d02raf| |nil| - |changeNameToObjf| |setCondition!| |represents| |f04faf| - |GospersMethod| |new| |acosh| |any| |elliptic| |regime| |atom?| - |genericRightDiscriminant| |indicialEquations| |bezoutDiscriminant| - |iicosh| |maxPoints| |compile| |monicLeftDivide| |opeval| |atanh| - |primextintfrac| |makeMulti| |csubst| |prefix?| |basisOfRightNucleus| - |nodeOf?| |objects| |problemPoints| |unit| |reduceLODE| |fixPredicate| - |LyndonCoordinates| |acoth| |prod| |normDeriv2| |setValue!| |cSinh| - |point?| |base| |approximate| |addPoint| |typeList| |sortConstraints| - |multiEuclidean| |find| |convert| |asech| - |initializeGroupForWordProblem| |alternatingGroup| |setchildren!| - |zeroSquareMatrix| |changeVar| |complex| |constantRight| |exQuo| - |cCosh| |sh| |hasTopPredicate?| |create| |lfintegrate| |s17ajf| - |zeroOf| |doubleDisc| |padicallyExpand| |setEpilogue!| |perfectSqrt| - |noValueMode| |numberOfHues| |multiple| |children| |mathieu23| - |multiplyCoefficients| |accuracyIF| |euclideanSize| |failed| |before?| - |defineProperty| |OMgetEndBind| |interpretString| - |createPrimitiveElement| |applyQuote| |f02xef| |fibonacci| - |leftExactQuotient| |bipolarCylindrical| |cAcsc| |alphanumeric?| - |BumInSepFFE| |localUnquote| |lowerCase?| |typeLists| |infix?| |orbit| - |seed| |cot2tan| |iisec| |eyeDistance| |outputArgs| |sinIfCan| - |conical| |degreePartition| |monicCompleteDecompose| |incr| |mask| - |prologue| |lazyGintegrate| |rightFactorIfCan| |lepol| |lyndon| - |updatD| |c06fqf| |distdfact| |rewriteIdealWithHeadRemainder| - |univariatePolynomial| |ruleset| |hi| |addmod| |Ci| |anticoord| - |showTheFTable| |OMsupportsSymbol?| |ScanFloatIgnoreSpaces| - |tanh2coth| |multMonom| |squareFree| |is?| |left| |summation| - |minimumDegree| |lambert| |subResultantGcdEuclidean| |allRootsOf| - |getIdentifier| |dot| |backOldPos| |denominator| |ddFact| |right| - |f01rdf| |maxColIndex| |linearDependenceOverZ| |setStatus!| - |printTypes| |newLine| |singleFactorBound| |rightRecip| |Frobenius| - |chebyshevT| |suchThat| |degreeSubResultantEuclidean| |primaryDecomp| - |showTheRoutinesTable| |morphism| |subResultantChain| |quadraticNorm| - |quartic| |clip| |padicFraction| |cRationalPower| |blue| |nsqfree| - |rename| |exprToXXP| |mainPrimitivePart| |previous| |delta| |node?| - |bumptab1| |callForm?| |linears| |constantKernel| |stirling1| - |typeForm| |gbasis| |degree| |primeFrobenius| |wholeRadix| |initial| - |df2st| |rightMinimalPolynomial| |dark| |move| |numFunEvals| - |isConnected?| |freeOf?| |palgLODE| |createMultiplicationTable| - |jacobiIdentity?| |next| |f01bsf| |badNum| |setRealSteps| |ldf2vmf| - |size?| |datalist| |key| |rightZero| |leftRemainder| |midpoint| - |localReal?| |gradient| |attributeData| |interval| - |cyclotomicDecomposition| |tanAn| |ksec| |normalDenom| |isobaric?| - |headReduced?| |generic| |derivationCoordinates| |conjug| |listLoops| - |forLoop| |withPredicates| |screenResolution| |filename| - |uncouplingMatrices| |ricDsolve| |resetVariableOrder| |ScanArabic| - |commaSeparate| |OMgetType| |sncndn| |pdf2ef| |just| |d01akf| - |particularSolution| |csc2sin| |radicalOfLeftTraceForm| |quasiRegular| - |s14aaf| |removeSinSq| |index?| |ran| |less?| |resultantEuclidean| - |pointColorDefault| |cot2trig| |parse| |makeYoungTableau| - |inverseIntegralMatrixAtInfinity| |setPrologue!| |triangular?| - |SturmHabichtCoefficients| |multinomial| |lambda| |code| - |supDimElseRittWu?| |lSpaceBasis| |bivariate?| |distFact| |rank| - |generate| |UpTriBddDenomInv| |integralMatrix| |bothWays| - |linearAssociatedLog| |triangularSystems| |pushdterm| |resultant| - |curve| |LowTriBddDenomInv| |e04jaf| |indicialEquationAtInfinity| - |torsion?| |conjunction| |ref| |standardBasisOfCyclicSubmodule| - |oneDimensionalArray| |symbolIfCan| |lookupFunction| |critM| - |getMultiplicationMatrix| |incrementBy| |OMconnectTCP| |printCode| - |float?| |prem| |upDateBranches| |e02ahf| |lineColorDefault| - |stoseInvertible?reg| |pointData| |representationType| |extractClosed| - |reorder| |e02agf| |stirling2| |logIfCan| |equality| - |prepareDecompose| |showArrayValues| |coHeight| |completeSmith| - |d03faf| |bfKeys| |submod| |rowEchelon| |internalZeroSetSplit| - |subSet| |cyclic?| |integralCoordinates| |tan2cot| |hexDigit| - |lintgcd| |symbol?| |printInfo| |removeCoshSq| |createPrimitivePoly| - |elseBranch| |associatedEquations| |leastAffineMultiple| - |basisOfMiddleNucleus| |extendedint| |rightExactQuotient| |gcdprim| - |rightPower| |hexDigit?| |OMputSymbol| |squareFreePrim| - |getVariableOrder| |complexSolve| |duplicates?| |currentCategoryFrame| - |OMgetError| |options| |solveLinearPolynomialEquationByRecursion| - |homogeneous?| |lists| |d02cjf| |infix| |innerEigenvectors| |po| - |tail| |integral| |dom| |subscriptedVariables| |palglimint0| - |irreducibleFactor| |mergeFactors| |curry| |tan2trig| - |indiceSubResultantEuclidean| |colorDef| |coord| |htrigs| - |completeHensel| |arg1| |entry| |support| |var2Steps| |identityMatrix| - |semiSubResultantGcdEuclidean1| |stoseLastSubResultant| - |rightCharacteristicPolynomial| |nil| |infinite| |arbitraryExponent| + |Record| |Union| |computeCycleEntry| |stoseIntegralLastSubResultant| + |lambert| |insertTop!| |arg2| |f02agf| |stronglyReduce| + |viewWriteAvailable| |string| |trunc| |integralAtInfinity?| + |makeResult| |upperCase!| |minimalPolynomial| + |semiResultantEuclidean2| |subResultantGcdEuclidean| |showAllElements| + |nand| |readLineIfCan!| |exportedOperators| |writable?| |say| + |nullSpace| |scalarMatrix| |constantToUnaryFunction| |imagE| + |allRootsOf| |solveLinear| |conditions| |matrixConcat3D| + |setVariableOrder| |linearAssociatedExp| |exponential1| + |basisOfCommutingElements| |palgRDE0| |d02bbf| + |solveLinearPolynomialEquation| |getIdentifier| |complementaryBasis| + |title| |f02aef| |match| |OMopenString| |insertMatch| + |primitiveElement| |reset| |raisePolynomial| |birth| |swapColumns!| + |rk4a| |arguments| |dot| |maximumExponent| |e02ajf| |mainContent| + |univariatePolynomialsGcds| |digamma| |inc| |permutationGroup| + |twoFactor| |setLabelValue| |dequeue!| |backOldPos| |idealiserMatrix| + |lighting| |s18acf| |lex| |leadingSupport| |write| |isTimes| + |showClipRegion| |testModulus| |hessian| |denominator| |e| |iilog| + |isNot| |save| |f02akf| |adaptive| |s17acf| |critT| + |extractSplittingLeaf| |e01bhf| |split| |ddFact| |mapExpon| |nothing| + |diff| |radicalEigenvalues| |cycles| |mindegTerm| |e04ucf| |argscript| + |iflist2Result| |pmintegrate| |f01rdf| |iiacsc| |binding| |signAround| + |var1Steps| |reseed| |leftTrace| |beauzamyBound| |rightDiscriminant| + |trailingCoefficient| |maxColIndex| |indices| |complete| |f04adf| + |top| |nextIrreduciblePoly| |Vectorise| |safetyMargin| |divideIfCan!| + |leastPower| |pow| |linearDependenceOverZ| |continue| |e02akf| + |fortranLogical| |zeroDim?| |generalizedEigenvectors| |e01sff| + |readUInt8!| |linearDependence| |palginfieldint| |content| + |setStatus!| |sn| |extensionDegree| |se2rfi| |revert| |principal?| + |integralMatrixAtInfinity| |parts| |f02aaf| |splitDenominator| + |enterPointData| |shiftLeft| |printTypes| |typeForm| |mdeg| |reopen!| + |pureLex| |palgextint0| |d01aqf| ** |hash| |functionIsFracPolynomial?| + |thetaCoord| |horizConcat| |s18adf| |newLine| |universe| + |nonLinearPart| |squareFreeLexTriangular| |doubleRank| + |numberOfComposites| |count| |linearElement| |viewpoint| + |separateFactors| |createThreeSpace| |singleFactorBound| |datalist| + |makeTerm| |fortranComplex| |lagrange| |bandedHessian| |determinant| + |divisor| |cdr| |copy!| |f04atf| |rightRecip| |primlimintfrac| + |bipolar| |OMputBVar| |radPoly| |getDatabase| |dictionary| + |ip4Address| |squareTop| |laguerre| |Frobenius| |constant| + |getGoodPrime| |green| |weierstrass| |tablePow| |ParCondList| |entry?| + |dimensionsOf| |iifact| |commutativeEquality| |chebyshevT| + |integralBasisAtInfinity| |returnTypeOf| |mantissa| |OMreadStr| + |endSubProgram| |multiplyExponents| |outputList| |traceMatrix| + |chiSquare1| |leftOne| |addBadValue| |degreeSubResultantEuclidean| + |stripCommentsAndBlanks| |lazyEvaluate| |sts2stst| |makeFR| |sign| + |c06fpf| |romberg| |numberOfFactors| |printHeader| |primaryDecomp| + |rank| |clipBoolean| |RittWuCompare| |c06gcf| |e01saf| |lexGroebner| + |extendIfCan| |asimpson| |maxdeg| |brillhartIrreducible?| |implies| + |showTheRoutinesTable| |check| |quotedOperators| |SturmHabicht| + |completeEchelonBasis| |subResultantGcd| |OMsend| + |monicDecomposeIfCan| |neglist| |open?| |morphism| |basisOfCentroid| + |legendre| |reflect| |OMputEndBVar| |sorted?| |resetNew| |component| + F2FG |decreasePrecision| |f02ajf| |subResultantChain| + |rightRegularRepresentation| |chebyshevU| |logical?| |red| GF2FG + |normalizedDivide| |checkPrecision| |hasPredicate?| |noKaratsuba| + |fortranLiteral| |firstDenom| |quadraticNorm| |diagonals| |heapSort| + |f01qdf| |cPower| |commonDenominator| |arrayStack| |isOp| |separant| + |nthr| |quartic| |leader| |e02bdf| |integralRepresents| |getBadValues| + |dual| UP2UTS |nthRootIfCan| |selectFiniteRoutines| |frst| |swapRows!| + |clip| |oddInfiniteProduct| |setEmpty!| |solid| |max| |rename!| + |integralBasis| |binarySearchTree| |categories| + |wordsForStrongGenerators| |cfirst| |coerceS| |lexico| |padicFraction| + |numer| |laplace| |lists| |retractIfCan| |usingTable?| |trivialIdeal?| + |member?| |possiblyInfinite?| |fintegrate| |associatorDependence| + |changeMeasure| |totalDifferential| |child?| |cRationalPower| |denom| + |s14baf| |complexEigenvalues| |extension| + |semiResultantReduitEuclidean| |elementary| |rightTrace| |polar| + |startTableInvSet!| |gcdcofact| |legendreP| |blue| |mathieu11| + |atrapezoidal| |OMgetObject| |algint| |trigs2explogs| + |createMultiplicationMatrix| |pushucoef| |createPrimitiveNormalPoly| + |setMaxPoints| |nsqfree| |pi| |in?| |closeComponent| + |absolutelyIrreducible?| |secIfCan| |euclideanGroebner| |closedCurve?| + |collectUnder| |toseLastSubResultant| |infinity| |rename| |jacobi| + |complexNumericIfCan| |s21baf| |clearDenominator| |critMonD1| + |genericLeftDiscriminant| |concat| |step| |cyclotomicFactorization| + |numericalIntegration| |iisqrt3| |factorSquareFree| |exprToXXP| + |clipParametric| |unaryFunction| |nextPrimitiveNormalPoly| + |semiResultantEuclideannaif| |range| |unrankImproperPartitions0| + |droot| |roughSubIdeal?| |bernoulliB| |continuedFraction| + |mainPrimitivePart| |coordinate| |internalIntegrate| + |nextLatticePermutation| |hdmpToP| |removeIrreducibleRedundantFactors| + |useEisensteinCriterion?| |denomRicDE| |kernel| |node?| |discriminant| + |simpleBounds?| |rightTraceMatrix| |pquo| |internalInfRittWu?| |init| + |nextSublist| |key?| |f04mbf| |list| |bumptab1| |ptree| + |topFortranOutputStack| |removeConstantTerm| |viewport2D| |number?| + |Beta| |lhs| |balancedBinaryTree| |showFortranOutputStack| |rk4| + |draw| |callForm?| |polyRDE| |leadingBasisTerm| |s15adf| |clearCache| + |bringDown| |fullDisplay| |rhs| |f01ref| |nthExpon| |iteratedInitials| + |linears| |rootProduct| |deleteRoutine!| |SturmHabichtSequence| + |derivative| |adaptive3D?| |isAnd| |constantKernel| |qroot| + |integral?| |semiResultantEuclidean1| |ratDsolve| |mainVariables| + |currentEnv| |systemSizeIF| |aLinear| |tableau| |stirling1| + |operation| |traverse| |zeroVector| |makeViewport3D| + |SturmHabichtMultiple| |shallowCopy| |resultantnaif| |charClass| + |irreducibleFactors| |makeObject| |gbasis| |parametersOf| + |solveRetract| |initials| |computeBasis| |gramschmidt| |middle| + |directory| |degree| |coef| |sizePascalTriangle| |exactQuotient| + |stoseSquareFreePart| |totalDegree| |getOperator| |expintfldpoly| + |powerAssociative?| |userOrdered?| |primeFrobenius| |pointPlot| + |relerror| |hcrf| |operators| |harmonic| |restorePrecision| + |schwerpunkt| |fortranCharacter| |wholeRadix| |reducedQPowers| + |stoseInvertible?sqfreg| |abs| |limitedint| |pushNewContour| + |bubbleSort!| |inconsistent?| |ode2| |df2st| |torsionIfCan| + |reciprocalPolynomial| |exponent| |kind| |evaluate| |setErrorBound| + |viewSizeDefault| |rightMinimalPolynomial| + |primPartElseUnitCanonical!| |exprHasWeightCosWXorSinWX| + |sylvesterSequence| |numericIfCan| |stosePrepareSubResAlgo| |op| + |minPoints3D| |colorFunction| |iiasinh| |dark| |kernels| + |branchPointAtInfinity?| |lastSubResultantEuclidean| + |resultantEuclideannaif| |cCsc| |presuper| |OMUnknownSymbol?| |minset| + |lquo| |move| |physicalLength| |c05adf| |cAsech| |leftFactorIfCan| + |LazardQuotient2| |operator| |more?| |constantOpIfCan| |outputGeneral| + |binaryTree| |expenseOfEvaluation| SEGMENT |notelem| |s18aef| + |countRealRootsMultiple| |sech2cosh| |quoted?| |singularAtInfinity?| + |plotPolar| |cCosh| |dflist| |nativeModuleExtension| |univariate| + |sort| |OMputFloat| |antisymmetricTensors| |nil?| |taylorIfCan| + |lieAdmissible?| |dn| |generalizedEigenvector| |child| |sh| + |pleskenSplit| |radicalEigenvectors| |dec| |algebraic?| + |virtualDegree| |unitsColorDefault| |readByte!| |iicot| + |wordInStrongGenerators| |hasTopPredicate?| |numberOfComputedEntries| + |OMgetFloat| |mathieu12| |LyndonWordsList| |mirror| |rightMult| + |union| |iprint| |normalized?| |create| |divisorCascade| |routines| + |getProperties| |randomR| |c05nbf| |factor| |round| |eulerE| + |showIntensityFunctions| |lfintegrate| |readInt8!| |viewWriteDefault| + |random| |ceiling| |mesh| |pastel| |sqrt| |unary?| |OMgetEndError| + |getCurve| |s17ajf| |comp| |pack!| |extendedResultant| |lifting| + |generalInfiniteProduct| |trim| |real| |oblateSpheroidal| |fi2df| + |e01bff| |zeroOf| |rotatex| |useSingleFactorBound?| + |nthFractionalTerm| |OMconnOutDevice| |imag| |linearlyDependentOverZ?| + |properties| |seriesToOutputForm| |univariatePolynomials| + |cycleSplit!| |doubleDisc| |copy| |directProduct| |rur| |OMgetBVar| + |modifyPointData| |unitNormalize| |radix| |super| |ocf2ocdf| + |getGraph| |translate| |OMgetEndBVar| |padicallyExpand| |rotatey| + |readable?| |drawCurves| |Aleph| |f02aff| |iiasech| |fortranTypeOf| + |depth| |wronskianMatrix| |setEpilogue!| |knownInfBasis| + |clipPointsDefault| |abelianGroup| |push!| |alternative?| |brace| + |symmetricSquare| |factorList| |decompose| |perfectSqrt| + |noLinearFactor?| |quasiComponent| |d01alf| |complexNormalize| + |characteristic| |destruct| |erf| |trapezoidalo| |critpOrder| |e02dff| + |noValueMode| |outputFixed| |algintegrate| |minordet| |OMlistSymbols| + |invertibleElseSplit?| |match?| |upperCase| |normal?| |simpsono| + |numberOfHues| |autoCoerce| |rewriteIdealWithRemainder| |writeBytes!| + |currentScope| |fractionFreeGauss!| |d03edf| |nextPartition| + |interactiveEnv| |basis| |children| |fill!| |nextSubsetGray| + |endOfFile?| |upperBound| |cyclicEqual?| |dilog| |rangeIsFinite| + |complex?| |s17dgf| |mathieu23| |digit| |leftZero| |expand| + |goodnessOfFit| |boundOfCauchy| |irreducible?| |monomial| |sin| + |constant?| |ranges| |radicalSimplify| |multiplyCoefficients| + |physicalLength!| |rowEchelonLocal| |filterWhile| |root| + |makingStats?| |multivariate| |stoseInvertibleSetreg| |close| |cos| + |lazyPseudoRemainder| |create3Space| |quasiRegular?| |accuracyIF| F + |rightUnit| |filterUntil| |karatsubaDivide| |leftDivide| + |discriminantEuclidean| |fractRagits| |variables| |tan| |normalForm| + |commutative?| |toseSquareFreePart| |euclideanSize| |select| + |PDESolve| |binaryFunction| |deepestTail| |scopes| |HenselLift| + |display| |cot| |optional?| |binary| |setlast!| |before?| |points| + |rootRadius| |diagonal?| |setleaves!| |innerint| |sec| |iicos| + |UnVectorise| |pushup| |defineProperty| |sumOfKthPowerDivisors| + |createZechTable| |parent| |exprToGenUPS| |symmetricRemainder| |csc| + |expenseOfEvaluationIF| |toroidal| |minus!| |OMgetEndBind| |factors| + |edf2df| |shrinkable| |members| |tensorProduct| |asin| |removeZero| + |critMTonD1| |pop!| |interpretString| |setAttributeButtonStep| + |alphabetic| |getPickedPoints| |qualifier| |debug| |nthRoot| |qelt| + |taylor| |acos| |predicate| |perfectNthPower?| |fTable| + |createGenericMatrix| |createPrimitiveElement| |binaryTournament| + |startPolynomial| |qsetelt| |vedf2vef| |irDef| |expt| D |laurent| + |input| |atan| |fortranInteger| |antiAssociative?| |ode| |f02xef| + |primitive?| |cAtan| |schema| |complexForm| |xRange| |nextColeman| + |puiseux| |library| |acot| |copyInto!| |OMencodingXML| |newTypeLists| + |fibonacci| EQ |modTree| |removeRoughlyRedundantFactorsInPol| |write!| + |groebnerFactorize| |youngGroup| |yRange| |asec| |jokerMode| |returns| + |primeFactor| |leftExactQuotient| |setFieldInfo| |fortranLinkerArgs| + |tube| |primitivePart!| |inv| |pToHdmp| |zRange| |acsc| |setProperty| + |box| |c05pbf| |totalGroebner| |bipolarCylindrical| + |extendedEuclidean| |read!| |cAcos| |ground?| |any?| |map!| + |OMreceive| |sinh| |OMgetString| |sPol| |transpose| |cAcsc| + |dualSignature| |dihedral| |e01daf| |qsetelt!| |elem?| |ground| + |resetBadValues| |set| |cosh| |leftRankPolynomial| + |internalIntegrate0| |semiDegreeSubResultantEuclidean| |alphanumeric?| + |double| |mapDown!| |rightExtendedGcd| |complexZeros| |sincos| + |intermediateResultsIF| |leadingMonomial| |transcendent?| |tanh| + |compBound| |unravel| |partition| |BumInSepFFE| |yellow| |scaleRoots| + |mapGen| |fixedPoint| |OMputEndAttr| |leadingCoefficient| + |outputSpacing| |coth| |expextendedint| |makeSeries| |normal01| + |localUnquote| |size| |permutation| |realRoots| |argument| |subset?| + |rubiksGroup| |primitiveMonomials| |parameters| |sech| |leftFactor| + |setright!| |s20acf| |lowerCase?| |mkcomm| |block| |groebgen| |d01anf| + |print| |chiSquare| |reductum| |csch| |mapBivariate| |e02daf| + |evaluateInverse| |typeLists| |finiteBound| |intPatternMatch| + |curryLeft| |resolve| |subCase?| |cSech| |acsch| |asinh| + |gcdPolynomial| |fglmIfCan| |cyclicEntries| |orbit| |skewSFunction| + |fortranDouble| |OMReadError?| |invmod| |norm| |acosh| |true| + |quoByVar| |Gamma| |besselJ| |category| |seed| |iiabs| |constDsolve| + |halfExtendedSubResultantGcd2| |limitedIntegrate| |f07aef| |f04asf| + |basisOfNucleus| |domain| |over| |optional| |dmp2rfi| |declare!| + |cot2tan| |deepestInitial| |insertionSort!| |coth2trigh| |factorset| + |epilogue| |linearPolynomials| |clikeUniv| |OMcloseConn| |integers| + |package| |iisec| |vectorise| |whileLoop| |OMgetAttr| |aromberg| + |infinite?| |insert| |maxIndex| |reindex| |exists?| |eyeDistance| + |readInt32!| |extract!| |cosSinInfo| |imagk| |recoverAfterFail| |show| + |iiacsch| |exprHasAlgebraicWeight| |discreteLog| |outputArgs| + |singularitiesOf| |search| |f04qaf| |dmpToP| |lazyVariations| + |lazyPremWithDefault| |rewriteSetWithReduction| |stopTableInvSet!| + UTS2UP |sinIfCan| |node| |solid?| |symmetricTensors| |rquo| + |pointColor| |c06fuf| |trace| |fmecg| |cTanh| |setAdaptive3D| + |conical| |has?| |partialQuotients| |cothIfCan| |iisech| + |zeroDimensional?| |capacity| |coefficient| |region| |degreePartition| + |iomode| |OMencodingBinary| |mapdiv| |e01sbf| |odd?| |stop| |ratpart| + |adaptive?| |segment| |monicCompleteDecompose| |sylvesterMatrix| + |nonSingularModel| |idealSimplify| |ListOfTerms| |setTex!| |OMputApp| + |alternating| |extractIfCan| |prologue| |quotient| |voidMode| + |setsubMatrix!| |prefixRagits| |listOfLists| |formula| |flatten| + |latex| |tanintegrate| |setScreenResolution3D| |lazyGintegrate| + |paraboloidal| |rootNormalize| |charpol| |d02gaf| |lllip| |subMatrix| + |extractBottom!| |mainVariable| |rightFactorIfCan| |reducedForm| + |graeffe| |isQuotient| |monicRightFactorIfCan| |writeInt8!| |getlo| + |doubleComplex?| |lepol| |sinhIfCan| |zero?| |trace2PowMod| + |zeroDimPrime?| |s18aff| |ideal| |dioSolve| |reify| |lyndon| |cAsec| + |pole?| |elliptic?| |augment| |purelyAlgebraic?| |nrows| + |OMUnknownCD?| |genericLeftTraceForm| |entries| |updatD| + |lastSubResultant| |axes| |exprHasLogarithmicWeights| |OMputVariable| + |lazyPrem| |ncols| |UP2ifCan| |c06fqf| |leftRecip| |controlPanel| + |changeBase| |incrementKthElement| |simplify| |conjugates| + |setIntersection| |ScanFloatIgnoreSpacesIfCan| |distdfact| |nullary?| + |ignore?| |mapUnivariateIfCan| |fortranCarriageReturn| |gcdcofactprim| + |height| |units| |log10| |mesh?| |setTopPredicate| |factorSFBRlcUnit| + |rewriteIdealWithHeadRemainder| |equation| |drawToScale| |s17aef| + |expIfCan| |null?| |mindeg| |basisOfLeftNucloid| |bitand| |cup| + |rationalPoints| |univariatePolynomial| |OMserve| |optpair| |leaves| + |outerProduct| |deriv| |bitior| |d02ejf| |setOrder| |addmod| + |genericLeftNorm| |pseudoQuotient| |roughUnitIdeal?| |shape| + |toseInvertible?| |radicalRoots| |triangSolve| |Ci| |cLog| + |divergence| |shallowExpand| |jacobian| |macroExpand| + |leftCharacteristicPolynomial| |distribute| |Is| |anticoord| + |elements| |bumptab| |linSolve| |closedCurve| |replaceKthElement| + |subNodeOf?| |readBytes!| |rightDivide| + |generalizedContinuumHypothesisAssumed?| |explimitedint| + |startTableGcd!| |numberOfVariables| |compdegd| |clearTheSymbolTable| + |df2fi| |inGroundField?| |iitanh| |tubeRadius| |hasHi| |besselI| + |insert!| |createNormalPoly| |pascalTriangle| |f02adf| |getOperands| + |rule| |tryFunctionalDecomposition?| |fprindINFO| |declare| |makeCrit| + |inRadical?| |resize| |ellipticCylindrical| |splitSquarefree| |common| + |rootBound| |linearlyDependent?| |mainMonomial| |atanIfCan| + |asinhIfCan| |mapUp!| |imaginary| |writeLine!| |minRowIndex| + |factorials| |exptMod| |d02gbf| |zoom| |hexDigit| |euler| + |numberOfPrimitivePoly| |PollardSmallFactor| |interReduce| |c06ecf| + |symmetricGroup| |deleteProperty!| |realEigenvectors| |lintgcd| + |zCoord| |lazy?| |elRow2!| |branchIfCan| |partialDenominators| + |iiasin| |leadingExponent| |d02kef| |matrix| |symbol?| + |domainTemplate| |HermiteIntegrate| |twist| |algSplitSimple| |Nul| + |edf2ef| |readUInt16!| |partitions| |removeCoshSq| |ord| |e02adf| + |var2StepsDefault| |Si| |isOpen?| |quotientByP| |ratDenom| |prevPrime| + |createPrimitivePoly| |groebner?| |dequeue| |generators| + |squareFreeFactors| Y |trapezoidal| |acosIfCan| |tanSum| |sec2cos| + |elseBranch| |extendedIntegrate| |isEquiv| |limitPlus| |linearPart| + |label| |internalLastSubResultant| |diagonalProduct| |ef2edf| |inR?| + |associatedEquations| |safeFloor| |makeGraphImage| |B1solve| |df2mf| + |escape| |sin2csc| |stiffnessAndStabilityFactor| |components| + |leastAffineMultiple| |deepCopy| |coerceP| + |numberOfImproperPartitions| |mainDefiningPolynomial| + |rangePascalTriangle| |pair?| |palgint0| |minPol| + |basisOfMiddleNucleus| |rightRankPolynomial| |univariateSolve| + |composites| |result| |zeroDimPrimary?| |iidsum| |listOfMonoms| + |categoryMode| |univariate?| |extendedint| |mkIntegral| |cSec| + |taylorRep| |d02raf| |vark| |enterInCache| |associatedSystem| + |laplacian| |rightExactQuotient| |noncommutativeJordanAlgebra?| + |f02fjf| |expint| |changeNameToObjf| |validExponential| |fixedDivisor| + |d01bbf| |bernoulli| |gcdprim| |showAll?| |setButtonValue| |cyclic| + |setCondition!| |constantOperator| |s17dhf| |setLength!| + |hypergeometric0F1| |constructor| |rightPower| |inverseIntegralMatrix| + |readIfCan!| |graphState| |represents| |approximants| |normalElement| + |substitute| |OMgetEndApp| |hexDigit?| |sum| |iibinom| |totalLex| + |bindings| |cTan| |option| |f04faf| |showSummary| |symbolTable| + |makeCos| |e02ddf| |e04gcf| |basicSet| |OMputSymbol| |leaf?| + |sechIfCan| |rdHack1| |GospersMethod| |curveColorPalette| + |squareFreePart| |getMatch| |front| |squareFreePrim| |symFunc| + |multiEuclideanTree| |s19acf| |elliptic| |pushFortranOutputStack| + |showAttributes| |lp| |d01gaf| |poisson| |badValues| |deref| + |getVariableOrder| |newSubProgram| |elaborateFile| |moduleSum| + |makeRecord| |regime| |popFortranOutputStack| |sturmSequence| |lllp| + |tab1| |realSolve| |complexSolve| |imagI| |saturate| |cAsin| |atom?| + |outputAsFortran| |insertRoot!| |vertConcat| |alphanumeric| + |prinpolINFO| |duplicates?| |OMgetInteger| |name| |bitLength| |d01asf| + |genericRightDiscriminant| |mergeDifference| |setMinPoints3D| + |parabolicCylindrical| |matrixGcd| |currentCategoryFrame| |rightTrim| + |redpps| |body| |prinb| |selectAndPolynomials| |indicialEquations| + |duplicates| |subresultantSequence| |kroneckerDelta| |e02zaf| + |OMgetError| |leftTrim| |untab| |high| |outputAsTex| + |bezoutDiscriminant| |null| |binomThmExpt| |karatsubaOnce| |e04fdf| + |shufflein| |solveLinearPolynomialEquationByRecursion| |stack| + |rootsOf| |linGenPos| |quasiAlgebraicSet| |iicosh| |not| |janko2| + |lazyIrreducibleFactors| |cAtanh| |s19abf| |homogeneous?| BY |cn| + |top!| |subtractIfCan| |ODESolve| |maxPoints| |and| |solve1| + |removeSuperfluousQuasiComponents| |setProperties| |weights| |d02cjf| + |simplifyPower| |categoryFrame| |diagonal| |monicLeftDivide| |or| + |getSyntaxFormsFromFile| |mpsode| |identitySquareMatrix| |curryRight| + |infix| |overset?| |eigenvalues| |magnitude| |opeval| |xor| |pdf2df| + |viewDefaults| |normFactors| |youngDiagram| |innerEigenvectors| + |s13aaf| |besselK| |numerator| |signature| |primextintfrac| |dim| + |case| |spherical| |OMgetEndAtp| |assert| |factorByRecursion| |hasoln| + |po| |port| |infiniteProduct| |leftUnits| |s13adf| |makeMulti| + |pattern| |Zero| |iiasec| |orthonormalBasis| |identification| |presub| + |integral| |rationalIfCan| |SFunction| |simpson| |csubst| |One| + |rationalApproximation| |lazyPseudoDivide| |patternMatchTimes| + |asechIfCan| |subscriptedVariables| |t| |selectNonFiniteRoutines| + |s13acf| |ScanRoman| |basisOfRightNucleus| |shift| NOT + |LyndonWordsList1| |FormatArabic| |shiftRight| |coordinates| |output| + |palglimint0| |powmod| |f04maf| |chainSubResultants| |nodeOf?| OR + |vector| |leadingIndex| |messagePrint| |eq?| |bracket| + |irreducibleFactor| |df2ef| |polyred| |expandLog| |problemPoints| + |message| AND |differentiate| |mapCoef| |integerIfCan| |getZechTable| + |multiset| |mergeFactors| |genus| |OMgetSymbol| |setrest!| |unit| + |cAcoth| |lazyPquo| |initTable!| |positive?| |fortran| |curry| |delay| + |iiexp| |initiallyReduce| |reduceLODE| |elt| |overlabel| |tanNa| + |hMonic| |henselFact| |tan2trig| |mainSquareFreePart| |finiteBasis| + |headReduce| |fixPredicate| |iFTable| |replace| |An| + |addMatchRestricted| |level| |indiceSubResultantEuclidean| + |generalSqFr| |coerceListOfPairs| |closed?| |LyndonCoordinates| + |outputBinaryFile| |zeroSetSplitIntoTriangularSystems| |startStats!| + |concat!| |colorDef| |numericalOptimization| + |factorSquareFreePolynomial| |enqueue!| |prod| |sizeLess?| + |removeSuperfluousCases| |branchPoint?| |palgintegrate| |coord| |cons| + |selectOptimizationRoutines| |double?| |sumSquares| |normDeriv2| + |addPoint2| |mainExpression| |s01eaf| |nodes| |htrigs| |cond| + |completeHermite| |negative?| |quadratic| |setValue!| |retract| + |leftNorm| |terms| |paren| |asinIfCan| |completeHensel| |makeSUP| + |clipSurface| |cSinh| |groebnerIdeal| |leftScalarTimes!| + |extractProperty| |subspace| |support| |interpolate| |prime| + |fractionPart| |point?| |second| * |s17akf| |subResultantsChain| + |multisect| |graphCurves| |var2Steps| |ridHack1| |invertIfCan| |row| + |addPoint| |third| |inrootof| |bfEntry| |basisOfRightNucloid| |nary?| + |identityMatrix| |tryFunctionalDecomposition| |setleft!| |reduction| + |typeList| |decrease| |putProperty| |semiSubResultantGcdEuclidean1| + |source| |void| |pushdown| |conditionsForIdempotents| |gensym| + |sortConstraints| |explogs2trigs| = |printStats!| |enumerate| + |dominantTerm| |stoseLastSubResultant| |e04dgf| |makeop| |mix| + |multiEuclidean| |createLowComplexityNormalBasis| + |numberOfIrreduciblePoly| |chvar| |symmetricPower| |script| + |rightCharacteristicPolynomial| |modulus| |mappingMode| |maxrank| + |find| |rationalPoint?| |readUInt32!| < |completeEval| |collectUpper| + |findConstructor| |plusInfinity| |initializeGroupForWordProblem| + |char| |deepExpand| |iCompose| > |iitan| |d02bhf| |minusInfinity| + |isOr| |s17def| |cotIfCan| |systemCommand| |alternatingGroup| + |totolex| <= |isPlus| |whatInfinity| |viewPhiDefault| |tex| |target| + |OMencodingUnknown| |qinterval| |inverseColeman| |s17aff| + |setchildren!| |rightRank| >= |imagJ| |ffactor| |factorPolynomial| + |pr2dmp| |newReduc| |retractable?| |pointColorPalette| + |zeroSquareMatrix| |expr| |roughBase?| |car| |eulerPhi| |mkPrim| + |isExpt| |normal| |changeVar| |s17ahf| |reduceByQuasiMonic| + |ramified?| |permutationRepresentation| |xCoord| |lookup| |isAtom| + |linear| |constantRight| |complexRoots| + |evenInfiniteProduct| + |partialNumerators| |createIrreduciblePoly| |type| |getOrder| + |firstNumer| |exactQuotient!| |exQuo| |s18dcf| - |float| |subPolSet?| + |mathieu22| |certainlySubVariety?| |nthFactor| |rootKerSimp| |f02bjf| + |polynomial| |leadingIdeal| |variable| |repSq| / |phiCoord| |solve| + |roughBasicSet| |postfix| |algebraicVariables| |oddlambert| + |iterators| |divisors| |pdct| |inputBinaryFile| |viewDeltaXDefault| + |rightGcd| |fullPartialFraction| |subresultantVector| |sin?| |inspect| + |maxint| |push| |solveLinearlyOverQ| |tanIfCan| |headAst| |readLine!| + |f02axf| |OMputEndBind| |coshIfCan| |tubePoints| |element?| + |mightHaveRoots| |sumOfDivisors| |s21bdf| |polarCoordinates| |id| + |copies| |hconcat| |fortranReal| |contours| |value| |triangular?| + |merge| |comparison| |generateIrredPoly| |updatF| |symbol| |lo| + |jordanAdmissible?| |modularFactor| |OMputEndAtp| |startTable!| + |SturmHabichtCoefficients| |compiledFunction| |removeSquaresIfCan| + |atanhIfCan| |f02wef| |expression| |lieAlgebra?| |rightUnits| |bit?| + |denomLODE| |multinomial| |s19aaf| |OMwrite| |charthRoot| |calcRanges| + |integer| |integer?| |nthExponent| |leftReducedSystem| GE |hex| + |minrank| |supDimElseRittWu?| |removeZeroes| |intersect| |medialSet| + |setPoly| |unitVector| |contains?| |rational?| GT |bitTruth| + |showRegion| |lSpaceBasis| |f01qcf| |principalAncestors| + |variationOfParameters| |hermite| |style| |eigenvectors| LE |pomopo!| + |e02gaf| |bivariate?| |createRandomElement| |zerosOf| + |createLowComplexityTable| |reduceBasisAtInfinity| |setelt!| + |reverseLex| LT |rotatez| |stopMusserTrials| |distFact| + |decomposeFunc| |extractTop!| |getMultiplicationTable| |crest| + |socf2socdf| |iterationVar| |c06gsf| |list?| |UpTriBddDenomInv| + |connect| |nor| |squareMatrix| |invertibleSet| + |numberOfFractionalTerms| |curve?| |computeCycleLength| |pile| + |integralMatrix| |OMbindTCP| |denominators| |monomial?| + |transcendenceDegree| |keys| |edf2efi| |expressIdealMember| |select!| + |bombieriNorm| |bothWays| |cos2sec| |unknownEndian| |unitNormal| + |separateDegrees| |numberOfOperations| |OMgetApp| |lyndonIfCan| + |singRicDE| |linearAssociatedLog| |cycleRagits| |leviCivitaSymbol| + |OMgetVariable| |primlimitedint| |index| |makeEq| |definingPolynomial| + |numberOfComponents| |order| |triangularSystems| |OMencodingSGML| + |repeatUntilLoop| |square?| |nextNormalPoly| |numeric| |s17dlf| + |shuffle| |cCoth| |polygon| |pushdterm| |hdmpToDmp| |rightNorm| + |gderiv| |redPo| |radical| |OMputBind| |patternMatch| |removeCosSq| + |fixedPointExquo| |resultant| |fortranDoubleComplex| |bivariateSLPEBR| + |reduced?| |rightQuotient| |pair| |open| |tree| |positiveRemainder| + |primPartElseUnitCanonical| |structuralConstants| |outlineRender| + |curve| |kmax| |bright| |setImagSteps| |rst| |graphStates| |tanQ| + |numberOfChildren| |thenBranch| |currentSubProgram| + |LowTriBddDenomInv| |plus!| |fortranCompilerName| |FormatRoman| + |useEisensteinCriterion| |critB| |eof?| |getRef| |algDsolve| |e04jaf| + |printingInfo?| |eval| |makeFloatFunction| |ode1| + |removeRoughlyRedundantFactorsInContents| |setUnion| |stFunc1| + |vspace| |scale| |indicialEquationAtInfinity| |writeByte!| + |expintegrate| |adjoint| |splitNodeOf!| |operations| |mapMatrixIfCan| + |selectOrPolynomials| |checkForZero| |normalizeAtInfinity| |torsion?| + |largest| |lfunc| |internalDecompose| |lowerBound| |bandedJacobian| + |e04mbf| |solveid| |OMreadFile| |interpret| |conjunction| |error| + |midpoints| |complexExpand| |selectIntegrationRoutines| |imagK| + |airyBi| |clearTable!| |f2df| |aQuartic| |ref| |setStatus| |groebner| + |normalize| |quadratic?| |lexTriangular| |pointSizeDefault| + |sayLength| |direction| |optimize| |standardBasisOfCyclicSubmodule| + |algebraicOf| |insertBottom!| |perspective| |sequence| |logGamma| + |function| |stoseInvertibleSet| |symmetricProduct| |OMmakeConn| + |oneDimensionalArray| |cAcsch| |rightOne| |symbolTableOf| + |createNormalElement| |lflimitedint| |tubeRadiusDefault| |subHeight| + |autoReduced?| |symbolIfCan| |matrixDimensions| |seriesSolve| + |reducedSystem| |llprop| |width| |ramifiedAtInfinity?| + |inputOutputBinaryFile| |makeUnit| |cyclicGroup| |lookupFunction| + |iiacoth| |rules| |topPredicate| |monicDivide| |aspFilename| + |primintegrate| |cubic| |dihedralGroup| |rectangularMatrix| |critM| + |explicitEntries?| |unitCanonical| |maxrow| |pseudoRemainder| + |rightRemainder| |divideIfCan| |sumOfSquares| |cCot| + |getMultiplicationMatrix| |tubePlot| |degreeSubResultant| + |extendedSubResultantGcd| |e02bbf| |bezoutResultant| |baseRDEsys| + |tracePowMod| |setMaxPoints3D| |OMconnectTCP| |countRealRoots| + |solveLinearPolynomialEquationByFractions| + |unprotectedRemoveRedundantFactors| |smith| + |leftRegularRepresentation| |queue| |someBasis| |logpart| |printCode| + |mr| |subscript| |selectsecond| |sinh2csch| |genericRightTrace| + |real?| |characteristicSerie| |length| |leftGcd| |redmat| |float?| + |upperCase?| |sort!| |rootPoly| |xn| |changeWeightLevel| |ratPoly| + |changeThreshhold| |scripts| |irreducibleRepresentation| |preprocess| + |prem| |rem| |purelyTranscendental?| |removeRedundantFactors| + |string?| |euclideanNormalForm| |npcoef| |numberOfNormalPoly| + |definingEquations| |scanOneDimSubspaces| |cycle| |selectPDERoutines| + |upDateBranches| |quo| |weakBiRank| |empty?| |argumentList!| + |buildSyntax| |cCos| |varList| |uniform01| |removeSinhSq| + |lfextlimint| |infieldIntegrate| |e02ahf| |intcompBasis| |mainKernel| + |every?| |LiePoly| |wreath| |lcm| |tanhIfCan| |headRemainder| + |normalise| |lineColorDefault| |div| |inf| |delete| |BasicMethod| + |vconcat| |isList| |external?| |graphs| |genericRightTraceForm| + |clearTheFTable| |stoseInvertible?reg| |exquo| |relativeApprox| + |digit?| |algebraicCoefficients?| |drawComplex| |bigEndian| |append| + |minPoints| |normalDeriv| |floor| |pointData| ~= |monicRightDivide| + |minGbasis| |composite| |wholeRagits| |irVar| |imagj| |gcd| + |OMlistCDs| |laurentIfCan| |representationType| |#| |subNode?| + |s15aef| |semiSubResultantGcdEuclidean2| |factorGroebnerBasis| + |OMputEndApp| |perfectSquare?| |false| |status| |delete!| + |factorOfDegree| |extractClosed| ~ |readInt16!| |realEigenvalues| + |aCubic| |mappingAst| |genericPosition| |randnum| |collectQuasiMonic| + |btwFact| |cross| |reorder| |hspace| |bumprow| |ravel| |rowEchLocal| + |att2Result| |complexEigenvectors| |realElementary| |cosIfCan| + |e02agf| |zeroSetSplit| |rk4f| |roman| |reshape| |oddintegers| + |sqfrFactor| |e02dcf| |setprevious!| |airyAi| |stirling2| |/\\| |bat| + |laguerreL| |selectODEIVPRoutines| |processTemplate| |f04axf| + |functorData| |moebiusMu| |plenaryPower| |modularGcdPrimitive| + |stopTableGcd!| |logIfCan| |\\/| |constantCoefficientRicDE| + |rootPower| |genericRightMinimalPolynomial| |innerSolve1| + |viewPosDefault| |apply| |coerce| |genericLeftMinimalPolynomial| + |flexibleArray| |s17adf| |equality| |tRange| |closed| |OMclose| + |d01fcf| |first| |construct| |setLegalFortranSourceExtensions| + |varselect| |idealiser| |internalSubPolSet?| |mainForm| + |prepareDecompose| |listexp| |f04mcf| |printInfo!| |stFunc2| |rest| + |cap| |contractSolve| |anfactor| |f07fdf| |rdregime| |showArrayValues| + |regularRepresentation| |character?| |ParCond| |extractIndex| |plus| + |update| |irCtor| |atoms| |inverseLaplace| |mkAnswer| |unvectorise| + |coHeight| |inHallBasis?| |dmpToHdmp| |groebSolve| |commutator| + |functionIsContinuousAtEndPoints| |critBonD| |meshPar1Var| + |completeSmith| |conjugate| |componentUpperBound| |algebraicSort| + |bytes| |computePowers| |exponential| |redPol| |palglimint| + |showTheSymbolTable| |d03faf| |isPower| |quote| |plot| |times| + |selectMultiDimensionalRoutines| |rootOf| |slex| |parents| + |lfextendedint| |c06ekf| |rspace| |bfKeys| + |selectSumOfSquaresRoutines| |leftMult| |addPointLast| |scalarTypeOf| + |f07adf| |tubePointsDefault| |expandPower| |submod| |sparsityIF| + |iiatan| |empty| |position| |subQuasiComponent?| |csch2sinh| + |printStatement| |s18def| |polygon?| |rationalFunction| + |numberOfDivisors| |rowEchelon| |listBranches| + |tableForDiscreteLogarithm| |even?| |radicalSolve| + |expandTrigProducts| |recur| |eigenMatrix| |OMunhandledSymbol| + |antiCommutator| |cycleTail| |doublyTransitive?| + |internalZeroSetSplit| |crushedSet| |collect| |split!| |reverse!| + |monom| |rootSplit| |lift| |conditionP| |sequences| |leftRank| |tab| + |failed?| |subSet| |getMeasure| |imports| |toseInvertibleSet| + |sdf2lst| |loadNativeModule| |fillPascalTriangle| |reduce| |power!| + |point| |exteriorDifferential| |powern| |mvar| |cyclic?| + |areEquivalent?| |iiatanh| |generalTwoFactor| |close!| + |strongGenerators| |polCase| |part?| |simplifyExp| |getConstant| + |rootOfIrreduciblePoly| |qqq| |integralCoordinates| |lazyResidueClass| + |yCoordinates| |moreAlgebraic?| |remainder| |nonQsign| |frobenius| + |remove!| |OMputEndError| |positiveSolve| + |semiIndiceSubResultantEuclidean| |tan2cot| |blankSeparate| + |mapUnivariate| |f04jgf| |generalPosition| |zeroMatrix| |gethi| + |comment| |padecf| |series| |factorAndSplit| |nullity| + |removeRedundantFactorsInContents| |partialFraction| |center| |f02awf| + |removeRedundantFactorsInPols| |integerBound| |infieldint| |log| + |pushuconst| |coerceImages| |expPot| |lastSubResultantElseSplit| + |associative?| |numFunEvals| |complement| |cExp| |OMputAttr| + |specialTrigs| |subTriSet?| |setelt| |nlde| |internal?| |powerSum| + |rewriteIdealWithQuasiMonicGenerators| |s17dcf| |isConnected?| + |OMputEndObject| |setClipValue| |extractPoint| |nthFlag| |quatern| + |leftUnit| |module| |swap| |selectPolynomials| |freeOf?| + |mainCoefficients| |singular?| |changeName| |contract| |minimize| + |maxRowIndex| |bottom!| |resultantReduitEuclidean| |min| + |outputFloating| |halfExtendedResultant1| |palgLODE| |nextPrime| + |hasSolution?| |ipow| |leadingCoefficientRicDE| |infinityNorm| + |outputForm| |setFormula!| |yCoord| |c02agf| |fixedPoints| + |createMultiplicationTable| |lazyIntegrate| |appendPoint| |monomials| + |cyclicParents| |setColumn!| |createNormalPrimitivePoly| + |measure2Result| |jacobiIdentity?| |flagFactor| |moduloP| + |listRepresentation| |sup| |setvalue!| |totalfract| |exprToUPS| + |bivariatePolynomials| |rootSimp| |iicsc| |figureUnits| |f01bsf| + |factorSquareFreeByRecursion| |property| |transcendentalDecompose| + |unmakeSUP| |unexpand| |f01maf| |d03eef| |numberOfCycles| |mat| + |prindINFO| |byte| |goodPoint| |generalizedInverse| |showScalarValues| + |omError| |separate| |badNum| |meatAxe| |OMputObject| |acothIfCan| + |errorInfo| |setref| |rootDirectory| |zero| |setRealSteps| |mulmod| + |reverse| |sinhcosh| |minColIndex| |algebraicDecompose| |mainValue| + |acschIfCan| |call| |prinshINFO| |myDegree| |pToDmp| |product| + |setRow!| |ldf2vmf| |KrullNumber| |rotate| |polyPart| |setOfMinN| |li| + |OMputError| |iisin| |difference| |OMopenFile| |multiple?| |And| + |viewport3D| |size?| |alphabetic?| |imagi| |mapSolve| |unparse| + |Lazard2| |unknown| |geometric| |makeVariable| |setScreenResolution| + |increasePrecision| |rCoord| |Or| |besselY| |reducedContinuedFraction| + |sturmVariationsOf| |mapmult| |rightZero| |screenResolution3D| |exp1| + |primitivePart| |elaborate| |column| |rightScalarTimes!| |findCycle| + |Not| |generalLambert| |bezoutMatrix| |build| |approxSqrt| |makeprod| + |signatureAst| |finite?| |leftRemainder| |identity| |cycleElt| + |mainMonomials| |setPredicates| |firstUncouplingMatrix| |pointLists| + |complexLimit| |d01ajf| |position!| |superscript| |getStream| + |midpoint| FG2F |weighted| |modifyPoint| |bsolve| |recip| |localReal?| + |int| |cschIfCan| |scripted?| |color| |coth2tanh| |listYoungTableaus| + |superHeight| |factorFraction| |minIndex| |root?| |cylindrical| + |OMputString| |basisOfLeftNucleus| |localAbs| |realZeros| + |useSingleFactorBound| |f01mcf| |gradient| |dimension| |symmetric?| + |decimal| |iisqrt2| |e02baf| |resultantReduit| |attributeData| + |innerSolve| |binomial| |cSin| |supRittWu?| |f02abf| |OMParseError?| + |repeating| |rk4qc| |Lazard| |trueEqual| |OMread| + |shanksDiscLogAlgorithm| |iiGamma| |distance| |stopTable!| + |loopPoints| |interval| |stoseInternalLastSubResultant| |test| + |exponents| |getProperty| |quickSort| |elaboration| |graphImage| + |cyclotomicDecomposition| |remove| |fortranLiteralLine| |power| + |nextNormalPrimitivePoly| |musserTrials| |host| |primes| + |argumentListOf| |probablyZeroDim?| |bat1| |factorsOfDegree| |kovacic| + |factorial| |functionIsOscillatory| |zag| |genericLeftTrace| |cAcosh| + |tanAn| |inverse| |removeDuplicates| |cartesian| + |quasiMonicPolynomials| |dAndcExp| |addMatch| |getButtonValue| |last| + |OMgetAtp| |patternVariable| |ksec| |reducedDiscriminant| |e04naf| + |extend| |cyclicSubmodule| |differentialVariables| |clearTheIFTable| + |nextPrimitivePoly| |wholePart| |assoc| |credPol| |coefChoose| + |errorKind| |normalDenom| |c06gbf| |leftLcm| |assign| |c02aff| + |ReduceOrder| |rewriteSetByReducingWithParticularGenerators| + |condition| |divide| |dimensions| |tower| + |generalizedContinuumHypothesisAssumed| |isobaric?| + |removeRoughlyRedundantFactorsInPols| |writeUInt8!| |parametric?| + |palgRDE| |rightFactorCandidate| |basisOfLeftAnnihilator| + |primintfldpoly| |whitePoint| |parabolic| |infLex?| |iiperm| |bits| + |e01sef| |light| |indiceSubResultant| |acscIfCan| |headReduced?| + |prefix| |nilFactor| |bounds| |stoseInvertibleSetsqfreg| |limit| + |s20adf| |uniform| |cyclicCopy| |const| |wrregime| |putProperties| + |generic| |leftExtendedGcd| |parseString| |setClosed| |polyRicDE| + |axesColorDefault| |weight| |localIntegralBasis| |tValues| + |laurentRep| |obj| |derivationCoordinates| |eq| |orbits| + |genericRightNorm| |meshFun2Var| |arbitrary| |putGraph| |coerceL| + |e02bef| |option?| |pade| |conjug| |cache| |monomialIntegrate| |iter| + |isMult| |setDifference| |flexible?| |Ei| |complexNumeric| + |lowerPolynomial| |e01baf| |variable?| |aQuadratic| |listLoops| + |setfirst!| |maxPoints3D| |infRittWu?| |linkToFortran| |solveInField| + |heap| |nextItem| |lfinfieldint| |stronglyReduced?| |forLoop| + |sizeMultiplication| |irForm| |shiftRoots| |perfectNthRoot| + |cycleLength| |e02aef| |permutations| |coleman| |RemainderList| + |withPredicates| |merge!| |firstSubsetGray| |compose| |fracPart| + |coefficients| |nullary| |digits| |isAbsolutelyIrreducible?| + |associates?| |f07fef| |screenResolution| |f01rcf| |normalizeIfCan| + |LiePolyIfCan| |eisensteinIrreducible?| |OMputInteger| |generic?| + |radicalEigenvector| |surface| |acotIfCan| |uncouplingMatrices| + |subst| |f2st| |mapExponents| |rightLcm| |roughEqualIdeals?| |low| + |substring?| |setAdaptive| |internalAugment| |leadingTerm| |monic?| + |packageCall| |ricDsolve| |exp| |debug3D| |iipow| |s19adf| + |applyRules| |exprex| |nthCoef| |quadraticForm| |froot| |acoshIfCan| + |clipWithRanges| |resetVariableOrder| |bag| |shellSort| |d01amf| |hue| + |map| |nextsousResultant2| |suffix?| |possiblyNewVariety?| + |cycleEntry| |s14abf| |mainVariable?| |ScanArabic| |environment| + |lifting1| |lyndon?| |one?| |table| |Hausdorff| |generator| + |palgLODE0| |getExplanations| |OMgetBind| |simplifyLog| + |commaSeparate| |nil| |explicitlyEmpty?| |semicolonSeparate| + |wordInGenerators| |asecIfCan| |integralLastSubResultant| |new| + |atanh| |basisOfCenter| |prefix?| |OMsupportsCD?| |encodingDirectory| + |antiCommutative?| |OMgetType| |compile| |complexIntegrate| |rischDE| + |principalIdeal| |quasiMonic?| |s21bbf| |OMconnInDevice| |acoth| + |linear?| |repeating?| |LyndonBasis| |e04ycf| |sncndn| |objects| + |iiacos| |directSum| |c06gqf| |normInvertible?| |predicates| + |fractRadix| |asech| |brillhartTrials| |randomLC| |supersub| + |halfExtendedSubResultantGcd1| |pdf2ef| |base| |approximate| |space| + |constantIfCan| |tanh2trigh| |convert| |leastMonomial| + |prolateSpheroidal| |polynomialZeros| |countable?| |minPoly| |just| + |complex| |coercePreimagesImages| |computeInt| |monomRDEsys| |belong?| + |d01gbf| |multiple| |drawComplexVectorField| |univcase| |makeSin| + |dimensionOfIrreducibleRepresentation| |d01akf| |lprop| |increment| + |cAcot| |optAttributes| |hostByteOrder| |applyQuote| + |factorsOfCyclicGroupSize| |mathieu24| |rroot| |monicModulo| |failed| + |particularSolution| |testDim| |overlap| |baseRDE| + |characteristicPolynomial| |invertible?| |infix?| |palgint| + |cosh2sech| |csc2sin| |gcdPrimitive| |refine| |integrate| |iisinh| + |cyclePartition| |balancedFactorisation| |compactFraction| |mask| + |satisfy?| |intensity| |radicalOfLeftTraceForm| |leftAlternative?| + |viewDeltaYDefault| |var1StepsDefault| |elRow1!| |compound?| |ruleset| + |incr| |setPosition| |cyclotomic| |biRank| |measure| |quasiRegular| + |purelyAlgebraicLeadingMonomial?| |transform| |OMgetEndAttr| |c06eaf| + |f01qef| |hi| |pmComplexintegrate| |hitherPlane| + |basisOfRightAnnihilator| |selectfirst| |s14aaf| |normalizedAssociate| + |chineseRemainder| |left| |stoseInvertible?| |convergents| |qPot| + |LazardQuotient| |head| |removeSinSq| |rotate!| |outputMeasure| + |updateStatus!| |leftMinimalPolynomial| |sqfree| |right| |suchThat| + |eigenvector| |rational| |sub| |stFuncN| |index?| |rischDEsys| + |palgextint| |primextendedint| |doubleFloatFormat| |monomRDE| |rowEch| + |nextsubResultant2| |squareFreePolynomial| |shade| |ran| + |rationalPower| |associator| |OMgetEndObject| |outputAsScript| + |prime?| |safeCeiling| |relationsIdeal| |previous| |less?| |delta| + |invmultisect| |curveColor| |integralDerivationMatrix| |consnewpol| + |pseudoDivide| |clearFortranOutputStack| |leftQuotient| + |rischNormalize| |halfExtendedResultant2| |resultantEuclidean| + |edf2fi| |rightAlternative?| |cAsinh| |initial| |diagonalMatrix| + |drawStyle| |iiacosh| |s17agf| |pol| |cscIfCan| |next| + |pointColorDefault| |goto| |explicitlyFinite?| |monomialIntPoly| + |precision| |central?| |s21bcf| |key| |hyperelliptic| + |listConjugateBases| |iidprod| |removeDuplicates!| |cot2trig| |f02bbf| + |putColorInfo| |antisymmetric?| |approxNthRoot| |slash| + |exponentialOrder| |intChoose| |makeYoungTableau| |prepareSubResAlgo| + |unit?| |choosemon| |taylorQuoByVar| |times!| |filename| |c06ebf| + |viewThetaDefault| |swap!| |psolve| |inverseIntegralMatrixAtInfinity| + |hostPlatform| |hclf| |dfRange| |companionBlocks| |powers| + |mainCharacterization| |splitLinear| |corrPoly| |e01bgf| |returnType!| + |qfactor| |setPrologue!| |connectTo| |f01brf| |evenlambert| + |combineFeatureCompatibility| |diag| |parse| |numberOfMonomials| + |arity| |littleEndian| |divideExponents| |recolor| |lambda| + |semiLastSubResultantEuclidean| |iicoth| |indicialEquation| |code| + |rombergo| |generate| |cardinality| |modularGcd| |byteBuffer| + |linearAssociatedOrder| |showTheFTable| |unrankImproperPartitions1| + |setMinPoints| |diophantineSystem| |setnext!| |trigs| + |symmetricDifference| |addiag| |log2| |sample| |OMsupportsSymbol?| + |highCommonTerms| |back| |karatsuba| |iroot| |initiallyReduced?| + |incrementBy| |getCode| |overbar| |checkRur| |disjunction| + |ScanFloatIgnoreSpaces| |numerators| |OMsetEncoding| |truncate| + |factor1| |e01bef| |lazyPseudoQuotient| |lowerCase| |isImplies| + |lowerCase!| |tanh2coth| |permanent| |externalList| |viewZoomDefault| + |constantLeft| |OMputAtp| |resetAttributeButtons| |elColumn2!| + |numFunEvals3D| |findBinding| |printInfo| |multMonom| |ldf2lst| + |doubleResultant| |splitConstant| |jordanAlgebra?| |d01apf| |rarrow| + |polygamma| |makeSketch| |cCsch| |squareFree| |ptFunc| |leftPower| + |complexElementary| |octon| |hermiteH| |leftDiscriminant| LODO2FUN + |stiffnessAndStabilityOfODEIF| |iiacot| |is?| |linearMatrix| + |useNagFunctions| |minimumExponent| |e02bcf| |scan| |options| + |increase| |equiv| |meshPar2Var| |makeViewport2D| |summation| |tail| + |dom| |any| |leftTraceMatrix| |triangulate| RF2UTS |bitCoef| |moebius| + |toScale| |definingInequation| |e02def| |characteristicSet| + |minimumDegree| |iicsch| |arg1| |c06frf| |entry| |f04arf| |iExquo| + |showTheIFTable| |internalSubQuasiComponent?| |LagrangeInterpolation| + |semiDiscriminantEuclidean| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 43073be2..28497f69 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5435 +1,5435 @@ -(3264121 . 3486916241) -((-3925 (((-112) (-1 (-112) |#2| |#2|) $) 86) 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((-576) $)) (-15 -4230 ((-576) $)) (-15 -2334 ((-784) $)) (-15 -2344 ((-784) $)) (-15 -2780 (|t#1| $ (-576) (-576))) (-15 -1741 (|t#1| $ (-576) (-576))) (-15 -2780 (|t#1| $ (-576) (-576) |t#1|)) (-15 -3520 (|t#2| $ (-576))) (-15 -1612 (|t#3| $ (-576))) (-15 -1448 ((-657 |t#1|) $)) (-15 -3719 (|t#1| $ (-576) (-576) |t#1|)) (-15 -1810 (|t#1| $ (-576) (-576) |t#1|)) (-15 -1327 ($ $ (-576) |t#2|)) (-15 -3960 ($ $ (-576) |t#3|)) (-15 -4071 ($ (-1 |t#1| |t#1|) $)) (-15 -1799 ($ (-1 |t#1| |t#1|) $)) (-15 -4071 ($ (-1 |t#1| |t#1| |t#1|) $ $)) (-15 -4071 ($ (-1 |t#1| |t#1| |t#1|) $ $ |t#1|)))) -(((-34) . T) ((-102) -2748 (|has| |#1| (-1122)) (|has| |#1| (-102))) ((-625 (-877)) -2748 (|has| |#1| (-1122)) (|has| |#1| (-625 (-877)))) ((-319 |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) ((-501 |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) ((-1122) |has| |#1| (-1122)) ((-1239) . T)) -((-3899 (((-59 |#2|) (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|) 16)) (-3662 ((|#2| (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|) 18)) (-4071 (((-59 |#2|) (-1 |#2| |#1|) (-59 |#1|)) 13))) -(((-58 |#1| |#2|) (-10 -7 (-15 -3899 ((-59 |#2|) (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -3662 (|#2| (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -4071 ((-59 |#2|) (-1 |#2| |#1|) (-59 |#1|)))) (-1239) (-1239)) (T -58)) -((-4071 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-59 *5)) (-4 *5 (-1239)) (-4 *6 (-1239)) (-5 *2 (-59 *6)) (-5 *1 (-58 *5 *6)))) (-3662 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-59 *5)) (-4 *5 (-1239)) (-4 *2 (-1239)) (-5 *1 (-58 *5 *2)))) (-3899 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-59 *6)) (-4 *6 (-1239)) (-4 *5 (-1239)) (-5 *2 (-59 *5)) (-5 *1 (-58 *6 *5))))) -(-10 -7 (-15 -3899 ((-59 |#2|) (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -3662 (|#2| (-1 |#2| |#1| |#2|) (-59 |#1|) |#2|)) (-15 -4071 ((-59 |#2|) (-1 |#2| |#1|) (-59 |#1|)))) -((-3423 (((-112) $ $) NIL (|has| |#1| (-102)))) (-3590 (((-1294) $ (-576) (-576)) NIL (|has| $ (-6 -4467)))) (-3925 (((-112) (-1 (-112) |#1| |#1|) $) NIL) (((-112) $) NIL (|has| |#1| (-862)))) (-1698 (($ (-1 (-112) |#1| |#1|) $) NIL (|has| $ (-6 -4467))) (($ $) NIL (-12 (|has| $ (-6 -4467)) (|has| |#1| (-862))))) (-1832 (($ (-1 (-112) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (-862)))) (-4284 (((-112) $ (-784)) NIL)) (-3719 ((|#1| $ (-576) |#1|) NIL (|has| $ (-6 -4467))) ((|#1| $ (-1256 (-576)) |#1|) NIL (|has| $ (-6 -4467)))) (-2007 (($ (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4466)))) (-2515 (($) NIL T CONST)) (-4072 (($ $) NIL (|has| $ (-6 -4467)))) (-3796 (($ $) NIL)) (-1620 (($ $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122))))) (-3901 (($ |#1| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122)))) (($ (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4466)))) (-3662 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) NIL (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122)))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (-6 -4466))) ((|#1| (-1 |#1| |#1| |#1|) $) NIL (|has| $ (-6 -4466)))) (-1810 ((|#1| $ (-576) |#1|) NIL (|has| $ (-6 -4467)))) (-1741 ((|#1| $ (-576)) NIL)) (-3619 (((-576) (-1 (-112) |#1|) $) NIL) (((-576) |#1| $) NIL (|has| |#1| (-1122))) (((-576) |#1| $ (-576)) NIL (|has| |#1| (-1122)))) (-1448 (((-657 |#1|) $) NIL (|has| $ (-6 -4466)))) (-4360 (($ (-657 |#1|)) 11) (($ (-784) |#1|) 14)) (-4096 (($ (-784) |#1|) 13)) (-1786 (((-112) $ (-784)) NIL)) (-3363 (((-576) $) NIL (|has| (-576) (-862)))) (-3740 (($ $ $) NIL (|has| |#1| (-862)))) (-1661 (($ (-1 (-112) |#1| |#1|) $ $) NIL) (($ $ $) NIL (|has| |#1| (-862)))) (-3855 (((-657 |#1|) $) NIL (|has| $ (-6 -4466)))) (-3326 (((-112) |#1| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122))))) (-1833 (((-576) $) NIL (|has| (-576) (-862)))) (-2249 (($ $ $) NIL (|has| |#1| (-862)))) (-1799 (($ (-1 |#1| |#1|) $) NIL (|has| $ (-6 -4467)))) (-4071 (($ (-1 |#1| |#1|) $) NIL) (($ (-1 |#1| |#1| |#1|) $ $) NIL)) (-4326 (((-112) $ (-784)) NIL)) (-1708 (((-1180) $) NIL (|has| |#1| (-1122)))) (-2225 (($ |#1| $ (-576)) NIL) (($ $ $ (-576)) NIL)) (-3309 (((-657 (-576)) $) NIL)) (-4324 (((-112) (-576) $) NIL)) (-1460 (((-1142) $) NIL (|has| |#1| (-1122)))) (-3528 ((|#1| $) NIL (|has| (-576) (-862)))) (-4135 (((-3 |#1| "failed") (-1 (-112) |#1|) $) NIL)) (-1495 (($ $ |#1|) NIL (|has| $ (-6 -4467)))) (-2372 (((-112) (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4466)))) (-3205 (($ $ (-657 (-304 |#1|))) NIL (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ (-304 |#1|)) NIL (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ |#1| |#1|) NIL (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ (-657 |#1|) (-657 |#1|)) NIL (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))))) (-3807 (((-112) $ $) NIL)) (-3010 (((-112) |#1| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122))))) (-3585 (((-657 |#1|) $) NIL)) (-1368 (((-112) $) NIL)) (-3340 (($) NIL)) (-2780 ((|#1| $ (-576) |#1|) NIL) ((|#1| $ (-576)) NIL) (($ $ (-1256 (-576))) 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(-12 (-5 *2 (-657 *3)) (-4 *3 (-1239)) (-5 *1 (-59 *3)))) (-4360 (*1 *1 *2 *3) (-12 (-5 *2 (-784)) (-5 *1 (-59 *3)) (-4 *3 (-1239))))) -(-13 (-19 |#1|) (-10 -8 (-15 -4360 ($ (-657 |#1|))) (-15 -4360 ($ (-784) |#1|)))) -((-3423 (((-112) $ $) NIL (|has| |#1| (-102)))) (-4284 (((-112) $ (-784)) NIL)) (-3719 ((|#1| $ (-576) (-576) |#1|) NIL)) (-1327 (($ $ (-576) (-59 |#1|)) NIL)) (-3960 (($ $ (-576) (-59 |#1|)) NIL)) (-2515 (($) NIL T CONST)) (-3520 (((-59 |#1|) $ (-576)) NIL)) (-1810 ((|#1| $ (-576) (-576) |#1|) NIL)) (-1741 ((|#1| $ (-576) (-576)) NIL)) (-1448 (((-657 |#1|) $) NIL)) (-2334 (((-784) $) NIL)) (-4096 (($ (-784) (-784) |#1|) NIL)) (-2344 (((-784) $) NIL)) (-1786 (((-112) $ (-784)) NIL)) (-4076 (((-576) $) NIL)) (-2581 (((-576) $) NIL)) (-3855 (((-657 |#1|) $) NIL (|has| $ (-6 -4466)))) (-3326 (((-112) |#1| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122))))) (-2898 (((-576) $) NIL)) (-4230 (((-576) $) NIL)) (-1799 (($ (-1 |#1| |#1|) $) NIL)) (-4071 (($ (-1 |#1| |#1|) $) 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T) ((-102) -2802 (|has| |#1| (-1122)) (|has| |#1| (-102))) ((-625 (-877)) -2802 (|has| |#1| (-1122)) (|has| |#1| (-625 (-877)))) ((-319 |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) ((-501 |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) ((-1122) |has| |#1| (-1122)) ((-1239) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1224)) ((-95) |has| |#1| (-1224)) ((-102) . T) ((-111 #0# #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2748 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2748 (|has| |#1| (-1060 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-877)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1044)) ((-626 (-171 (-390))) |has| |#1| (-1044)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-908 (-390))) |has| |#1| (-626 (-908 (-390)))) ((-626 (-908 (-576))) |has| |#1| (-626 (-908 (-576)))) ((-626 #1=(-1194 |#1|)) . 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T) ((-464) -2748 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1224)) ((-526 (-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2748 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-659 #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-661 #2=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-653 |#1|) . T) ((-653 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-652 #2#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-730 |#1|) . T) ((-730 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-737 |#1| #1#) . T) ((-739) . T) ((-912 $ #3=(-1198)) -2748 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-918 (-1198)) |has| |#1| (-918 (-1198))) ((-920 #3#) -2748 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-902 (-390)) |has| |#1| (-902 (-390))) ((-902 (-576)) |has| |#1| (-902 (-576))) ((-900 |#1|) . T) ((-929) -12 (|has| |#1| (-317)) (|has| |#1| (-929))) ((-940) -2748 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1024) -12 (|has| |#1| (-1024)) (|has| |#1| (-1224))) ((-1060 (-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((-1060 (-576)) |has| |#1| (-1060 (-576))) ((-1060 |#1|) . T) ((-1073 #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1073 |#1|) . T) ((-1073 $) . T) ((-1078 #0#) -2748 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1078 |#1|) . T) ((-1078 $) . T) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1174) |has| |#1| (-360)) ((-1224) |has| |#1| (-1224)) ((-1227) |has| |#1| (-1224)) ((-1239) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1224)) ((-95) |has| |#1| (-1224)) ((-102) . T) ((-111 #0# #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2802 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2802 (|has| |#1| (-1060 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-877)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1044)) ((-626 (-171 (-390))) |has| |#1| (-1044)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-908 (-390))) |has| |#1| (-626 (-908 (-390)))) ((-626 (-908 (-576))) |has| |#1| (-626 (-908 (-576)))) ((-626 #1=(-1194 |#1|)) . T) ((-234 $) -2802 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) -2802 (|has| |#1| (-360)) (|has| |#1| (-238))) ((-237) -2802 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-294) |has| |#1| (-1224)) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) -2802 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-317) -2802 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-414) |has| |#1| (-360)) ((-379) -2802 (|has| |#1| (-379)) (|has| |#1| (-360))) ((-360) |has| |#1| (-360)) ((-381 |#1| #1#) . T) ((-421 |#1| #1#) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-423 |#1|) . T) ((-464) -2802 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1224)) ((-526 (-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2802 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-659 #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-661 #2=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-653 |#1|) . T) ((-653 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-652 #2#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-730 |#1|) . T) ((-730 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-737 |#1| #1#) . T) ((-739) . T) ((-912 $ #3=(-1198)) -2802 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-918 (-1198)) |has| |#1| (-918 (-1198))) ((-920 #3#) -2802 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-902 (-390)) |has| |#1| (-902 (-390))) ((-902 (-576)) |has| |#1| (-902 (-576))) ((-900 |#1|) . T) ((-929) -12 (|has| |#1| (-317)) (|has| |#1| (-929))) ((-940) -2802 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1024) -12 (|has| |#1| (-1024)) (|has| |#1| (-1224))) ((-1060 (-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((-1060 (-576)) |has| |#1| (-1060 (-576))) ((-1060 |#1|) . T) ((-1073 #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1073 |#1|) . T) ((-1073 $) . T) ((-1078 #0#) -2802 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1078 |#1|) . T) ((-1078 $) . T) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1174) |has| |#1| (-360)) ((-1224) |has| |#1| (-1224)) ((-1227) |has| |#1| (-1224)) ((-1239) . 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(-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2748 (|has| |#2| (-1122)) (|has| |#2| (-1071)) (|has| |#2| (-862)) (|has| |#2| (-806)) (|has| |#2| (-739)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2748 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2748 (|has| |#2| (-1071)) (|has| |#2| (-806)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122))) ((-628 (-576)) -2748 (|has| |#2| (-1071)) (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122)))) ((-628 |#2|) |has| |#2| (-1122)) ((-625 (-877)) -2748 (|has| |#2| (-1122)) (|has| |#2| (-1071)) (|has| |#2| (-862)) (|has| |#2| (-806)) (|has| |#2| (-739)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-877))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1289 |#2|)) . T) ((-234 $) -2748 (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1071)))) ((-232 |#2|) |has| |#2| (-1071)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1071))) ((-237) -2748 (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1071)))) ((-272 |#2|) |has| |#2| (-1071)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1071)) ((-423 |#2|) |has| |#2| (-1122)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((-659 (-576)) -2748 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-659 |#2|) -2748 (|has| |#2| (-1071)) (|has| |#2| (-739)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-659 $) |has| |#2| (-1071)) ((-661 #2=(-576)) -12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071))) ((-661 |#2|) -2748 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-661 $) |has| |#2| (-1071)) ((-653 |#2|) -2748 (|has| |#2| (-739)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-652 #2#) -12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071))) ((-652 |#2|) |has| |#2| (-1071)) ((-730 |#2|) -2748 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-739) |has| |#2| (-1071)) ((-805) |has| |#2| (-806)) ((-806) |has| |#2| (-806)) ((-807) |has| |#2| (-806)) ((-808) |has| |#2| (-806)) ((-862) -2748 (|has| |#2| (-862)) (|has| |#2| (-806))) ((-865) -2748 (|has| |#2| (-862)) (|has| |#2| (-806))) ((-912 $ #3=(-1198)) -2748 (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071))) (-12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071)))) ((-918 (-1198)) -12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071))) ((-920 #3#) -2748 (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071))) (-12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071)))) ((-1060 #0#) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122))) ((-1060 (-576)) -12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122))) ((-1060 |#2|) |has| |#2| (-1122)) ((-1073 |#2|) -2748 (|has| |#2| (-1071)) (|has| |#2| (-739)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1078 |#2|) -2748 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1071) |has| |#2| (-1071)) ((-1080) |has| |#2| (-1071)) ((-1134) |has| |#2| (-1071)) ((-1122) -2748 (|has| |#2| (-1122)) (|has| |#2| (-1071)) (|has| |#2| (-862)) (|has| |#2| (-806)) (|has| |#2| (-739)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1239) . T) ((-1296 |#2|) |has| |#2| (-374))) -((-3899 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3662 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4071 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -3899 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3662 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4071 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-784) (-1239) (-1239)) (T -244)) -((-4071 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-784)) (-4 *6 (-1239)) (-4 *7 (-1239)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3662 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-784)) (-4 *6 (-1239)) (-4 *2 (-1239)) (-5 *1 (-244 *5 *6 *2)))) (-3899 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-784)) (-4 *7 (-1239)) (-4 *5 (-1239)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 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(|has| |#2| (-1071))) (($ $ |#2|) 44 (|has| |#2| (-739))) (($ |#2| $) 45 (|has| |#2| (-739))) (($ (-576) $) NIL (|has| |#2| (-21))) (($ (-784) $) NIL (|has| |#2| (-23))) (($ (-941) $) NIL (|has| |#2| (-25)))) (-3437 (((-784) $) NIL (|has| $ (-6 -4466))))) +((-1924 (*1 *1 *2) (-12 (-5 *2 (-1289 *4)) (-4 *4 (-1239)) (-4 *1 (-243 *3 *4)))) (-3110 (*1 *1 *2) (-12 (-5 *2 (-941)) (-4 *1 (-243 *3 *4)) (-4 *4 (-1071)) (-4 *4 (-1239)))) (-1374 (*1 *2 *1 *1) (-12 (-4 *1 (-243 *3 *2)) (-4 *2 (-1239)) (-4 *2 (-1071))))) +(-13 (-616 (-576) |t#2|) (-625 (-1289 |t#2|)) (-10 -8 (-6 -4466) (-15 -1924 ($ (-1289 |t#2|))) (IF (|has| |t#2| (-1122)) (-6 (-423 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1071)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-232 |t#2|)) (-6 (-388 |t#2|)) (-15 -3110 ($ (-941))) (-15 -1374 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-739)) (-6 (-653 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-379)) (-6 (-379)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-730 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4463)) (-6 -4463) |%noBranch|) (IF (|has| |t#2| (-862)) (-6 (-862)) |%noBranch|) (IF (|has| |t#2| (-806)) (-6 (-806)) |%noBranch|) (IF (|has| |t#2| (-374)) (-6 (-1296 |t#2|)) |%noBranch|))) +(((-21) -2802 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -2802 (|has| |#2| (-1071)) (|has| |#2| (-806)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2802 (|has| |#2| (-1071)) (|has| |#2| (-806)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2802 (|has| |#2| (-1122)) (|has| |#2| (-1071)) (|has| |#2| (-862)) (|has| |#2| (-806)) (|has| |#2| (-739)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2802 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2802 (|has| |#2| (-1071)) (|has| |#2| (-806)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122))) ((-628 (-576)) -2802 (|has| |#2| (-1071)) (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122)))) ((-628 |#2|) |has| |#2| (-1122)) ((-625 (-877)) -2802 (|has| |#2| (-1122)) (|has| |#2| (-1071)) (|has| |#2| (-862)) (|has| |#2| (-806)) (|has| |#2| (-739)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-877))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1289 |#2|)) . T) ((-234 $) -2802 (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1071)))) ((-232 |#2|) |has| |#2| (-1071)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1071))) ((-237) -2802 (-12 (|has| |#2| (-237)) (|has| |#2| (-1071))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1071)))) ((-272 |#2|) |has| |#2| (-1071)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1071)) ((-423 |#2|) |has| |#2| (-1122)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((-659 (-576)) -2802 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-659 |#2|) -2802 (|has| |#2| (-1071)) (|has| |#2| (-739)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-659 $) |has| |#2| (-1071)) ((-661 #2=(-576)) -12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071))) ((-661 |#2|) -2802 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-661 $) |has| |#2| (-1071)) ((-653 |#2|) -2802 (|has| |#2| (-739)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-652 #2#) -12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071))) ((-652 |#2|) |has| |#2| (-1071)) ((-730 |#2|) -2802 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-739) |has| |#2| (-1071)) ((-805) |has| |#2| (-806)) ((-806) |has| |#2| (-806)) ((-807) |has| |#2| (-806)) ((-808) |has| |#2| (-806)) ((-862) -2802 (|has| |#2| (-862)) (|has| |#2| (-806))) ((-865) -2802 (|has| |#2| (-862)) (|has| |#2| (-806))) ((-912 $ #3=(-1198)) -2802 (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071))) (-12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071)))) ((-918 (-1198)) -12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071))) ((-920 #3#) -2802 (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071))) (-12 (|has| |#2| (-918 (-1198))) (|has| |#2| (-1071)))) ((-1060 #0#) -12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122))) ((-1060 (-576)) -12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122))) ((-1060 |#2|) |has| |#2| (-1122)) ((-1073 |#2|) -2802 (|has| |#2| (-1071)) (|has| |#2| (-739)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1078 |#2|) -2802 (|has| |#2| (-1071)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1071) |has| |#2| (-1071)) ((-1080) |has| |#2| (-1071)) ((-1134) |has| |#2| (-1071)) ((-1122) -2802 (|has| |#2| (-1122)) (|has| |#2| (-1071)) (|has| |#2| (-862)) (|has| |#2| (-806)) (|has| |#2| (-739)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1239) . T) ((-1296 |#2|) |has| |#2| (-374))) +((-4417 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3622 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4083 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -4417 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3622 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4083 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-784) (-1239) (-1239)) (T -244)) +((-4083 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-784)) (-4 *6 (-1239)) (-4 *7 (-1239)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3622 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-784)) (-4 *6 (-1239)) (-4 *2 (-1239)) (-5 *1 (-244 *5 *6 *2)))) (-4417 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-784)) (-4 *7 (-1239)) (-4 *5 (-1239)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) +(-10 -7 (-15 -4417 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3622 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4083 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) +((-3429 (((-112) $ $) NIL (|has| |#2| (-102)))) (-2364 (((-112) $) NIL (|has| |#2| (-23)))) (-3110 (($ (-941)) 62 (|has| |#2| (-1071)))) (-4313 (((-1294) $ (-576) (-576)) NIL (|has| $ (-6 -4467)))) (-3733 (($ $ $) 68 (|has| |#2| (-806)))) (-2721 (((-3 $ "failed") $ $) 53 (|has| |#2| (-132)))) (-3793 (((-112) $ (-784)) NIL)) (-2193 (((-784)) NIL (|has| |#2| (-379)))) (-3682 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4467)))) (-4359 (($) NIL T CONST)) (-1624 (((-3 (-576) "failed") $) NIL (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122)))) (((-3 (-419 (-576)) "failed") $) NIL (-12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122)))) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1122)))) (-2884 (((-576) $) NIL (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122)))) (((-419 (-576)) $) NIL (-12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122)))) ((|#2| $) 28 (|has| |#2| (-1122)))) (-3306 (((-702 (-576)) (-702 $)) NIL (-12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071)))) (((-2 (|:| -3750 (-702 (-576))) (|:| |vec| (-1289 (-576)))) (-702 $) (-1289 $)) NIL (-12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071)))) (((-2 (|:| -3750 (-702 |#2|)) (|:| |vec| (-1289 |#2|))) (-702 $) (-1289 $)) NIL (|has| |#2| (-1071))) (((-702 |#2|) (-702 $)) NIL (|has| |#2| (-1071)))) (-3843 (((-3 $ "failed") $) 58 (|has| |#2| (-1071)))) (-1892 (($) NIL (|has| |#2| (-379)))) (-2158 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4467)))) (-2083 ((|#2| $ (-576)) 56)) (-1458 (((-657 |#2|) $) 14 (|has| $ (-6 -4466)))) (-4094 (((-112) $) NIL (|has| |#2| (-1071)))) (-1833 (((-112) $ (-784)) NIL)) (-3853 (((-576) $) 19 (|has| (-576) (-862)))) (-3707 (($ $ $) NIL (|has| |#2| (-862)))) (-2070 (((-657 |#2|) $) NIL (|has| $ (-6 -4466)))) (-1627 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#2| (-1122))))) 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NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1198)) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1071))) (($ $ (-1 |#2| |#2|) (-784)) NIL (|has| |#2| (-1071)))) (-1482 (((-784) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4466))) (((-784) |#2| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#2| (-1122))))) (-1923 (($ $) NIL)) (-3501 (((-1289 |#2|) $) 9) (($ (-576)) NIL (-2802 (-12 (|has| |#2| (-1060 (-576))) (|has| |#2| (-1122))) (|has| |#2| (-1071)))) (($ (-419 (-576))) NIL (-12 (|has| |#2| (-1060 (-419 (-576)))) (|has| |#2| (-1122)))) (($ |#2|) 12 (|has| |#2| (-1122))) (((-877) $) NIL (|has| |#2| (-625 (-877))))) (-1960 (((-784)) NIL (|has| |#2| (-1071)) CONST)) (-2046 (((-112) $ $) NIL (|has| |#2| (-102)))) (-2147 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4466)))) (-2769 (($) 36 (|has| |#2| (-23)) CONST)) (-2779 (($) 40 (|has| |#2| (-1071)) CONST)) (-2097 (($ $ (-784)) NIL (-12 (|has| |#2| (-237)) (|has| |#2| 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -2748 (|has| |#1| (-1060 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 |#2|) . T) ((-628 |#3|) . T) ((-628 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-625 (-877)) . T) ((-174) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| |#1| (-626 (-548))) (|has| |#3| (-626 (-548)))) ((-626 (-908 (-390))) -12 (|has| |#1| (-626 (-908 (-390)))) (|has| |#3| (-626 (-908 (-390))))) ((-626 (-908 (-576))) -12 (|has| |#1| (-626 (-908 (-576)))) (|has| |#3| (-626 (-908 (-576))))) ((-234 $) -2748 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2748 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-300) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-319 $) . T) ((-336 |#1| |#4|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2748 (|has| |#1| (-929)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-238)) ((-526 |#2| $) |has| |#1| (-238)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-568) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-659 #0#) |has| |#1| (-38 (-419 (-576)))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #0#) |has| |#1| (-38 (-419 (-576)))) ((-661 #1=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #0#) |has| |#1| (-38 (-419 (-576)))) ((-653 |#1|) |has| |#1| (-174)) ((-653 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-652 #1#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #0#) |has| |#1| (-38 (-419 (-576)))) ((-730 |#1|) |has| |#1| (-174)) ((-730 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-739) . T) ((-912 $ #2=(-1198)) -2748 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-912 $ |#3|) . T) ((-918 (-1198)) |has| |#1| (-918 (-1198))) ((-918 |#3|) . T) ((-920 #2#) -2748 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-920 |#3|) . T) ((-902 (-390)) -12 (|has| |#1| (-902 (-390))) (|has| |#3| (-902 (-390)))) ((-902 (-576)) -12 (|has| |#1| (-902 (-576))) (|has| |#3| (-902 (-576)))) ((-969 |#1| |#4| |#3|) . T) ((-929) |has| |#1| (-929)) ((-1060 (-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((-1060 (-576)) |has| |#1| (-1060 (-576))) ((-1060 |#1|) . T) ((-1060 |#2|) . T) ((-1060 |#3|) . T) ((-1073 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1073 |#1|) . T) ((-1073 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1078 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1078 |#1|) . T) ((-1078 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1239) . T) ((-1243) |has| |#1| (-929))) -((-3423 (((-112) $ $) 20 (|has| |#1| (-102)))) (-1753 ((|#1| $) 55)) (-1425 ((|#1| $) 45)) (-4284 (((-112) $ (-784)) 8)) (-2515 (($) 7 T CONST)) (-1528 (($ $) 61)) (-4072 (($ $) 49)) (-3240 ((|#1| |#1| $) 47)) (-2477 ((|#1| $) 46)) (-1448 (((-657 |#1|) $) 31 (|has| $ (-6 -4466)))) (-1786 (((-112) $ (-784)) 9)) (-3855 (((-657 |#1|) $) 30 (|has| $ (-6 -4466)))) (-3326 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466))))) (-1799 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4467)))) (-4071 (($ (-1 |#1| |#1|) $) 36)) (-4326 (((-112) $ (-784)) 10)) (-3041 (((-784) $) 62)) (-1708 (((-1180) $) 23 (|has| |#1| (-1122)))) (-3107 ((|#1| $) 40)) (-1548 ((|#1| |#1| $) 53)) (-3436 ((|#1| |#1| $) 52)) (-2701 (($ |#1| $) 41)) (-2363 (((-784) $) 56)) (-1460 (((-1142) $) 22 (|has| |#1| (-1122)))) (-2727 ((|#1| $) 63)) (-2341 ((|#1| $) 51)) (-3582 ((|#1| $) 50)) (-2184 ((|#1| $) 42)) (-2372 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4466)))) (-3205 (($ $ (-657 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ (-657 |#1|) (-657 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))))) (-3807 (((-112) $ $) 14)) (-3513 ((|#1| |#1| $) 59)) (-1368 (((-112) $) 11)) (-3340 (($) 12)) (-3608 ((|#1| $) 60)) (-2404 (($) 58) (($ (-657 |#1|)) 57)) (-3106 (((-784) $) 44)) (-1469 (((-784) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4466))) (((-784) |#1| $) 29 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466))))) (-1899 (($ $) 13)) (-3515 (((-877) $) 18 (|has| |#1| (-625 (-877))))) (-1926 ((|#1| $) 54)) (-4166 (((-112) $ $) 21 (|has| |#1| (-102)))) (-1636 (($ (-657 |#1|)) 43)) (-3292 ((|#1| $) 64)) (-3258 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4466)))) (-2881 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3437 (((-784) $) 6 (|has| $ (-6 -4466))))) +((-3801 (*1 *2 *3) (-12 (-4 *4 (-1071)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-806)) (-5 *2 (-1 *1 (-784))) (-4 *1 (-260 *4 *3 *5 *6)))) (-3928 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-806)) (-5 *2 (-657 *4)))) (-3182 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1071)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-806)) (-5 *2 (-784)))) (-3182 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-806)) (-5 *2 (-784)))) (-1770 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1071)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-806)) (-5 *2 (-784)))) (-2728 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-806)) (-5 *2 (-657 (-784))))) (-3983 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-806)) (-5 *2 (-784)))) (-2728 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1071)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-806)) (-5 *2 (-657 (-784))))) (-3983 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1071)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-806)) (-5 *2 (-784)))) (-3948 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-806)) (-5 *2 (-112)))) (-1597 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *2 *5)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-806)) (-4 *2 (-275 *4)))) (-4276 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1071)) (-4 *3 (-862)) (-4 *4 (-275 *3)) (-4 *5 (-806)))) (-1594 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1071)) (-4 *3 (-862)) (-4 *4 (-275 *3)) (-4 *5 (-806)))) (-3801 (*1 *2 *1) (-12 (-4 *3 (-238)) (-4 *3 (-1071)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-806)) (-5 *2 (-1 *1 (-784))) (-4 *1 (-260 *3 *4 *5 *6))))) +(-13 (-969 |t#1| |t#4| |t#3|) (-232 |t#1|) (-1060 |t#2|) (-10 -8 (-15 -3801 ((-1 $ (-784)) |t#2|)) (-15 -3928 ((-657 |t#2|) $)) (-15 -3182 ((-784) $ |t#2|)) (-15 -3182 ((-784) $)) (-15 -1770 ((-784) $ |t#2|)) (-15 -2728 ((-657 (-784)) $)) (-15 -3983 ((-784) $)) (-15 -2728 ((-657 (-784)) $ |t#2|)) (-15 -3983 ((-784) $ |t#2|)) (-15 -3948 ((-112) $)) (-15 -1597 (|t#3| $)) (-15 -4276 ($ $)) (-15 -1594 ($ $)) (IF (|has| |t#1| (-238)) (PROGN (-6 (-526 |t#2| |t#1|)) (-6 (-526 |t#2| $)) (-6 (-319 $)) (-15 -3801 ((-1 $ (-784)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -2802 (|has| |#1| (-1060 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 |#2|) . T) ((-628 |#3|) . T) ((-628 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-625 (-877)) . T) ((-174) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| |#1| (-626 (-548))) (|has| |#3| (-626 (-548)))) ((-626 (-908 (-390))) -12 (|has| |#1| (-626 (-908 (-390)))) (|has| |#3| (-626 (-908 (-390))))) ((-626 (-908 (-576))) -12 (|has| |#1| (-626 (-908 (-576)))) (|has| |#3| (-626 (-908 (-576))))) ((-234 $) -2802 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2802 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-300) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-319 $) . T) ((-336 |#1| |#4|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2802 (|has| |#1| (-929)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-238)) ((-526 |#2| $) |has| |#1| (-238)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-568) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-659 #0#) |has| |#1| (-38 (-419 (-576)))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #0#) |has| |#1| (-38 (-419 (-576)))) ((-661 #1=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #0#) |has| |#1| (-38 (-419 (-576)))) ((-653 |#1|) |has| |#1| (-174)) ((-653 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-652 #1#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #0#) |has| |#1| (-38 (-419 (-576)))) ((-730 |#1|) |has| |#1| (-174)) ((-730 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-739) . T) ((-912 $ #2=(-1198)) -2802 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-912 $ |#3|) . T) ((-918 (-1198)) |has| |#1| (-918 (-1198))) ((-918 |#3|) . T) ((-920 #2#) -2802 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-920 |#3|) . T) ((-902 (-390)) -12 (|has| |#1| (-902 (-390))) (|has| |#3| (-902 (-390)))) ((-902 (-576)) -12 (|has| |#1| (-902 (-576))) (|has| |#3| (-902 (-576)))) ((-969 |#1| |#4| |#3|) . T) ((-929) |has| |#1| (-929)) ((-1060 (-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((-1060 (-576)) |has| |#1| (-1060 (-576))) ((-1060 |#1|) . T) ((-1060 |#2|) . T) ((-1060 |#3|) . T) ((-1073 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1073 |#1|) . T) ((-1073 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1078 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1078 |#1|) . T) ((-1078 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1239) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) . T) ((-628 (-576)) . T) ((-628 #1=(-1198)) |has| |#1| (-1060 (-1198))) ((-628 |#1|) . T) ((-628 $) . T) ((-625 (-877)) . T) ((-174) . T) ((-626 (-227)) |has| |#1| (-1044)) ((-626 (-390)) |has| |#1| (-1044)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-908 (-390))) |has| |#1| (-626 (-908 (-390)))) ((-626 (-908 (-576))) |has| |#1| (-626 (-908 (-576)))) ((-234 $) -2802 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2802 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) . T) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) . T) ((-317) . T) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-464) . T) ((-526 (-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) . T) ((-659 #0#) . T) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #0#) . T) ((-661 #2=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #0#) . T) ((-653 |#1|) . T) ((-653 $) . T) ((-652 #2#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #0#) . T) ((-730 |#1|) . T) ((-730 $) . T) ((-739) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2748 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2748 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1198)) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-1198)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . 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T) ((-661 |#2|) |has| |#1| (-374)) ((-661 $) . T) ((-653 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-653 |#1|) |has| |#1| (-174)) ((-653 |#2|) |has| |#1| (-374)) ((-653 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-652 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) ((-652 |#2|) |has| |#1| (-374)) ((-730 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-730 |#1|) |has| |#1| (-174)) ((-730 |#2|) |has| |#1| (-374)) ((-730 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-739) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1198)) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-1198)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-877)) . T) ((-174) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1044))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1044))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-908 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-908 (-390))))) ((-626 (-908 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-908 (-576))))) ((-234 $) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1134)) ((-300) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1198) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1198) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-659 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 |#2|) |has| |#1| (-374)) ((-659 $) . T) ((-661 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-661 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) ((-661 |#1|) . T) ((-661 |#2|) |has| |#1| (-374)) ((-661 $) . T) ((-653 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-653 |#1|) |has| |#1| (-174)) ((-653 |#2|) |has| |#1| (-374)) ((-653 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-652 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) ((-652 |#2|) |has| |#1| (-374)) ((-730 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-730 |#1|) |has| |#1| (-174)) ((-730 |#2|) |has| |#1| (-374)) ((-730 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-739) . T) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-805) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-808) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-833) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-861) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-862) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-833)))) ((-865) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-833)))) ((-912 $ #4=(-1198)) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-920 (-1198)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198))))) ((-918 (-1198)) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198))))) ((-920 #4#) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-920 (-1198)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198))))) ((-902 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-902 (-390)))) ((-902 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-902 (-576)))) ((-900 |#2|) |has| |#1| (-374)) ((-929) -12 (|has| |#1| (-374)) (|has| |#2| (-929))) ((-995 |#1| #0# (-1104)) . T) ((-940) |has| |#1| (-374)) ((-1014 |#2|) |has| |#1| (-374)) ((-1024) |has| |#1| (-38 (-419 (-576)))) ((-1044) -12 (|has| |#1| (-374)) (|has| |#2| (-1044))) ((-1060 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-576)))) ((-1060 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-576)))) ((-1060 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-1198)))) ((-1060 |#2|) . T) ((-1073 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1073 |#1|) . T) ((-1073 |#2|) |has| |#1| (-374)) ((-1073 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1078 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1078 |#1|) . T) ((-1078 |#2|) |has| |#1| (-374)) ((-1078 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1174) -12 (|has| |#1| (-374)) (|has| |#2| (-1174))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1227) |has| |#1| (-38 (-419 (-576)))) ((-1239) . T) ((-1243) |has| |#1| (-374)) ((-1249 |#1|) . T) ((-1267 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-784)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2748 (|has| |#1| (-1060 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1104)) . T) ((-628 |#1|) . T) ((-628 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-877)) . T) ((-174) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1104) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-908 (-390))) -12 (|has| (-1104) (-626 (-908 (-390)))) (|has| |#1| (-626 (-908 (-390))))) ((-626 (-908 (-576))) -12 (|has| (-1104) (-626 (-908 (-576)))) (|has| |#1| (-626 (-908 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2748 (|has| |#1| (-929)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-659 #1#) |has| |#1| (-38 (-419 (-576)))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #1#) |has| |#1| (-38 (-419 (-576)))) ((-661 #3=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #1#) |has| |#1| (-38 (-419 (-576)))) ((-653 |#1|) |has| |#1| (-174)) ((-653 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-652 #3#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #1#) |has| |#1| (-38 (-419 (-576)))) ((-730 |#1|) |has| |#1| (-174)) ((-730 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-739) . T) ((-912 $ #2#) . T) ((-912 $ #4=(-1198)) -2748 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-918 #2#) . T) ((-918 (-1198)) |has| |#1| (-918 (-1198))) ((-920 #2#) . T) ((-920 #4#) -2748 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-902 (-390)) -12 (|has| (-1104) (-902 (-390))) (|has| |#1| (-902 (-390)))) ((-902 (-576)) -12 (|has| (-1104) (-902 (-576))) (|has| |#1| (-902 (-576)))) ((-969 |#1| #0# #2#) . T) ((-929) |has| |#1| (-929)) ((-940) |has| |#1| (-374)) ((-1060 (-419 (-576))) |has| |#1| (-1060 (-419 (-576)))) ((-1060 (-576)) |has| |#1| (-1060 (-576))) ((-1060 #2#) . T) ((-1060 |#1|) . T) ((-1073 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1073 |#1|) . T) ((-1073 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1078 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1078 |#1|) . T) ((-1078 $) -2748 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1174) |has| |#1| (-1174)) ((-1239) . T) ((-1243) |has| |#1| (-929))) -((-1998 (((-657 (-1104)) $) 34)) (-2165 (($ $) 31)) (-1974 (($ |#2| |#3|) NIL) (($ $ (-1104) |#3|) 28) (($ $ (-657 (-1104)) (-657 |#3|)) 27)) (-2129 (($ $) 14)) (-2141 ((|#2| $) 12)) (-4265 ((|#3| $) 10))) -(((-1266 |#1| |#2| |#3|) (-10 -8 (-15 -1998 ((-657 (-1104)) |#1|)) (-15 -1974 (|#1| |#1| (-657 (-1104)) (-657 |#3|))) (-15 -1974 (|#1| |#1| (-1104) |#3|)) (-15 -2165 (|#1| |#1|)) (-15 -1974 (|#1| |#2| |#3|)) (-15 -4265 (|#3| |#1|)) (-15 -2129 (|#1| |#1|)) (-15 -2141 (|#2| |#1|))) (-1267 |#2| |#3|) (-1071) (-805)) (T -1266)) -NIL -(-10 -8 (-15 -1998 ((-657 (-1104)) |#1|)) (-15 -1974 (|#1| |#1| (-657 (-1104)) (-657 |#3|))) (-15 -1974 (|#1| |#1| (-1104) |#3|)) (-15 -2165 (|#1| |#1|)) (-15 -1974 (|#1| |#2| |#3|)) (-15 -4265 (|#3| |#1|)) (-15 -2129 (|#1| |#1|)) (-15 -2141 (|#2| |#1|))) -((-3423 (((-112) $ $) 7)) (-2044 (((-112) $) 17)) (-1998 (((-657 (-1104)) $) 86)) (-2993 (((-1198) $) 118)) (-3422 (((-2 (|:| -4119 $) (|:| -4453 $) (|:| |associate| $)) 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T) ((-23) . T) ((-47 |#1| #0=(-784)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2802 (|has| |#1| (-1060 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1104)) . T) ((-628 |#1|) . T) ((-628 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-877)) . T) ((-174) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1104) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-908 (-390))) -12 (|has| (-1104) (-626 (-908 (-390)))) (|has| |#1| (-626 (-908 (-390))))) ((-626 (-908 (-576))) -12 (|has| (-1104) (-626 (-908 (-576)))) (|has| |#1| (-626 (-908 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2802 (|has| |#1| (-929)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-659 #1#) |has| |#1| (-38 (-419 (-576)))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-661 #1#) |has| |#1| (-38 (-419 (-576)))) ((-661 #3=(-576)) |has| |#1| (-652 (-576))) ((-661 |#1|) . T) ((-661 $) . T) ((-653 #1#) |has| |#1| (-38 (-419 (-576)))) ((-653 |#1|) |has| |#1| (-174)) ((-653 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-652 #3#) |has| |#1| (-652 (-576))) ((-652 |#1|) . T) ((-730 #1#) |has| |#1| (-38 (-419 (-576)))) ((-730 |#1|) |has| |#1| (-174)) ((-730 $) -2802 (|has| |#1| (-929)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-739) . T) ((-912 $ #2#) . T) ((-912 $ #4=(-1198)) -2802 (|has| |#1| (-920 (-1198))) (|has| |#1| (-918 (-1198)))) ((-918 #2#) . T) ((-918 (-1198)) |has| |#1| (-918 (-1198))) ((-920 #2#) . 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T) ((-653 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-653 |#1|) |has| |#1| (-174)) ((-653 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-730 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-730 |#1|) |has| |#1| (-174)) ((-730 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-739) . T) ((-912 $ #2=(-1198)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-918 (-1198)))) ((-918 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-918 (-1198)))) ((-920 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-918 (-1198)))) ((-995 |#1| #0# (-1104)) . T) ((-940) |has| |#1| (-374)) ((-1024) |has| |#1| (-38 (-419 (-576)))) ((-1060 |#2|) . T) ((-1073 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1073 |#1|) . T) ((-1073 $) -2748 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1078 #1#) -2748 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1078 |#1|) . 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3251558 3253326 3255298 "ZDSOLVE" 3260388 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1315 3250804 3250945 3251134 "YSTREAM" 3251404 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1314 3250232 3250478 3250591 "YDIAGRAM" 3250713 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1313 3248006 3249533 3249737 "XRPOLY" 3250075 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3244559 3245877 3246452 "XPR" 3247478 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1311 3242280 3243890 3244094 "XPOLY" 3244390 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1310 3239919 3241287 3241342 "XPOLYC" 3241630 NIL XPOLYC (NIL T T) -9 NIL 3241743 NIL) (-1309 3236295 3238436 3238824 "XPBWPOLY" 3239577 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1308 3231976 3234271 3234313 "XF" 3234934 NIL XF (NIL T) -9 NIL 3235334 NIL) (-1307 3231597 3231685 3231854 "XF-" 3231859 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1306 3226779 3228068 3228123 "XFALG" 3230295 NIL XFALG (NIL T T) -9 NIL 3231084 NIL) (-1305 3225912 3226016 3226221 "XEXPPKG" 3226671 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1304 3224021 3225762 3225858 "XDPOLY" 3225863 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1303 3222814 3223414 3223457 "XALG" 3223462 NIL XALG (NIL T) -9 NIL 3223573 NIL) (-1302 3216256 3220791 3221285 "WUTSET" 3222406 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1301 3214512 3215308 3215631 "WP" 3216067 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1300 3214114 3214334 3214404 "WHILEAST" 3214464 T WHILEAST (NIL) -8 NIL NIL NIL) (-1299 3213586 3213831 3213925 "WHEREAST" 3214042 T WHEREAST (NIL) -8 NIL NIL NIL) (-1298 3212472 3212670 3212965 "WFFINTBS" 3213383 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1297 3210376 3210803 3211265 "WEIER" 3212044 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1296 3209408 3209858 3209900 "VSPACE" 3210036 NIL VSPACE (NIL T) -9 NIL 3210110 NIL) (-1295 3209246 3209273 3209364 "VSPACE-" 3209369 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1294 3209055 3209097 3209165 "VOID" 3209200 T VOID (NIL) -8 NIL NIL NIL) (-1293 3207191 3207550 3207956 "VIEW" 3208671 T VIEW (NIL) -7 NIL NIL NIL) (-1292 3203615 3204254 3204991 "VIEWDEF" 3206476 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1291 3192919 3195163 3197336 "VIEW3D" 3201464 T VIEW3D (NIL) -8 NIL NIL NIL) (-1290 3185170 3186830 3188409 "VIEW2D" 3191362 T VIEW2D (NIL) -8 NIL NIL NIL) (-1289 3180526 3184940 3185032 "VECTOR" 3185113 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1288 3179103 3179362 3179680 "VECTOR2" 3180256 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1287 3172501 3176807 3176850 "VECTCAT" 3177845 NIL VECTCAT (NIL T) -9 NIL 3178432 NIL) (-1286 3171515 3171769 3172159 "VECTCAT-" 3172164 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1285 3170969 3171166 3171286 "VARIABLE" 3171430 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1284 3170902 3170907 3170937 "UTYPE" 3170942 T UTYPE (NIL) -9 NIL NIL NIL) (-1283 3169732 3169886 3170148 "UTSODETL" 3170728 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1282 3167172 3167632 3168156 "UTSODE" 3169273 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1281 3159120 3164933 3165413 "UTS" 3166750 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1280 3149684 3155054 3155097 "UTSCAT" 3156209 NIL UTSCAT (NIL T) -9 NIL 3156967 NIL) (-1279 3147032 3147754 3148743 "UTSCAT-" 3148748 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1278 3146659 3146702 3146835 "UTS2" 3146983 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1277 3140860 3143469 3143512 "URAGG" 3145582 NIL URAGG (NIL T) -9 NIL 3146305 NIL) (-1276 3137799 3138662 3139785 "URAGG-" 3139790 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1275 3133508 3136434 3136899 "UPXSSING" 3137463 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1274 3125684 3132890 3133154 "UPXS" 3133302 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1273 3118757 3125588 3125660 "UPXSCONS" 3125665 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1272 3108164 3114960 3115022 "UPXSCCA" 3115596 NIL UPXSCCA (NIL T T) -9 NIL 3115829 NIL) (-1271 3107802 3107887 3108061 "UPXSCCA-" 3108066 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1270 3097061 3103630 3103673 "UPXSCAT" 3104321 NIL UPXSCAT (NIL T) -9 NIL 3104930 NIL) (-1269 3096491 3096570 3096749 "UPXS2" 3096976 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1268 3095145 3095398 3095749 "UPSQFREE" 3096234 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1267 3088353 3091413 3091468 "UPSCAT" 3092548 NIL UPSCAT (NIL T T) -9 NIL 3093313 NIL) (-1266 3087557 3087764 3088091 "UPSCAT-" 3088096 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1265 3072639 3080684 3080727 "UPOLYC" 3082828 NIL UPOLYC (NIL T) -9 NIL 3084049 NIL) (-1264 3063967 3066393 3069540 "UPOLYC-" 3069545 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1263 3063594 3063637 3063770 "UPOLYC2" 3063918 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1262 3055129 3063277 3063406 "UP" 3063513 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1261 3054468 3054575 3054739 "UPMP" 3055018 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1260 3054021 3054102 3054241 "UPDIVP" 3054381 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1259 3052589 3052838 3053154 "UPDECOMP" 3053770 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1258 3051820 3051932 3052118 "UPCDEN" 3052473 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1257 3051339 3051408 3051557 "UP2" 3051745 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1256 3049806 3050543 3050820 "UNISEG" 3051097 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1255 3049021 3049148 3049353 "UNISEG2" 3049649 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1254 3048081 3048261 3048487 "UNIFACT" 3048837 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1253 3030833 3047393 3047635 "ULS" 3047897 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1252 3018463 3030737 3030809 "ULSCONS" 3030814 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1251 2999184 3011544 3011606 "ULSCCAT" 3012244 NIL ULSCCAT (NIL T T) -9 NIL 3012533 NIL) (-1250 2998234 2998479 2998867 "ULSCCAT-" 2998872 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 2987298 2993781 2993824 "ULSCAT" 2994687 NIL ULSCAT (NIL T) -9 NIL 2995418 NIL) (-1248 2986728 2986807 2986986 "ULS2" 2987213 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1247 2985847 2986357 2986464 "UINT8" 2986575 T UINT8 (NIL) -8 NIL NIL 2986660) (-1246 2984965 2985475 2985582 "UINT64" 2985693 T UINT64 (NIL) -8 NIL NIL 2985778) (-1245 2984083 2984593 2984700 "UINT32" 2984811 T UINT32 (NIL) -8 NIL NIL 2984896) (-1244 2983201 2983711 2983818 "UINT16" 2983929 T UINT16 (NIL) -8 NIL NIL 2984014) (-1243 2981490 2982447 2982477 "UFD" 2982689 T UFD (NIL) -9 NIL 2982803 NIL) (-1242 2981284 2981330 2981425 "UFD-" 2981430 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1241 2980366 2980549 2980765 "UDVO" 2981090 T UDVO (NIL) -7 NIL NIL NIL) (-1240 2978182 2978591 2979062 "UDPO" 2979930 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1239 2978115 2978120 2978150 "TYPE" 2978155 T TYPE (NIL) -9 NIL NIL NIL) (-1238 2977875 2978070 2978101 "TYPEAST" 2978106 T TYPEAST (NIL) -8 NIL NIL NIL) (-1237 2976846 2977048 2977288 "TWOFACT" 2977669 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1236 2975869 2976255 2976490 "TUPLE" 2976646 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1235 2973560 2974079 2974618 "TUBETOOL" 2975352 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1234 2972409 2972614 2972855 "TUBE" 2973353 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1233 2967138 2971381 2971664 "TS" 2972161 NIL TS (NIL T) -8 NIL NIL NIL) (-1232 2955778 2959897 2959994 "TSETCAT" 2965263 NIL TSETCAT (NIL T T T T) -9 NIL 2966794 NIL) (-1231 2950510 2952110 2954001 "TSETCAT-" 2954006 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1230 2945149 2945996 2946925 "TRMANIP" 2949646 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1229 2944590 2944653 2944816 "TRIMAT" 2945081 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1228 2942456 2942693 2943050 "TRIGMNIP" 2944339 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1227 2941976 2942089 2942119 "TRIGCAT" 2942332 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1226 2941645 2941724 2941865 "TRIGCAT-" 2941870 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1225 2938493 2940503 2940784 "TREE" 2941399 NIL TREE (NIL T) -8 NIL NIL NIL) (-1224 2937767 2938295 2938325 "TRANFUN" 2938360 T TRANFUN (NIL) -9 NIL 2938426 NIL) (-1223 2937046 2937237 2937517 "TRANFUN-" 2937522 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1222 2936850 2936882 2936943 "TOPSP" 2937007 T TOPSP (NIL) -7 NIL NIL NIL) (-1221 2936198 2936313 2936467 "TOOLSIGN" 2936731 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1220 2934832 2935375 2935614 "TEXTFILE" 2935981 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1219 2932744 2933285 2933714 "TEX" 2934425 T TEX (NIL) -8 NIL NIL NIL) (-1218 2932525 2932556 2932628 "TEX1" 2932707 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1217 2932173 2932236 2932326 "TEMUTL" 2932457 T TEMUTL (NIL) -7 NIL NIL NIL) (-1216 2930327 2930607 2930932 "TBCMPPK" 2931896 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1215 2922036 2928413 2928469 "TBAGG" 2928869 NIL TBAGG (NIL T T) -9 NIL 2929080 NIL) (-1214 2917106 2918594 2920348 "TBAGG-" 2920353 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1213 2916490 2916597 2916742 "TANEXP" 2916995 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1212 2916001 2916265 2916355 "TALGOP" 2916435 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1211 2909397 2915858 2915951 "TABLE" 2915956 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1210 2908809 2908908 2909046 "TABLEAU" 2909294 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1209 2903417 2904637 2905885 "TABLBUMP" 2907595 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1208 2902639 2902786 2902967 "SYSTEM" 2903258 T SYSTEM (NIL) -8 NIL NIL NIL) (-1207 2899098 2899797 2900580 "SYSSOLP" 2901890 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1206 2898896 2899053 2899084 "SYSPTR" 2899089 T SYSPTR (NIL) -8 NIL NIL NIL) (-1205 2897932 2898437 2898556 "SYSNNI" 2898742 NIL SYSNNI (NIL NIL) -8 NIL NIL 2898827) (-1204 2897231 2897690 2897769 "SYSINT" 2897829 NIL SYSINT (NIL NIL) -8 NIL NIL 2897874) (-1203 2893563 2894509 2895219 "SYNTAX" 2896543 T SYNTAX (NIL) -8 NIL NIL NIL) (-1202 2890721 2891323 2891955 "SYMTAB" 2892953 T SYMTAB (NIL) -8 NIL NIL NIL) (-1201 2885970 2886872 2887855 "SYMS" 2889760 T SYMS (NIL) -8 NIL NIL NIL) (-1200 2883205 2885428 2885658 "SYMPOLY" 2885775 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1199 2882722 2882797 2882920 "SYMFUNC" 2883117 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1198 2878742 2880034 2880847 "SYMBOL" 2881931 T SYMBOL (NIL) -8 NIL NIL NIL) (-1197 2872281 2873970 2875690 "SWITCH" 2877044 T SWITCH (NIL) -8 NIL NIL NIL) (-1196 2865625 2871237 2871531 "SUTS" 2872045 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1195 2857801 2865007 2865271 "SUPXS" 2865419 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2849284 2857419 2857545 "SUP" 2857710 NIL SUP (NIL T) -8 NIL NIL NIL) (-1193 2848443 2848570 2848787 "SUPFRACF" 2849152 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1192 2848064 2848123 2848236 "SUP2" 2848378 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1191 2846512 2846786 2847142 "SUMRF" 2847763 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1190 2845847 2845913 2846105 "SUMFS" 2846433 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1189 2828634 2845159 2845401 "SULS" 2845663 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1188 2828236 2828456 2828526 "SUCHTAST" 2828586 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1187 2827531 2827761 2827901 "SUCH" 2828144 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1186 2821398 2822437 2823396 "SUBSPACE" 2826619 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1185 2820828 2820918 2821082 "SUBRESP" 2821286 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1184 2814196 2815493 2816804 "STTF" 2819564 NIL STTF (NIL T) -7 NIL NIL NIL) (-1183 2808369 2809489 2810636 "STTFNC" 2813096 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1182 2799682 2801551 2803345 "STTAYLOR" 2806610 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1181 2792818 2799546 2799629 "STRTBL" 2799634 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1180 2787779 2792527 2792626 "STRING" 2792741 T STRING (NIL) -8 NIL NIL NIL) (-1179 2780535 2785398 2786009 "STREAM" 2787203 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1178 2780045 2780122 2780266 "STREAM3" 2780452 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1177 2779027 2779210 2779445 "STREAM2" 2779858 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1176 2778715 2778767 2778860 "STREAM1" 2778969 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1175 2777731 2777912 2778143 "STINPROD" 2778531 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1174 2777269 2777479 2777509 "STEP" 2777589 T STEP (NIL) -9 NIL 2777667 NIL) (-1173 2776456 2776758 2776906 "STEPAST" 2777143 T STEPAST (NIL) -8 NIL NIL NIL) (-1172 2769894 2776355 2776432 "STBL" 2776437 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1171 2764964 2769057 2769100 "STAGG" 2769253 NIL STAGG (NIL T) -9 NIL 2769342 NIL) (-1170 2762666 2763268 2764140 "STAGG-" 2764145 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1169 2760816 2762436 2762528 "STACK" 2762609 NIL STACK (NIL T) -8 NIL NIL NIL) (-1168 2753511 2758957 2759413 "SREGSET" 2760446 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1167 2745936 2747305 2748818 "SRDCMPK" 2752117 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1166 2738773 2743295 2743325 "SRAGG" 2744628 T SRAGG (NIL) -9 NIL 2745236 NIL) (-1165 2737790 2738045 2738424 "SRAGG-" 2738429 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1164 2731974 2736737 2737158 "SQMATRIX" 2737416 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1163 2725662 2728692 2729419 "SPLTREE" 2731319 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1162 2721625 2722318 2722964 "SPLNODE" 2725088 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1161 2720672 2720905 2720935 "SPFCAT" 2721379 T SPFCAT (NIL) -9 NIL NIL NIL) (-1160 2719409 2719619 2719883 "SPECOUT" 2720430 T SPECOUT (NIL) -7 NIL NIL NIL) (-1159 2710505 2712377 2712407 "SPADXPT" 2717083 T SPADXPT (NIL) -9 NIL 2719247 NIL) (-1158 2710266 2710306 2710375 "SPADPRSR" 2710458 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1157 2708315 2710221 2710252 "SPADAST" 2710257 T SPADAST (NIL) -8 NIL NIL NIL) (-1156 2700246 2702019 2702062 "SPACEC" 2706435 NIL SPACEC (NIL T) -9 NIL 2708251 NIL) (-1155 2698376 2700178 2700227 "SPACE3" 2700232 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1154 2697128 2697299 2697590 "SORTPAK" 2698181 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1153 2695220 2695523 2695935 "SOLVETRA" 2696792 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1152 2694270 2694492 2694753 "SOLVESER" 2694993 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1151 2689574 2690462 2691457 "SOLVERAD" 2693322 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1150 2685389 2685998 2686727 "SOLVEFOR" 2688941 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1149 2679659 2684738 2684835 "SNTSCAT" 2684840 NIL SNTSCAT (NIL T T T T) -9 NIL 2684910 NIL) (-1148 2673765 2677982 2678373 "SMTS" 2679349 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1147 2668174 2673653 2673730 "SMP" 2673735 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1146 2666333 2666634 2667032 "SMITH" 2667871 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1145 2658437 2662912 2663015 "SMATCAT" 2664366 NIL SMATCAT (NIL NIL T T T) -9 NIL 2664916 NIL) (-1144 2655377 2656200 2657378 "SMATCAT-" 2657383 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1143 2653018 2654585 2654628 "SKAGG" 2654889 NIL SKAGG (NIL T) -9 NIL 2655024 NIL) (-1142 2649208 2652491 2652675 "SINT" 2652827 T SINT (NIL) -8 NIL NIL 2652989) (-1141 2648980 2649018 2649084 "SIMPAN" 2649164 T SIMPAN (NIL) -7 NIL NIL NIL) (-1140 2648259 2648515 2648655 "SIG" 2648862 T SIG (NIL) -8 NIL NIL NIL) (-1139 2647097 2647318 2647593 "SIGNRF" 2648018 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1138 2645930 2646081 2646365 "SIGNEF" 2646926 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1137 2645236 2645513 2645637 "SIGAST" 2645828 T SIGAST (NIL) -8 NIL NIL NIL) (-1136 2642926 2643380 2643886 "SHP" 2644777 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1135 2636755 2642827 2642903 "SHDP" 2642908 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1134 2636314 2636506 2636536 "SGROUP" 2636629 T SGROUP (NIL) -9 NIL 2636691 NIL) (-1133 2636172 2636198 2636271 "SGROUP-" 2636276 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1132 2632963 2633661 2634384 "SGCF" 2635471 T SGCF (NIL) -7 NIL NIL NIL) (-1131 2627331 2632410 2632507 "SFRTCAT" 2632512 NIL SFRTCAT (NIL T T T T) -9 NIL 2632551 NIL) (-1130 2620752 2621770 2622906 "SFRGCD" 2626314 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1129 2613878 2614951 2616137 "SFQCMPK" 2619685 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1128 2613498 2613587 2613698 "SFORT" 2613819 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1127 2612616 2613338 2613459 "SEXOF" 2613464 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1126 2611723 2612497 2612565 "SEX" 2612570 T SEX (NIL) -8 NIL NIL NIL) (-1125 2607504 2608219 2608314 "SEXCAT" 2610936 NIL SEXCAT (NIL T T T T T) -9 NIL 2611496 NIL) (-1124 2604657 2607438 2607486 "SET" 2607491 NIL SET (NIL T) -8 NIL NIL NIL) (-1123 2602881 2603370 2603675 "SETMN" 2604398 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1122 2602447 2602599 2602629 "SETCAT" 2602746 T SETCAT (NIL) -9 NIL 2602831 NIL) (-1121 2602227 2602279 2602378 "SETCAT-" 2602383 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1120 2598588 2600688 2600731 "SETAGG" 2601601 NIL SETAGG (NIL T) -9 NIL 2601941 NIL) (-1119 2598046 2598162 2598399 "SETAGG-" 2598404 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1118 2597489 2597742 2597843 "SEQAST" 2597967 T SEQAST (NIL) -8 NIL NIL NIL) (-1117 2596688 2596982 2597043 "SEGXCAT" 2597329 NIL SEGXCAT (NIL T T) -9 NIL 2597449 NIL) (-1116 2595694 2596354 2596536 "SEG" 2596541 NIL SEG (NIL T) -8 NIL NIL NIL) (-1115 2594673 2594887 2594930 "SEGCAT" 2595452 NIL SEGCAT (NIL T) -9 NIL 2595673 NIL) (-1114 2593605 2594036 2594244 "SEGBIND" 2594500 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1113 2593226 2593285 2593398 "SEGBIND2" 2593540 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1112 2592799 2593027 2593104 "SEGAST" 2593171 T SEGAST (NIL) -8 NIL NIL NIL) (-1111 2592018 2592144 2592348 "SEG2" 2592643 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1110 2591389 2591953 2592000 "SDVAR" 2592005 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1109 2583640 2591159 2591289 "SDPOL" 2591294 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1108 2582233 2582499 2582818 "SCPKG" 2583355 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1107 2581397 2581569 2581761 "SCOPE" 2582063 T SCOPE (NIL) -8 NIL NIL NIL) (-1106 2580617 2580751 2580930 "SCACHE" 2581252 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1105 2580249 2580435 2580465 "SASTCAT" 2580470 T SASTCAT (NIL) -9 NIL 2580483 NIL) (-1104 2579736 2580084 2580160 "SAOS" 2580195 T SAOS (NIL) -8 NIL NIL NIL) (-1103 2579301 2579336 2579509 "SAERFFC" 2579695 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1102 2572964 2579198 2579278 "SAE" 2579283 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1101 2572557 2572592 2572751 "SAEFACT" 2572923 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1100 2570878 2571192 2571593 "RURPK" 2572223 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1099 2569515 2569821 2570126 "RULESET" 2570712 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1098 2566738 2567268 2567726 "RULE" 2569196 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1097 2566350 2566532 2566615 "RULECOLD" 2566690 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1096 2566140 2566168 2566239 "RTVALUE" 2566301 T RTVALUE (NIL) -8 NIL NIL NIL) (-1095 2565611 2565857 2565951 "RSTRCAST" 2566068 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1094 2560459 2561254 2562174 "RSETGCD" 2564810 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1093 2549689 2554768 2554865 "RSETCAT" 2558984 NIL RSETCAT (NIL T T T T) -9 NIL 2560081 NIL) (-1092 2547616 2548155 2548979 "RSETCAT-" 2548984 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1091 2540002 2541378 2542898 "RSDCMPK" 2546215 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1090 2537967 2538434 2538508 "RRCC" 2539594 NIL RRCC (NIL T T) -9 NIL 2539938 NIL) (-1089 2537318 2537492 2537771 "RRCC-" 2537776 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1088 2536761 2537014 2537115 "RPTAST" 2537239 T RPTAST (NIL) -8 NIL NIL NIL) (-1087 2510237 2519873 2519940 "RPOLCAT" 2530606 NIL RPOLCAT (NIL T T T) -9 NIL 2533766 NIL) (-1086 2501735 2504075 2507197 "RPOLCAT-" 2507202 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1085 2492672 2499946 2500428 "ROUTINE" 2501275 T ROUTINE (NIL) -8 NIL NIL NIL) (-1084 2489333 2492298 2492438 "ROMAN" 2492554 T ROMAN (NIL) -8 NIL NIL NIL) (-1083 2487577 2488193 2488453 "ROIRC" 2489138 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1082 2483781 2486066 2486096 "RNS" 2486400 T RNS (NIL) -9 NIL 2486674 NIL) (-1081 2482290 2482673 2483207 "RNS-" 2483282 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1080 2481679 2482087 2482117 "RNG" 2482122 T RNG (NIL) -9 NIL 2482143 NIL) (-1079 2480682 2481044 2481246 "RNGBIND" 2481530 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1078 2480067 2480455 2480498 "RMODULE" 2480503 NIL RMODULE (NIL T) -9 NIL 2480530 NIL) (-1077 2478903 2478997 2479333 "RMCAT2" 2479968 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1076 2475753 2478249 2478546 "RMATRIX" 2478665 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1075 2468580 2470840 2470955 "RMATCAT" 2474314 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2475296 NIL) (-1074 2467955 2468102 2468409 "RMATCAT-" 2468414 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1073 2467570 2467742 2467785 "RLINSET" 2467847 NIL RLINSET (NIL T) -9 NIL 2467891 NIL) (-1072 2467137 2467212 2467340 "RINTERP" 2467489 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1071 2466181 2466735 2466765 "RING" 2466821 T RING (NIL) -9 NIL 2466913 NIL) (-1070 2465973 2466017 2466114 "RING-" 2466119 NIL RING- (NIL T) -8 NIL NIL NIL) (-1069 2464814 2465051 2465309 "RIDIST" 2465737 T RIDIST (NIL) -7 NIL NIL NIL) (-1068 2456103 2464282 2464488 "RGCHAIN" 2464662 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1067 2455439 2455845 2455886 "RGBCSPC" 2455944 NIL RGBCSPC (NIL T) -9 NIL 2455996 NIL) (-1066 2454583 2454964 2455005 "RGBCMDL" 2455237 NIL RGBCMDL (NIL T) -9 NIL 2455351 NIL) (-1065 2451577 2452191 2452861 "RF" 2453947 NIL RF (NIL T) -7 NIL NIL NIL) (-1064 2451223 2451286 2451389 "RFFACTOR" 2451508 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1063 2450948 2450983 2451080 "RFFACT" 2451182 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1062 2449065 2449429 2449811 "RFDIST" 2450588 T RFDIST (NIL) -7 NIL NIL NIL) (-1061 2448518 2448610 2448773 "RETSOL" 2448967 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1060 2448154 2448234 2448277 "RETRACT" 2448410 NIL RETRACT (NIL T) -9 NIL 2448497 NIL) (-1059 2448003 2448028 2448115 "RETRACT-" 2448120 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1058 2447605 2447825 2447895 "RETAST" 2447955 T RETAST (NIL) -8 NIL NIL NIL) (-1057 2440349 2447258 2447385 "RESULT" 2447500 T RESULT (NIL) -8 NIL NIL NIL) (-1056 2438940 2439618 2439817 "RESRING" 2440252 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1055 2438576 2438625 2438723 "RESLATC" 2438877 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1054 2438281 2438316 2438423 "REPSQ" 2438535 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1053 2435703 2436283 2436885 "REP" 2437701 T REP (NIL) -7 NIL NIL NIL) (-1052 2435400 2435435 2435546 "REPDB" 2435662 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1051 2429300 2430689 2431912 "REP2" 2434212 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1050 2425677 2426358 2427166 "REP1" 2428527 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1049 2418373 2423818 2424274 "REGSET" 2425307 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1048 2417138 2417521 2417771 "REF" 2418158 NIL REF (NIL T) -8 NIL NIL NIL) (-1047 2416515 2416618 2416785 "REDORDER" 2417022 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1046 2412483 2415728 2415955 "RECLOS" 2416343 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1045 2411535 2411716 2411931 "REALSOLV" 2412290 T REALSOLV (NIL) -7 NIL NIL NIL) (-1044 2411381 2411422 2411452 "REAL" 2411457 T REAL (NIL) -9 NIL 2411492 NIL) (-1043 2407864 2408666 2409550 "REAL0Q" 2410546 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1042 2403465 2404453 2405514 "REAL0" 2406845 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1041 2402936 2403182 2403276 "RDUCEAST" 2403393 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1040 2402341 2402413 2402620 "RDIV" 2402858 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1039 2401409 2401583 2401796 "RDIST" 2402163 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1038 2400006 2400293 2400665 "RDETRS" 2401117 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1037 2397818 2398272 2398810 "RDETR" 2399548 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1036 2396443 2396721 2397118 "RDEEFS" 2397534 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1035 2394952 2395258 2395683 "RDEEF" 2396131 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1034 2388985 2391906 2391936 "RCFIELD" 2393231 T RCFIELD (NIL) -9 NIL 2393962 NIL) (-1033 2387049 2387553 2388249 "RCFIELD-" 2388324 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1032 2383293 2385122 2385165 "RCAGG" 2386249 NIL RCAGG (NIL T) -9 NIL 2386714 NIL) (-1031 2382921 2383015 2383178 "RCAGG-" 2383183 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1030 2382256 2382368 2382533 "RATRET" 2382805 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1029 2381809 2381876 2381997 "RATFACT" 2382184 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1028 2381117 2381237 2381389 "RANDSRC" 2381679 T RANDSRC (NIL) -7 NIL NIL NIL) (-1027 2380851 2380895 2380968 "RADUTIL" 2381066 T RADUTIL (NIL) -7 NIL NIL NIL) (-1026 2373679 2379682 2379993 "RADIX" 2380574 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1025 2364139 2373521 2373651 "RADFF" 2373656 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1024 2363786 2363861 2363891 "RADCAT" 2364051 T RADCAT (NIL) -9 NIL NIL NIL) (-1023 2363568 2363616 2363716 "RADCAT-" 2363721 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1022 2361669 2363338 2363430 "QUEUE" 2363511 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1021 2357930 2361602 2361650 "QUAT" 2361655 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1020 2357561 2357604 2357735 "QUATCT2" 2357881 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1019 2350359 2353984 2354026 "QUATCAT" 2354817 NIL QUATCAT (NIL T) -9 NIL 2355583 NIL) (-1018 2346498 2347535 2348925 "QUATCAT-" 2349021 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1017 2343938 2345546 2345589 "QUAGG" 2345970 NIL QUAGG (NIL T) -9 NIL 2346145 NIL) (-1016 2343540 2343760 2343830 "QQUTAST" 2343890 T QQUTAST (NIL) -8 NIL NIL NIL) (-1015 2342553 2343053 2343218 "QFORM" 2343421 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1014 2332885 2338400 2338442 "QFCAT" 2339110 NIL QFCAT (NIL T) -9 NIL 2340111 NIL) (-1013 2328452 2329653 2331247 "QFCAT-" 2331343 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1012 2328083 2328126 2328257 "QFCAT2" 2328403 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1011 2327538 2327648 2327780 "QEQUAT" 2327973 T QEQUAT (NIL) -8 NIL NIL NIL) (-1010 2320664 2321737 2322923 "QCMPACK" 2326471 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1009 2318202 2318650 2319080 "QALGSET" 2320319 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1008 2317437 2317613 2317849 "QALGSET2" 2318020 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1007 2316122 2316346 2316665 "PWFFINTB" 2317210 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1006 2314297 2314465 2314821 "PUSHVAR" 2315936 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1005 2310186 2311240 2311283 "PTRANFN" 2313194 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1004 2308577 2308868 2309192 "PTPACK" 2309897 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1003 2308206 2308263 2308374 "PTFUNC2" 2308514 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1002 2302601 2306995 2307038 "PTCAT" 2307338 NIL PTCAT (NIL T) -9 NIL 2307491 NIL) (-1001 2302256 2302291 2302417 "PSQFR" 2302560 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1000 2300846 2301144 2301480 "PSEUDLIN" 2301954 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-999 2287609 2289980 2292304 "PSETPK" 2298606 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-998 2280627 2283367 2283463 "PSETCAT" 2286484 NIL PSETCAT (NIL T T T T) -9 NIL 2287298 NIL) (-997 2278463 2279097 2279918 "PSETCAT-" 2279923 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-996 2277812 2277977 2278005 "PSCURVE" 2278273 T PSCURVE (NIL) -9 NIL 2278440 NIL) (-995 2273796 2275312 2275377 "PSCAT" 2276221 NIL PSCAT (NIL T T T) -9 NIL 2276461 NIL) (-994 2272859 2273075 2273475 "PSCAT-" 2273480 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-993 2271218 2271928 2272191 "PRTITION" 2272616 T PRTITION (NIL) -8 NIL NIL NIL) (-992 2270693 2270939 2271031 "PRTDAST" 2271146 T PRTDAST (NIL) -8 NIL NIL NIL) (-991 2259783 2261997 2264185 "PRS" 2268555 NIL PRS (NIL T T) -7 NIL NIL NIL) (-990 2257569 2259105 2259145 "PRQAGG" 2259328 NIL PRQAGG (NIL T) -9 NIL 2259430 NIL) (-989 2256905 2257210 2257238 "PROPLOG" 2257377 T PROPLOG (NIL) -9 NIL 2257492 NIL) (-988 2256509 2256566 2256689 "PROPFUN2" 2256828 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-987 2255824 2255945 2256117 "PROPFUN1" 2256370 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-986 2254005 2254571 2254868 "PROPFRML" 2255560 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-985 2253474 2253581 2253709 "PROPERTY" 2253897 T PROPERTY (NIL) -8 NIL NIL NIL) (-984 2247532 2251640 2252460 "PRODUCT" 2252700 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-983 2244810 2246990 2247224 "PR" 2247343 NIL PR (NIL T T) -8 NIL NIL NIL) (-982 2244606 2244638 2244697 "PRINT" 2244771 T PRINT (NIL) -7 NIL NIL NIL) (-981 2243946 2244063 2244215 "PRIMES" 2244486 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-980 2242011 2242412 2242878 "PRIMELT" 2243525 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-979 2241740 2241789 2241817 "PRIMCAT" 2241941 T PRIMCAT (NIL) -9 NIL NIL NIL) (-978 2237858 2241678 2241723 "PRIMARR" 2241728 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-977 2236865 2237043 2237271 "PRIMARR2" 2237676 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-976 2236508 2236564 2236675 "PREASSOC" 2236803 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-975 2235983 2236116 2236144 "PPCURVE" 2236349 T PPCURVE (NIL) -9 NIL 2236485 NIL) (-974 2235578 2235778 2235861 "PORTNUM" 2235920 T PORTNUM (NIL) -8 NIL NIL NIL) (-973 2232937 2233336 2233928 "POLYROOT" 2235159 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-972 2226843 2232541 2232701 "POLY" 2232810 NIL POLY (NIL T) -8 NIL NIL NIL) (-971 2226226 2226284 2226518 "POLYLIFT" 2226779 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-970 2222501 2222950 2223579 "POLYCATQ" 2225771 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-969 2208843 2214248 2214313 "POLYCAT" 2217827 NIL POLYCAT (NIL T T T) -9 NIL 2219705 NIL) (-968 2202292 2204154 2206538 "POLYCAT-" 2206543 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2201879 2201947 2202067 "POLY2UP" 2202218 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-966 2201511 2201568 2201677 "POLY2" 2201816 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-965 2200196 2200435 2200711 "POLUTIL" 2201285 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-964 2198551 2198828 2199159 "POLTOPOL" 2199918 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-963 2194017 2198485 2198532 "POINT" 2198537 NIL POINT (NIL T) -8 NIL NIL NIL) (-962 2192204 2192561 2192936 "PNTHEORY" 2193662 T PNTHEORY (NIL) -7 NIL NIL NIL) (-961 2190662 2190959 2191358 "PMTOOLS" 2191902 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-960 2190255 2190333 2190450 "PMSYM" 2190578 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-959 2189763 2189832 2190007 "PMQFCAT" 2190180 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-958 2189118 2189228 2189384 "PMPRED" 2189640 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-957 2188511 2188597 2188759 "PMPREDFS" 2189019 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-956 2187175 2187383 2187761 "PMPLCAT" 2188273 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-955 2186707 2186786 2186938 "PMLSAGG" 2187090 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-954 2186180 2186256 2186438 "PMKERNEL" 2186625 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-953 2185797 2185872 2185985 "PMINS" 2186099 NIL PMINS (NIL T) -7 NIL NIL NIL) (-952 2185239 2185308 2185517 "PMFS" 2185722 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-951 2184467 2184585 2184790 "PMDOWN" 2185116 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-950 2183634 2183792 2183973 "PMASS" 2184306 T PMASS (NIL) -7 NIL NIL NIL) (-949 2182907 2183017 2183180 "PMASSFS" 2183521 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-948 2182562 2182630 2182724 "PLOTTOOL" 2182833 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-947 2177169 2178373 2179521 "PLOT" 2181434 T PLOT (NIL) -8 NIL NIL NIL) (-946 2172973 2174017 2174938 "PLOT3D" 2176268 T PLOT3D (NIL) -8 NIL NIL NIL) (-945 2171885 2172062 2172297 "PLOT1" 2172777 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-944 2147276 2151951 2156802 "PLEQN" 2167151 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-943 2146594 2146716 2146896 "PINTERP" 2147141 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-942 2146287 2146334 2146437 "PINTERPA" 2146541 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-941 2145503 2146051 2146138 "PI" 2146178 T PI (NIL) -8 NIL NIL 2146245) (-940 2143786 2144761 2144789 "PID" 2144971 T PID (NIL) -9 NIL 2145105 NIL) (-939 2143537 2143574 2143649 "PICOERCE" 2143743 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-938 2142857 2142996 2143172 "PGROEB" 2143393 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-937 2138444 2139258 2140163 "PGE" 2141972 T PGE (NIL) -7 NIL NIL NIL) (-936 2136567 2136814 2137180 "PGCD" 2138161 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-935 2135905 2136008 2136169 "PFRPAC" 2136451 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-934 2132545 2134453 2134806 "PFR" 2135584 NIL PFR (NIL T) -8 NIL NIL NIL) (-933 2130934 2131178 2131503 "PFOTOOLS" 2132292 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-932 2129467 2129706 2130057 "PFOQ" 2130691 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-931 2127968 2128180 2128536 "PFO" 2129251 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-930 2124521 2127857 2127926 "PF" 2127931 NIL PF (NIL NIL) -8 NIL NIL NIL) (-929 2121841 2123112 2123140 "PFECAT" 2123725 T PFECAT (NIL) -9 NIL 2124109 NIL) (-928 2121286 2121440 2121654 "PFECAT-" 2121659 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-927 2119889 2120141 2120442 "PFBRU" 2121035 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-926 2117755 2118107 2118539 "PFBR" 2119540 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-925 2113801 2115267 2115914 "PERM" 2117141 NIL PERM (NIL T) -8 NIL NIL NIL) (-924 2109035 2110008 2110878 "PERMGRP" 2112964 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-923 2107099 2108059 2108100 "PERMCAT" 2108500 NIL PERMCAT (NIL T) -9 NIL 2108798 NIL) (-922 2106752 2106793 2106917 "PERMAN" 2107052 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-921 2104243 2106417 2106539 "PENDTREE" 2106663 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-920 2103172 2103387 2103428 "PDSPC" 2103961 NIL PDSPC (NIL T) -9 NIL 2104206 NIL) (-919 2102275 2102493 2102855 "PDSPC-" 2102860 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-918 2101157 2101925 2101966 "PDRING" 2101971 NIL PDRING (NIL T) -9 NIL 2101999 NIL) (-917 2100044 2100662 2100716 "PDMOD" 2100721 NIL PDMOD (NIL T T) -9 NIL 2100825 NIL) (-916 2097259 2098037 2098705 "PDEPROB" 2099396 T PDEPROB (NIL) -8 NIL NIL NIL) (-915 2094804 2095308 2095863 "PDEPACK" 2096724 T PDEPACK (NIL) -7 NIL NIL NIL) (-914 2093716 2093906 2094157 "PDECOMP" 2094603 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-913 2091281 2092124 2092152 "PDECAT" 2092939 T PDECAT (NIL) -9 NIL 2093652 NIL) (-912 2090910 2090965 2091019 "PDDOM" 2091184 NIL PDDOM (NIL T T) -9 NIL 2091264 NIL) (-911 2090729 2090759 2090866 "PDDOM-" 2090871 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-910 2090480 2090513 2090603 "PCOMP" 2090690 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-909 2088658 2089281 2089578 "PBWLB" 2090209 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-908 2081131 2082731 2084069 "PATTERN" 2087341 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-907 2080763 2080820 2080929 "PATTERN2" 2081068 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-906 2078520 2078908 2079365 "PATTERN1" 2080352 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-905 2075888 2076469 2076950 "PATRES" 2078085 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-904 2075452 2075519 2075651 "PATRES2" 2075815 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-903 2073335 2073740 2074147 "PATMATCH" 2075119 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-902 2072831 2073040 2073081 "PATMAB" 2073188 NIL PATMAB (NIL T) -9 NIL 2073271 NIL) (-901 2071349 2071685 2071943 "PATLRES" 2072636 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-900 2070895 2071018 2071059 "PATAB" 2071064 NIL PATAB (NIL T) -9 NIL 2071236 NIL) (-899 2069077 2069472 2069895 "PARTPERM" 2070492 T PARTPERM (NIL) -7 NIL NIL NIL) (-898 2068698 2068761 2068863 "PARSURF" 2069008 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-897 2068330 2068387 2068496 "PARSU2" 2068635 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-896 2068094 2068134 2068201 "PARSER" 2068283 T PARSER (NIL) -7 NIL NIL NIL) (-895 2067715 2067778 2067880 "PARSCURV" 2068025 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-894 2067347 2067404 2067513 "PARSC2" 2067652 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-893 2066986 2067044 2067141 "PARPCURV" 2067283 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-892 2066618 2066675 2066784 "PARPC2" 2066923 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-891 2065679 2065991 2066173 "PARAMAST" 2066456 T PARAMAST (NIL) -8 NIL NIL NIL) (-890 2065199 2065285 2065404 "PAN2EXPR" 2065580 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-889 2063976 2064320 2064548 "PALETTE" 2064991 T PALETTE (NIL) -8 NIL NIL NIL) (-888 2062369 2062981 2063341 "PAIR" 2063662 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-887 2055961 2061626 2061821 "PADICRC" 2062223 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-886 2048877 2055305 2055490 "PADICRAT" 2055808 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-885 2047192 2048814 2048859 "PADIC" 2048864 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-884 2044288 2045852 2045892 "PADICCT" 2046473 NIL PADICCT (NIL NIL) -9 NIL 2046755 NIL) (-883 2043245 2043445 2043713 "PADEPAC" 2044075 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-882 2042457 2042590 2042796 "PADE" 2043107 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-881 2040844 2041665 2041945 "OWP" 2042261 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-880 2040337 2040550 2040647 "OVERSET" 2040767 T OVERSET (NIL) -8 NIL NIL NIL) (-879 2039383 2039942 2040114 "OVAR" 2040205 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-878 2038647 2038768 2038929 "OUT" 2039242 T OUT (NIL) -7 NIL NIL NIL) (-877 2027519 2029756 2031956 "OUTFORM" 2036467 T OUTFORM (NIL) -8 NIL NIL NIL) (-876 2026855 2027116 2027243 "OUTBFILE" 2027412 T OUTBFILE (NIL) -8 NIL NIL NIL) (-875 2026162 2026327 2026355 "OUTBCON" 2026673 T OUTBCON (NIL) -9 NIL 2026839 NIL) (-874 2025763 2025875 2026032 "OUTBCON-" 2026037 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-873 2025143 2025492 2025581 "OSI" 2025694 T OSI (NIL) -8 NIL NIL NIL) (-872 2024646 2024984 2025012 "OSGROUP" 2025017 T OSGROUP (NIL) -9 NIL 2025039 NIL) (-871 2023391 2023618 2023903 "ORTHPOL" 2024393 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-870 2020942 2023226 2023347 "OREUP" 2023352 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-869 2018345 2020633 2020760 "ORESUP" 2020884 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-868 2015873 2016373 2016934 "OREPCTO" 2017834 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-867 2009545 2011746 2011787 "OREPCAT" 2014135 NIL OREPCAT (NIL T) -9 NIL 2015239 NIL) (-866 2006692 2007474 2008532 "OREPCAT-" 2008537 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-865 2005939 2006162 2006190 "ORDTYPE" 2006499 T ORDTYPE (NIL) -9 NIL 2006662 NIL) (-864 2005282 2005456 2005711 "ORDTYPE-" 2005716 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-863 2004708 2005021 2005179 "ORDSTRCT" 2005184 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-862 2004278 2004576 2004604 "ORDSET" 2004609 T ORDSET (NIL) -9 NIL 2004631 NIL) (-861 2002816 2003607 2003635 "ORDRING" 2003837 T ORDRING (NIL) -9 NIL 2003962 NIL) (-860 2002461 2002555 2002699 "ORDRING-" 2002704 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-859 2001814 2002277 2002305 "ORDMON" 2002310 T ORDMON (NIL) -9 NIL 2002331 NIL) (-858 2000976 2001123 2001318 "ORDFUNS" 2001663 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-857 2000287 2000706 2000734 "ORDFIN" 2000799 T ORDFIN (NIL) -9 NIL 2000873 NIL) (-856 1996846 1998873 1999282 "ORDCOMP" 1999911 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-855 1996112 1996239 1996425 "ORDCOMP2" 1996706 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-854 1992693 1993603 1994417 "OPTPROB" 1995318 T OPTPROB (NIL) -8 NIL NIL NIL) (-853 1989495 1990134 1990838 "OPTPACK" 1992009 T OPTPACK (NIL) -7 NIL NIL NIL) (-852 1987168 1987934 1987962 "OPTCAT" 1988781 T OPTCAT (NIL) -9 NIL 1989431 NIL) (-851 1986552 1986845 1986950 "OPSIG" 1987083 T OPSIG (NIL) -8 NIL NIL NIL) (-850 1986320 1986359 1986425 "OPQUERY" 1986506 T OPQUERY (NIL) -7 NIL NIL NIL) (-849 1983451 1984631 1985135 "OP" 1985849 NIL OP (NIL T) -8 NIL NIL NIL) (-848 1982811 1983037 1983078 "OPERCAT" 1983290 NIL OPERCAT (NIL T) -9 NIL 1983387 NIL) (-847 1982566 1982622 1982739 "OPERCAT-" 1982744 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-846 1979379 1981363 1981732 "ONECOMP" 1982230 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-845 1978684 1978799 1978973 "ONECOMP2" 1979251 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-844 1978103 1978209 1978339 "OMSERVER" 1978574 T OMSERVER (NIL) -7 NIL NIL NIL) (-843 1974965 1977543 1977583 "OMSAGG" 1977644 NIL OMSAGG (NIL T) -9 NIL 1977708 NIL) (-842 1973588 1973851 1974133 "OMPKG" 1974703 T OMPKG (NIL) -7 NIL NIL NIL) (-841 1973018 1973121 1973149 "OM" 1973448 T OM (NIL) -9 NIL NIL NIL) (-840 1971565 1972567 1972736 "OMLO" 1972899 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-839 1970525 1970672 1970892 "OMEXPR" 1971391 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-838 1969816 1970071 1970207 "OMERR" 1970409 T OMERR (NIL) -8 NIL NIL NIL) (-837 1968967 1969237 1969397 "OMERRK" 1969676 T OMERRK (NIL) -8 NIL NIL NIL) (-836 1968418 1968644 1968752 "OMENC" 1968879 T OMENC (NIL) -8 NIL NIL NIL) (-835 1962313 1963498 1964669 "OMDEV" 1967267 T OMDEV (NIL) -8 NIL NIL NIL) (-834 1961382 1961553 1961747 "OMCONN" 1962139 T OMCONN (NIL) -8 NIL NIL NIL) (-833 1959876 1960852 1960880 "OINTDOM" 1960885 T OINTDOM (NIL) -9 NIL 1960906 NIL) (-832 1957214 1958564 1958901 "OFMONOID" 1959571 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-831 1956586 1957151 1957196 "ODVAR" 1957201 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-830 1954009 1956331 1956486 "ODR" 1956491 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-829 1946314 1953785 1953911 "ODPOL" 1953916 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-828 1940113 1946186 1946291 "ODP" 1946296 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-827 1938879 1939094 1939369 "ODETOOLS" 1939887 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-826 1935846 1936504 1937220 "ODESYS" 1938212 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-825 1930728 1931636 1932661 "ODERTRIC" 1934921 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-824 1930154 1930236 1930430 "ODERED" 1930640 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-823 1927042 1927590 1928267 "ODERAT" 1929577 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-822 1924001 1924466 1925063 "ODEPRRIC" 1926571 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-821 1921944 1922540 1923026 "ODEPROB" 1923535 T ODEPROB (NIL) -8 NIL NIL NIL) (-820 1918464 1918949 1919596 "ODEPRIM" 1921423 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-819 1917713 1917815 1918075 "ODEPAL" 1918356 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-818 1913875 1914666 1915530 "ODEPACK" 1916869 T ODEPACK (NIL) -7 NIL NIL NIL) (-817 1912936 1913043 1913265 "ODEINT" 1913764 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-816 1907037 1908462 1909909 "ODEIFTBL" 1911509 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-815 1902435 1903221 1904173 "ODEEF" 1906196 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-814 1901784 1901873 1902096 "ODECONST" 1902340 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-813 1899895 1900556 1900584 "ODECAT" 1901189 T ODECAT (NIL) -9 NIL 1901720 NIL) (-812 1896750 1899600 1899722 "OCT" 1899805 NIL OCT (NIL T) -8 NIL NIL NIL) (-811 1896388 1896431 1896558 "OCTCT2" 1896701 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-810 1890995 1893431 1893471 "OC" 1894568 NIL OC (NIL T) -9 NIL 1895426 NIL) (-809 1888222 1888970 1889960 "OC-" 1890054 NIL OC- (NIL T T) -8 NIL NIL NIL) (-808 1887547 1888015 1888043 "OCAMON" 1888048 T OCAMON (NIL) -9 NIL 1888069 NIL) (-807 1887051 1887392 1887420 "OASGP" 1887425 T OASGP (NIL) -9 NIL 1887445 NIL) (-806 1886285 1886774 1886802 "OAMONS" 1886842 T OAMONS (NIL) -9 NIL 1886885 NIL) (-805 1885672 1886105 1886133 "OAMON" 1886138 T OAMON (NIL) -9 NIL 1886158 NIL) (-804 1884903 1885421 1885449 "OAGROUP" 1885454 T OAGROUP (NIL) -9 NIL 1885474 NIL) (-803 1884593 1884643 1884731 "NUMTUBE" 1884847 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-802 1878166 1879684 1881220 "NUMQUAD" 1883077 T NUMQUAD (NIL) -7 NIL NIL NIL) (-801 1873922 1874910 1875935 "NUMODE" 1877161 T NUMODE (NIL) -7 NIL NIL NIL) (-800 1871263 1872143 1872171 "NUMINT" 1873094 T NUMINT (NIL) -9 NIL 1873858 NIL) (-799 1870211 1870408 1870626 "NUMFMT" 1871065 T NUMFMT (NIL) -7 NIL NIL NIL) (-798 1856570 1859515 1862047 "NUMERIC" 1867718 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-797 1850940 1856019 1856114 "NTSCAT" 1856119 NIL NTSCAT (NIL T T T T) -9 NIL 1856158 NIL) (-796 1850134 1850299 1850492 "NTPOLFN" 1850779 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-795 1837935 1846959 1847771 "NSUP" 1849355 NIL NSUP (NIL T) -8 NIL NIL NIL) (-794 1837567 1837624 1837733 "NSUP2" 1837872 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-793 1827517 1837341 1837474 "NSMP" 1837479 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-792 1825949 1826250 1826607 "NREP" 1827205 NIL NREP (NIL T) -7 NIL NIL NIL) (-791 1824540 1824792 1825150 "NPCOEF" 1825692 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-790 1823606 1823721 1823937 "NORMRETR" 1824421 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-789 1821647 1821937 1822346 "NORMPK" 1823314 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-788 1821332 1821360 1821484 "NORMMA" 1821613 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-787 1821132 1821289 1821318 "NONE" 1821323 T NONE (NIL) -8 NIL NIL NIL) (-786 1820921 1820950 1821019 "NONE1" 1821096 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-785 1820418 1820480 1820659 "NODE1" 1820853 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-784 1818699 1819550 1819805 "NNI" 1820152 T NNI (NIL) -8 NIL NIL 1820387) (-783 1817119 1817432 1817796 "NLINSOL" 1818367 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-782 1813360 1814355 1815254 "NIPROB" 1816240 T NIPROB (NIL) -8 NIL NIL NIL) (-781 1812117 1812351 1812653 "NFINTBAS" 1813122 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-780 1811291 1811767 1811808 "NETCLT" 1811980 NIL NETCLT (NIL T) -9 NIL 1812062 NIL) (-779 1809999 1810230 1810511 "NCODIV" 1811059 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-778 1809761 1809798 1809873 "NCNTFRAC" 1809956 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-777 1807941 1808305 1808725 "NCEP" 1809386 NIL NCEP (NIL T) -7 NIL NIL NIL) (-776 1806778 1807551 1807579 "NASRING" 1807689 T NASRING (NIL) -9 NIL 1807769 NIL) (-775 1806573 1806617 1806711 "NASRING-" 1806716 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-774 1805666 1806191 1806219 "NARNG" 1806336 T NARNG (NIL) -9 NIL 1806427 NIL) (-773 1805358 1805425 1805559 "NARNG-" 1805564 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-772 1804237 1804444 1804679 "NAGSP" 1805143 T NAGSP (NIL) -7 NIL NIL NIL) (-771 1795509 1797193 1798866 "NAGS" 1802584 T NAGS (NIL) -7 NIL NIL NIL) (-770 1794057 1794365 1794696 "NAGF07" 1795198 T NAGF07 (NIL) -7 NIL NIL NIL) (-769 1788595 1789886 1791193 "NAGF04" 1792770 T NAGF04 (NIL) -7 NIL NIL NIL) (-768 1781563 1783177 1784810 "NAGF02" 1786982 T NAGF02 (NIL) -7 NIL NIL NIL) (-767 1776787 1777887 1779004 "NAGF01" 1780466 T NAGF01 (NIL) -7 NIL NIL NIL) (-766 1770415 1771981 1773566 "NAGE04" 1775222 T NAGE04 (NIL) -7 NIL NIL NIL) (-765 1761584 1763705 1765835 "NAGE02" 1768305 T NAGE02 (NIL) -7 NIL NIL NIL) (-764 1757537 1758484 1759448 "NAGE01" 1760640 T NAGE01 (NIL) -7 NIL NIL NIL) (-763 1755332 1755866 1756424 "NAGD03" 1756999 T NAGD03 (NIL) -7 NIL NIL NIL) (-762 1747082 1749010 1750964 "NAGD02" 1753398 T NAGD02 (NIL) -7 NIL NIL NIL) (-761 1740893 1742318 1743758 "NAGD01" 1745662 T NAGD01 (NIL) -7 NIL NIL NIL) (-760 1737102 1737924 1738761 "NAGC06" 1740076 T NAGC06 (NIL) -7 NIL NIL NIL) (-759 1735567 1735899 1736255 "NAGC05" 1736766 T NAGC05 (NIL) -7 NIL NIL NIL) (-758 1734943 1735062 1735206 "NAGC02" 1735443 T NAGC02 (NIL) -7 NIL NIL NIL) (-757 1733888 1734471 1734511 "NAALG" 1734590 NIL NAALG (NIL T) -9 NIL 1734651 NIL) (-756 1733723 1733752 1733842 "NAALG-" 1733847 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-755 1727673 1728781 1729968 "MULTSQFR" 1732619 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-754 1726992 1727067 1727251 "MULTFACT" 1727585 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-753 1719663 1723577 1723630 "MTSCAT" 1724700 NIL MTSCAT (NIL T T) -9 NIL 1725215 NIL) (-752 1719375 1719429 1719521 "MTHING" 1719603 NIL MTHING (NIL T) -7 NIL NIL NIL) (-751 1719167 1719200 1719260 "MSYSCMD" 1719335 T MSYSCMD (NIL) -7 NIL NIL NIL) (-750 1715249 1717922 1718242 "MSET" 1718880 NIL MSET (NIL T) -8 NIL NIL NIL) (-749 1712318 1714810 1714851 "MSETAGG" 1714856 NIL MSETAGG (NIL T) -9 NIL 1714890 NIL) (-748 1708160 1709697 1710442 "MRING" 1711618 NIL MRING (NIL T T) -8 NIL NIL NIL) (-747 1707726 1707793 1707924 "MRF2" 1708087 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-746 1707344 1707379 1707523 "MRATFAC" 1707685 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-745 1704956 1705251 1705682 "MPRFF" 1707049 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-744 1698977 1704810 1704907 "MPOLY" 1704912 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-743 1698467 1698502 1698710 "MPCPF" 1698936 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-742 1697981 1698024 1698208 "MPC3" 1698418 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-741 1697176 1697257 1697478 "MPC2" 1697896 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695477 1695814 1696204 "MONOTOOL" 1696836 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-739 1694688 1695005 1695033 "MONOID" 1695252 T MONOID (NIL) -9 NIL 1695399 NIL) (-738 1694234 1694353 1694534 "MONOID-" 1694539 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-737 1683824 1690054 1690113 "MONOGEN" 1690787 NIL MONOGEN (NIL T T) -9 NIL 1691243 NIL) (-736 1681042 1681777 1682777 "MONOGEN-" 1682896 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-735 1679861 1680307 1680335 "MONADWU" 1680727 T MONADWU (NIL) -9 NIL 1680965 NIL) (-734 1679233 1679392 1679640 "MONADWU-" 1679645 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-733 1678578 1678822 1678850 "MONAD" 1679057 T MONAD (NIL) -9 NIL 1679169 NIL) (-732 1678263 1678341 1678473 "MONAD-" 1678478 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-731 1676552 1677176 1677455 "MOEBIUS" 1678016 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-730 1675816 1676220 1676260 "MODULE" 1676265 NIL MODULE (NIL T) -9 NIL 1676304 NIL) (-729 1675384 1675480 1675670 "MODULE-" 1675675 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-728 1673064 1673748 1674075 "MODRING" 1675208 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-727 1670008 1671169 1671690 "MODOP" 1672593 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-726 1668596 1669075 1669352 "MODMONOM" 1669871 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-725 1658364 1666887 1667301 "MODMON" 1668233 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-724 1655520 1657208 1657484 "MODFIELD" 1658239 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-723 1654497 1654801 1654991 "MMLFORM" 1655350 T MMLFORM (NIL) -8 NIL NIL NIL) (-722 1654023 1654066 1654245 "MMAP" 1654448 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-721 1652088 1652855 1652896 "MLO" 1653319 NIL MLO (NIL T) -9 NIL 1653561 NIL) (-720 1649454 1649970 1650572 "MLIFT" 1651569 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-719 1648845 1648929 1649083 "MKUCFUNC" 1649365 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-718 1648444 1648514 1648637 "MKRECORD" 1648768 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-717 1647491 1647653 1647881 "MKFUNC" 1648255 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-716 1646879 1646983 1647139 "MKFLCFN" 1647374 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-715 1646156 1646258 1646443 "MKBCFUNC" 1646772 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-714 1642745 1645710 1645846 "MINT" 1646040 T MINT (NIL) -8 NIL NIL NIL) (-713 1641557 1641800 1642077 "MHROWRED" 1642500 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-712 1636937 1640092 1640497 "MFLOAT" 1641172 T MFLOAT (NIL) -8 NIL NIL NIL) (-711 1636294 1636370 1636541 "MFINFACT" 1636849 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-710 1632609 1633457 1634341 "MESH" 1635430 T MESH (NIL) -7 NIL NIL NIL) (-709 1630999 1631311 1631664 "MDDFACT" 1632296 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-708 1627769 1630130 1630171 "MDAGG" 1630426 NIL MDAGG (NIL T) -9 NIL 1630569 NIL) (-707 1616463 1627062 1627269 "MCMPLX" 1627582 T MCMPLX (NIL) -8 NIL NIL NIL) (-706 1615600 1615746 1615947 "MCDEN" 1616312 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-705 1613490 1613760 1614140 "MCALCFN" 1615330 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-704 1612415 1612655 1612888 "MAYBE" 1613296 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-703 1610027 1610550 1611112 "MATSTOR" 1611886 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-702 1605939 1609399 1609647 "MATRIX" 1609812 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-701 1601705 1602412 1603148 "MATLIN" 1605296 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-700 1591531 1594762 1594839 "MATCAT" 1599871 NIL MATCAT (NIL T T T) -9 NIL 1601343 NIL) (-699 1587724 1588794 1590207 "MATCAT-" 1590212 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-698 1586318 1586471 1586804 "MATCAT2" 1587559 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-697 1584430 1584754 1585138 "MAPPKG3" 1585993 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-696 1583411 1583584 1583806 "MAPPKG2" 1584254 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-695 1581910 1582194 1582521 "MAPPKG1" 1583117 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-694 1580989 1581316 1581493 "MAPPAST" 1581753 T MAPPAST (NIL) -8 NIL NIL NIL) (-693 1580600 1580658 1580781 "MAPHACK3" 1580925 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-692 1580192 1580253 1580367 "MAPHACK2" 1580532 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-691 1579630 1579733 1579875 "MAPHACK1" 1580083 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-690 1577709 1578330 1578634 "MAGMA" 1579358 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-689 1577188 1577433 1577524 "MACROAST" 1577638 T MACROAST (NIL) -8 NIL NIL NIL) (-688 1573609 1575427 1575888 "M3D" 1576760 NIL M3D (NIL T) -8 NIL NIL NIL) (-687 1567659 1571920 1571961 "LZSTAGG" 1572743 NIL LZSTAGG (NIL T) -9 NIL 1573038 NIL) (-686 1563617 1564790 1566247 "LZSTAGG-" 1566252 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-685 1560704 1561508 1561995 "LWORD" 1563162 NIL LWORD (NIL T) -8 NIL NIL NIL) (-684 1560280 1560508 1560583 "LSTAST" 1560649 T LSTAST (NIL) -8 NIL NIL NIL) (-683 1553170 1560051 1560185 "LSQM" 1560190 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-682 1552394 1552533 1552761 "LSPP" 1553025 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-681 1550206 1550507 1550963 "LSMP" 1552083 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-680 1546985 1547659 1548389 "LSMP1" 1549508 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-679 1540787 1546075 1546116 "LSAGG" 1546178 NIL LSAGG (NIL T) -9 NIL 1546256 NIL) (-678 1537482 1538406 1539619 "LSAGG-" 1539624 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-677 1535081 1536626 1536875 "LPOLY" 1537277 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-676 1534663 1534748 1534871 "LPEFRAC" 1534990 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-675 1532984 1533757 1534010 "LO" 1534495 NIL LO (NIL T T T) -8 NIL NIL NIL) (-674 1532596 1532734 1532762 "LOGIC" 1532873 T LOGIC (NIL) -9 NIL 1532954 NIL) (-673 1532458 1532481 1532552 "LOGIC-" 1532557 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-672 1531651 1531791 1531984 "LODOOPS" 1532314 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-671 1529074 1531567 1531633 "LODO" 1531638 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-670 1527612 1527847 1528200 "LODOF" 1528821 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-669 1523816 1526247 1526288 "LODOCAT" 1526726 NIL LODOCAT (NIL T) -9 NIL 1526937 NIL) (-668 1523549 1523607 1523734 "LODOCAT-" 1523739 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-667 1520869 1523390 1523508 "LODO2" 1523513 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-666 1518304 1520806 1520851 "LODO1" 1520856 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-665 1517185 1517350 1517655 "LODEEF" 1518127 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-664 1512463 1515351 1515392 "LNAGG" 1516254 NIL LNAGG (NIL T) -9 NIL 1516689 NIL) (-663 1511610 1511824 1512166 "LNAGG-" 1512171 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-662 1507746 1508535 1509174 "LMOPS" 1511025 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-661 1507135 1507523 1507564 "LMODULE" 1507569 NIL LMODULE (NIL T) -9 NIL 1507595 NIL) (-660 1504336 1506780 1506903 "LMDICT" 1507045 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-659 1503954 1504126 1504167 "LLINSET" 1504228 NIL LLINSET (NIL T) -9 NIL 1504272 NIL) (-658 1503653 1503862 1503922 "LITERAL" 1503927 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-657 1496819 1502587 1502891 "LIST" 1503382 NIL LIST (NIL T) -8 NIL NIL NIL) (-656 1496344 1496418 1496557 "LIST3" 1496739 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-655 1495351 1495529 1495757 "LIST2" 1496162 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-654 1493485 1493797 1494196 "LIST2MAP" 1494998 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-653 1493116 1493304 1493345 "LINSET" 1493350 NIL LINSET (NIL T) -9 NIL 1493384 NIL) (-652 1491529 1492143 1492184 "LINEXP" 1492674 NIL LINEXP (NIL T) -9 NIL 1492947 NIL) (-651 1490421 1490991 1491167 "LINELT" 1491405 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-650 1488998 1489258 1489569 "LINDEP" 1490173 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485765 1486484 1487261 "LIMITRF" 1488253 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1484068 1484364 1484773 "LIMITPS" 1485460 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478496 1483579 1483807 "LIE" 1483889 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1477430 1477899 1477939 "LIECAT" 1478079 NIL LIECAT (NIL T) -9 NIL 1478230 NIL) (-645 1477271 1477298 1477386 "LIECAT-" 1477391 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469864 1476811 1476967 "LIB" 1477135 T LIB (NIL) -8 NIL NIL NIL) (-643 1465499 1466382 1467317 "LGROBP" 1468981 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463497 1463771 1464121 "LF" 1465220 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1462337 1463029 1463057 "LFCAT" 1463264 T LFCAT (NIL) -9 NIL 1463403 NIL) (-640 1459239 1459869 1460557 "LEXTRIPK" 1461701 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455983 1456809 1457312 "LEXP" 1458819 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455459 1455704 1455796 "LETAST" 1455911 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453857 1454170 1454571 "LEADCDET" 1455141 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1453047 1453121 1453350 "LAZM3PK" 1453778 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447964 1451124 1451662 "LAUPOL" 1452559 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447543 1447587 1447748 "LAPLACE" 1447914 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445482 1446644 1446895 "LA" 1447376 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444462 1445046 1445087 "LALG" 1445149 NIL LALG (NIL T) -9 NIL 1445208 NIL) (-631 1444176 1444235 1444371 "LALG-" 1444376 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1444011 1444035 1444076 "KVTFROM" 1444138 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442934 1443378 1443563 "KTVLOGIC" 1443846 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442769 1442793 1442834 "KRCFROM" 1442896 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441673 1441860 1442159 "KOVACIC" 1442569 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441508 1441532 1441573 "KONVERT" 1441635 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1441343 1441367 1441408 "KOERCE" 1441470 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1439174 1439936 1440313 "KERNEL" 1440999 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438670 1438751 1438883 "KERNEL2" 1439088 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1432381 1437147 1437201 "KDAGG" 1437578 NIL KDAGG (NIL T T) -9 NIL 1437784 NIL) (-621 1431910 1432034 1432239 "KDAGG-" 1432244 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1425058 1431571 1431726 "KAFILE" 1431788 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419486 1424569 1424797 "JORDAN" 1424879 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418865 1419135 1419256 "JOINAST" 1419385 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418711 1418770 1418825 "JAVACODE" 1418830 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414938 1416888 1416942 "IXAGG" 1417871 NIL IXAGG (NIL T T) -9 NIL 1418330 NIL) (-615 1413857 1414163 1414582 "IXAGG-" 1414587 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1409390 1413779 1413838 "IVECTOR" 1413843 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1408156 1408393 1408659 "ITUPLE" 1409157 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406658 1406835 1407130 "ITRIGMNP" 1407978 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1405403 1405607 1405890 "ITFUN3" 1406434 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1405035 1405092 1405201 "ITFUN2" 1405340 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1404194 1404515 1404689 "ITFORM" 1404881 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1402155 1403214 1403492 "ITAYLOR" 1403949 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1391100 1396292 1397455 "ISUPS" 1401025 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1390204 1390344 1390580 "ISUMP" 1390947 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385582 1390149 1390190 "ISTRING" 1390195 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1385058 1385303 1385395 "ISAST" 1385510 T ISAST (NIL) -8 NIL NIL NIL) (-603 1384267 1384349 1384565 "IRURPK" 1384972 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1383203 1383404 1383644 "IRSN" 1384047 T IRSN (NIL) -7 NIL NIL NIL) (-601 1381274 1381629 1382058 "IRRF2F" 1382841 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1381021 1381059 1381135 "IRREDFFX" 1381230 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379636 1379895 1380194 "IROOT" 1380754 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1376240 1377320 1378012 "IR" 1378976 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1375445 1375733 1375884 "IRFORM" 1376109 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1373058 1373553 1374119 "IR2" 1374923 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1372158 1372271 1372485 "IR2F" 1372941 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371949 1371983 1372043 "IPRNTPK" 1372118 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368530 1371838 1371907 "IPF" 1371912 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366857 1368455 1368512 "IPADIC" 1368517 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1366169 1366417 1366547 "IP4ADDR" 1366747 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365543 1365798 1365930 "IOMODE" 1366057 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364616 1365140 1365267 "IOBFILE" 1365436 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1364104 1364520 1364548 "IOBCON" 1364553 T IOBCON (NIL) -9 NIL 1364574 NIL) (-587 1363615 1363673 1363856 "INVLAPLA" 1364040 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1353263 1355617 1358003 "INTTR" 1361279 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349598 1350340 1351205 "INTTOOLS" 1352448 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1349184 1349275 1349392 "INTSLPE" 1349501 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1347137 1349107 1349166 "INTRVL" 1349171 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344739 1345251 1345826 "INTRF" 1346622 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1344150 1344247 1344389 "INTRET" 1344637 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1342147 1342536 1343006 "INTRAT" 1343758 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1339410 1339993 1340612 "INTPM" 1341632 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1336155 1336754 1337492 "INTPAF" 1338796 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1331334 1332296 1333347 "INTPACK" 1335124 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1328146 1331131 1331240 "INT" 1331245 T INT (NIL) -8 NIL NIL NIL) (-575 1327398 1327550 1327758 "INTHERTR" 1327988 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326837 1326917 1327105 "INTHERAL" 1327312 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324683 1325126 1325583 "INTHEORY" 1326400 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1316089 1317710 1319482 "INTG0" 1323035 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296662 1301452 1306262 "INTFTBL" 1311299 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295911 1296049 1296222 "INTFACT" 1296521 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1293338 1293784 1294341 "INTEF" 1295465 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291691 1292430 1292458 "INTDOM" 1292759 T INTDOM (NIL) -9 NIL 1292966 NIL) (-567 1291060 1291234 1291476 "INTDOM-" 1291481 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1287420 1289349 1289403 "INTCAT" 1290202 NIL INTCAT (NIL T) -9 NIL 1290523 NIL) (-565 1286892 1286995 1287123 "INTBIT" 1287312 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285591 1285745 1286052 "INTALG" 1286737 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1285074 1285164 1285321 "INTAF" 1285495 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1278423 1284884 1285024 "INTABL" 1285029 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277756 1278222 1278287 "INT8" 1278321 T INT8 (NIL) -8 NIL NIL 1278366) (-560 1277088 1277554 1277619 "INT64" 1277653 T INT64 (NIL) -8 NIL NIL 1277698) (-559 1276420 1276886 1276951 "INT32" 1276985 T INT32 (NIL) -8 NIL NIL 1277030) (-558 1275752 1276218 1276283 "INT16" 1276317 T INT16 (NIL) -8 NIL NIL 1276362) (-557 1270447 1273300 1273328 "INS" 1274262 T INS (NIL) -9 NIL 1274927 NIL) (-556 1267687 1268458 1269432 "INS-" 1269505 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266462 1266689 1266987 "INPSIGN" 1267440 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265580 1265697 1265894 "INPRODPF" 1266342 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264474 1264591 1264828 "INPRODFF" 1265460 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263474 1263626 1263886 "INNMFACT" 1264310 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262671 1262768 1262956 "INMODGCD" 1263373 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1261179 1261424 1261748 "INFSP" 1262416 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1260363 1260480 1260663 "INFPROD0" 1261059 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1257218 1258428 1258943 "INFORM" 1259856 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256828 1256888 1256986 "INFORM1" 1257153 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1256351 1256440 1256554 "INFINITY" 1256734 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255527 1256071 1256172 "INETCLTS" 1256270 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1254143 1254393 1254714 "INEP" 1255275 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1253348 1254040 1254105 "INDE" 1254110 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252912 1252980 1253097 "INCRMAPS" 1253275 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251730 1252181 1252387 "INBFILE" 1252726 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1247029 1247966 1248910 "INBFF" 1250818 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245937 1246206 1246234 "INBCON" 1246747 T INBCON (NIL) -9 NIL 1247013 NIL) (-538 1245189 1245412 1245688 "INBCON-" 1245693 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244668 1244913 1245004 "INAST" 1245118 T INAST (NIL) -8 NIL NIL NIL) (-536 1244095 1244347 1244453 "IMPTAST" 1244582 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240496 1243939 1244043 "IMATRIX" 1244048 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1239204 1239327 1239643 "IMATQF" 1240352 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237424 1237651 1237988 "IMATLIN" 1238960 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1232005 1237348 1237406 "ILIST" 1237411 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229913 1231865 1231978 "IIARRAY2" 1231983 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1225311 1229824 1229888 "IFF" 1229893 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224658 1224928 1225044 "IFAST" 1225215 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219656 1223950 1224138 "IFARRAY" 1224515 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218836 1219560 1219633 "IFAMON" 1219638 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218420 1218485 1218539 "IEVALAB" 1218746 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1218095 1218163 1218323 "IEVALAB-" 1218328 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217542 1218010 1218072 "IDPO" 1218077 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216750 1217431 1217506 "IDPOAMS" 1217511 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1216015 1216639 1216714 "IDPOAM" 1216719 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214561 1215022 1215074 "IDPC" 1215586 NIL IDPC (NIL T T) -9 NIL 1215867 NIL) (-520 1213989 1214453 1214526 "IDPAM" 1214531 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213881 1213954 "IDPAG" 1213959 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -2085 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) (-162 267683 267911 267986 "COMMAAST" 268052 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266932 267126 267154 "COMBOPC" 267492 T COMBOPC (NIL) -9 NIL 267667 NIL) (-160 265828 266038 266280 "COMBINAT" 266722 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 262285 262859 263486 "COMBF" 265250 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 261043 261401 261636 "COLOR" 262070 T COLOR (NIL) -8 NIL NIL NIL) (-157 260519 260764 260856 "COLONAST" 260971 T COLONAST (NIL) -8 NIL NIL NIL) (-156 260159 260206 260331 "CMPLXRT" 260466 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259607 259859 259958 "CLLCTAST" 260080 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 255109 256137 257217 "CLIP" 258547 T CLIP (NIL) -7 NIL NIL NIL) (-153 253450 254210 254450 "CLIF" 254936 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249600 251568 251609 "CLAGG" 252538 NIL CLAGG (NIL T) -9 NIL 253074 NIL) (-151 248022 248479 249062 "CLAGG-" 249067 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247566 247651 247791 "CINTSLPE" 247931 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 245067 245538 246086 "CHVAR" 247094 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 244227 244781 244809 "CHARZ" 244814 T CHARZ (NIL) -9 NIL 244829 NIL) (-147 243981 244021 244099 "CHARPOL" 244181 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 243025 243612 243640 "CHARNZ" 243687 T CHARNZ (NIL) -9 NIL 243743 NIL) (-145 240931 241679 242032 "CHAR" 242692 T CHAR (NIL) -8 NIL NIL NIL) (-144 240657 240718 240746 "CFCAT" 240857 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239898 240009 240192 "CDEN" 240541 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235863 239051 239331 "CCLASS" 239638 T CCLASS (NIL) -8 NIL NIL NIL) (-141 235114 235271 235448 "CATEGORY" 235706 T -10 (NIL) -8 NIL NIL NIL) (-140 234687 235033 235081 "CATCTOR" 235086 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 234138 234390 234488 "CATAST" 234609 T CATAST (NIL) -8 NIL NIL NIL) (-138 233614 233859 233951 "CASEAST" 234066 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228752 229771 230515 "CARTEN" 232926 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227860 228008 228229 "CARTEN2" 228599 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 226176 227010 227267 "CARD" 227623 T CARD (NIL) -8 NIL NIL NIL) (-134 225752 225980 226055 "CAPSLAST" 226121 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 225242 225450 225478 "CACHSET" 225610 T CACHSET (NIL) -9 NIL 225688 NIL) (-132 224698 225020 225048 "CABMON" 225098 T CABMON (NIL) -9 NIL 225154 NIL) (-131 224171 224402 224512 "BYTEORD" 224608 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 223148 223700 223842 "BYTE" 224005 T BYTE (NIL) -8 NIL NIL 224127) (-129 218501 222653 222825 "BYTEBUF" 222996 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 216013 218193 218300 "BTREE" 218427 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213465 215661 215783 "BTOURN" 215923 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210810 212907 212948 "BTCAT" 213016 NIL BTCAT (NIL T) -9 NIL 213093 NIL) (-125 210477 210557 210706 "BTCAT-" 210711 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205842 209723 209751 "BTAGG" 209865 T BTAGG (NIL) -9 NIL 209975 NIL) (-123 205332 205457 205663 "BTAGG-" 205668 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 202330 204610 204825 "BSTREE" 205149 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201468 201594 201778 "BRILL" 202186 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 198095 200166 200207 "BRAGG" 200856 NIL BRAGG (NIL T) -9 NIL 201114 NIL) (-119 196624 197030 197585 "BRAGG-" 197590 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189540 195968 196153 "BPADICRT" 196471 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187855 189477 189522 "BPADIC" 189527 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187553 187583 187697 "BOUNDZRO" 187819 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182781 183979 184891 "BOP" 186661 T BOP (NIL) -8 NIL NIL NIL) (-114 180562 180966 181441 "BOP1" 182339 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 180263 180324 180352 "BOOLE" 180463 T BOOLE (NIL) -9 NIL 180545 NIL) (-112 179088 179837 179986 "BOOLEAN" 180134 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 178353 178757 178811 "BMODULE" 178816 NIL BMODULE (NIL T T) -9 NIL 178881 NIL) (-110 174154 178151 178224 "BITS" 178300 T BITS (NIL) -8 NIL NIL NIL) (-109 173575 173694 173834 "BINDING" 174034 T BINDING (NIL) -8 NIL NIL NIL) (-108 167294 173170 173319 "BINARY" 173446 T BINARY (NIL) -8 NIL NIL NIL) (-107 165049 166521 166562 "BGAGG" 166822 NIL BGAGG (NIL T) -9 NIL 166959 NIL) (-106 164880 164912 165003 "BGAGG-" 165008 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163951 164264 164469 "BFUNCT" 164695 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162641 162819 163107 "BEZOUT" 163775 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 159113 161493 161823 "BBTREE" 162344 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158714 158792 158820 "BASTYPE" 158997 T BASTYPE (NIL) -9 NIL 159096 NIL) (-101 158390 158471 158606 "BASTYPE-" 158611 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157824 157900 158052 "BALFACT" 158301 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156680 157239 157425 "AUTOMOR" 157669 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156406 156411 156437 "ATTREG" 156442 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154658 155103 155455 "ATTRBUT" 156072 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154266 154486 154552 "ATTRAST" 154610 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153802 153915 153941 "ATRIG" 154142 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153611 153652 153739 "ATRIG-" 153744 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153242 153428 153454 "ASTCAT" 153459 T ASTCAT (NIL) -9 NIL 153489 NIL) (-92 152969 153028 153147 "ASTCAT-" 153152 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151121 152745 152833 "ASTACK" 152912 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149626 149923 150288 "ASSOCEQ" 150803 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148658 149285 149409 "ASP9" 149533 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148421 148606 148645 "ASP8" 148650 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147289 148026 148168 "ASP80" 148310 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146187 146924 147056 "ASP7" 147188 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145141 145864 145982 "ASP78" 146100 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144110 144821 144938 "ASP77" 145055 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 143022 143748 143879 "ASP74" 144010 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141922 142657 142789 "ASP73" 142921 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 141026 141748 141848 "ASP6" 141853 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139973 140703 140821 "ASP55" 140939 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138922 139647 139766 "ASP50" 139885 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 138010 138623 138733 "ASP4" 138843 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137098 137711 137821 "ASP49" 137931 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135882 136637 136805 "ASP42" 136987 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134659 135415 135585 "ASP41" 135769 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133609 134336 134454 "ASP35" 134572 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133374 133557 133596 "ASP34" 133601 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133111 133178 133254 "ASP33" 133329 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 132005 132746 132878 "ASP31" 133010 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131770 131953 131992 "ASP30" 131997 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131505 131574 131650 "ASP29" 131725 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131270 131453 131492 "ASP28" 131497 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 131035 131218 131257 "ASP27" 131262 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130119 130733 130844 "ASP24" 130955 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129196 129921 130033 "ASP20" 130038 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128284 128897 129007 "ASP1" 129117 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127227 127958 128077 "ASP19" 128196 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126964 127031 127107 "ASP12" 127182 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125816 126563 126707 "ASP10" 126851 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123670 125660 125751 "ARRAY2" 125756 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119438 123318 123432 "ARRAY1" 123587 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118470 118643 118864 "ARRAY12" 119261 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112757 114672 114747 "ARR2CAT" 117377 NIL ARR2CAT (NIL T T T) -9 NIL 118135 NIL) (-56 110191 110935 111889 "ARR2CAT-" 111894 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109508 109818 109943 "ARITY" 110084 T ARITY (NIL) -8 NIL NIL NIL) (-54 108284 108436 108735 "APPRULE" 109344 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107935 107983 108102 "APPLYORE" 108230 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107289 107528 107648 "ANY" 107833 T ANY (NIL) -8 NIL NIL NIL) (-51 106567 106690 106847 "ANY1" 107163 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104097 105004 105331 "ANTISYM" 106291 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103589 103804 103900 "ANON" 104019 T ANON (NIL) -8 NIL NIL NIL) (-48 97589 102128 102582 "AN" 103153 T AN (NIL) -8 NIL NIL NIL) (-47 93473 94861 94912 "AMR" 95660 NIL AMR (NIL T T) -9 NIL 96260 NIL) (-46 92585 92806 93169 "AMR-" 93174 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 77030 92502 92563 "ALIST" 92568 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73835 76624 76793 "ALGSC" 76948 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70391 70945 71552 "ALGPKG" 73275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69668 69769 69953 "ALGMFACT" 70277 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65703 66282 66876 "ALGMANIP" 69252 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55914 65329 65479 "ALGFF" 65636 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55110 55241 55420 "ALGFACT" 55772 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54037 54637 54675 "ALGEBRA" 54680 NIL ALGEBRA (NIL T) -9 NIL 54721 NIL) (-37 53755 53814 53946 "ALGEBRA-" 53951 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35692 51592 51644 "ALAGG" 51780 NIL ALAGG (NIL T T) -9 NIL 51941 NIL) (-35 35228 35341 35367 "AHYP" 35568 T AHYP (NIL) -9 NIL NIL NIL) (-34 34159 34407 34433 "AGG" 34932 T AGG (NIL) -9 NIL 35211 NIL) (-33 33593 33755 33969 "AGG-" 33974 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31399 31822 32227 "AF" 33235 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30879 31124 31214 "ADDAST" 31327 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30147 30406 30562 "ACPLOT" 30741 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18770 27079 27117 "ACFS" 27724 NIL ACFS (NIL T) -9 NIL 27963 NIL) (-28 16797 17287 18049 "ACFS-" 18054 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12901 14830 14856 "ACF" 15735 T ACF (NIL) -9 NIL 16148 NIL) (-26 11605 11939 12432 "ACF-" 12437 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11163 11358 11384 "ABELSG" 11476 T ABELSG (NIL) -9 NIL 11541 NIL) (-24 11030 11055 11121 "ABELSG-" 11126 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10359 10646 10672 "ABELMON" 10842 T ABELMON (NIL) -9 NIL 10954 NIL) (-22 10023 10107 10245 "ABELMON-" 10250 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9357 9729 9755 "ABELGRP" 9827 T ABELGRP (NIL) -9 NIL 9902 NIL) (-20 8820 8949 9165 "ABELGRP-" 9170 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8082 8121 "A1AGG" 8126 NIL A1AGG (NIL T) -9 NIL 8166 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3264106 3264111 3264116 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3264091 3264096 3264101 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3264076 3264081 3264086 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3264061 3264066 3264071 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1318 3263204 3263936 3264013 "ZMOD" 3264018 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1317 3262258 3262422 3262645 "ZLINDEP" 3263036 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1316 3251558 3253326 3255298 "ZDSOLVE" 3260388 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1315 3250804 3250945 3251134 "YSTREAM" 3251404 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1314 3250232 3250478 3250591 "YDIAGRAM" 3250713 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1313 3248006 3249533 3249737 "XRPOLY" 3250075 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3244559 3245877 3246452 "XPR" 3247478 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1311 3242280 3243890 3244094 "XPOLY" 3244390 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1310 3239919 3241287 3241342 "XPOLYC" 3241630 NIL XPOLYC (NIL T T) -9 NIL 3241743 NIL) (-1309 3236295 3238436 3238824 "XPBWPOLY" 3239577 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1308 3231976 3234271 3234313 "XF" 3234934 NIL XF (NIL T) -9 NIL 3235334 NIL) (-1307 3231597 3231685 3231854 "XF-" 3231859 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1306 3226779 3228068 3228123 "XFALG" 3230295 NIL XFALG (NIL T T) -9 NIL 3231084 NIL) (-1305 3225912 3226016 3226221 "XEXPPKG" 3226671 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1304 3224021 3225762 3225858 "XDPOLY" 3225863 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1303 3222814 3223414 3223457 "XALG" 3223462 NIL XALG (NIL T) -9 NIL 3223573 NIL) (-1302 3216256 3220791 3221285 "WUTSET" 3222406 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1301 3214512 3215308 3215631 "WP" 3216067 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1300 3214114 3214334 3214404 "WHILEAST" 3214464 T WHILEAST (NIL) -8 NIL NIL NIL) (-1299 3213586 3213831 3213925 "WHEREAST" 3214042 T WHEREAST (NIL) -8 NIL NIL NIL) (-1298 3212472 3212670 3212965 "WFFINTBS" 3213383 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1297 3210376 3210803 3211265 "WEIER" 3212044 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1296 3209408 3209858 3209900 "VSPACE" 3210036 NIL VSPACE (NIL T) -9 NIL 3210110 NIL) (-1295 3209246 3209273 3209364 "VSPACE-" 3209369 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1294 3209055 3209097 3209165 "VOID" 3209200 T VOID (NIL) -8 NIL NIL NIL) (-1293 3207191 3207550 3207956 "VIEW" 3208671 T VIEW (NIL) -7 NIL NIL NIL) (-1292 3203615 3204254 3204991 "VIEWDEF" 3206476 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1291 3192919 3195163 3197336 "VIEW3D" 3201464 T VIEW3D (NIL) -8 NIL NIL NIL) (-1290 3185170 3186830 3188409 "VIEW2D" 3191362 T VIEW2D (NIL) -8 NIL NIL NIL) (-1289 3180526 3184940 3185032 "VECTOR" 3185113 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1288 3179103 3179362 3179680 "VECTOR2" 3180256 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1287 3172501 3176807 3176850 "VECTCAT" 3177845 NIL VECTCAT (NIL T) -9 NIL 3178432 NIL) (-1286 3171515 3171769 3172159 "VECTCAT-" 3172164 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1285 3170969 3171166 3171286 "VARIABLE" 3171430 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1284 3170902 3170907 3170937 "UTYPE" 3170942 T UTYPE (NIL) -9 NIL NIL NIL) (-1283 3169732 3169886 3170148 "UTSODETL" 3170728 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1282 3167172 3167632 3168156 "UTSODE" 3169273 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1281 3159120 3164933 3165413 "UTS" 3166750 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1280 3149684 3155054 3155097 "UTSCAT" 3156209 NIL UTSCAT (NIL T) -9 NIL 3156967 NIL) (-1279 3147032 3147754 3148743 "UTSCAT-" 3148748 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1278 3146659 3146702 3146835 "UTS2" 3146983 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1277 3140860 3143469 3143512 "URAGG" 3145582 NIL URAGG (NIL T) -9 NIL 3146305 NIL) (-1276 3137799 3138662 3139785 "URAGG-" 3139790 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1275 3133508 3136434 3136899 "UPXSSING" 3137463 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1274 3125684 3132890 3133154 "UPXS" 3133302 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1273 3118757 3125588 3125660 "UPXSCONS" 3125665 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1272 3108164 3114960 3115022 "UPXSCCA" 3115596 NIL UPXSCCA (NIL T T) -9 NIL 3115829 NIL) (-1271 3107802 3107887 3108061 "UPXSCCA-" 3108066 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1270 3097061 3103630 3103673 "UPXSCAT" 3104321 NIL UPXSCAT (NIL T) -9 NIL 3104930 NIL) (-1269 3096491 3096570 3096749 "UPXS2" 3096976 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1268 3095145 3095398 3095749 "UPSQFREE" 3096234 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1267 3088353 3091413 3091468 "UPSCAT" 3092548 NIL UPSCAT (NIL T T) -9 NIL 3093313 NIL) (-1266 3087557 3087764 3088091 "UPSCAT-" 3088096 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1265 3072639 3080684 3080727 "UPOLYC" 3082828 NIL UPOLYC (NIL T) -9 NIL 3084049 NIL) (-1264 3063967 3066393 3069540 "UPOLYC-" 3069545 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1263 3063594 3063637 3063770 "UPOLYC2" 3063918 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1262 3055129 3063277 3063406 "UP" 3063513 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1261 3054468 3054575 3054739 "UPMP" 3055018 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1260 3054021 3054102 3054241 "UPDIVP" 3054381 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1259 3052589 3052838 3053154 "UPDECOMP" 3053770 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1258 3051820 3051932 3052118 "UPCDEN" 3052473 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1257 3051339 3051408 3051557 "UP2" 3051745 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1256 3049806 3050543 3050820 "UNISEG" 3051097 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1255 3049021 3049148 3049353 "UNISEG2" 3049649 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1254 3048081 3048261 3048487 "UNIFACT" 3048837 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1253 3030833 3047393 3047635 "ULS" 3047897 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1252 3018463 3030737 3030809 "ULSCONS" 3030814 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1251 2999184 3011544 3011606 "ULSCCAT" 3012244 NIL ULSCCAT (NIL T T) -9 NIL 3012533 NIL) (-1250 2998234 2998479 2998867 "ULSCCAT-" 2998872 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 2987298 2993781 2993824 "ULSCAT" 2994687 NIL ULSCAT (NIL T) -9 NIL 2995418 NIL) (-1248 2986728 2986807 2986986 "ULS2" 2987213 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1247 2985847 2986357 2986464 "UINT8" 2986575 T UINT8 (NIL) -8 NIL NIL 2986660) (-1246 2984965 2985475 2985582 "UINT64" 2985693 T UINT64 (NIL) -8 NIL NIL 2985778) (-1245 2984083 2984593 2984700 "UINT32" 2984811 T UINT32 (NIL) -8 NIL NIL 2984896) (-1244 2983201 2983711 2983818 "UINT16" 2983929 T UINT16 (NIL) -8 NIL NIL 2984014) (-1243 2981490 2982447 2982477 "UFD" 2982689 T UFD (NIL) -9 NIL 2982803 NIL) (-1242 2981284 2981330 2981425 "UFD-" 2981430 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1241 2980366 2980549 2980765 "UDVO" 2981090 T UDVO (NIL) -7 NIL NIL NIL) (-1240 2978182 2978591 2979062 "UDPO" 2979930 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1239 2978115 2978120 2978150 "TYPE" 2978155 T TYPE (NIL) -9 NIL NIL NIL) (-1238 2977875 2978070 2978101 "TYPEAST" 2978106 T TYPEAST (NIL) -8 NIL NIL NIL) (-1237 2976846 2977048 2977288 "TWOFACT" 2977669 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1236 2975869 2976255 2976490 "TUPLE" 2976646 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1235 2973560 2974079 2974618 "TUBETOOL" 2975352 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1234 2972409 2972614 2972855 "TUBE" 2973353 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1233 2967138 2971381 2971664 "TS" 2972161 NIL TS (NIL T) -8 NIL NIL NIL) (-1232 2955778 2959897 2959994 "TSETCAT" 2965263 NIL TSETCAT (NIL T T T T) -9 NIL 2966794 NIL) (-1231 2950510 2952110 2954001 "TSETCAT-" 2954006 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1230 2945149 2945996 2946925 "TRMANIP" 2949646 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1229 2944590 2944653 2944816 "TRIMAT" 2945081 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1228 2942456 2942693 2943050 "TRIGMNIP" 2944339 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1227 2941976 2942089 2942119 "TRIGCAT" 2942332 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1226 2941645 2941724 2941865 "TRIGCAT-" 2941870 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1225 2938493 2940503 2940784 "TREE" 2941399 NIL TREE (NIL T) -8 NIL NIL NIL) (-1224 2937767 2938295 2938325 "TRANFUN" 2938360 T TRANFUN (NIL) -9 NIL 2938426 NIL) (-1223 2937046 2937237 2937517 "TRANFUN-" 2937522 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1222 2936850 2936882 2936943 "TOPSP" 2937007 T TOPSP (NIL) -7 NIL NIL NIL) (-1221 2936198 2936313 2936467 "TOOLSIGN" 2936731 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1220 2934832 2935375 2935614 "TEXTFILE" 2935981 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1219 2932744 2933285 2933714 "TEX" 2934425 T TEX (NIL) -8 NIL NIL NIL) (-1218 2932525 2932556 2932628 "TEX1" 2932707 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1217 2932173 2932236 2932326 "TEMUTL" 2932457 T TEMUTL (NIL) -7 NIL NIL NIL) (-1216 2930327 2930607 2930932 "TBCMPPK" 2931896 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1215 2922036 2928413 2928469 "TBAGG" 2928869 NIL TBAGG (NIL T T) -9 NIL 2929080 NIL) (-1214 2917106 2918594 2920348 "TBAGG-" 2920353 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1213 2916490 2916597 2916742 "TANEXP" 2916995 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1212 2916001 2916265 2916355 "TALGOP" 2916435 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1211 2909397 2915858 2915951 "TABLE" 2915956 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1210 2908809 2908908 2909046 "TABLEAU" 2909294 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1209 2903417 2904637 2905885 "TABLBUMP" 2907595 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1208 2902639 2902786 2902967 "SYSTEM" 2903258 T SYSTEM (NIL) -8 NIL NIL NIL) (-1207 2899098 2899797 2900580 "SYSSOLP" 2901890 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1206 2898896 2899053 2899084 "SYSPTR" 2899089 T SYSPTR (NIL) -8 NIL NIL NIL) (-1205 2897932 2898437 2898556 "SYSNNI" 2898742 NIL SYSNNI (NIL NIL) -8 NIL NIL 2898827) (-1204 2897231 2897690 2897769 "SYSINT" 2897829 NIL SYSINT (NIL NIL) -8 NIL NIL 2897874) (-1203 2893563 2894509 2895219 "SYNTAX" 2896543 T SYNTAX (NIL) -8 NIL NIL NIL) (-1202 2890721 2891323 2891955 "SYMTAB" 2892953 T SYMTAB (NIL) -8 NIL NIL NIL) (-1201 2885970 2886872 2887855 "SYMS" 2889760 T SYMS (NIL) -8 NIL NIL NIL) (-1200 2883205 2885428 2885658 "SYMPOLY" 2885775 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1199 2882722 2882797 2882920 "SYMFUNC" 2883117 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1198 2878742 2880034 2880847 "SYMBOL" 2881931 T SYMBOL (NIL) -8 NIL NIL NIL) (-1197 2872281 2873970 2875690 "SWITCH" 2877044 T SWITCH (NIL) -8 NIL NIL NIL) (-1196 2865625 2871237 2871531 "SUTS" 2872045 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1195 2857801 2865007 2865271 "SUPXS" 2865419 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2849284 2857419 2857545 "SUP" 2857710 NIL SUP (NIL T) -8 NIL NIL NIL) (-1193 2848443 2848570 2848787 "SUPFRACF" 2849152 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1192 2848064 2848123 2848236 "SUP2" 2848378 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1191 2846512 2846786 2847142 "SUMRF" 2847763 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1190 2845847 2845913 2846105 "SUMFS" 2846433 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1189 2828634 2845159 2845401 "SULS" 2845663 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1188 2828236 2828456 2828526 "SUCHTAST" 2828586 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1187 2827531 2827761 2827901 "SUCH" 2828144 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1186 2821398 2822437 2823396 "SUBSPACE" 2826619 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1185 2820828 2820918 2821082 "SUBRESP" 2821286 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1184 2814196 2815493 2816804 "STTF" 2819564 NIL STTF (NIL T) -7 NIL NIL NIL) (-1183 2808369 2809489 2810636 "STTFNC" 2813096 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1182 2799682 2801551 2803345 "STTAYLOR" 2806610 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1181 2792818 2799546 2799629 "STRTBL" 2799634 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1180 2787779 2792527 2792626 "STRING" 2792741 T STRING (NIL) -8 NIL NIL NIL) (-1179 2780535 2785398 2786009 "STREAM" 2787203 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1178 2780045 2780122 2780266 "STREAM3" 2780452 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1177 2779027 2779210 2779445 "STREAM2" 2779858 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1176 2778715 2778767 2778860 "STREAM1" 2778969 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1175 2777731 2777912 2778143 "STINPROD" 2778531 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1174 2777269 2777479 2777509 "STEP" 2777589 T STEP (NIL) -9 NIL 2777667 NIL) (-1173 2776456 2776758 2776906 "STEPAST" 2777143 T STEPAST (NIL) -8 NIL NIL NIL) (-1172 2769894 2776355 2776432 "STBL" 2776437 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1171 2764964 2769057 2769100 "STAGG" 2769253 NIL STAGG (NIL T) -9 NIL 2769342 NIL) (-1170 2762666 2763268 2764140 "STAGG-" 2764145 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1169 2760816 2762436 2762528 "STACK" 2762609 NIL STACK (NIL T) -8 NIL NIL NIL) (-1168 2753511 2758957 2759413 "SREGSET" 2760446 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1167 2745936 2747305 2748818 "SRDCMPK" 2752117 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1166 2738773 2743295 2743325 "SRAGG" 2744628 T SRAGG (NIL) -9 NIL 2745236 NIL) (-1165 2737790 2738045 2738424 "SRAGG-" 2738429 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1164 2731974 2736737 2737158 "SQMATRIX" 2737416 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1163 2725662 2728692 2729419 "SPLTREE" 2731319 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1162 2721625 2722318 2722964 "SPLNODE" 2725088 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1161 2720672 2720905 2720935 "SPFCAT" 2721379 T SPFCAT (NIL) -9 NIL NIL NIL) (-1160 2719409 2719619 2719883 "SPECOUT" 2720430 T SPECOUT (NIL) -7 NIL NIL NIL) (-1159 2710505 2712377 2712407 "SPADXPT" 2717083 T SPADXPT (NIL) -9 NIL 2719247 NIL) (-1158 2710266 2710306 2710375 "SPADPRSR" 2710458 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1157 2708315 2710221 2710252 "SPADAST" 2710257 T SPADAST (NIL) -8 NIL NIL NIL) (-1156 2700246 2702019 2702062 "SPACEC" 2706435 NIL SPACEC (NIL T) -9 NIL 2708251 NIL) (-1155 2698376 2700178 2700227 "SPACE3" 2700232 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1154 2697128 2697299 2697590 "SORTPAK" 2698181 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1153 2695220 2695523 2695935 "SOLVETRA" 2696792 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1152 2694270 2694492 2694753 "SOLVESER" 2694993 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1151 2689574 2690462 2691457 "SOLVERAD" 2693322 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1150 2685389 2685998 2686727 "SOLVEFOR" 2688941 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1149 2679659 2684738 2684835 "SNTSCAT" 2684840 NIL SNTSCAT (NIL T T T T) -9 NIL 2684910 NIL) (-1148 2673765 2677982 2678373 "SMTS" 2679349 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1147 2668174 2673653 2673730 "SMP" 2673735 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1146 2666333 2666634 2667032 "SMITH" 2667871 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1145 2658437 2662912 2663015 "SMATCAT" 2664366 NIL SMATCAT (NIL NIL T T T) -9 NIL 2664916 NIL) (-1144 2655377 2656200 2657378 "SMATCAT-" 2657383 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1143 2653018 2654585 2654628 "SKAGG" 2654889 NIL SKAGG (NIL T) -9 NIL 2655024 NIL) (-1142 2649208 2652491 2652675 "SINT" 2652827 T SINT (NIL) -8 NIL NIL 2652989) (-1141 2648980 2649018 2649084 "SIMPAN" 2649164 T SIMPAN (NIL) -7 NIL NIL NIL) (-1140 2648259 2648515 2648655 "SIG" 2648862 T SIG (NIL) -8 NIL NIL NIL) (-1139 2647097 2647318 2647593 "SIGNRF" 2648018 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1138 2645930 2646081 2646365 "SIGNEF" 2646926 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1137 2645236 2645513 2645637 "SIGAST" 2645828 T SIGAST (NIL) -8 NIL NIL NIL) (-1136 2642926 2643380 2643886 "SHP" 2644777 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1135 2636755 2642827 2642903 "SHDP" 2642908 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1134 2636314 2636506 2636536 "SGROUP" 2636629 T SGROUP (NIL) -9 NIL 2636691 NIL) (-1133 2636172 2636198 2636271 "SGROUP-" 2636276 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1132 2632963 2633661 2634384 "SGCF" 2635471 T SGCF (NIL) -7 NIL NIL NIL) (-1131 2627331 2632410 2632507 "SFRTCAT" 2632512 NIL SFRTCAT (NIL T T T T) -9 NIL 2632551 NIL) (-1130 2620752 2621770 2622906 "SFRGCD" 2626314 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1129 2613878 2614951 2616137 "SFQCMPK" 2619685 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1128 2613498 2613587 2613698 "SFORT" 2613819 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1127 2612616 2613338 2613459 "SEXOF" 2613464 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1126 2611723 2612497 2612565 "SEX" 2612570 T SEX (NIL) -8 NIL NIL NIL) (-1125 2607504 2608219 2608314 "SEXCAT" 2610936 NIL SEXCAT (NIL T T T T T) -9 NIL 2611496 NIL) (-1124 2604657 2607438 2607486 "SET" 2607491 NIL SET (NIL T) -8 NIL NIL NIL) (-1123 2602881 2603370 2603675 "SETMN" 2604398 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1122 2602447 2602599 2602629 "SETCAT" 2602746 T SETCAT (NIL) -9 NIL 2602831 NIL) (-1121 2602227 2602279 2602378 "SETCAT-" 2602383 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1120 2598588 2600688 2600731 "SETAGG" 2601601 NIL SETAGG (NIL T) -9 NIL 2601941 NIL) (-1119 2598046 2598162 2598399 "SETAGG-" 2598404 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1118 2597489 2597742 2597843 "SEQAST" 2597967 T SEQAST (NIL) -8 NIL NIL NIL) (-1117 2596688 2596982 2597043 "SEGXCAT" 2597329 NIL SEGXCAT (NIL T T) -9 NIL 2597449 NIL) (-1116 2595694 2596354 2596536 "SEG" 2596541 NIL SEG (NIL T) -8 NIL NIL NIL) (-1115 2594673 2594887 2594930 "SEGCAT" 2595452 NIL SEGCAT (NIL T) -9 NIL 2595673 NIL) (-1114 2593605 2594036 2594244 "SEGBIND" 2594500 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1113 2593226 2593285 2593398 "SEGBIND2" 2593540 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1112 2592799 2593027 2593104 "SEGAST" 2593171 T SEGAST (NIL) -8 NIL NIL NIL) (-1111 2592018 2592144 2592348 "SEG2" 2592643 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1110 2591389 2591953 2592000 "SDVAR" 2592005 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1109 2583640 2591159 2591289 "SDPOL" 2591294 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1108 2582233 2582499 2582818 "SCPKG" 2583355 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1107 2581397 2581569 2581761 "SCOPE" 2582063 T SCOPE (NIL) -8 NIL NIL NIL) (-1106 2580617 2580751 2580930 "SCACHE" 2581252 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1105 2580249 2580435 2580465 "SASTCAT" 2580470 T SASTCAT (NIL) -9 NIL 2580483 NIL) (-1104 2579736 2580084 2580160 "SAOS" 2580195 T SAOS (NIL) -8 NIL NIL NIL) (-1103 2579301 2579336 2579509 "SAERFFC" 2579695 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1102 2572964 2579198 2579278 "SAE" 2579283 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1101 2572557 2572592 2572751 "SAEFACT" 2572923 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1100 2570878 2571192 2571593 "RURPK" 2572223 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1099 2569515 2569821 2570126 "RULESET" 2570712 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1098 2566738 2567268 2567726 "RULE" 2569196 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1097 2566350 2566532 2566615 "RULECOLD" 2566690 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1096 2566140 2566168 2566239 "RTVALUE" 2566301 T RTVALUE (NIL) -8 NIL NIL NIL) (-1095 2565611 2565857 2565951 "RSTRCAST" 2566068 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1094 2560459 2561254 2562174 "RSETGCD" 2564810 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1093 2549689 2554768 2554865 "RSETCAT" 2558984 NIL RSETCAT (NIL T T T T) -9 NIL 2560081 NIL) (-1092 2547616 2548155 2548979 "RSETCAT-" 2548984 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1091 2540002 2541378 2542898 "RSDCMPK" 2546215 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1090 2537967 2538434 2538508 "RRCC" 2539594 NIL RRCC (NIL T T) -9 NIL 2539938 NIL) (-1089 2537318 2537492 2537771 "RRCC-" 2537776 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1088 2536761 2537014 2537115 "RPTAST" 2537239 T RPTAST (NIL) -8 NIL NIL NIL) (-1087 2510237 2519873 2519940 "RPOLCAT" 2530606 NIL RPOLCAT (NIL T T T) -9 NIL 2533766 NIL) (-1086 2501735 2504075 2507197 "RPOLCAT-" 2507202 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1085 2492672 2499946 2500428 "ROUTINE" 2501275 T ROUTINE (NIL) -8 NIL NIL NIL) (-1084 2489333 2492298 2492438 "ROMAN" 2492554 T ROMAN (NIL) -8 NIL NIL NIL) (-1083 2487577 2488193 2488453 "ROIRC" 2489138 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1082 2483781 2486066 2486096 "RNS" 2486400 T RNS (NIL) -9 NIL 2486674 NIL) (-1081 2482290 2482673 2483207 "RNS-" 2483282 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1080 2481679 2482087 2482117 "RNG" 2482122 T RNG (NIL) -9 NIL 2482143 NIL) (-1079 2480682 2481044 2481246 "RNGBIND" 2481530 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1078 2480067 2480455 2480498 "RMODULE" 2480503 NIL RMODULE (NIL T) -9 NIL 2480530 NIL) (-1077 2478903 2478997 2479333 "RMCAT2" 2479968 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1076 2475753 2478249 2478546 "RMATRIX" 2478665 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1075 2468580 2470840 2470955 "RMATCAT" 2474314 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2475296 NIL) (-1074 2467955 2468102 2468409 "RMATCAT-" 2468414 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1073 2467570 2467742 2467785 "RLINSET" 2467847 NIL RLINSET (NIL T) -9 NIL 2467891 NIL) (-1072 2467137 2467212 2467340 "RINTERP" 2467489 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1071 2466181 2466735 2466765 "RING" 2466821 T RING (NIL) -9 NIL 2466913 NIL) (-1070 2465973 2466017 2466114 "RING-" 2466119 NIL RING- (NIL T) -8 NIL NIL NIL) (-1069 2464814 2465051 2465309 "RIDIST" 2465737 T RIDIST (NIL) -7 NIL NIL NIL) (-1068 2456103 2464282 2464488 "RGCHAIN" 2464662 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1067 2455439 2455845 2455886 "RGBCSPC" 2455944 NIL RGBCSPC (NIL T) -9 NIL 2455996 NIL) (-1066 2454583 2454964 2455005 "RGBCMDL" 2455237 NIL RGBCMDL (NIL T) -9 NIL 2455351 NIL) (-1065 2451577 2452191 2452861 "RF" 2453947 NIL RF (NIL T) -7 NIL NIL NIL) (-1064 2451223 2451286 2451389 "RFFACTOR" 2451508 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1063 2450948 2450983 2451080 "RFFACT" 2451182 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1062 2449065 2449429 2449811 "RFDIST" 2450588 T RFDIST (NIL) -7 NIL NIL NIL) (-1061 2448518 2448610 2448773 "RETSOL" 2448967 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1060 2448154 2448234 2448277 "RETRACT" 2448410 NIL RETRACT (NIL T) -9 NIL 2448497 NIL) (-1059 2448003 2448028 2448115 "RETRACT-" 2448120 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1058 2447605 2447825 2447895 "RETAST" 2447955 T RETAST (NIL) -8 NIL NIL NIL) (-1057 2440349 2447258 2447385 "RESULT" 2447500 T RESULT (NIL) -8 NIL NIL NIL) (-1056 2438940 2439618 2439817 "RESRING" 2440252 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1055 2438576 2438625 2438723 "RESLATC" 2438877 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1054 2438281 2438316 2438423 "REPSQ" 2438535 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1053 2435703 2436283 2436885 "REP" 2437701 T REP (NIL) -7 NIL NIL NIL) (-1052 2435400 2435435 2435546 "REPDB" 2435662 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1051 2429300 2430689 2431912 "REP2" 2434212 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1050 2425677 2426358 2427166 "REP1" 2428527 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1049 2418373 2423818 2424274 "REGSET" 2425307 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1048 2417138 2417521 2417771 "REF" 2418158 NIL REF (NIL T) -8 NIL NIL NIL) (-1047 2416515 2416618 2416785 "REDORDER" 2417022 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1046 2412483 2415728 2415955 "RECLOS" 2416343 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1045 2411535 2411716 2411931 "REALSOLV" 2412290 T REALSOLV (NIL) -7 NIL NIL NIL) (-1044 2411381 2411422 2411452 "REAL" 2411457 T REAL (NIL) -9 NIL 2411492 NIL) (-1043 2407864 2408666 2409550 "REAL0Q" 2410546 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1042 2403465 2404453 2405514 "REAL0" 2406845 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1041 2402936 2403182 2403276 "RDUCEAST" 2403393 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1040 2402341 2402413 2402620 "RDIV" 2402858 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1039 2401409 2401583 2401796 "RDIST" 2402163 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1038 2400006 2400293 2400665 "RDETRS" 2401117 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1037 2397818 2398272 2398810 "RDETR" 2399548 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1036 2396443 2396721 2397118 "RDEEFS" 2397534 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1035 2394952 2395258 2395683 "RDEEF" 2396131 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1034 2388985 2391906 2391936 "RCFIELD" 2393231 T RCFIELD (NIL) -9 NIL 2393962 NIL) (-1033 2387049 2387553 2388249 "RCFIELD-" 2388324 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1032 2383293 2385122 2385165 "RCAGG" 2386249 NIL RCAGG (NIL T) -9 NIL 2386714 NIL) (-1031 2382921 2383015 2383178 "RCAGG-" 2383183 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1030 2382256 2382368 2382533 "RATRET" 2382805 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1029 2381809 2381876 2381997 "RATFACT" 2382184 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1028 2381117 2381237 2381389 "RANDSRC" 2381679 T RANDSRC (NIL) -7 NIL NIL NIL) (-1027 2380851 2380895 2380968 "RADUTIL" 2381066 T RADUTIL (NIL) -7 NIL NIL NIL) (-1026 2373679 2379682 2379993 "RADIX" 2380574 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1025 2364139 2373521 2373651 "RADFF" 2373656 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1024 2363786 2363861 2363891 "RADCAT" 2364051 T RADCAT (NIL) -9 NIL NIL NIL) (-1023 2363568 2363616 2363716 "RADCAT-" 2363721 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1022 2361669 2363338 2363430 "QUEUE" 2363511 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1021 2357930 2361602 2361650 "QUAT" 2361655 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1020 2357561 2357604 2357735 "QUATCT2" 2357881 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1019 2350359 2353984 2354026 "QUATCAT" 2354817 NIL QUATCAT (NIL T) -9 NIL 2355583 NIL) (-1018 2346498 2347535 2348925 "QUATCAT-" 2349021 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1017 2343938 2345546 2345589 "QUAGG" 2345970 NIL QUAGG (NIL T) -9 NIL 2346145 NIL) (-1016 2343540 2343760 2343830 "QQUTAST" 2343890 T QQUTAST (NIL) -8 NIL NIL NIL) (-1015 2342553 2343053 2343218 "QFORM" 2343421 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1014 2332885 2338400 2338442 "QFCAT" 2339110 NIL QFCAT (NIL T) -9 NIL 2340111 NIL) (-1013 2328452 2329653 2331247 "QFCAT-" 2331343 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1012 2328083 2328126 2328257 "QFCAT2" 2328403 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1011 2327538 2327648 2327780 "QEQUAT" 2327973 T QEQUAT (NIL) -8 NIL NIL NIL) (-1010 2320664 2321737 2322923 "QCMPACK" 2326471 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1009 2318202 2318650 2319080 "QALGSET" 2320319 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1008 2317437 2317613 2317849 "QALGSET2" 2318020 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1007 2316122 2316346 2316665 "PWFFINTB" 2317210 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1006 2314297 2314465 2314821 "PUSHVAR" 2315936 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1005 2310186 2311240 2311283 "PTRANFN" 2313194 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1004 2308577 2308868 2309192 "PTPACK" 2309897 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1003 2308206 2308263 2308374 "PTFUNC2" 2308514 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1002 2302601 2306995 2307038 "PTCAT" 2307338 NIL PTCAT (NIL T) -9 NIL 2307491 NIL) (-1001 2302256 2302291 2302417 "PSQFR" 2302560 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1000 2300846 2301144 2301480 "PSEUDLIN" 2301954 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-999 2287609 2289980 2292304 "PSETPK" 2298606 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-998 2280627 2283367 2283463 "PSETCAT" 2286484 NIL PSETCAT (NIL T T T T) -9 NIL 2287298 NIL) (-997 2278463 2279097 2279918 "PSETCAT-" 2279923 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-996 2277812 2277977 2278005 "PSCURVE" 2278273 T PSCURVE (NIL) -9 NIL 2278440 NIL) (-995 2273796 2275312 2275377 "PSCAT" 2276221 NIL PSCAT (NIL T T T) -9 NIL 2276461 NIL) (-994 2272859 2273075 2273475 "PSCAT-" 2273480 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-993 2271218 2271928 2272191 "PRTITION" 2272616 T PRTITION (NIL) -8 NIL NIL NIL) (-992 2270693 2270939 2271031 "PRTDAST" 2271146 T PRTDAST (NIL) -8 NIL NIL NIL) (-991 2259783 2261997 2264185 "PRS" 2268555 NIL PRS (NIL T T) -7 NIL NIL NIL) (-990 2257569 2259105 2259145 "PRQAGG" 2259328 NIL PRQAGG (NIL T) -9 NIL 2259430 NIL) (-989 2256905 2257210 2257238 "PROPLOG" 2257377 T PROPLOG (NIL) -9 NIL 2257492 NIL) (-988 2256509 2256566 2256689 "PROPFUN2" 2256828 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-987 2255824 2255945 2256117 "PROPFUN1" 2256370 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-986 2254005 2254571 2254868 "PROPFRML" 2255560 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-985 2253474 2253581 2253709 "PROPERTY" 2253897 T PROPERTY (NIL) -8 NIL NIL NIL) (-984 2247532 2251640 2252460 "PRODUCT" 2252700 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-983 2244810 2246990 2247224 "PR" 2247343 NIL PR (NIL T T) -8 NIL NIL NIL) (-982 2244606 2244638 2244697 "PRINT" 2244771 T PRINT (NIL) -7 NIL NIL NIL) (-981 2243946 2244063 2244215 "PRIMES" 2244486 NIL PRIMES 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2214313 "POLYCAT" 2217827 NIL POLYCAT (NIL T T T) -9 NIL 2219705 NIL) (-968 2202292 2204154 2206538 "POLYCAT-" 2206543 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2201879 2201947 2202067 "POLY2UP" 2202218 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-966 2201511 2201568 2201677 "POLY2" 2201816 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-965 2200196 2200435 2200711 "POLUTIL" 2201285 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-964 2198551 2198828 2199159 "POLTOPOL" 2199918 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-963 2194017 2198485 2198532 "POINT" 2198537 NIL POINT (NIL T) -8 NIL NIL NIL) (-962 2192204 2192561 2192936 "PNTHEORY" 2193662 T PNTHEORY (NIL) -7 NIL NIL NIL) (-961 2190662 2190959 2191358 "PMTOOLS" 2191902 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-960 2190255 2190333 2190450 "PMSYM" 2190578 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-959 2189763 2189832 2190007 "PMQFCAT" 2190180 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-958 2189118 2189228 2189384 "PMPRED" 2189640 NIL PMPRED (NIL T) -7 NIL 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NIL NIL NIL) (-945 2171885 2172062 2172297 "PLOT1" 2172777 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-944 2147276 2151951 2156802 "PLEQN" 2167151 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-943 2146594 2146716 2146896 "PINTERP" 2147141 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-942 2146287 2146334 2146437 "PINTERPA" 2146541 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-941 2145503 2146051 2146138 "PI" 2146178 T PI (NIL) -8 NIL NIL 2146245) (-940 2143786 2144761 2144789 "PID" 2144971 T PID (NIL) -9 NIL 2145105 NIL) (-939 2143537 2143574 2143649 "PICOERCE" 2143743 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-938 2142857 2142996 2143172 "PGROEB" 2143393 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-937 2138444 2139258 2140163 "PGE" 2141972 T PGE (NIL) -7 NIL NIL NIL) (-936 2136567 2136814 2137180 "PGCD" 2138161 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-935 2135905 2136008 2136169 "PFRPAC" 2136451 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-934 2132545 2134453 2134806 "PFR" 2135584 NIL PFR (NIL T) -8 NIL NIL NIL) (-933 2130934 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"ORDSET" 2004609 T ORDSET (NIL) -9 NIL 2004631 NIL) (-861 2002816 2003607 2003635 "ORDRING" 2003837 T ORDRING (NIL) -9 NIL 2003962 NIL) (-860 2002461 2002555 2002699 "ORDRING-" 2002704 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-859 2001814 2002277 2002305 "ORDMON" 2002310 T ORDMON (NIL) -9 NIL 2002331 NIL) (-858 2000976 2001123 2001318 "ORDFUNS" 2001663 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-857 2000287 2000706 2000734 "ORDFIN" 2000799 T ORDFIN (NIL) -9 NIL 2000873 NIL) (-856 1996846 1998873 1999282 "ORDCOMP" 1999911 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-855 1996112 1996239 1996425 "ORDCOMP2" 1996706 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-854 1992693 1993603 1994417 "OPTPROB" 1995318 T OPTPROB (NIL) -8 NIL NIL NIL) (-853 1989495 1990134 1990838 "OPTPACK" 1992009 T OPTPACK (NIL) -7 NIL NIL NIL) (-852 1987168 1987934 1987962 "OPTCAT" 1988781 T OPTCAT (NIL) -9 NIL 1989431 NIL) (-851 1986552 1986845 1986950 "OPSIG" 1987083 T OPSIG (NIL) -8 NIL NIL NIL) (-850 1986320 1986359 1986425 "OPQUERY" 1986506 T OPQUERY (NIL) -7 NIL NIL NIL) (-849 1983451 1984631 1985135 "OP" 1985849 NIL OP (NIL T) -8 NIL NIL NIL) (-848 1982811 1983037 1983078 "OPERCAT" 1983290 NIL OPERCAT (NIL T) -9 NIL 1983387 NIL) (-847 1982566 1982622 1982739 "OPERCAT-" 1982744 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-846 1979379 1981363 1981732 "ONECOMP" 1982230 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-845 1978684 1978799 1978973 "ONECOMP2" 1979251 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-844 1978103 1978209 1978339 "OMSERVER" 1978574 T OMSERVER (NIL) -7 NIL NIL NIL) (-843 1974965 1977543 1977583 "OMSAGG" 1977644 NIL OMSAGG (NIL T) -9 NIL 1977708 NIL) (-842 1973588 1973851 1974133 "OMPKG" 1974703 T OMPKG (NIL) -7 NIL NIL NIL) (-841 1973018 1973121 1973149 "OM" 1973448 T OM (NIL) -9 NIL NIL NIL) (-840 1971565 1972567 1972736 "OMLO" 1972899 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-839 1970525 1970672 1970892 "OMEXPR" 1971391 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-838 1969816 1970071 1970207 "OMERR" 1970409 T OMERR (NIL) -8 NIL NIL NIL) (-837 1968967 1969237 1969397 "OMERRK" 1969676 T OMERRK (NIL) -8 NIL NIL NIL) (-836 1968418 1968644 1968752 "OMENC" 1968879 T OMENC (NIL) -8 NIL NIL NIL) (-835 1962313 1963498 1964669 "OMDEV" 1967267 T OMDEV (NIL) -8 NIL NIL NIL) (-834 1961382 1961553 1961747 "OMCONN" 1962139 T OMCONN (NIL) -8 NIL NIL NIL) (-833 1959876 1960852 1960880 "OINTDOM" 1960885 T OINTDOM (NIL) -9 NIL 1960906 NIL) (-832 1957214 1958564 1958901 "OFMONOID" 1959571 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-831 1956586 1957151 1957196 "ODVAR" 1957201 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-830 1954009 1956331 1956486 "ODR" 1956491 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-829 1946314 1953785 1953911 "ODPOL" 1953916 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-828 1940113 1946186 1946291 "ODP" 1946296 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-827 1938879 1939094 1939369 "ODETOOLS" 1939887 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-826 1935846 1936504 1937220 "ODESYS" 1938212 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-825 1930728 1931636 1932661 "ODERTRIC" 1934921 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-824 1930154 1930236 1930430 "ODERED" 1930640 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-823 1927042 1927590 1928267 "ODERAT" 1929577 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-822 1924001 1924466 1925063 "ODEPRRIC" 1926571 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-821 1921944 1922540 1923026 "ODEPROB" 1923535 T ODEPROB (NIL) -8 NIL NIL NIL) (-820 1918464 1918949 1919596 "ODEPRIM" 1921423 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-819 1917713 1917815 1918075 "ODEPAL" 1918356 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-818 1913875 1914666 1915530 "ODEPACK" 1916869 T ODEPACK (NIL) -7 NIL NIL NIL) (-817 1912936 1913043 1913265 "ODEINT" 1913764 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-816 1907037 1908462 1909909 "ODEIFTBL" 1911509 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-815 1902435 1903221 1904173 "ODEEF" 1906196 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-814 1901784 1901873 1902096 "ODECONST" 1902340 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-813 1899895 1900556 1900584 "ODECAT" 1901189 T ODECAT (NIL) -9 NIL 1901720 NIL) (-812 1896750 1899600 1899722 "OCT" 1899805 NIL OCT (NIL T) -8 NIL NIL NIL) (-811 1896388 1896431 1896558 "OCTCT2" 1896701 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-810 1890995 1893431 1893471 "OC" 1894568 NIL OC (NIL T) -9 NIL 1895426 NIL) (-809 1888222 1888970 1889960 "OC-" 1890054 NIL OC- (NIL T T) -8 NIL NIL NIL) (-808 1887547 1888015 1888043 "OCAMON" 1888048 T OCAMON (NIL) -9 NIL 1888069 NIL) (-807 1887051 1887392 1887420 "OASGP" 1887425 T OASGP (NIL) -9 NIL 1887445 NIL) (-806 1886285 1886774 1886802 "OAMONS" 1886842 T OAMONS (NIL) -9 NIL 1886885 NIL) (-805 1885672 1886105 1886133 "OAMON" 1886138 T OAMON (NIL) -9 NIL 1886158 NIL) (-804 1884903 1885421 1885449 "OAGROUP" 1885454 T OAGROUP (NIL) -9 NIL 1885474 NIL) (-803 1884593 1884643 1884731 "NUMTUBE" 1884847 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-802 1878166 1879684 1881220 "NUMQUAD" 1883077 T NUMQUAD (NIL) -7 NIL NIL NIL) (-801 1873922 1874910 1875935 "NUMODE" 1877161 T NUMODE (NIL) -7 NIL NIL NIL) (-800 1871263 1872143 1872171 "NUMINT" 1873094 T NUMINT (NIL) -9 NIL 1873858 NIL) (-799 1870211 1870408 1870626 "NUMFMT" 1871065 T NUMFMT (NIL) -7 NIL NIL NIL) (-798 1856570 1859515 1862047 "NUMERIC" 1867718 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-797 1850940 1856019 1856114 "NTSCAT" 1856119 NIL NTSCAT (NIL T T T T) -9 NIL 1856158 NIL) (-796 1850134 1850299 1850492 "NTPOLFN" 1850779 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-795 1837935 1846959 1847771 "NSUP" 1849355 NIL NSUP (NIL T) -8 NIL NIL NIL) (-794 1837567 1837624 1837733 "NSUP2" 1837872 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-793 1827517 1837341 1837474 "NSMP" 1837479 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-792 1825949 1826250 1826607 "NREP" 1827205 NIL NREP (NIL T) -7 NIL NIL NIL) (-791 1824540 1824792 1825150 "NPCOEF" 1825692 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-790 1823606 1823721 1823937 "NORMRETR" 1824421 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-789 1821647 1821937 1822346 "NORMPK" 1823314 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-788 1821332 1821360 1821484 "NORMMA" 1821613 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-787 1821132 1821289 1821318 "NONE" 1821323 T NONE (NIL) -8 NIL NIL NIL) (-786 1820921 1820950 1821019 "NONE1" 1821096 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-785 1820418 1820480 1820659 "NODE1" 1820853 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-784 1818699 1819550 1819805 "NNI" 1820152 T NNI (NIL) -8 NIL NIL 1820387) (-783 1817119 1817432 1817796 "NLINSOL" 1818367 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-782 1813360 1814355 1815254 "NIPROB" 1816240 T NIPROB (NIL) -8 NIL NIL NIL) (-781 1812117 1812351 1812653 "NFINTBAS" 1813122 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-780 1811291 1811767 1811808 "NETCLT" 1811980 NIL NETCLT (NIL T) -9 NIL 1812062 NIL) (-779 1809999 1810230 1810511 "NCODIV" 1811059 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-778 1809761 1809798 1809873 "NCNTFRAC" 1809956 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-777 1807941 1808305 1808725 "NCEP" 1809386 NIL NCEP (NIL T) -7 NIL NIL NIL) (-776 1806778 1807551 1807579 "NASRING" 1807689 T NASRING (NIL) -9 NIL 1807769 NIL) (-775 1806573 1806617 1806711 "NASRING-" 1806716 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-774 1805666 1806191 1806219 "NARNG" 1806336 T NARNG (NIL) -9 NIL 1806427 NIL) (-773 1805358 1805425 1805559 "NARNG-" 1805564 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-772 1804237 1804444 1804679 "NAGSP" 1805143 T NAGSP (NIL) -7 NIL NIL NIL) (-771 1795509 1797193 1798866 "NAGS" 1802584 T NAGS (NIL) -7 NIL NIL NIL) (-770 1794057 1794365 1794696 "NAGF07" 1795198 T NAGF07 (NIL) -7 NIL NIL NIL) (-769 1788595 1789886 1791193 "NAGF04" 1792770 T NAGF04 (NIL) -7 NIL NIL NIL) (-768 1781563 1783177 1784810 "NAGF02" 1786982 T NAGF02 (NIL) -7 NIL NIL NIL) (-767 1776787 1777887 1779004 "NAGF01" 1780466 T NAGF01 (NIL) -7 NIL NIL NIL) (-766 1770415 1771981 1773566 "NAGE04" 1775222 T NAGE04 (NIL) -7 NIL NIL NIL) (-765 1761584 1763705 1765835 "NAGE02" 1768305 T NAGE02 (NIL) -7 NIL NIL NIL) (-764 1757537 1758484 1759448 "NAGE01" 1760640 T NAGE01 (NIL) -7 NIL NIL NIL) (-763 1755332 1755866 1756424 "NAGD03" 1756999 T NAGD03 (NIL) -7 NIL NIL NIL) (-762 1747082 1749010 1750964 "NAGD02" 1753398 T NAGD02 (NIL) -7 NIL NIL NIL) (-761 1740893 1742318 1743758 "NAGD01" 1745662 T NAGD01 (NIL) -7 NIL NIL NIL) (-760 1737102 1737924 1738761 "NAGC06" 1740076 T NAGC06 (NIL) -7 NIL NIL NIL) (-759 1735567 1735899 1736255 "NAGC05" 1736766 T NAGC05 (NIL) -7 NIL NIL NIL) (-758 1734943 1735062 1735206 "NAGC02" 1735443 T NAGC02 (NIL) -7 NIL NIL NIL) (-757 1733888 1734471 1734511 "NAALG" 1734590 NIL NAALG (NIL T) -9 NIL 1734651 NIL) (-756 1733723 1733752 1733842 "NAALG-" 1733847 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-755 1727673 1728781 1729968 "MULTSQFR" 1732619 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-754 1726992 1727067 1727251 "MULTFACT" 1727585 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-753 1719663 1723577 1723630 "MTSCAT" 1724700 NIL MTSCAT (NIL T T) -9 NIL 1725215 NIL) (-752 1719375 1719429 1719521 "MTHING" 1719603 NIL MTHING (NIL T) -7 NIL NIL NIL) (-751 1719167 1719200 1719260 "MSYSCMD" 1719335 T MSYSCMD (NIL) -7 NIL NIL NIL) (-750 1715249 1717922 1718242 "MSET" 1718880 NIL MSET (NIL T) -8 NIL NIL NIL) (-749 1712318 1714810 1714851 "MSETAGG" 1714856 NIL MSETAGG (NIL T) -9 NIL 1714890 NIL) (-748 1708160 1709697 1710442 "MRING" 1711618 NIL MRING (NIL T T) -8 NIL NIL NIL) (-747 1707726 1707793 1707924 "MRF2" 1708087 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-746 1707344 1707379 1707523 "MRATFAC" 1707685 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-745 1704956 1705251 1705682 "MPRFF" 1707049 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-744 1698977 1704810 1704907 "MPOLY" 1704912 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-743 1698467 1698502 1698710 "MPCPF" 1698936 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-742 1697981 1698024 1698208 "MPC3" 1698418 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-741 1697176 1697257 1697478 "MPC2" 1697896 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695477 1695814 1696204 "MONOTOOL" 1696836 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-739 1694688 1695005 1695033 "MONOID" 1695252 T MONOID (NIL) -9 NIL 1695399 NIL) (-738 1694234 1694353 1694534 "MONOID-" 1694539 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-737 1683824 1690054 1690113 "MONOGEN" 1690787 NIL MONOGEN (NIL T T) -9 NIL 1691243 NIL) (-736 1681042 1681777 1682777 "MONOGEN-" 1682896 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-735 1679861 1680307 1680335 "MONADWU" 1680727 T MONADWU (NIL) -9 NIL 1680965 NIL) (-734 1679233 1679392 1679640 "MONADWU-" 1679645 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-733 1678578 1678822 1678850 "MONAD" 1679057 T MONAD (NIL) -9 NIL 1679169 NIL) (-732 1678263 1678341 1678473 "MONAD-" 1678478 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-731 1676552 1677176 1677455 "MOEBIUS" 1678016 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-730 1675816 1676220 1676260 "MODULE" 1676265 NIL MODULE (NIL T) -9 NIL 1676304 NIL) (-729 1675384 1675480 1675670 "MODULE-" 1675675 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-728 1673064 1673748 1674075 "MODRING" 1675208 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-727 1670008 1671169 1671690 "MODOP" 1672593 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-726 1668596 1669075 1669352 "MODMONOM" 1669871 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-725 1658364 1666887 1667301 "MODMON" 1668233 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-724 1655520 1657208 1657484 "MODFIELD" 1658239 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-723 1654497 1654801 1654991 "MMLFORM" 1655350 T MMLFORM (NIL) -8 NIL NIL NIL) (-722 1654023 1654066 1654245 "MMAP" 1654448 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-721 1652088 1652855 1652896 "MLO" 1653319 NIL MLO (NIL T) -9 NIL 1653561 NIL) (-720 1649454 1649970 1650572 "MLIFT" 1651569 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-719 1648845 1648929 1649083 "MKUCFUNC" 1649365 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-718 1648444 1648514 1648637 "MKRECORD" 1648768 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-717 1647491 1647653 1647881 "MKFUNC" 1648255 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-716 1646879 1646983 1647139 "MKFLCFN" 1647374 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-715 1646156 1646258 1646443 "MKBCFUNC" 1646772 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-714 1642745 1645710 1645846 "MINT" 1646040 T MINT (NIL) -8 NIL NIL NIL) (-713 1641557 1641800 1642077 "MHROWRED" 1642500 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-712 1636937 1640092 1640497 "MFLOAT" 1641172 T MFLOAT (NIL) -8 NIL NIL NIL) (-711 1636294 1636370 1636541 "MFINFACT" 1636849 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-710 1632609 1633457 1634341 "MESH" 1635430 T MESH (NIL) -7 NIL NIL NIL) (-709 1630999 1631311 1631664 "MDDFACT" 1632296 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-708 1627769 1630130 1630171 "MDAGG" 1630426 NIL MDAGG (NIL T) -9 NIL 1630569 NIL) (-707 1616463 1627062 1627269 "MCMPLX" 1627582 T MCMPLX (NIL) -8 NIL NIL NIL) (-706 1615600 1615746 1615947 "MCDEN" 1616312 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-705 1613490 1613760 1614140 "MCALCFN" 1615330 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-704 1612415 1612655 1612888 "MAYBE" 1613296 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-703 1610027 1610550 1611112 "MATSTOR" 1611886 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-702 1605939 1609399 1609647 "MATRIX" 1609812 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-701 1601705 1602412 1603148 "MATLIN" 1605296 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-700 1591531 1594762 1594839 "MATCAT" 1599871 NIL MATCAT (NIL T T T) -9 NIL 1601343 NIL) (-699 1587724 1588794 1590207 "MATCAT-" 1590212 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-698 1586318 1586471 1586804 "MATCAT2" 1587559 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-697 1584430 1584754 1585138 "MAPPKG3" 1585993 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-696 1583411 1583584 1583806 "MAPPKG2" 1584254 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-695 1581910 1582194 1582521 "MAPPKG1" 1583117 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-694 1580989 1581316 1581493 "MAPPAST" 1581753 T MAPPAST (NIL) -8 NIL NIL NIL) (-693 1580600 1580658 1580781 "MAPHACK3" 1580925 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-692 1580192 1580253 1580367 "MAPHACK2" 1580532 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-691 1579630 1579733 1579875 "MAPHACK1" 1580083 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-690 1577709 1578330 1578634 "MAGMA" 1579358 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-689 1577188 1577433 1577524 "MACROAST" 1577638 T MACROAST (NIL) -8 NIL NIL NIL) (-688 1573609 1575427 1575888 "M3D" 1576760 NIL M3D (NIL T) -8 NIL NIL NIL) (-687 1567659 1571920 1571961 "LZSTAGG" 1572743 NIL LZSTAGG (NIL T) -9 NIL 1573038 NIL) (-686 1563617 1564790 1566247 "LZSTAGG-" 1566252 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-685 1560704 1561508 1561995 "LWORD" 1563162 NIL LWORD (NIL T) -8 NIL NIL NIL) (-684 1560280 1560508 1560583 "LSTAST" 1560649 T LSTAST (NIL) -8 NIL NIL NIL) (-683 1553170 1560051 1560185 "LSQM" 1560190 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-682 1552394 1552533 1552761 "LSPP" 1553025 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-681 1550206 1550507 1550963 "LSMP" 1552083 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-680 1546985 1547659 1548389 "LSMP1" 1549508 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-679 1540787 1546075 1546116 "LSAGG" 1546178 NIL LSAGG (NIL T) -9 NIL 1546256 NIL) (-678 1537482 1538406 1539619 "LSAGG-" 1539624 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-677 1535081 1536626 1536875 "LPOLY" 1537277 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-676 1534663 1534748 1534871 "LPEFRAC" 1534990 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-675 1532984 1533757 1534010 "LO" 1534495 NIL LO (NIL T T T) -8 NIL NIL NIL) (-674 1532596 1532734 1532762 "LOGIC" 1532873 T LOGIC (NIL) -9 NIL 1532954 NIL) (-673 1532458 1532481 1532552 "LOGIC-" 1532557 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-672 1531651 1531791 1531984 "LODOOPS" 1532314 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-671 1529074 1531567 1531633 "LODO" 1531638 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-670 1527612 1527847 1528200 "LODOF" 1528821 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-669 1523816 1526247 1526288 "LODOCAT" 1526726 NIL LODOCAT (NIL T) -9 NIL 1526937 NIL) (-668 1523549 1523607 1523734 "LODOCAT-" 1523739 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-667 1520869 1523390 1523508 "LODO2" 1523513 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-666 1518304 1520806 1520851 "LODO1" 1520856 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-665 1517185 1517350 1517655 "LODEEF" 1518127 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-664 1512463 1515351 1515392 "LNAGG" 1516254 NIL LNAGG (NIL T) -9 NIL 1516689 NIL) (-663 1511610 1511824 1512166 "LNAGG-" 1512171 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-662 1507746 1508535 1509174 "LMOPS" 1511025 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-661 1507135 1507523 1507564 "LMODULE" 1507569 NIL LMODULE (NIL T) -9 NIL 1507595 NIL) (-660 1504336 1506780 1506903 "LMDICT" 1507045 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-659 1503954 1504126 1504167 "LLINSET" 1504228 NIL LLINSET (NIL T) -9 NIL 1504272 NIL) (-658 1503653 1503862 1503922 "LITERAL" 1503927 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-657 1496819 1502587 1502891 "LIST" 1503382 NIL LIST (NIL T) -8 NIL NIL NIL) (-656 1496344 1496418 1496557 "LIST3" 1496739 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-655 1495351 1495529 1495757 "LIST2" 1496162 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-654 1493485 1493797 1494196 "LIST2MAP" 1494998 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-653 1493116 1493304 1493345 "LINSET" 1493350 NIL LINSET (NIL T) -9 NIL 1493384 NIL) (-652 1491529 1492143 1492184 "LINEXP" 1492674 NIL LINEXP (NIL T) -9 NIL 1492947 NIL) (-651 1490421 1490991 1491167 "LINELT" 1491405 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-650 1488998 1489258 1489569 "LINDEP" 1490173 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485765 1486484 1487261 "LIMITRF" 1488253 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1484068 1484364 1484773 "LIMITPS" 1485460 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478496 1483579 1483807 "LIE" 1483889 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1477430 1477899 1477939 "LIECAT" 1478079 NIL LIECAT (NIL T) -9 NIL 1478230 NIL) (-645 1477271 1477298 1477386 "LIECAT-" 1477391 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469864 1476811 1476967 "LIB" 1477135 T LIB (NIL) -8 NIL NIL NIL) (-643 1465499 1466382 1467317 "LGROBP" 1468981 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463497 1463771 1464121 "LF" 1465220 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1462337 1463029 1463057 "LFCAT" 1463264 T LFCAT (NIL) -9 NIL 1463403 NIL) (-640 1459239 1459869 1460557 "LEXTRIPK" 1461701 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455983 1456809 1457312 "LEXP" 1458819 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455459 1455704 1455796 "LETAST" 1455911 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453857 1454170 1454571 "LEADCDET" 1455141 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1453047 1453121 1453350 "LAZM3PK" 1453778 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447964 1451124 1451662 "LAUPOL" 1452559 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447543 1447587 1447748 "LAPLACE" 1447914 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445482 1446644 1446895 "LA" 1447376 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444462 1445046 1445087 "LALG" 1445149 NIL LALG (NIL T) -9 NIL 1445208 NIL) (-631 1444176 1444235 1444371 "LALG-" 1444376 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1444011 1444035 1444076 "KVTFROM" 1444138 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442934 1443378 1443563 "KTVLOGIC" 1443846 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442769 1442793 1442834 "KRCFROM" 1442896 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441673 1441860 1442159 "KOVACIC" 1442569 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441508 1441532 1441573 "KONVERT" 1441635 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1441343 1441367 1441408 "KOERCE" 1441470 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1439174 1439936 1440313 "KERNEL" 1440999 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438670 1438751 1438883 "KERNEL2" 1439088 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1432381 1437147 1437201 "KDAGG" 1437578 NIL KDAGG (NIL T T) -9 NIL 1437784 NIL) (-621 1431910 1432034 1432239 "KDAGG-" 1432244 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1425058 1431571 1431726 "KAFILE" 1431788 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419486 1424569 1424797 "JORDAN" 1424879 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418865 1419135 1419256 "JOINAST" 1419385 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418711 1418770 1418825 "JAVACODE" 1418830 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414938 1416888 1416942 "IXAGG" 1417871 NIL IXAGG (NIL T T) -9 NIL 1418330 NIL) (-615 1413857 1414163 1414582 "IXAGG-" 1414587 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1409390 1413779 1413838 "IVECTOR" 1413843 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1408156 1408393 1408659 "ITUPLE" 1409157 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406658 1406835 1407130 "ITRIGMNP" 1407978 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1405403 1405607 1405890 "ITFUN3" 1406434 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1405035 1405092 1405201 "ITFUN2" 1405340 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1404194 1404515 1404689 "ITFORM" 1404881 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1402155 1403214 1403492 "ITAYLOR" 1403949 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1391100 1396292 1397455 "ISUPS" 1401025 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1390204 1390344 1390580 "ISUMP" 1390947 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385582 1390149 1390190 "ISTRING" 1390195 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1385058 1385303 1385395 "ISAST" 1385510 T ISAST (NIL) -8 NIL NIL NIL) (-603 1384267 1384349 1384565 "IRURPK" 1384972 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1383203 1383404 1383644 "IRSN" 1384047 T IRSN (NIL) -7 NIL NIL NIL) (-601 1381274 1381629 1382058 "IRRF2F" 1382841 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1381021 1381059 1381135 "IRREDFFX" 1381230 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379636 1379895 1380194 "IROOT" 1380754 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1376240 1377320 1378012 "IR" 1378976 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1375445 1375733 1375884 "IRFORM" 1376109 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1373058 1373553 1374119 "IR2" 1374923 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1372158 1372271 1372485 "IR2F" 1372941 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371949 1371983 1372043 "IPRNTPK" 1372118 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368530 1371838 1371907 "IPF" 1371912 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366857 1368455 1368512 "IPADIC" 1368517 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1366169 1366417 1366547 "IP4ADDR" 1366747 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365543 1365798 1365930 "IOMODE" 1366057 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364616 1365140 1365267 "IOBFILE" 1365436 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1364104 1364520 1364548 "IOBCON" 1364553 T IOBCON (NIL) -9 NIL 1364574 NIL) (-587 1363615 1363673 1363856 "INVLAPLA" 1364040 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1353263 1355617 1358003 "INTTR" 1361279 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349598 1350340 1351205 "INTTOOLS" 1352448 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1349184 1349275 1349392 "INTSLPE" 1349501 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1347137 1349107 1349166 "INTRVL" 1349171 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344739 1345251 1345826 "INTRF" 1346622 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1344150 1344247 1344389 "INTRET" 1344637 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1342147 1342536 1343006 "INTRAT" 1343758 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1339410 1339993 1340612 "INTPM" 1341632 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1336155 1336754 1337492 "INTPAF" 1338796 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1331334 1332296 1333347 "INTPACK" 1335124 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1328146 1331131 1331240 "INT" 1331245 T INT (NIL) -8 NIL NIL NIL) (-575 1327398 1327550 1327758 "INTHERTR" 1327988 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326837 1326917 1327105 "INTHERAL" 1327312 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324683 1325126 1325583 "INTHEORY" 1326400 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1316089 1317710 1319482 "INTG0" 1323035 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296662 1301452 1306262 "INTFTBL" 1311299 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295911 1296049 1296222 "INTFACT" 1296521 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1293338 1293784 1294341 "INTEF" 1295465 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291691 1292430 1292458 "INTDOM" 1292759 T INTDOM (NIL) -9 NIL 1292966 NIL) (-567 1291060 1291234 1291476 "INTDOM-" 1291481 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1287420 1289349 1289403 "INTCAT" 1290202 NIL INTCAT (NIL T) -9 NIL 1290523 NIL) (-565 1286892 1286995 1287123 "INTBIT" 1287312 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285591 1285745 1286052 "INTALG" 1286737 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1285074 1285164 1285321 "INTAF" 1285495 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1278423 1284884 1285024 "INTABL" 1285029 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277756 1278222 1278287 "INT8" 1278321 T INT8 (NIL) -8 NIL NIL 1278366) (-560 1277088 1277554 1277619 "INT64" 1277653 T INT64 (NIL) -8 NIL NIL 1277698) (-559 1276420 1276886 1276951 "INT32" 1276985 T INT32 (NIL) -8 NIL NIL 1277030) (-558 1275752 1276218 1276283 "INT16" 1276317 T INT16 (NIL) -8 NIL NIL 1276362) (-557 1270447 1273300 1273328 "INS" 1274262 T INS (NIL) -9 NIL 1274927 NIL) (-556 1267687 1268458 1269432 "INS-" 1269505 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266462 1266689 1266987 "INPSIGN" 1267440 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265580 1265697 1265894 "INPRODPF" 1266342 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264474 1264591 1264828 "INPRODFF" 1265460 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263474 1263626 1263886 "INNMFACT" 1264310 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262671 1262768 1262956 "INMODGCD" 1263373 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1261179 1261424 1261748 "INFSP" 1262416 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1260363 1260480 1260663 "INFPROD0" 1261059 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1257218 1258428 1258943 "INFORM" 1259856 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256828 1256888 1256986 "INFORM1" 1257153 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1256351 1256440 1256554 "INFINITY" 1256734 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255527 1256071 1256172 "INETCLTS" 1256270 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1254143 1254393 1254714 "INEP" 1255275 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1253348 1254040 1254105 "INDE" 1254110 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252912 1252980 1253097 "INCRMAPS" 1253275 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251730 1252181 1252387 "INBFILE" 1252726 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1247029 1247966 1248910 "INBFF" 1250818 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245937 1246206 1246234 "INBCON" 1246747 T INBCON (NIL) -9 NIL 1247013 NIL) (-538 1245189 1245412 1245688 "INBCON-" 1245693 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244668 1244913 1245004 "INAST" 1245118 T INAST (NIL) -8 NIL NIL NIL) (-536 1244095 1244347 1244453 "IMPTAST" 1244582 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240496 1243939 1244043 "IMATRIX" 1244048 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1239204 1239327 1239643 "IMATQF" 1240352 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237424 1237651 1237988 "IMATLIN" 1238960 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1232005 1237348 1237406 "ILIST" 1237411 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229913 1231865 1231978 "IIARRAY2" 1231983 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1225311 1229824 1229888 "IFF" 1229893 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224658 1224928 1225044 "IFAST" 1225215 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219656 1223950 1224138 "IFARRAY" 1224515 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218836 1219560 1219633 "IFAMON" 1219638 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218420 1218485 1218539 "IEVALAB" 1218746 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1218095 1218163 1218323 "IEVALAB-" 1218328 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217542 1218010 1218072 "IDPO" 1218077 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216750 1217431 1217506 "IDPOAMS" 1217511 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1216015 1216639 1216714 "IDPOAM" 1216719 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214561 1215022 1215074 "IDPC" 1215586 NIL IDPC (NIL T T) -9 NIL 1215867 NIL) (-520 1213989 1214453 1214526 "IDPAM" 1214531 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213881 1213954 "IDPAG" 1213959 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -2118 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) (-162 267683 267911 267986 "COMMAAST" 268052 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266932 267126 267154 "COMBOPC" 267492 T COMBOPC (NIL) -9 NIL 267667 NIL) (-160 265828 266038 266280 "COMBINAT" 266722 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 262285 262859 263486 "COMBF" 265250 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 261043 261401 261636 "COLOR" 262070 T COLOR (NIL) -8 NIL NIL NIL) (-157 260519 260764 260856 "COLONAST" 260971 T COLONAST (NIL) -8 NIL NIL NIL) (-156 260159 260206 260331 "CMPLXRT" 260466 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259607 259859 259958 "CLLCTAST" 260080 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 255109 256137 257217 "CLIP" 258547 T CLIP (NIL) -7 NIL NIL NIL) (-153 253450 254210 254450 "CLIF" 254936 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249600 251568 251609 "CLAGG" 252538 NIL CLAGG (NIL T) -9 NIL 253074 NIL) (-151 248022 248479 249062 "CLAGG-" 249067 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247566 247651 247791 "CINTSLPE" 247931 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 245067 245538 246086 "CHVAR" 247094 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 244227 244781 244809 "CHARZ" 244814 T CHARZ (NIL) -9 NIL 244829 NIL) (-147 243981 244021 244099 "CHARPOL" 244181 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 243025 243612 243640 "CHARNZ" 243687 T CHARNZ (NIL) -9 NIL 243743 NIL) (-145 240931 241679 242032 "CHAR" 242692 T CHAR (NIL) -8 NIL NIL NIL) (-144 240657 240718 240746 "CFCAT" 240857 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239898 240009 240192 "CDEN" 240541 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235863 239051 239331 "CCLASS" 239638 T CCLASS (NIL) -8 NIL NIL NIL) (-141 235114 235271 235448 "CATEGORY" 235706 T -10 (NIL) -8 NIL NIL NIL) (-140 234687 235033 235081 "CATCTOR" 235086 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 234138 234390 234488 "CATAST" 234609 T CATAST (NIL) -8 NIL NIL NIL) (-138 233614 233859 233951 "CASEAST" 234066 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228752 229771 230515 "CARTEN" 232926 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227860 228008 228229 "CARTEN2" 228599 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 226176 227010 227267 "CARD" 227623 T CARD (NIL) -8 NIL NIL NIL) (-134 225752 225980 226055 "CAPSLAST" 226121 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 225242 225450 225478 "CACHSET" 225610 T CACHSET (NIL) -9 NIL 225688 NIL) (-132 224698 225020 225048 "CABMON" 225098 T CABMON (NIL) -9 NIL 225154 NIL) (-131 224171 224402 224512 "BYTEORD" 224608 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 223148 223700 223842 "BYTE" 224005 T BYTE (NIL) -8 NIL NIL 224127) (-129 218501 222653 222825 "BYTEBUF" 222996 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 216013 218193 218300 "BTREE" 218427 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213465 215661 215783 "BTOURN" 215923 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210810 212907 212948 "BTCAT" 213016 NIL BTCAT (NIL T) -9 NIL 213093 NIL) (-125 210477 210557 210706 "BTCAT-" 210711 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205842 209723 209751 "BTAGG" 209865 T BTAGG (NIL) -9 NIL 209975 NIL) (-123 205332 205457 205663 "BTAGG-" 205668 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 202330 204610 204825 "BSTREE" 205149 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201468 201594 201778 "BRILL" 202186 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 198095 200166 200207 "BRAGG" 200856 NIL BRAGG (NIL T) -9 NIL 201114 NIL) (-119 196624 197030 197585 "BRAGG-" 197590 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189540 195968 196153 "BPADICRT" 196471 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187855 189477 189522 "BPADIC" 189527 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187553 187583 187697 "BOUNDZRO" 187819 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182781 183979 184891 "BOP" 186661 T BOP (NIL) -8 NIL NIL NIL) (-114 180562 180966 181441 "BOP1" 182339 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 180263 180324 180352 "BOOLE" 180463 T BOOLE (NIL) -9 NIL 180545 NIL) (-112 179088 179837 179986 "BOOLEAN" 180134 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 178353 178757 178811 "BMODULE" 178816 NIL BMODULE (NIL T T) -9 NIL 178881 NIL) (-110 174154 178151 178224 "BITS" 178300 T BITS (NIL) -8 NIL NIL NIL) (-109 173575 173694 173834 "BINDING" 174034 T BINDING (NIL) -8 NIL NIL NIL) (-108 167294 173170 173319 "BINARY" 173446 T BINARY (NIL) -8 NIL NIL NIL) (-107 165049 166521 166562 "BGAGG" 166822 NIL BGAGG (NIL T) -9 NIL 166959 NIL) (-106 164880 164912 165003 "BGAGG-" 165008 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163951 164264 164469 "BFUNCT" 164695 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162641 162819 163107 "BEZOUT" 163775 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 159113 161493 161823 "BBTREE" 162344 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158714 158792 158820 "BASTYPE" 158997 T BASTYPE (NIL) -9 NIL 159096 NIL) (-101 158390 158471 158606 "BASTYPE-" 158611 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157824 157900 158052 "BALFACT" 158301 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156680 157239 157425 "AUTOMOR" 157669 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156406 156411 156437 "ATTREG" 156442 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154658 155103 155455 "ATTRBUT" 156072 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154266 154486 154552 "ATTRAST" 154610 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153802 153915 153941 "ATRIG" 154142 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153611 153652 153739 "ATRIG-" 153744 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153242 153428 153454 "ASTCAT" 153459 T ASTCAT (NIL) -9 NIL 153489 NIL) (-92 152969 153028 153147 "ASTCAT-" 153152 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151121 152745 152833 "ASTACK" 152912 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149626 149923 150288 "ASSOCEQ" 150803 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148658 149285 149409 "ASP9" 149533 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148421 148606 148645 "ASP8" 148650 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147289 148026 148168 "ASP80" 148310 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146187 146924 147056 "ASP7" 147188 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145141 145864 145982 "ASP78" 146100 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144110 144821 144938 "ASP77" 145055 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 143022 143748 143879 "ASP74" 144010 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141922 142657 142789 "ASP73" 142921 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 141026 141748 141848 "ASP6" 141853 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139973 140703 140821 "ASP55" 140939 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138922 139647 139766 "ASP50" 139885 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 138010 138623 138733 "ASP4" 138843 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137098 137711 137821 "ASP49" 137931 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135882 136637 136805 "ASP42" 136987 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134659 135415 135585 "ASP41" 135769 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133609 134336 134454 "ASP35" 134572 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133374 133557 133596 "ASP34" 133601 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133111 133178 133254 "ASP33" 133329 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 132005 132746 132878 "ASP31" 133010 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131770 131953 131992 "ASP30" 131997 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131505 131574 131650 "ASP29" 131725 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131270 131453 131492 "ASP28" 131497 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 131035 131218 131257 "ASP27" 131262 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130119 130733 130844 "ASP24" 130955 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129196 129921 130033 "ASP20" 130038 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128284 128897 129007 "ASP1" 129117 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127227 127958 128077 "ASP19" 128196 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126964 127031 127107 "ASP12" 127182 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125816 126563 126707 "ASP10" 126851 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123670 125660 125751 "ARRAY2" 125756 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119438 123318 123432 "ARRAY1" 123587 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118470 118643 118864 "ARRAY12" 119261 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112757 114672 114747 "ARR2CAT" 117377 NIL ARR2CAT (NIL T T T) -9 NIL 118135 NIL) (-56 110191 110935 111889 "ARR2CAT-" 111894 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109508 109818 109943 "ARITY" 110084 T ARITY (NIL) -8 NIL NIL NIL) (-54 108284 108436 108735 "APPRULE" 109344 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107935 107983 108102 "APPLYORE" 108230 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107289 107528 107648 "ANY" 107833 T ANY (NIL) -8 NIL NIL NIL) (-51 106567 106690 106847 "ANY1" 107163 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104097 105004 105331 "ANTISYM" 106291 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103589 103804 103900 "ANON" 104019 T ANON (NIL) -8 NIL NIL NIL) (-48 97589 102128 102582 "AN" 103153 T AN (NIL) -8 NIL NIL NIL) (-47 93473 94861 94912 "AMR" 95660 NIL AMR (NIL T T) -9 NIL 96260 NIL) (-46 92585 92806 93169 "AMR-" 93174 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 77030 92502 92563 "ALIST" 92568 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73835 76624 76793 "ALGSC" 76948 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70391 70945 71552 "ALGPKG" 73275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69668 69769 69953 "ALGMFACT" 70277 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65703 66282 66876 "ALGMANIP" 69252 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55914 65329 65479 "ALGFF" 65636 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55110 55241 55420 "ALGFACT" 55772 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54037 54637 54675 "ALGEBRA" 54680 NIL ALGEBRA (NIL T) -9 NIL 54721 NIL) (-37 53755 53814 53946 "ALGEBRA-" 53951 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35692 51592 51644 "ALAGG" 51780 NIL ALAGG (NIL T T) -9 NIL 51941 NIL) (-35 35228 35341 35367 "AHYP" 35568 T AHYP (NIL) -9 NIL NIL NIL) (-34 34159 34407 34433 "AGG" 34932 T AGG (NIL) -9 NIL 35211 NIL) (-33 33593 33755 33969 "AGG-" 33974 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31399 31822 32227 "AF" 33235 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30879 31124 31214 "ADDAST" 31327 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30147 30406 30562 "ACPLOT" 30741 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18770 27079 27117 "ACFS" 27724 NIL ACFS (NIL T) -9 NIL 27963 NIL) (-28 16797 17287 18049 "ACFS-" 18054 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12901 14830 14856 "ACF" 15735 T ACF (NIL) -9 NIL 16148 NIL) (-26 11605 11939 12432 "ACF-" 12437 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11163 11358 11384 "ABELSG" 11476 T ABELSG (NIL) -9 NIL 11541 NIL) (-24 11030 11055 11121 "ABELSG-" 11126 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10359 10646 10672 "ABELMON" 10842 T ABELMON (NIL) -9 NIL 10954 NIL) (-22 10023 10107 10245 "ABELMON-" 10250 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9357 9729 9755 "ABELGRP" 9827 T ABELGRP (NIL) -9 NIL 9902 NIL) (-20 8820 8949 9165 "ABELGRP-" 9170 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8082 8121 "A1AGG" 8126 NIL A1AGG (NIL T) -9 NIL 8166 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 53671d0b..436640d0 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,29 +1,30 @@ -(731775 . 3486916220) -(((*1 *2 *1) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-1194 *3))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) - (-4 *3 (-1087 *5 *6 *7)) - (-5 *2 (-657 (-2 (|:| |val| *3) (|:| -3941 *4)))) - (-5 *1 (-1130 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-568)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3431 *3))) +(731775 . 3486967789) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -1701 *4))) (-5 *1 (-991 *4 *3)) (-4 *3 (-1265 *4))))) -(((*1 *1 *2) - (-12 (-5 *2 (-784)) (-5 *1 (-688 *3)) (-4 *3 (-1071)) - (-4 *3 (-1122))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-941)) (-5 *3 (-657 (-270))) (-5 *1 (-268)))) - ((*1 *1 *2) (-12 (-5 *2 (-941)) (-5 *1 (-270))))) -(((*1 *2 *1) - (-12 (-4 *1 (-923 *3)) (-4 *3 (-1122)) (-5 *2 (-1124 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-1124 *3)) (-5 *1 (-924 *3)) (-4 *3 (-1122))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-657 *4)) (-4 *4 (-374)) (-4 *2 (-1265 *4)) + (-5 *1 (-942 *4 *2))))) +(((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862)) + (-4 *7 (-1087 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1010 *4 *5 *6 *7 *3)) (-4 *3 (-1093 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862)) + (-4 *7 (-1087 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1129 *4 *5 *6 *7 *3)) (-4 *3 (-1093 *4 *5 *6 *7))))) +(((*1 *1) (-5 *1 (-816)))) +(((*1 *1 *1 *1 *2) + (|partial| -12 (-5 *2 (-112)) (-5 *1 (-607 *3)) (-4 *3 (-1071))))) +(((*1 *2 *3 *4 *3 *4 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *2 (-1057)) + (-5 *1 (-769))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) - (|:| -3936 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) + (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 @@ -41,7 +42,7 @@ (-3 (|:| |str| (-1179 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3936 + (|:| -1685 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -49,418 +50,403 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-571))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-1180)) (-5 *5 (-702 (-227))) + (-5 *2 (-1057)) (-5 *1 (-760))))) (((*1 *2 *2 *3) (-12 (-5 *1 (-692 *2 *3)) (-4 *2 (-1122)) (-4 *3 (-1122))))) -(((*1 *2 *3 *2 *4 *5) - (-12 (-5 *2 (-657 *3)) (-5 *5 (-941)) (-4 *3 (-1265 *4)) - (-4 *4 (-317)) (-5 *1 (-472 *4 *3))))) (((*1 *2 *2) - (-12 (-4 *3 (-464)) (-5 *1 (-1230 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1224)))))) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1024)))))) +(((*1 *2 *1) (-12 (-4 *1 (-336 *3 *2)) (-4 *3 (-1071)) (-4 *2 (-805)))) + ((*1 *2 *1) (-12 (-4 *1 (-721 *3)) (-4 *3 (-1071)) (-5 *2 (-784)))) + ((*1 *2 *1) (-12 (-4 *1 (-867 *3)) (-4 *3 (-1071)) (-5 *2 (-784)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-657 *6)) (-4 *1 (-969 *4 *5 *6)) (-4 *4 (-1071)) + (-4 *5 (-806)) (-4 *6 (-862)) (-5 *2 (-657 (-784))))) + ((*1 *2 *1 *3) + (-12 (-4 *1 (-969 *4 *5 *3)) (-4 *4 (-1071)) (-4 *5 (-806)) + (-4 *3 (-862)) (-5 *2 (-784))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-657 *6)) (-4 *6 (-1087 *3 *4 *5)) + (-4 *3 (-568)) (-4 *4 (-806)) (-4 *5 (-862)) + (-5 *1 (-1302 *3 *4 *5 *6)))) + ((*1 *1 *2 *3 *4) + (|partial| -12 (-5 *2 (-657 *8)) (-5 *3 (-1 (-112) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1087 *5 *6 *7)) (-4 *5 (-568)) + (-4 *6 (-806)) (-4 *7 (-862)) (-5 *1 (-1302 *5 *6 *7 *8))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *2 (-1057)) + (-5 *1 (-765))))) +(((*1 *2 *1) + (-12 (-4 *2 (-969 *3 *5 *4)) (-5 *1 (-1009 *3 *4 *5 *2)) + (-4 *3 (-464)) (-4 *4 (-862)) (-4 *5 (-806))))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-1 (-963 (-227)) (-963 (-227)))) (-5 *3 (-657 (-270))) - (-5 *1 (-268)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1 (-963 (-227)) (-963 (-227)))) (-5 *1 (-270)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-657 (-493 *5 *6))) (-5 *3 (-493 *5 *6)) - (-14 *5 (-657 (-1198))) (-4 *6 (-464)) (-5 *2 (-1289 *6)) - (-5 *1 (-643 *5 *6))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-158)) (-5 *2 (-1294)) (-5 *1 (-1291))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-784)) (-4 *5 (-568)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-991 *5 *3)) (-4 *3 (-1265 *5))))) -(((*1 *2 *2) - (-12 (-4 *3 (-464)) (-5 *1 (-1230 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1224)))))) + (-12 (-5 *2 (-112)) (-5 *3 (-657 (-270))) (-5 *1 (-268)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-270))))) +(((*1 *1 *2 *2 *2 *2) (-12 (-5 *1 (-731 *2)) (-4 *2 (-374))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-565))))) +(((*1 *2 *3) + (-12 (-5 *3 (-419 *5)) (-4 *5 (-1265 *4)) (-4 *4 (-568)) + (-4 *4 (-1071)) (-4 *2 (-1280 *4)) (-5 *1 (-1283 *4 *5 *6 *2)) + (-4 *6 (-669 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *5 *4)) (-4 *4 (-1122)) (-4 *5 (-1122)) - (-5 *2 (-1 *5)) (-5 *1 (-696 *4 *5))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-430 *3)) (-4 *3 (-568)) (-5 *1 (-431 *3))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-576)) (-5 *1 (-430 *2)) (-4 *2 (-568))))) -(((*1 *2 *3 *4 *4 *5 *3 *6) - (|partial| -12 (-5 *4 (-624 *3)) (-5 *5 (-657 *3)) (-5 *6 (-1194 *3)) - (-4 *3 (-13 (-442 *7) (-27) (-1224))) - (-4 *7 (-13 (-464) (-1060 (-576)) (-148) (-652 (-576)))) - (-5 *2 - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-657 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-572 *7 *3 *8)) (-4 *8 (-1122)))) - ((*1 *2 *3 *4 *4 *5 *4 *3 *6) - (|partial| -12 (-5 *4 (-624 *3)) (-5 *5 (-657 *3)) - (-5 *6 (-419 (-1194 *3))) (-4 *3 (-13 (-442 *7) (-27) (-1224))) - (-4 *7 (-13 (-464) (-1060 (-576)) (-148) (-652 (-576)))) - (-5 *2 - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-657 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-572 *7 *3 *8)) (-4 *8 (-1122))))) -(((*1 *2 *2) (-12 (-5 *2 (-326 (-227))) (-5 *1 (-212))))) + (-12 (-4 *5 (-374)) + (-5 *2 + (-2 (|:| A (-702 *5)) + (|:| |eqs| + (-657 + (-2 (|:| C (-702 *5)) (|:| |g| (-1289 *5)) (|:| -3989 *6) + (|:| |rh| *5)))))) + (-5 *1 (-826 *5 *6)) (-5 *3 (-702 *5)) (-5 *4 (-1289 *5)) + (-4 *6 (-669 *5)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-374)) (-4 *6 (-669 *5)) + (-5 *2 (-2 (|:| -3750 (-702 *6)) (|:| |vec| (-1289 *5)))) + (-5 *1 (-826 *5 *6)) (-5 *3 (-702 *6)) (-5 *4 (-1289 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1289 *1)) (-4 *1 (-378 *4)) (-4 *4 (-174)) + (-5 *2 (-702 *4)))) + ((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-702 *4)) (-5 *1 (-428 *3 *4)) + (-4 *3 (-429 *4)))) + ((*1 *2) (-12 (-4 *1 (-429 *3)) (-4 *3 (-174)) (-5 *2 (-702 *3))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1126)) (-5 *3 (-787)) (-5 *1 (-52))))) (((*1 *2 *1) (-12 (-5 *2 (-1126)) (-5 *1 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*4 *5)) @@ -1488,12 +1706,12 @@ (-4 *3 (-38 (-419 (-576)))) (-4 *5 (-626 (-1198))) (-4 *3 (-1071)) (-4 *4 (-806)) (-4 *5 (-862)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-657 *7)) (|:| -3941 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-657 *7)) (|:| -3946 *8))) (-4 *7 (-1087 *4 *5 *6)) (-4 *8 (-1093 *4 *5 *6 *7)) (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862)) (-5 *2 (-1180)) (-5 *1 (-1091 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-657 *7)) (|:| -3941 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-657 *7)) (|:| -3946 *8))) (-4 *7 (-1087 *4 *5 *6)) (-4 *8 (-1131 *4 *5 *6 *7)) (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862)) (-5 *2 (-1180)) (-5 *1 (-1167 *4 *5 *6 *7 *8)))) @@ -1525,33 +1743,16 @@ (-4 *4 (-13 (-861) (-317) (-148) (-1044))) (-14 *6 (-657 (-1198))) (-5 *2 (-657 (-793 *4 (-879 *6)))) (-5 *1 (-1316 *4 *5 *6)) (-14 *5 (-657 (-1198)))))) -(((*1 *2 *3 *1) - (|partial| -12 (-5 *3 (-1 (-112) *2)) (-4 *1 (-152 *2)) - (-4 *2 (-1239))))) -(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-657 *1)) 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*3 (-657 (-270))) (-5 *2 (-1155 (-227))) (-5 *1 (-268)))) + ((*1 *1 *2) (-12 (-5 *2 (-1155 (-227))) (-5 *1 (-270))))) (((*1 *2 *1 *3) (-12 (-5 *2 (-419 (-576))) (-5 *1 (-118 *4)) (-14 *4 *3) (-5 *3 (-576)))) @@ -1568,23 +1769,30 @@ (-4 *3 (-1265 *2)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-1267 *2 *3)) (-4 *3 (-805)) - (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3515 (*2 (-1198)))) + (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3501 (*2 (-1198)))) (-4 *2 (-1071))))) (((*1 *2 *1) (-12 (-5 *2 (-1157)) (-5 *1 (-31)))) ((*1 *2) (-12 (-4 *1 (-416)) (-5 *2 (-941)))) ((*1 *1) (-4 *1 (-557))) ((*1 *2 *2) (-12 (-5 *2 (-941)) (-5 *1 (-712)))) ((*1 *2 *1) (-12 (-5 *2 (-657 *3)) (-5 *1 (-924 *3)) (-4 *3 (-1122))))) -(((*1 *2 *1) (-12 (-4 *1 (-1156 *3)) (-4 *3 (-1071)) (-5 *2 (-112))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) -(((*1 *1 *1 *2) - (-12 (-5 *1 (-1162 *2 *3)) (-4 *2 (-13 (-1122) (-34))) - (-4 *3 (-13 (-1122) (-34)))))) -(((*1 *2 *2 *3) - (-12 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(-1265 (-576)))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -1601,51 +1809,49 @@ ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) +(((*1 *1 *2 *2) + (-12 (-5 *2 (-657 (-576))) (-5 *1 (-1026 *3)) (-14 *3 (-576))))) (((*1 *2 *1) - (-12 (-5 *2 (-657 (-2 (|:| |k| (-685 *3)) (|:| |c| *4)))) - (-5 *1 (-639 *3 *4 *5)) (-4 *3 (-862)) - (-4 *4 (-13 (-174) (-730 (-419 (-576))))) (-14 *5 (-941))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 (-112) *6)) (-4 *6 (-13 (-1122) (-1060 *5))) - (-4 *5 (-902 *4)) (-4 *4 (-1122)) (-5 *2 (-1 (-112) *5)) - (-5 *1 (-951 *4 *5 *6))))) + (-12 (-5 *2 (-657 (-52))) (-5 *1 (-908 *3)) (-4 *3 (-1122))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-374)) (-4 *7 (-1265 *5)) (-4 *4 (-737 *5 *7)) - (-5 *2 (-2 (|:| -3962 (-702 *6)) (|:| |vec| (-1289 *5)))) - (-5 *1 (-824 *5 *6 *7 *4 *3)) (-4 *6 (-669 *5)) (-4 *3 (-669 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-657 (-390))) (-5 *1 (-270)))) - ((*1 *1) - (|partial| -12 (-4 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(-5 *2 - (-2 (|:| -1500 (-784)) (|:| |curves| (-784)) + (-2 (|:| -2047 (-784)) (|:| |curves| (-784)) (|:| |polygons| (-784)) (|:| |constructs| (-784))))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1162 *4 *5)) (-4 *4 (-13 (-1122) (-34))) - (-4 *5 (-13 (-1122) (-34))) (-5 *2 (-112)) (-5 *1 (-1163 *4 *5))))) -(((*1 *2) - (-12 (-4 *3 (-568)) (-5 *2 (-657 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-429 *3))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-1166)) (-5 *2 (-112))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-657 *6)) (-5 *4 (-657 (-1179 *7))) (-4 *6 (-862)) - (-4 *7 (-969 *5 (-543 *6) *6)) (-4 *5 (-1071)) - (-5 *2 (-1 (-1179 *7) *7)) (-5 *1 (-1148 *5 *6 *7))))) -(((*1 *1 *2) - (-12 (-5 *2 (-657 (-2 (|:| |gen| *3) (|:| -4056 *4)))) - (-4 *3 (-1122)) (-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-662 *3 *4 *5))))) -(((*1 *2 *3 *4 *3) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1265 *5)) (-4 *5 (-374)) - (-5 *2 (-2 (|:| -3579 (-419 *6)) (|:| |coeff| (-419 *6)))) - (-5 *1 (-586 *5 *6)) (-5 *3 (-419 *6))))) + (-12 (-4 *4 (-374)) (-5 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- (-12 (-5 *3 (-115)) (-4 *4 (-1071)) (-5 *1 (-727 *4 *2)) - (-4 *2 (-661 *4)))) - ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-849 *2)) (-4 *2 (-1071))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-568)) (-4 *3 (-1071)) - (-5 *2 (-2 (|:| -2192 *1) (|:| -3951 *1))) (-4 *1 (-867 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-568)) (-4 *5 (-1071)) - (-5 *2 (-2 (|:| -2192 *3) (|:| -3951 *3))) (-5 *1 (-868 *5 *3)) - (-4 *3 (-867 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-1198)) (-5 *3 (-657 (-548))) (-5 *1 (-548))))) -(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-947))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1024)))))) -(((*1 *2 *3) - (-12 (|has| *2 (-6 (-4468 "*"))) (-4 *5 (-384 *2)) (-4 *6 (-384 *2)) - (-4 *2 (-1071)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1265 *2)) - (-4 *4 (-700 *2 *5 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-835)) (-5 *1 (-834))))) +(((*1 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(-1198)) + (-5 *6 + (-1 + (-3 + (-2 (|:| |mainpart| *4) + (|:| |limitedlogs| + (-657 (-2 (|:| |coeff| *4) (|:| |logand| *4))))) + "failed") + *4 (-657 *4))) + (-5 *7 + (-1 (-3 (-2 (|:| -2322 *4) (|:| |coeff| *4)) "failed") *4 *4)) + (-4 *4 (-13 (-1224) (-27) (-442 *8))) + (-4 *8 (-13 (-464) (-148) (-1060 *3) (-652 *3))) (-5 *3 (-576)) + (-5 *2 (-2 (|:| |ans| *4) (|:| -4236 *4) (|:| |sol?| (-112)))) + (-5 *1 (-1035 *8 *4))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1198)) + (-4 *4 (-13 (-317) (-148) (-1060 (-576)) (-652 (-576)))) + (-5 *1 (-438 *4 *2)) (-4 *2 (-13 (-1224) (-29 *4))))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-13 (-374) (-148) (-1060 (-419 (-576))))) - (-4 *4 (-1265 *5)) (-5 *2 (-657 (-2 (|:| -3713 *4) (|:| -2371 *4)))) - (-5 *1 (-820 *5 *4 *6 *3)) (-4 *6 (-669 *4)) - (-4 *3 (-669 (-419 *4)))))) + (-12 (-5 *3 (-419 (-972 *5))) (-5 *4 (-1198)) (-4 *5 (-148)) + (-4 *5 (-13 (-464) (-1060 (-576)) (-652 (-576)))) (-5 *2 (-326 *5)) + (-5 *1 (-601 *5))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1198)) (-5 *3 (-657 (-548))) (-5 *1 (-548))))) +(((*1 *2 *1) (-12 (-5 *2 (-1198)) (-5 *1 (-835))))) (((*1 *2) - (-12 (-5 *2 (-419 (-972 *3))) (-5 *1 (-465 *3 *4 *5 *6)) - (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-941)) - (-14 *5 (-657 (-1198))) (-14 *6 (-1289 (-702 *3)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1125 *3 *4 *5 *6 *7)) (-4 *3 (-1122)) (-4 *4 (-1122)) - (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *7 (-1122)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *5 *6 *7 *7 *8) - (-12 - (-5 *3 - (-2 (|:| |det| *12) (|:| |rows| (-657 (-576))) - (|:| |cols| (-657 (-576))))) - (-5 *4 (-702 *12)) (-5 *5 (-657 (-419 (-972 *9)))) - (-5 *6 (-657 (-657 *12))) (-5 *7 (-784)) (-5 *8 (-576)) - (-4 *9 (-13 (-317) (-148))) (-4 *12 (-969 *9 *11 *10)) - (-4 *10 (-13 (-862) (-626 (-1198)))) (-4 *11 (-806)) - (-5 *2 - (-2 (|:| |eqzro| (-657 *12)) (|:| |neqzro| (-657 *12)) - (|:| |wcond| (-657 (-972 *9))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1289 (-419 (-972 *9)))) - (|:| -2469 (-657 (-1289 (-419 (-972 *9))))))))) - (-5 *1 (-944 *9 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(-5 *2 (-1057)) (-5 *1 (-765))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-336 *2 *3)) (-4 *2 (-1071)) (-4 *3 (-805))))) +(((*1 *1 *2 *2) + (-12 + (-5 *2 + (-3 (|:| I (-326 (-576))) (|:| -2022 (-326 (-390))) + (|:| CF (-326 (-171 (-390)))) (|:| |switch| (-1197)))) + (-5 *1 (-1197))))) (((*1 *2 *3) (-12 (-4 *4 (-464)) (-5 *2 @@ -7589,6 +7750,33 @@ (|:| |eigmult| (-784)) (|:| |eigvec| (-657 (-702 (-419 (-972 *4)))))))) (-5 *1 (-302 *4)) (-5 *3 (-702 (-419 (-972 *4))))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1180)) (-5 *3 (-657 (-270))) (-5 *1 (-268)))) + ((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-270))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1194 (-576))) (-5 *1 (-962)) (-5 *3 (-576)))) + ((*1 *2 *2) + (-12 (-4 *3 (-317)) (-4 *4 (-384 *3)) (-4 *5 (-384 *3)) + (-5 *1 (-1146 *3 *4 *5 *2)) (-4 *2 (-700 *3 *4 *5))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *5 (-657 *4)) (-4 *4 (-374)) (-5 *2 (-1289 *4)) + (-5 *1 (-827 *4 *3)) (-4 *3 (-669 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-657 (-185 (-140)))) (-5 *1 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(-856 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-782)))) ((*1 *2 *1) @@ -9170,13 +9253,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-227))) (|:| -1679 (-657 (-227))) + (-2 (|:| |fn| (-326 (-227))) (|:| -1706 (-657 (-227))) (|:| |lb| (-657 (-856 (-227)))) (|:| |cf| (-657 (-326 (-227)))) (|:| |ub| (-657 (-856 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-657 (-326 (-227)))) - (|:| -1679 (-657 (-227))))))) + (|:| -1706 (-657 (-227))))))) (-5 *1 (-854)))) ((*1 *2 *1) (-12 @@ -9195,26 +9278,26 @@ (-4 *4 (-806)) (-4 *5 (-862)) (-4 *1 (-998 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1060 *2)) (-4 *2 (-1239)))) ((*1 *1 *2) - (-2748 + (-2802 (-12 (-5 *2 (-972 *3)) - (-12 (-2665 (-4 *3 (-38 (-419 (-576))))) - (-2665 (-4 *3 (-38 (-576)))) (-4 *5 (-626 (-1198)))) + (-12 (-2712 (-4 *3 (-38 (-419 (-576))))) + (-2712 (-4 *3 (-38 (-576)))) (-4 *5 (-626 (-1198)))) (-4 *3 (-1071)) (-4 *1 (-1087 *3 *4 *5)) (-4 *4 (-806)) (-4 *5 (-862))) (-12 (-5 *2 (-972 *3)) - (-12 (-2665 (-4 *3 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(-34))) + (-5 *2 (-112)) (-5 *1 (-1163 *5 *6))))) +(((*1 *1 *1 *2 *2) + (|partial| -12 (-5 *2 (-941)) (-5 *1 (-1123 *3 *4)) (-14 *3 *2) + (-14 *4 *2)))) +(((*1 *2 *1) + (-12 (-4 *1 (-1156 *3)) (-4 *3 (-1071)) (-5 *2 (-657 (-963 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-657 (-963 *3))) (-4 *3 (-1071)) (-4 *1 (-1156 *3)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-657 (-657 *3))) (-4 *1 (-1156 *3)) (-4 *3 (-1071)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-657 (-963 *3))) (-4 *1 (-1156 *3)) (-4 *3 (-1071))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-657 *8)) (-5 *4 (-657 *7)) (-4 *7 (-862)) + (-4 *8 (-969 *5 *6 *7)) (-4 *5 (-568)) (-4 *6 (-806)) + (-5 *2 + (-2 (|:| |particular| (-3 (-1289 (-419 *8)) "failed")) + (|:| -1985 (-657 (-1289 (-419 *8)))))) + (-5 *1 (-682 *5 *6 *7 *8))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-657 (-657 (-657 *5)))) (-5 *3 (-1 (-112) *5 *5)) + (-5 *4 (-657 *5)) (-4 *5 (-862)) (-5 *1 (-1209 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-657 (-1157))) (-5 *1 (-684)))) + ((*1 *2 *1) + (-12 (-5 *2 (-657 (-941))) (-5 *1 (-1123 *3 *4)) (-14 *3 (-941)) + (-14 *4 (-941))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-657 *6)) (-5 *4 (-657 (-253 *5 *6))) (-4 *6 (-464)) + (-5 *2 (-253 *5 *6)) (-14 *5 (-657 (-1198))) (-5 *1 (-643 *5 *6))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1122)) (-4 *6 (-902 *5)) (-5 *2 (-901 *5 *6 (-657 *6))) (-5 *1 (-903 *5 *6 *4)) (-5 *3 (-657 *6)) (-4 *4 (-626 (-908 *5))))) @@ -11597,12 +11429,49 @@ ((*1 *2 *3 *4) (-12 (-4 *5 (-1122)) (-5 *2 (-657 (-304 (-972 *3)))) (-5 *1 (-903 *5 *3 *4)) (-4 *3 (-1071)) - (-2665 (-4 *3 (-1060 (-1198)))) (-4 *3 (-902 *5)) + (-2712 (-4 *3 (-1060 (-1198)))) (-4 *3 (-902 *5)) (-4 *4 (-626 (-908 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1122)) (-5 *2 (-905 *5 *3)) (-5 *1 (-903 *5 *3 *4)) - (-2665 (-4 *3 (-1060 (-1198)))) (-2665 (-4 *3 (-1071))) + (-2712 (-4 *3 (-1060 (-1198)))) (-2712 (-4 *3 (-1071))) (-4 *3 (-902 *5)) (-4 *4 (-626 (-908 *5)))))) +(((*1 *1 *1 *1) (-4 *1 (-312))) ((*1 *1 *1) (-4 *1 (-312)))) +(((*1 *2 *1) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-1194 *3))))) +(((*1 *2 *2 *3) (-12 (-5 *2 (-1157)) (-5 *3 (-301)) (-5 *1 (-169))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1289 (-326 (-227)))) (-5 *4 (-657 (-1198))) + (-5 *2 (-702 (-326 (-227)))) (-5 *1 (-207)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-1122)) (-4 *6 (-918 *5)) (-5 *2 (-702 *6)) + (-5 *1 (-705 *5 *6 *3 *4)) (-4 *3 (-384 *6)) + (-4 *4 (-13 (-384 *5) (-10 -7 (-6 -4466))))))) +(((*1 *2 *1) + (-12 (-5 *2 (-877)) (-5 *1 (-402 *3 *4 *5)) (-14 *3 (-784)) + (-14 *4 (-784)) (-4 *5 (-174))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1122)) (-4 *2 (-918 *5)) (-5 *1 (-705 *5 *2 *3 *4)) + (-4 *3 (-384 *2)) (-4 *4 (-13 (-384 *5) (-10 -7 (-6 -4466))))))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) +(((*1 *1 *1) (-4 *1 (-641))) + ((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-642 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1024) (-1224)))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-657 (-972 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-861) (-317) (-148) (-1044))) + (-5 *2 (-657 (-1068 *5 *6))) (-5 *1 (-1316 *5 *6 *7)) + (-14 *6 (-657 (-1198))) (-14 *7 (-657 (-1198))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-657 (-972 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-861) (-317) (-148) (-1044))) + (-5 *2 (-657 (-1068 *5 *6))) (-5 *1 (-1316 *5 *6 *7)) + (-14 *6 (-657 (-1198))) (-14 *7 (-657 (-1198))))) + ((*1 *2 *3) + (-12 (-5 *3 (-657 (-972 *4))) + (-4 *4 (-13 (-861) (-317) (-148) (-1044))) + (-5 *2 (-657 (-1068 *4 *5))) (-5 *1 (-1316 *4 *5 *6)) + (-14 *5 (-657 (-1198))) (-14 *6 (-657 (-1198)))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-419 (-972 *5))) (-5 *4 (-1198)) (-4 *5 (-13 (-317) (-148))) (-5 *2 (-657 (-326 *5))) @@ -11611,12 +11480,61 @@ (-12 (-5 *3 (-657 (-419 (-972 *5)))) (-5 *4 (-657 (-1198))) (-4 *5 (-13 (-317) (-148))) (-5 *2 (-657 (-657 (-326 *5)))) (-5 *1 (-1151 *5))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) + (-4 *3 (-1087 *5 *6 *7)) (-5 *2 (-112)) + (-5 *1 (-1094 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) + (-4 *3 (-1087 *5 *6 *7)) + (-5 *2 (-657 (-2 (|:| |val| (-112)) (|:| -3946 *4)))) + (-5 *1 (-1094 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-993)) (-5 *1 (-1314))))) +(((*1 *2 *1) + (-12 (-4 *1 (-998 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-806)) + (-4 *5 (-862)) (-4 *6 (-1087 *3 *4 *5)) (-4 *3 (-568)) + (-5 *2 (-112))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1071)) (-4 *2 (-568))))) +(((*1 *2 *1) + (-12 (-5 *2 (-419 (-972 *3))) (-5 *1 (-465 *3 *4 *5 *6)) + (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-941)) + (-14 *5 (-657 (-1198))) (-14 *6 (-1289 (-702 *3)))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-557)))) (((*1 *2 *3) (-12 (-5 *3 (-657 *4)) (-4 *4 (-1122)) (-5 *2 (-1294)) (-5 *1 (-1240 *4)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-657 *4)) (-4 *4 (-1122)) (-5 *2 (-1294)) (-5 *1 (-1240 *4))))) +(((*1 *2 *3 *4 *4 *5 *4 *3 *6 *3 *4 *7 *8 *9 *10) + (-12 (-5 *4 (-576)) (-5 *5 (-1180)) (-5 *6 (-702 (-227))) + (-5 *7 (-3 (|:| |fn| (-400)) (|:| |fp| (-89 G)))) + (-5 *8 (-3 (|:| |fn| (-400)) (|:| |fp| (-86 FCN)))) + (-5 *9 (-3 (|:| |fn| (-400)) (|:| |fp| (-71 PEDERV)))) + (-5 *10 (-3 (|:| |fn| (-400)) (|:| |fp| (-88 OUTPUT)))) + (-5 *3 (-227)) (-5 *2 (-1057)) (-5 *1 (-762))))) +(((*1 *1 *1 *1) (-5 *1 (-130))) + ((*1 *1 *1 *1) (-12 (-5 *1 (-1205 *2)) (-14 *2 (-941)))) + ((*1 *1 *1 *1) (-5 *1 (-1244))) ((*1 *1 *1 *1) (-5 *1 (-1245))) + ((*1 *1 *1 *1) (-5 *1 (-1246))) ((*1 *1 *1 *1) (-5 *1 (-1247)))) +(((*1 *2 *2) + (-12 (-5 *2 (-1179 *3)) (-4 *3 (-1071)) (-5 *1 (-1182 *3))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1287 *3)) (-4 *3 (-1239)) (-4 *3 (-1071)) + (-5 *2 (-702 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1032 *3)) (-4 *3 (-1239)) (-5 *2 (-657 *3))))) +(((*1 *2 *2) + (|partial| -12 (-5 *2 (-657 (-908 *3))) (-5 *1 (-908 *3)) + (-4 *3 (-1122))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1142)) (-5 *2 (-1294)) (-5 *1 (-844))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-784)) (-5 *2 (-1262 *5 *4)) (-5 *1 (-1196 *4 *5 *6)) + (-4 *4 (-1071)) (-14 *5 (-1198)) (-14 *6 *4))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-784)) (-5 *2 (-1262 *5 *4)) (-5 *1 (-1281 *4 *5 *6)) + (-4 *4 (-1071)) (-14 *5 (-1198)) (-14 *6 *4)))) (((*1 *2) (-12 (-4 *4 (-1243)) (-4 *5 (-1265 *4)) (-4 *6 (-1265 (-419 *5))) (-5 *2 (-657 (-657 *4))) (-5 *1 (-352 *3 *4 *5 *6)) @@ -11624,59 +11542,27 @@ ((*1 *2) (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1243)) (-4 *4 (-1265 *3)) (-4 *5 (-1265 (-419 *4))) (-4 *3 (-379)) (-5 *2 (-657 (-657 *3)))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-657 (-1198))) (-5 *3 (-52)) (-5 *1 (-908 *4)) - (-4 *4 (-1122))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-1180)) (-5 *2 (-390)) (-5 *1 (-799))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1200 (-419 (-576)))) (-5 *1 (-192))))) (((*1 *1 *1 *1) (-5 *1 (-130))) ((*1 *1 *1 *1) (-12 (-5 *1 (-1205 *2)) (-14 *2 (-941)))) ((*1 *1 *1 *1) (-5 *1 (-1244))) ((*1 *1 *1 *1) (-5 *1 (-1245))) ((*1 *1 *1 *1) (-5 *1 (-1246))) ((*1 *1 *1 *1) (-5 *1 (-1247)))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1287 *3)) (-4 *3 (-1239)) (-4 *3 (-1071)) - (-5 *2 (-702 *3))))) +(((*1 *2) + (-12 (-4 *3 (-568)) (-5 *2 (-657 (-702 *3))) (-5 *1 (-43 *3 *4)) + (-4 *4 (-429 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-784)) (-5 *1 (-1186 *3 *4)) (-14 *3 (-941)) - (-4 *4 (-1071))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1216 *4 *5)) - (-4 *4 (-1122)) (-4 *5 (-1122))))) -(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) + (-12 (-4 *1 (-1306 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1071)) + (-5 *2 (-832 *3)))) + ((*1 *2 *1) + (-12 (-4 *2 (-859)) (-5 *1 (-1312 *3 *2)) (-4 *3 (-1071))))) (((*1 *2 *1) - (-12 (-5 *2 (-1194 (-419 (-972 *3)))) (-5 *1 (-465 *3 *4 *5 *6)) - (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-941)) - (-14 *5 (-657 (-1198))) (-14 *6 (-1289 (-702 *3)))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-784)) (-5 *1 (-871 *2)) (-4 *2 (-174)))) - ((*1 *2 *3 *3 *2) - (-12 (-5 *3 (-784)) (-5 *1 (-871 *2)) (-4 *2 (-174))))) -(((*1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-1084)))) - ((*1 *1 *2) (-12 (-5 *2 (-1198)) (-5 *1 (-1084))))) -(((*1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-877))))) -(((*1 *2 *2 *2 *2 *2) - (-12 (-4 *2 (-13 (-374) (-10 -8 (-15 ** ($ $ (-419 (-576))))))) - (-5 *1 (-1150 *3 *2)) (-4 *3 (-1265 *2))))) + (-12 (-4 *1 (-1125 *3 *4 *5 *6 *7)) (-4 *3 (-1122)) (-4 *4 (-1122)) + (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *7 (-1122)) (-5 *2 (-112))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1005 *2)) (-4 *2 (-1224))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1057)) (-5 *1 (-771))))) -(((*1 *1 *1 *1) (-5 *1 (-130))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-1205 *2)) (-14 *2 (-941)))) - ((*1 *1 *1 *1) (-5 *1 (-1244))) ((*1 *1 *1 *1) (-5 *1 (-1245))) - ((*1 *1 *1 *1) (-5 *1 (-1246))) ((*1 *1 *1 *1) (-5 *1 (-1247)))) -(((*1 *1 *2) - (-12 (-5 *2 (-657 *1)) (-4 *1 (-1156 *3)) (-4 *3 (-1071)))) - ((*1 *2 *2 *1) - (|partial| -12 (-5 *2 (-419 *1)) (-4 *1 (-1265 *3)) (-4 *3 (-1071)) - (-4 *3 (-568)))) - ((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-1265 *2)) (-4 *2 (-1071)) (-4 *2 (-568))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1093 *4 *5 *6 *3)) (-4 *4 (-464)) (-4 *5 (-806)) - (-4 *6 (-862)) (-4 *3 (-1087 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *1 *2) (-12 (-5 *2 (-657 (-877))) (-5 *1 (-877)))) - ((*1 *1 *1 *1) (-5 *1 (-877)))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4466)) (-4 *1 (-501 *4)) - (-4 *4 (-1239)) (-5 *2 (-112))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479))))) (((*1 *1 *2 *2) (-12 (-5 *1 (-304 *2)) (-4 *2 (-1239)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-1198)) (-5 *3 (-1180)) (-5 *1 (-1011)))) ((*1 *1 *2 *3) @@ -11685,26 +11571,21 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1198)) (-5 *3 (-1116 *4)) (-4 *4 (-1239)) (-5 *1 (-1114 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-657 (-1198))) (-5 *2 (-1294)) (-5 *1 (-1201)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-657 (-1198))) (-5 *3 (-1198)) (-5 *2 (-1294)) - (-5 *1 (-1201)))) - ((*1 *2 *3 *4 *1) - (-12 (-5 *4 (-657 (-1198))) (-5 *3 (-1198)) (-5 *2 (-1294)) - (-5 *1 (-1201))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-657 *2)) (-4 *2 (-969 *4 *5 *6)) (-4 *4 (-317)) - (-4 *5 (-806)) (-4 *6 (-862)) (-5 *1 (-459 *4 *5 *6 *2))))) +(((*1 *2 *2 *1) + (-12 (-5 *2 (-657 *6)) (-4 *1 (-998 *3 *4 *5 *6)) (-4 *3 (-1071)) + (-4 *4 (-806)) (-4 *5 (-862)) (-4 *6 (-1087 *3 *4 *5)) + (-4 *3 (-568))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-419 *6)) (-4 *5 (-1243)) (-4 *6 (-1265 *5)) - (-5 *2 (-2 (|:| -2128 (-784)) (|:| -1735 *3) (|:| |radicand| *6))) - (-5 *1 (-149 *5 *6 *7)) (-5 *4 (-784)) (-4 *7 (-1265 *3))))) -(((*1 *2 *1) - (-12 (-4 *2 (-1122)) (-5 *1 (-984 *3 *2)) (-4 *3 (-1122))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-657 (-1194 *4))) (-5 *3 (-1194 *4)) - (-4 *4 (-929)) (-5 *1 (-676 *4))))) + (-12 (-5 *3 (-657 *7)) (-4 *7 (-862)) (-4 *5 (-929)) (-4 *6 (-806)) + (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-430 (-1194 *8))) + (-5 *1 (-926 *5 *6 *7 *8)) (-5 *4 (-1194 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-929)) (-4 *5 (-1265 *4)) (-5 *2 (-430 (-1194 *5))) + (-5 *1 (-927 *4 *5)) (-5 *3 (-1194 *5))))) +(((*1 *1 *1 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(-4 *6 (-862)) (-5 *2 (-112)) + (-5 *1 (-1129 *4 *5 *6 *7 *8))))) +(((*1 *2 *3) (-12 (-5 *3 (-503)) (-5 *2 (-704 (-591))) (-5 *1 (-591))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1122)) (-4 *5 (-1122)) + (-4 *6 (-1122)) (-5 *2 (-1 *6 *5)) (-5 *1 (-697 *4 *5 *6))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *5 (-1 (-598 *3) *3 (-1198))) + (-5 *6 + (-1 (-3 (-2 (|:| |special| *3) (|:| |integrand| *3)) "failed") *3 + (-1198))) + (-4 *3 (-294)) (-4 *3 (-641)) (-4 *3 (-1060 *4)) (-4 *3 (-442 *7)) + (-5 *4 (-1198)) (-4 *7 (-626 (-908 (-576)))) (-4 *7 (-464)) + (-4 *7 (-902 (-576))) (-4 *7 (-1122)) (-5 *2 (-598 *3)) + (-5 *1 (-585 *7 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-657 (-856 (-227)))) (-5 *4 (-227)) (-5 *2 (-657 *4)) + (-5 *1 (-276))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-657 + (-657 + (-3 (|:| -2676 (-1198)) + (|:| -3968 (-657 (-3 (|:| S (-1198)) (|:| P (-972 (-576)))))))))) + (-5 *1 (-1202))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-661 *3)) (-4 *3 (-1071)) + (-5 *1 (-727 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1071)) (-5 *1 (-849 *3))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *5 *3 *3 *3 *6 *4 *3) + (-12 (-5 *4 (-702 (-227))) (-5 *5 (-702 (-576))) (-5 *6 (-227)) + (-5 *3 (-576)) (-5 *2 (-1057)) (-5 *1 (-765))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1071)) (-4 *7 (-1071)) + (-4 *6 (-1265 *5)) (-5 *2 (-1194 (-1194 *7))) + (-5 *1 (-513 *5 *6 *4 *7)) (-4 *4 (-1265 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -12729,10 +12510,10 @@ (-12 (-4 *1 (-393 *2 *3)) (-4 *2 (-1071)) (-4 *3 (-1122)))) ((*1 *1 *1) (-12 (-14 *2 (-657 (-1198))) (-4 *3 (-174)) - (-4 *5 (-243 (-3437 *2) (-784))) + (-4 *5 (-243 (-3440 *2) (-784))) (-14 *6 - (-1 (-112) (-2 (|:| -3146 *4) (|:| -2128 *5)) - (-2 (|:| -3146 *4) (|:| -2128 *5)))) + (-1 (-112) (-2 (|:| -3178 *4) (|:| -1801 *5)) + (-2 (|:| -3178 *4) (|:| -1801 *5)))) (-5 *1 (-473 *2 *3 *4 *5 *6 *7)) (-4 *4 (-862)) (-4 *7 (-969 *3 *5 (-879 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-521 *2 *3)) (-4 *2 (-102)) (-4 *3 (-865)))) @@ -12748,37 +12529,29 @@ (-4 *2 (-862)))) ((*1 *1 *1) (-12 (-5 *1 (-1312 *2 *3)) (-4 *2 (-1071)) (-4 *3 (-859))))) +(((*1 *2 *3) (-12 (-5 *3 (-784)) (-5 *2 (-1 (-390))) (-5 *1 (-1062))))) (((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-877)))) ((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1294)) (-5 *1 (-982))))) -(((*1 *2 *1) (-12 (-5 *2 (-657 (-963 (-227)))) (-5 *1 (-1290))))) -(((*1 *2 *3) (-12 (-5 *3 (-326 (-227))) (-5 *2 (-227)) (-5 *1 (-315))))) -(((*1 *1 *1) - (-12 (-5 *1 (-1186 *2 *3)) (-14 *2 (-941)) (-4 *3 (-1071))))) -(((*1 *2 *3 *2) - (-12 (-4 *2 (-13 (-374) (-861))) (-5 *1 (-183 *2 *3)) - (-4 *3 (-1265 (-171 *2))))) - ((*1 *2 *3) - (-12 (-4 *2 (-13 (-374) (-861))) (-5 *1 (-183 *2 *3)) - (-4 *3 (-1265 (-171 *2)))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1087 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-806)) - (-4 *4 (-862))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-374)) (-5 *2 (-2 (|:| -2192 *3) (|:| -3951 *3))) - (-5 *1 (-779 *3 *4)) (-4 *3 (-721 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-374)) (-4 *3 (-1071)) - (-5 *2 (-2 (|:| -2192 *1) (|:| -3951 *1))) (-4 *1 (-867 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-374)) (-4 *5 (-1071)) - (-5 *2 (-2 (|:| -2192 *3) (|:| -3951 *3))) (-5 *1 (-868 *5 *3)) - (-4 *3 (-867 *5))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) - (-4 *4 (-1122))))) +(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) + (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-64 G)))) (-5 *2 (-1057)) + (-5 *1 (-761))))) (((*1 *2 *3) - (-12 (-4 *2 (-374)) (-4 *2 (-861)) (-5 *1 (-965 *2 *3)) - (-4 *3 (-1265 *2))))) + (-12 (-14 *4 (-657 (-1198))) (-4 *5 (-464)) + (-5 *2 + (-2 (|:| |glbase| (-657 (-253 *4 *5))) (|:| |glval| (-657 (-576))))) + (-5 *1 (-643 *4 *5)) (-5 *3 (-657 (-253 *4 *5)))))) +(((*1 *1 *2) (-12 (-5 *2 (-657 (-340))) (-5 *1 (-340))))) +(((*1 *1 *1 *1) (-5 *1 (-163))) + ((*1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-163))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1057)) (-5 *1 (-771))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4467)) (-4 *1 (-120 *2)) (-4 *2 (-1239))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-374)) (-5 *1 (-914 *2 *3)) + (-4 *2 (-1265 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -12800,15 +12573,23 @@ (((*1 *2 *1) (-12 (-4 *3 (-1071)) (-4 *4 (-806)) (-4 *5 (-862)) (-5 *2 (-657 *1)) (-4 *1 (-969 *3 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1220))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-875)) (-5 *3 (-129)) (-5 *2 (-784))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1265 *6)) - (-4 *6 (-13 (-27) (-442 *5))) (-4 *5 (-13 (-568) (-1060 (-576)))) - (-4 *8 (-1265 (-419 *7))) (-5 *2 (-598 *3)) - (-5 *1 (-564 *5 *6 *7 *8 *3)) (-4 *3 (-353 *6 *7 *8))))) -(((*1 *2 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-121 *3)) (-4 *3 (-1265 (-576)))))) +(((*1 *2) (-12 (-5 *2 (-924 (-576))) (-5 *1 (-937))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1120 *3)) (-4 *3 (-1122)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1224)))) + ((*1 *2 *1) (-12 (-5 *1 (-341 *2)) (-4 *2 (-862)))) + ((*1 *2 *1) (-12 (-5 *2 (-657 *3)) (-5 *1 (-624 *3)) (-4 *3 (-1122))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-657 (-419 (-972 (-576))))) (-5 *4 (-657 (-1198))) + (-5 *2 (-657 (-657 *5))) (-5 *1 (-391 *5)) + (-4 *5 (-13 (-861) (-374))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-419 (-972 (-576)))) (-5 *2 (-657 *4)) (-5 *1 (-391 *4)) + (-4 *4 (-13 (-861) (-374)))))) +(((*1 *1 *1 *1) (-4 *1 (-144))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-159 *3 *2)) (-4 *2 (-442 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-557))))) (((*1 *2) (-12 (-14 *4 *2) (-4 *5 (-1239)) (-5 *2 (-784)) (-5 *1 (-242 *3 *4 *5)) (-4 *3 (-243 *4 *5)))) @@ -12834,11 +12615,26 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-861) (-374))) (-5 *1 (-1083 *2 *3)) (-4 *3 (-1265 *2))))) -(((*1 *2 *3) - (-12 (-5 *3 (-657 (-941))) (-5 *2 (-924 (-576))) (-5 *1 (-937))))) -(((*1 *2 *1) (-12 (-4 *1 (-401)) (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) -(((*1 *1 *2) (-12 (-5 *1 (-229 *2)) (-4 *2 (-13 (-374) (-1224)))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-657 (-1198))) (-4 *4 (-1122)) + (-4 *5 (-13 (-1071) (-902 *4) (-626 (-908 *4)))) + (-5 *1 (-54 *4 *5 *2)) + (-4 *2 (-13 (-442 *5) (-902 *4) (-626 (-908 *4))))))) +(((*1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1062))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1048 (-856 (-576)))) + (-5 *3 (-1179 (-2 (|:| |k| (-576)) (|:| |c| *4)))) (-4 *4 (-1071)) + (-5 *1 (-607 *4))))) +(((*1 *2 *3 *4 *5 *3) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4236 *6) (|:| |sol?| (-112))) (-576) + *6)) + (-4 *6 (-374)) (-4 *7 (-1265 *6)) + (-5 *2 + (-3 (-2 (|:| |answer| (-419 *7)) (|:| |a0| *6)) + (-2 (|:| -2322 (-419 *7)) (|:| |coeff| (-419 *7))) "failed")) + (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -12848,9 +12644,6 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) - (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) ((*1 *1 *1) (-4 *1 (-505))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) @@ -12858,19 +12651,7 @@ ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-576)) (-4 *4 (-13 (-568) (-148))) (-5 *1 (-549 *4 *2)) - (-4 *2 (-1280 *4)))) - ((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-576)) (-4 *4 (-13 (-374) (-379) (-626 *3))) - (-4 *5 (-1265 *4)) (-4 *6 (-737 *4 *5)) (-5 *1 (-553 *4 *5 *6 *2)) - (-4 *2 (-1280 *6)))) - ((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-576)) (-4 *4 (-13 (-374) (-379) (-626 *3))) - (-5 *1 (-554 *4 *2)) (-4 *2 (-1280 *4)))) - ((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-1179 *4)) (-5 *3 (-576)) (-4 *4 (-13 (-568) (-148))) - (-5 *1 (-1175 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-784)) (-5 *2 (-1294)) (-5 *1 (-390))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-805)) (-4 *2 (-1071)))) ((*1 *2 *1) (-12 (-4 *2 (-1071)) (-5 *1 (-50 *2 *3)) (-14 *3 (-657 (-1198))))) @@ -12880,10 +12661,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-393 *2 *3)) (-4 *3 (-1122)) (-4 *2 (-1071)))) ((*1 *2 *1) - (-12 (-14 *3 (-657 (-1198))) (-4 *5 (-243 (-3437 *3) (-784))) + (-12 (-14 *3 (-657 (-1198))) (-4 *5 (-243 (-3440 *3) (-784))) (-14 *6 - (-1 (-112) (-2 (|:| -3146 *4) (|:| -2128 *5)) - (-2 (|:| -3146 *4) (|:| -2128 *5)))) + (-1 (-112) (-2 (|:| -3178 *4) (|:| -1801 *5)) + (-2 (|:| -3178 *4) (|:| -1801 *5)))) (-4 *2 (-174)) (-5 *1 (-473 *3 *2 *4 *5 *6 *7)) (-4 *4 (-862)) (-4 *7 (-969 *2 *5 (-879 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-521 *2 *3)) (-4 *3 (-865)) (-4 *2 (-102)))) @@ -12900,33 +12681,40 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1087 *3 *4 *2)) (-4 *3 (-1071)) (-4 *4 (-806)) (-4 *2 (-862))))) -(((*1 *2 *1) (-12 (-4 *1 (-1014 *2)) (-4 *2 (-568)) (-4 *2 (-557)))) - ((*1 *1 *1) (-4 *1 (-1082)))) -(((*1 *2) - (-12 (-4 *3 (-806)) (-4 *4 (-862)) (-4 *2 (-929)) - (-5 *1 (-469 *3 *4 *2 *5)) (-4 *5 (-969 *2 *3 *4)))) - ((*1 *2) - (-12 (-4 *3 (-806)) (-4 *4 (-862)) (-4 *2 (-929)) - (-5 *1 (-926 *2 *3 *4 *5)) (-4 *5 (-969 *2 *3 *4)))) - ((*1 *2) (-12 (-4 *2 (-929)) (-5 *1 (-927 *2 *3)) (-4 *3 (-1265 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-227)) (-5 *1 (-835))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1232 *4 *5 *3 *6)) (-4 *4 (-568)) (-4 *5 (-806)) - (-4 *3 (-862)) (-4 *6 (-1087 *4 *5 *3)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-4 *1 (-1308 *3)) (-4 *3 (-374)) (-5 *2 (-112))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-941)) (-5 *1 (-1052 *2)) - (-4 *2 (-13 (-1122) (-10 -8 (-15 -2971 ($ $ $)))))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1294)) (-5 *1 (-835))))) -(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-128 *2)) (-4 *2 (-1122)))) - ((*1 *1 *2) (-12 (-5 *1 (-128 *2)) (-4 *2 (-1122))))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-13 (-568) (-148))) (-5 *1 (-1259 *3 *2)) - (-4 *2 (-1265 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-568)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4351 *4))) - (-5 *1 (-991 *4 *3)) (-4 *3 (-1265 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *2 *2)) (-5 *1 (-695 *2)) (-4 *2 (-1122)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1 (-657 *5) (-657 *5))) (-5 *4 (-576)) + (-5 *2 (-657 *5)) (-5 *1 (-695 *5)) (-4 *5 (-1122))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-333 *3 *4)) (-4 *3 (-1122)) + (-4 *4 (-132)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1122)) (-5 *1 (-372 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-397 *3)) (-4 *3 (-1122)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1122)) (-5 *1 (-662 *3 *4 *5)) + (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-1071)) (-5 *1 (-456 *3 *2)) (-4 *2 (-1265 *3))))) +(((*1 *1) (-5 *1 (-158)))) +(((*1 *2 *2) + (-12 + (-5 *2 + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) + (|:| |xpnt| (-576)))) + (-4 *4 (-13 (-1265 *3) (-568) (-10 -8 (-15 -3436 ($ $ $))))) + (-4 *3 (-568)) (-5 *1 (-1268 *3 *4))))) +(((*1 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-557)))) + ((*1 *1 *2) (-12 (-5 *2 (-657 (-941))) (-5 *1 (-993))))) +(((*1 *1 *2) + (-12 (-5 *2 (-657 *5)) (-4 *5 (-174)) (-5 *1 (-137 *3 *4 *5)) + (-14 *3 (-576)) (-14 *4 (-784))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-657 *3)) (-4 *3 (-1265 *5)) (-4 *5 (-317)) + (-5 *2 (-784)) (-5 *1 (-467 *5 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -12946,18 +12734,16 @@ ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-374)) (-5 *2 (-657 *3)) (-5 *1 (-965 *4 *3)) - (-4 *3 (-1265 *4))))) +(((*1 *2 *1) (-12 (-4 *1 (-1308 *3)) (-4 *3 (-374)) (-5 *2 (-112))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1071)) (-4 *3 (-805)))) ((*1 *2 *1) (-12 (-4 *1 (-393 *3 *2)) (-4 *3 (-1071)) (-4 *2 (-1122)))) ((*1 *2 *1) (-12 (-14 *3 (-657 (-1198))) (-4 *4 (-174)) - (-4 *6 (-243 (-3437 *3) (-784))) + (-4 *6 (-243 (-3440 *3) (-784))) (-14 *7 - (-1 (-112) (-2 (|:| -3146 *5) (|:| -2128 *6)) - (-2 (|:| -3146 *5) (|:| -2128 *6)))) + (-1 (-112) (-2 (|:| -3178 *5) (|:| -1801 *6)) + (-2 (|:| -3178 *5) (|:| -1801 *6)))) (-5 *2 (-726 *5 *6 *7)) (-5 *1 (-473 *3 *4 *5 *6 *7 *8)) (-4 *5 (-862)) (-4 *8 (-969 *4 *6 (-879 *3))))) ((*1 *2 *1) @@ -12966,55 +12752,59 @@ ((*1 *1 *1) (-12 (-4 *1 (-995 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-805)) (-4 *4 (-862))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1274 *3 *4 *5)) (-5 *1 (-329 *3 *4 *5)) (-4 *3 (-374)) - (-14 *4 (-1198)) (-14 *5 *3))) - ((*1 *2 *1) (-12 (-4 *1 (-416)) (-5 *2 (-576)))) - ((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-430 *3)) (-4 *3 (-568)))) - ((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-712)))) - ((*1 *2 *1) - (-12 (-4 *2 (-1122)) (-5 *1 (-726 *3 *2 *4)) (-4 *3 (-862)) - (-14 *4 - (-1 (-112) (-2 (|:| -3146 *3) (|:| -2128 *2)) - (-2 (|:| -3146 *3) (|:| -2128 *2))))))) -(((*1 *1 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1082)))) - ((*1 *1 *1) - (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) - (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) - ((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *2 *1) (-12 (-4 *1 (-810 *2)) (-4 *2 (-174)) (-4 *2 (-1082)))) - ((*1 *1 *1) (-4 *1 (-861))) - ((*1 *2 *1) (-12 (-4 *1 (-1019 *2)) (-4 *2 (-174)) (-4 *2 (-1082)))) - ((*1 *1 *1) (-4 *1 (-1082))) ((*1 *1 *1) (-4 *1 (-1161)))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-576)) (-5 *1 (-390))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) - (-4 *3 (-1087 *5 *6 *7)) - (-5 *2 (-657 (-2 (|:| |val| *3) (|:| -3941 *4)))) - (-5 *1 (-1130 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1289 (-326 (-227)))) (|:| |yinit| (-657 (-227))) + (|:| |intvals| (-657 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-390)) (-5 *1 (-207))))) +(((*1 *2 *3) + (-12 (-4 *4 (-38 (-419 (-576)))) + (-5 *2 (-2 (|:| -2004 (-1179 *4)) (|:| -2017 (-1179 *4)))) + (-5 *1 (-1184 *4)) (-5 *3 (-1179 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-657 (-972 *6))) (-5 *4 (-657 (-1198))) - (-4 *6 (-13 (-568) (-1060 *5))) (-4 *5 (-568)) - (-5 *2 (-657 (-657 (-304 (-419 (-972 *6)))))) (-5 *1 (-1061 *5 *6))))) + (-12 (-5 *2 (-657 (-171 *4))) (-5 *1 (-156 *3 *4)) + (-4 *3 (-1265 (-171 (-576)))) (-4 *4 (-13 (-374) (-861))))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-374) (-861))) (-5 *2 (-657 (-171 *4))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1265 (-171 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-374) (-861))) (-5 *2 (-657 (-171 *4))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1265 (-171 *4)))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-374)) (-4 *3 (-1071)) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4097 *1))) + (-4 *1 (-867 *3))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 (-657 *2) *2 *2 *2)) (-4 *2 (-1122)) + (-5 *1 (-103 *2)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1122)) (-5 *1 (-103 *2))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-941)) (-5 *1 (-1052 *2)) + (-4 *2 (-13 (-1122) (-10 -8 (-15 -3012 ($ $ $)))))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-784)) (-4 *5 (-568)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-991 *5 *3)) (-4 *3 (-1265 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1198)) (-5 *4 (-972 (-576))) (-5 *2 (-340)) - (-5 *1 (-342))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-353 *4 *3 *5)) (-4 *4 (-1243)) (-4 *3 (-1265 *4)) - (-4 *5 (-1265 (-419 *3))) (-5 *2 (-112)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1243)) (-4 *4 (-1265 *3)) - (-4 *5 (-1265 (-419 *4))) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1243)) (-4 *4 (-1265 *3)) - (-4 *5 (-1265 (-419 *4))) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1198)) - (-5 *2 - (-2 (|:| |zeros| (-1179 (-227))) (|:| |ones| (-1179 (-227))) - (|:| |singularities| (-1179 (-227))))) - (-5 *1 (-105))))) + (-12 (-5 *4 (-1198)) + (-4 *5 (-13 (-317) (-148) (-1060 (-576)) (-652 (-576)))) + (-5 *2 (-598 *3)) (-5 *1 (-438 *5 *3)) + (-4 *3 (-13 (-1224) (-29 *5)))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-1194 (-972 *4))) (-5 *1 (-428 *3 *4)) + (-4 *3 (-429 *4)))) + ((*1 *2) + (-12 (-4 *1 (-429 *3)) (-4 *3 (-174)) (-4 *3 (-374)) + (-5 *2 (-1194 (-972 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1194 (-419 (-972 *3)))) (-5 *1 (-465 *3 *4 *5 *6)) + (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-941)) + (-14 *5 (-657 (-1198))) (-14 *6 (-1289 (-702 *3)))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13037,31 +12827,47 @@ (((*1 *1 *2) (-12 (-5 *2 (-657 *3)) (-4 *3 (-1122)) (-4 *1 (-1120 *3)))) ((*1 *1) (-12 (-4 *1 (-1120 *2)) (-4 *2 (-1122))))) +(((*1 *1 *1) (-12 (-5 *1 (-908 *2)) (-4 *2 (-1122))))) (((*1 *2 *1) (-12 (-4 *1 (-336 *2 *3)) (-4 *3 (-805)) (-4 *2 (-1071)))) ((*1 *2 *1) (-12 (-4 *1 (-442 *2)) (-4 *2 (-1122))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-657 (-795 *3))) (-5 *1 (-795 *3)) (-4 *3 (-568)) - (-4 *3 (-1071))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *2 (-702 *3)) (-4 *3 (-1071)) (-5 *1 (-703 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-378 *2)) (-4 *2 (-174))))) -(((*1 *2 *1) (-12 (-5 *2 (-1157)) (-5 *1 (-1299))))) -(((*1 *2 *2) - (-12 (-5 *2 (-657 (-2 (|:| |val| (-657 *6)) (|:| -3941 *7)))) - (-4 *6 (-1087 *3 *4 *5)) (-4 *7 (-1093 *3 *4 *5 *6)) (-4 *3 (-464)) - (-4 *4 (-806)) (-4 *5 (-862)) (-5 *1 (-1010 *3 *4 *5 *6 *7)))) - ((*1 *2 *2) - (-12 (-5 *2 (-657 (-2 (|:| |val| (-657 *6)) (|:| -3941 *7)))) - (-4 *6 (-1087 *3 *4 *5)) (-4 *7 (-1093 *3 *4 *5 *6)) (-4 *3 (-464)) - (-4 *4 (-806)) (-4 *5 (-862)) (-5 *1 (-1129 *3 *4 *5 *6 *7))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-598 *3)) (-4 *3 (-374))))) +(((*1 *2 *1 *3 *3 *2) + (-12 (-5 *3 (-576)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1239)) + (-4 *4 (-384 *2)) (-4 *5 (-384 *2)))) + ((*1 *2 *1 *3 *2) + (-12 (|has| *1 (-6 -4467)) (-4 *1 (-298 *3 *2)) (-4 *3 (-1122)) + (-4 *2 (-1239))))) +(((*1 *2 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *2 (-1057)) + (-5 *1 (-764))))) (((*1 *2 *3) - (-12 (-4 *4 (-568)) (-4 *5 (-806)) (-4 *6 (-862)) - (-4 *7 (-1087 *4 *5 *6)) - (-5 *2 (-657 (-2 (|:| -1988 *1) (|:| -3179 (-657 *7))))) - (-5 *3 (-657 *7)) (-4 *1 (-1232 *4 *5 *6 *7))))) -(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-1166)) (-5 *2 (-1256 (-576)))))) -(((*1 *1 *1) (-4 *1 (-95))) - ((*1 *2 *2) + (-12 (-5 *3 (-941)) (-5 *2 (-1200 (-419 (-576)))) (-5 *1 (-192))))) +(((*1 *2 *1) (-12 (-4 *1 (-187)) (-5 *2 (-657 (-112)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-784)) (-4 *5 (-174)))) + ((*1 *1 *1) + (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-576)) (-14 *3 (-784)) + (-4 *4 (-174)))) + ((*1 *1 *1) + (-12 (-4 *1 (-700 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-384 *2)) + (-4 *4 (-384 *2)))) + ((*1 *1 *2) + (-12 (-4 *3 (-1071)) (-4 *1 (-700 *3 *2 *4)) (-4 *2 (-384 *3)) + (-4 *4 (-384 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1164 *2 *3)) (-14 *2 (-784)) (-4 *3 (-1071))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-784)) (|:| |poli| *2) + (|:| |polj| *2))) + (-4 *5 (-806)) (-4 *2 (-969 *4 *5 *6)) (-5 *1 (-461 *4 *5 *6 *2)) + (-4 *4 (-464)) (-4 *6 (-862))))) +(((*1 *2 *1) (-12 (-5 *2 (-1180)) (-5 *1 (-835))))) +(((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) ((*1 *2 *2) @@ -13070,50 +12876,54 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) + (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) + ((*1 *1 *1) (-4 *1 (-505))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *1 *1 *1) (-5 *1 (-877)))) +(((*1 *2 *3) (-12 (-5 *3 (-834)) (-5 *2 (-52)) (-5 *1 (-844))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1239)) + (-4 *4 (-384 *3)) (-4 *5 (-384 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4467)) (-4 *1 (-501 *3)) + (-4 *3 (-1239))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4466)) (-4 *1 (-501 *4)) + (-4 *4 (-1239)) (-5 *2 (-112))))) (((*1 *2 *1) (-12 (-4 *1 (-336 *3 *4)) (-4 *3 (-1071)) (-4 *4 (-805)) (-5 *2 (-112)))) ((*1 *2 *1) (-12 (-4 *1 (-442 *3)) (-4 *3 (-1122)) (-5 *2 (-112))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-1087 *3 *4 *2)) (-4 *3 (-1071)) (-4 *4 (-806)) - (-4 *2 (-862)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1087 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-806)) - (-4 *4 (-862))))) -(((*1 *2 *3) - (|partial| -12 (-5 *2 (-576)) (-5 *1 (-581 *3)) (-4 *3 (-1060 *2))))) -(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-877))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-784)) (-4 *1 (-1265 *3)) (-4 *3 (-1071))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -1735 *3) (|:| |gap| (-784)) (|:| -2192 (-795 *3)) - (|:| -3951 (-795 *3)))) - (-5 *1 (-795 *3)) (-4 *3 (-1071)))) - ((*1 *2 *1 *1 *3) - (-12 (-4 *4 (-1071)) (-4 *5 (-806)) (-4 *3 (-862)) - (-5 *2 - (-2 (|:| -1735 *1) (|:| |gap| (-784)) (|:| -2192 *1) - (|:| -3951 *1))) - (-4 *1 (-1087 *4 *5 *3)))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) +(((*1 *2 *1) + (-12 (-4 *1 (-375 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1122))))) +(((*1 *2 *1 *1 *1) + (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) + (-4 *1 (-317)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-1071)) (-4 *4 (-806)) (-4 *5 (-862)) - (-5 *2 - (-2 (|:| -1735 *1) (|:| |gap| (-784)) (|:| -2192 *1) - (|:| -3951 *1))) - (-4 *1 (-1087 *3 *4 *5))))) + (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4097 *1))) + (-4 *1 (-317))))) (((*1 *2 *3) - (-12 (-5 *3 (-702 (-419 (-972 (-576))))) - (-5 *2 (-657 (-702 (-326 (-576))))) (-5 *1 (-1053))))) -(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) + (-12 (-5 *2 (-1 (-963 *3) (-963 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-374) (-1224) (-1024)))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-657 (-972 *4))) (-5 *3 (-657 (-1198))) (-4 *4 (-464)) + (-5 *1 (-938 *4))))) +(((*1 *2 *3 *3 *3 *4 *5 *3 *6) + (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *5 (-227)) + (-5 *6 (-3 (|:| |fn| (-400)) (|:| |fp| (-74 FCN)))) (-5 *2 (-1057)) + (-5 *1 (-759))))) +(((*1 *1 *2) (-12 (-5 *2 (-657 *1)) (-4 *1 (-312)))) + ((*1 *1 *1) (-4 *1 (-312))) ((*1 *1 *1) (-5 *1 (-877)))) +(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-787)) (-5 *1 (-115)))) + ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1180)) (-5 *3 (-787)) (-5 *1 (-115))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -13130,7 +12940,10 @@ ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-972 (-227))) (-5 *2 (-227)) (-5 *1 (-315))))) +(((*1 *2 *1) (-12 (-4 *1 (-996)) (-5 *2 (-1116 (-227)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-972 *5)) (-4 *5 (-1071)) (-5 *2 (-493 *4 *5)) + (-5 *1 (-964 *4 *5)) (-14 *4 (-657 (-1198)))))) (((*1 *1 *1) (-4 *1 (-248))) ((*1 *1 *1) (-12 (-4 *2 (-174)) (-5 *1 (-299 *2 *3 *4 *5 *6 *7)) @@ -13138,7 +12951,7 @@ (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-2748 (-12 (-5 *1 (-304 *2)) (-4 *2 (-374)) (-4 *2 (-1239))) + (-2802 (-12 (-5 *1 (-304 *2)) (-4 *2 (-374)) (-4 *2 (-1239))) (-12 (-5 *1 (-304 *2)) (-4 *2 (-485)) (-4 *2 (-1239))))) ((*1 *1 *1) (-4 *1 (-485))) ((*1 *2 *2) (-12 (-5 *2 (-1289 *3)) (-4 *3 (-360)) (-5 *1 (-540 *3)))) @@ -13147,22 +12960,32 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *1) (-12 (-4 *1 (-810 *2)) (-4 *2 (-174)) (-4 *2 (-374))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1180)) (-5 *2 (-657 (-1203))) (-5 *1 (-896))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1087 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-806)) + (-4 *4 (-862)) (-4 *2 (-464))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-227)) (-5 *5 (-576)) (-5 *2 (-1234 *3)) + (-5 *1 (-803 *3)) (-4 *3 (-996)))) + ((*1 *1 *2 *3 *4) + (-12 (-5 *3 (-657 (-657 (-963 (-227))))) (-5 *4 (-112)) + (-5 *1 (-1234 *2)) (-4 *2 (-996))))) +(((*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-772))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1194 *5)) (-4 *5 (-374)) (-5 *2 (-657 *6)) - (-5 *1 (-544 *5 *6 *4)) (-4 *6 (-374)) (-4 *4 (-13 (-374) (-861)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-657 (-576))) (-5 *2 (-924 (-576))) (-5 *1 (-937)))) - ((*1 *2) (-12 (-5 *2 (-924 (-576))) (-5 *1 (-937))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-1071)) (-5 *1 (-1261 *3 *2)) (-4 *2 (-1265 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-833)) (-14 *5 (-1198)) (-5 *2 (-657 (-1262 *5 *4))) - (-5 *1 (-1136 *4 *5)) (-5 *3 (-1262 *5 *4))))) + (-12 (-5 *3 (-1289 (-657 (-2 (|:| -3071 *4) (|:| -3178 (-1142)))))) + (-4 *4 (-360)) (-5 *2 (-1294)) (-5 *1 (-540 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-657 *3)) (-4 *3 (-862)) (-5 *1 (-752 *3))))) -(((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-862))))) + (|partial| -12 (-4 *3 (-374)) (-5 *1 (-779 *2 *3)) (-4 *2 (-721 *3)))) + ((*1 *1 *1 *1) + (|partial| -12 (-4 *1 (-867 *2)) (-4 *2 (-1071)) (-4 *2 (-374))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-576)) (-5 *1 (-430 *2)) (-4 *2 (-568))))) +(((*1 *1 *2) (-12 (-5 *2 (-326 (-171 (-390)))) (-5 *1 (-340)))) + ((*1 *1 *2) (-12 (-5 *2 (-326 (-576))) (-5 *1 (-340)))) + ((*1 *1 *2) (-12 (-5 *2 (-326 (-390))) (-5 *1 (-340)))) + ((*1 *1 *2) (-12 (-5 *2 (-326 (-707))) (-5 *1 (-340)))) + ((*1 *1 *2) (-12 (-5 *2 (-326 (-714))) (-5 *1 (-340)))) + ((*1 *1 *2) (-12 (-5 *2 (-326 (-712))) (-5 *1 (-340)))) + ((*1 *1) (-5 *1 (-340)))) +(((*1 *1) (-5 *1 (-609)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -13179,28 +13002,47 @@ ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1156 *3)) (-4 *3 (-1071)) - (-5 *2 (-657 (-657 (-657 (-963 *3)))))))) +(((*1 *2 *1) (-12 (-4 *1 (-975)) (-5 *2 (-1116 (-227))))) + ((*1 *2 *1) (-12 (-4 *1 (-996)) (-5 *2 (-1116 (-227)))))) (((*1 *2 *3) - (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-576))) (-5 *1 (-1069))))) + (-12 (-5 *3 (-657 (-576))) (-5 *2 (-924 (-576))) (-5 *1 (-937)))) + ((*1 *2 *3) (-12 (-5 *3 (-993)) (-5 *2 (-924 (-576))) (-5 *1 (-937))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-317) (-148))) (-4 *5 (-806)) (-4 *6 (-862)) + (-4 *7 (-969 *4 *5 *6)) (-5 *2 (-657 (-657 *7))) + (-5 *1 (-460 *4 *5 *6 *7)) (-5 *3 (-657 *7)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-317) (-148))) (-4 *6 (-806)) + (-4 *7 (-862)) (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-657 (-657 *8))) + (-5 *1 (-460 *5 *6 *7 *8)) (-5 *3 (-657 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-317) (-148))) (-4 *5 (-806)) (-4 *6 (-862)) + (-4 *7 (-969 *4 *5 *6)) (-5 *2 (-657 (-657 *7))) + (-5 *1 (-460 *4 *5 *6 *7)) (-5 *3 (-657 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-317) (-148))) (-4 *6 (-806)) + (-4 *7 (-862)) (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-657 (-657 *8))) + (-5 *1 (-460 *5 *6 *7 *8)) (-5 *3 (-657 *8))))) +(((*1 *2 *1 *2) + (-12 (-4 *1 (-375 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1122))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-657 *2)) (-4 *2 (-1087 *4 *5 *6)) (-4 *4 (-568)) + (-4 *5 (-806)) (-4 *6 (-862)) (-5 *1 (-999 *4 *5 *6 *2))))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-889)) (-5 *3 (-657 (-270))) (-5 *1 (-268))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-439 *3 *2)) (-4 *3 (-13 (-174) (-38 (-419 (-576))))) - (-4 *2 (-13 (-862) (-21)))))) + (-12 (-5 *2 (-657 *3)) (-4 *3 (-317)) (-5 *1 (-181 *3))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-326 (-576))) (|:| -1995 (-326 (-390))) + (-3 (|:| I (-326 (-576))) (|:| -2022 (-326 (-390))) (|:| CF (-326 (-171 (-390)))) (|:| |switch| (-1197)))) (-5 *1 (-1197))))) -(((*1 *1) (-12 (-4 *1 (-339 *2)) (-4 *2 (-379)) (-4 *2 (-374)))) - ((*1 *2 *3) - (-12 (-5 *3 (-941)) (-5 *2 (-1289 *4)) (-5 *1 (-540 *4)) - (-4 *4 (-360))))) -(((*1 *2 *3) (-12 (-5 *2 (-115)) (-5 *1 (-114 *3)) (-4 *3 (-1122))))) -(((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-227))) +(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) +(((*1 *2 *1) (-12 (-5 *2 (-1126)) (-5 *1 (-1202))))) +(((*1 *1) (-5 *1 (-836)))) +(((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-576)) (|has| *1 (-6 -4467)) (-4 *1 (-384 *3)) + (-4 *3 (-1239))))) +(((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13210,18 +13052,12 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) - (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) - ((*1 *1 *1 *1) (-5 *1 (-390))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1194 (-576))) (-5 *2 (-576)) (-5 *1 (-962))))) (((*1 *1 *2) (-12 (-5 *2 (-400)) (-5 *1 (-644))))) (((*1 *2 *3) (-12 (-5 *3 (-1198)) @@ -13257,37 +13093,39 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-419 (-576))) (-4 *4 (-1071)) (-4 *1 (-1272 *4 *3)) (-4 *3 (-1249 *4))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-112) *2)) (-4 *2 (-133)) (-5 *1 (-1106 *2)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-576) *2 *2)) (-4 *2 (-133)) (-5 *1 (-1106 *2))))) -(((*1 *2 *3) - (-12 (-5 *3 (-657 *2)) (-4 *2 (-442 *4)) (-5 *1 (-159 *4 *2)) - (-4 *4 (-568))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1125 *3 *4 *5 *6 *7)) (-4 *3 (-1122)) (-4 *4 (-1122)) - (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *7 (-1122)) (-5 *2 (-112))))) -(((*1 *2 *2) - (-12 (-4 *3 (-464)) (-5 *1 (-1230 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1224)))))) -(((*1 *2 *3 *3 *4 *5 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-464)) (-4 *7 (-806)) (-4 *8 (-862)) - (-4 *3 (-1087 *6 *7 *8)) - (-5 *2 (-657 (-2 (|:| |val| *3) (|:| -3941 *4)))) - (-5 *1 (-1094 *6 *7 *8 *3 *4)) (-4 *4 (-1093 *6 *7 *8 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-657 (-2 (|:| |val| (-657 *8)) (|:| -3941 *9)))) - (-5 *5 (-112)) (-4 *8 (-1087 *6 *7 *4)) (-4 *9 (-1093 *6 *7 *4 *8)) - (-4 *6 (-464)) (-4 *7 (-806)) (-4 *4 (-862)) - (-5 *2 (-657 (-2 (|:| |val| *8) (|:| -3941 *9)))) - (-5 *1 (-1094 *6 *7 *4 *8 *9))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1005 *2)) (-4 *2 (-1224))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-541)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-589)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-876))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-702 (-576))) (-5 *3 (-657 (-576))) (-5 *1 (-1132))))) +(((*1 *2 *1) (-12 (-4 *1 (-975)) (-5 *2 (-1116 (-227))))) + ((*1 *2 *1) (-12 (-4 *1 (-996)) (-5 *2 (-1116 (-227)))))) (((*1 *2 *3) - (-12 (-5 *3 (-326 (-227))) (-5 *2 (-326 (-390))) (-5 *1 (-315))))) -(((*1 *1 *1) (-4 *1 (-95))) + (-12 (-4 *4 (-13 (-568) (-1060 (-576)))) (-5 *2 (-171 (-326 *4))) + (-5 *1 (-190 *4 *3)) (-4 *3 (-13 (-27) (-1224) (-442 (-171 *4)))))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-464) (-1060 (-576)) (-652 (-576)))) + (-5 *2 (-171 *3)) (-5 *1 (-1228 *4 *3)) + (-4 *3 (-13 (-27) (-1224) (-442 *4)))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) (-5 *2 (-657 (-784))) (-5 *1 (-991 *4 *3)) + (-4 *3 (-1265 *4))))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) +(((*1 *2 *1) (-12 (-4 *1 (-360)) (-5 *2 (-112)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1194 *4)) (-4 *4 (-360)) (-5 *2 (-112)) + (-5 *1 (-368 *4))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-112)) (-5 *5 (-702 (-171 (-227)))) + (-5 *2 (-1057)) (-5 *1 (-768))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *2 (-657 *2))) (-5 *4 (-657 *5)) + (-4 *5 (-38 (-419 (-576)))) (-4 *2 (-1280 *5)) + (-5 *1 (-1282 *5 *2))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-377 *3 *4)) + (-4 *3 (-378 *4)))) + ((*1 *2) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *1) (-5 *1 (-449)))) +(((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-227))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13300,6 +13138,7 @@ ((*1 *1 *1) (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) + ((*1 *1 *1 *1) (-5 *1 (-390))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3)))) @@ -13310,13 +13149,6 @@ (|partial| -12 (-5 *2 (-1 (-548) (-657 (-548)))) (-5 *1 (-115)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-548) (-657 (-548)))) (-5 *1 (-115)))) ((*1 *1) (-5 *1 (-590)))) -(((*1 *2 *1) - (-12 (-14 *3 (-657 (-1198))) (-4 *4 (-174)) - (-14 *6 - (-1 (-112) (-2 (|:| -3146 *5) (|:| -2128 *2)) - (-2 (|:| -3146 *5) (|:| -2128 *2)))) - (-4 *2 (-243 (-3437 *3) (-784))) (-5 *1 (-473 *3 *4 *5 *2 *6 *7)) - (-4 *5 (-862)) (-4 *7 (-969 *4 *2 (-879 *3)))))) (((*1 *2 *3) (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-464) (-1060 (-576)) (-652 (-576)))) (-5 *2 (-52)) @@ -13368,41 +13200,61 @@ (-12 (-5 *3 (-784)) (-4 *1 (-920 *2)) (-4 *2 (-1122)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-657 *3)) (-4 *1 (-920 *3)) (-4 *3 (-1122))))) -(((*1 *2 *3) (-12 (-5 *3 (-941)) (-5 *2 (-924 (-576))) (-5 *1 (-937)))) - ((*1 *2 *3) - (-12 (-5 *3 (-657 (-576))) (-5 *2 (-924 (-576))) (-5 *1 (-937))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-159 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1198)) (-4 *4 (-568)) (-5 *1 (-159 *4 *2)) - (-4 *2 (-442 *4)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-161)) (-5 *2 (-1198)))) - ((*1 *1 *1) (-4 *1 (-161)))) -(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-62 *3)) (-14 *3 (-1198)))) - ((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-69 *3)) (-14 *3 (-1198)))) - ((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-72 *3)) (-14 *3 (-1198)))) - ((*1 *2 *1) (-12 (-4 *1 (-407)) (-5 *2 (-1294)))) - ((*1 *2 *3) (-12 (-5 *3 (-400)) (-5 *2 (-1294)) (-5 *1 (-409)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1180)) (-5 *4 (-877)) (-5 *2 (-1294)) (-5 *1 (-1160)))) - ((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1294)) (-5 *1 (-1160)))) - ((*1 *2 *3) - (-12 (-5 *3 (-657 (-877))) (-5 *2 (-1294)) (-5 *1 (-1160))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1087 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-806)) - (-4 *4 (-862))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-454 *3)) (-4 *3 (-1265 (-576)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-390)) (-5 *3 (-657 (-270))) (-5 *1 (-268)))) - ((*1 *1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-270))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-135))))) -(((*1 *2 *1) (-12 (-5 *2 (-657 (-1157))) (-5 *1 (-684)))) - ((*1 *2 *1) - (-12 (-5 *2 (-657 (-941))) (-5 *1 (-1123 *3 *4)) (-14 *3 (-941)) - (-14 *4 (-941))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-941)) (-5 *1 (-1054 *2)) + (-4 *2 (-13 (-1122) (-10 -8 (-15 * ($ $ $)))))))) +(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-518)) (-5 *3 (-609)) (-5 *1 (-597))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1289 (-326 (-227)))) (-5 *2 (-1289 (-326 (-390)))) + (-5 *1 (-315))))) +(((*1 *2 *1 *3 *2) + (-12 (-5 *3 (-784)) (-5 *1 (-215 *4 *2)) (-14 *4 (-941)) + (-4 *2 (-1122))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-374) (-861))) + (-5 *2 (-2 (|:| |start| *3) (|:| -2067 (-430 *3)))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1265 (-171 *4)))))) +(((*1 *1 *2) (-12 (-5 *2 (-657 *3)) (-4 *3 (-862)) (-5 *1 (-127 *3))))) +(((*1 *1) (-4 *1 (-360)))) +(((*1 *2 *3) + (-12 (-5 *3 (-784)) (-5 *2 (-702 (-972 *4))) (-5 *1 (-1050 *4)) + (-4 *4 (-1071))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-657 + (-2 + (|:| -4291 + (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) + (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -4440 + (-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| (-1179 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1685 + (-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 (-571))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-784)) (-5 *2 (-112)) (-5 *1 (-599 *3)) (-4 *3 (-557))))) (((*1 *2 *3) (-12 (-5 *3 (-908 *4)) (-4 *4 (-1122)) (-5 *2 (-1 (-112) *5)) (-5 *1 (-906 *4 *5)) (-4 *5 (-1239)))) @@ -13426,8 +13278,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1071)) (-4 *2 (-568))))) (((*1 *2 *3) (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-464) (-1060 (-576)) (-652 (-576)))) (-5 *2 (-52)) @@ -13470,36 +13320,43 @@ (-5 *1 (-471 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1251 *3 *2)) (-4 *3 (-1071)) (-4 *2 (-1280 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-947))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-657 (-908 *3))) (-5 *1 (-908 *3)) - (-4 *3 (-1122))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-576)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-384 *2)) + (-4 *5 (-384 *2)) (-4 *2 (-1239)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-784)) (-4 *2 (-1122)) (-5 *1 (-215 *4 *2)) + (-14 *4 (-941)))) + ((*1 *2 *1 *3) + (-12 (-4 *1 (-298 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1239)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-576)) (-4 *1 (-1075 *4 *5 *2 *6 *7)) + (-4 *6 (-243 *5 *2)) (-4 *7 (-243 *4 *2)) (-4 *2 (-1071))))) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1194 *7)) - (-4 *5 (-1071)) (-4 *7 (-1071)) (-4 *2 (-1265 *5)) - (-5 *1 (-513 *5 *2 *6 *7)) (-4 *6 (-1265 *2))))) -(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-403))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1290)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1291))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-941)) (-5 *4 (-889)) (-5 *2 (-1294)) (-5 *1 (-1290)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-941)) (-5 *4 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1290)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1291))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1071))))) -(((*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) - ((*1 *2 *1) - (-12 (-4 *3 (-374)) (-4 *4 (-806)) (-4 *5 (-862)) (-5 *2 (-112)) - (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-969 *3 *4 *5)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1090 *4 *3)) (-4 *4 (-13 (-861) (-374))) - (-4 *3 (-1265 *4)) (-5 *2 (-112))))) -(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) + (-12 (-5 *3 (-430 *5)) (-4 *5 (-568)) + (-5 *2 + (-2 (|:| -1801 (-784)) (|:| -1771 *5) (|:| |radicand| (-657 *5)))) + (-5 *1 (-330 *5)) (-5 *4 (-784)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1024)) (-5 *2 (-576))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-947))))) +(((*1 *2 *1) (-12 (-5 *2 (-1157)) (-5 *1 (-1299))))) +(((*1 *2 *1) (-12 (-5 *2 (-657 (-963 (-227)))) (-5 *1 (-1290))))) +(((*1 *1) (-5 *1 (-142)))) +(((*1 *2 *2) (-12 (-5 *2 (-390)) (-5 *1 (-97))))) +(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-52)) (-5 *1 (-1217))))) +(((*1 *2 *1) (-12 (-4 *1 (-1143 *2)) (-4 *2 (-1239))))) (((*1 *2 *2) + (-12 + (-5 *2 + (-657 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-784)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-806)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-464)) (-4 *5 (-862)) + (-5 *1 (-461 *3 *4 *5 *6))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1232 *3 *4 *5 *2)) (-4 *3 (-568)) (-4 *4 (-806)) + (-4 *5 (-862)) (-4 *2 (-1087 *3 *4 *5))))) +(((*1 *1 *1) (-4 *1 (-95))) + ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) ((*1 *2 *2) @@ -13508,59 +13365,58 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) + (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) - (-5 *1 (-1184 *3)))) - ((*1 *1 *1) (-4 *1 (-1227)))) -(((*1 *2 *3 *4 *5 *4 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *7 *4) - (-12 (-5 *3 (-1180)) (-5 *5 (-702 (-227))) (-5 *6 (-227)) - (-5 *7 (-702 (-576))) (-5 *4 (-576)) (-5 *2 (-1057)) (-5 *1 (-765))))) -(((*1 *2 *3) (-12 (-5 *3 (-400)) (-5 *2 (-1294)) (-5 *1 (-403)))) - ((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-403))))) + (-5 *1 (-1184 *3))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-702 *3)) (-4 *3 (-1071)) (-5 *1 (-1050 *3)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-657 (-702 *3))) (-4 *3 (-1071)) (-5 *1 (-1050 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-702 *3)) (-4 *3 (-1071)) (-5 *1 (-1050 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-657 (-702 *3))) (-4 *3 (-1071)) (-5 *1 (-1050 *3))))) +(((*1 *2 *1) + (-12 (|has| *1 (-6 -4466)) (-4 *1 (-501 *3)) (-4 *3 (-1239)) + (-5 *2 (-657 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-657 *3)) (-5 *1 (-750 *3)) (-4 *3 (-1122)))) + ((*1 *2 *1) (-12 (-5 *2 (-657 (-451))) (-5 *1 (-880))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-337 *3)) (-4 *3 (-1239)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1239)) + (-14 *4 (-576))))) +(((*1 *2 *3) (-12 (-5 *3 (-326 (-227))) (-5 *2 (-227)) (-5 *1 (-315))))) +(((*1 *2 *1) + (-12 (-5 *2 (-657 (-2 (|:| |gen| *3) (|:| -4067 (-576))))) + (-5 *1 (-372 *3)) (-4 *3 (-1122)))) + ((*1 *2 *1) + (-12 (-4 *1 (-397 *3)) (-4 *3 (-1122)) + (-5 *2 (-657 (-2 (|:| |gen| *3) (|:| -4067 (-784))))))) + ((*1 *2 *1) + (-12 (-5 *2 (-657 (-2 (|:| -1885 *3) (|:| -1801 (-576))))) + (-5 *1 (-430 *3)) (-4 *3 (-568))))) +(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-702 *3)) (-4 *3 (-1071)) (-5 *1 (-703 *3)))) + ((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-702 *3)) (-4 *3 (-1071)) (-5 *1 (-703 *3))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-963 *3) (-963 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-374) (-1224) (-1024)))))) (((*1 *2 *3) (-12 (-5 *3 - (-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| (-1179 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3936 - (-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 (-1057)) (-5 *1 (-315))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1232 *2 *3 *4 *5)) (-4 *2 (-568)) (-4 *3 (-806)) - (-4 *4 (-862)) (-4 *5 (-1087 *2 *3 *4))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-464)) (-4 *4 (-862)) (-4 *5 (-806)) - (-5 *2 (-112)) (-5 *1 (-1009 *3 *4 *5 *6)) - (-4 *6 (-969 *3 *5 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1162 *3 *4)) (-4 *3 (-13 (-1122) (-34))) - (-4 *4 (-13 (-1122) (-34)))))) -(((*1 *2 *1) (-12 (-4 *1 (-810 *2)) (-4 *2 (-174))))) -(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-947))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-449))))) + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1289 (-326 (-227)))) (|:| |yinit| (-657 (-227))) + (|:| |intvals| (-657 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-390)) (-5 *1 (-207))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13577,41 +13433,53 @@ (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3)))) ((*1 *1 *1) (-4 *1 (-1227)))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1200 (-419 (-576)))) (-5 *1 (-192))))) -(((*1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1062))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-657 (-1289 *5))) (-5 *4 (-576)) (-5 *2 (-1289 *5)) - (-5 *1 (-1051 *5)) (-4 *5 (-374)) (-4 *5 (-379)) (-4 *5 (-1071))))) +(((*1 *1 *1 *1) (-4 *1 (-557)))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-112)) (-4 *6 (-13 (-464) (-1060 (-576)) (-652 (-576)))) + (-4 *3 (-13 (-27) (-1224) (-442 *6) (-10 -8 (-15 -3501 ($ *7))))) + (-4 *7 (-861)) + (-4 *8 + (-13 (-1267 *3 *7) (-374) (-1224) + (-10 -8 (-15 -2815 ($ $)) (-15 -4190 ($ $))))) + (-5 *2 + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1180)) (|:| |prob| (-1180)))))) + (-5 *1 (-434 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1180)) (-4 *9 (-1005 *8)) + (-14 *10 (-1198))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1186 *2 *3)) (-14 *2 (-941)) (-4 *3 (-1071))))) (((*1 *2 *3) - (-12 (-4 *4 (-568)) (-5 *2 (-1194 *3)) (-5 *1 (-41 *4 *3)) + (-12 (-5 *3 (-1194 *4)) (-4 *4 (-360)) (-5 *2 (-978 (-1142))) + (-5 *1 (-357 *4))))) +(((*1 *2 *2 *3) (-12 (-5 *2 (-576)) (-5 *3 (-784)) (-5 *1 (-573))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-657 (-784))) (-5 *3 (-173)) (-5 *1 (-1186 *4 *5)) + (-14 *4 (-941)) (-4 *5 (-1071))))) +(((*1 *2 *2 *3) + (-12 (-4 *4 (-806)) + (-4 *3 (-13 (-862) (-10 -8 (-15 -4148 ((-1198) $))))) (-4 *5 (-568)) + (-5 *1 (-745 *4 *3 *5 *2)) (-4 *2 (-969 (-419 (-972 *5)) *4 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *4 (-1071)) (-4 *5 (-806)) (-4 *3 - (-13 (-374) (-312) - (-10 -8 (-15 -1590 ((-1147 *4 (-624 $)) $)) - (-15 -1602 ((-1147 *4 (-624 $)) $)) - (-15 -3515 ($ (-1147 *4 (-624 $)))))))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-568) (-1060 (-576)))) (-5 *2 (-112)) - (-5 *1 (-190 *4 *3)) (-4 *3 (-13 (-27) (-1224) (-442 (-171 *4)))))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-446)))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-464) (-1060 (-576)) (-652 (-576)))) (-5 *2 (-112)) - (-5 *1 (-1228 *4 *3)) (-4 *3 (-13 (-27) (-1224) (-442 *4)))))) + (-13 (-862) + (-10 -8 (-15 -4148 ((-1198) $)) + (-15 -3032 ((-3 $ "failed") (-1198)))))) + (-5 *1 (-1006 *4 *5 *3 *2)) (-4 *2 (-969 (-972 *4) *5 *3)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-657 *6)) + (-4 *6 + (-13 (-862) + (-10 -8 (-15 -4148 ((-1198) $)) + (-15 -3032 ((-3 $ "failed") (-1198)))))) + (-4 *4 (-1071)) (-4 *5 (-806)) (-5 *1 (-1006 *4 *5 *6 *2)) + (-4 *2 (-969 (-972 *4) *5 *6))))) (((*1 *1 *2) - (-12 (-5 *2 (-657 *3)) (-4 *3 (-1122)) (-5 *1 (-1022 *3))))) -(((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4468 "*"))) (-4 *5 (-384 *2)) (-4 *6 (-384 *2)) - (-4 *2 (-1071)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1265 *2)) - (-4 *4 (-700 *2 *5 *6))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-568)) - (-5 *2 (-2 (|:| -2192 *3) (|:| -3951 *3))) (-5 *1 (-1260 *4 *3)) - (-4 *3 (-1265 *4))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -3579 *6) (|:| |coeff| *6)) "failed") *6)) - (-4 *6 (-374)) (-4 *7 (-1265 *6)) - (-5 *2 (-2 (|:| |answer| (-598 (-419 *7))) (|:| |a0| *6))) - (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) + (-12 (-5 *2 (-1289 *3)) (-4 *3 (-1071)) (-5 *1 (-725 *3 *4)) + (-4 *4 (-1265 *3))))) +(((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1024)))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13628,38 +13496,36 @@ (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3)))) ((*1 *1 *1) (-4 *1 (-1227)))) -(((*1 *2) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1243)) (-4 *4 (-1265 *3)) - (-4 *5 (-1265 (-419 *4))) (-5 *2 (-112))))) -(((*1 *2 *3) (-12 (-5 *3 (-390)) (-5 *2 (-227)) (-5 *1 (-1292)))) - ((*1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-1292))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) - (-4 *3 (-1087 *5 *6 *7)) (-5 *2 (-657 *4)) - (-5 *1 (-1130 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-657 (-2 (|:| -4286 (-1198)) (|:| -4440 (-449))))) - (-5 *1 (-1202))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-657 (-793 *5 (-879 *6)))) (-5 *4 (-112)) (-4 *5 (-464)) - (-14 *6 (-657 (-1198))) (-5 *2 (-657 (-1068 *5 *6))) - (-5 *1 (-640 *5 *6))))) -(((*1 *2) - (-12 (-5 *2 (-1294)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) - (-4 *4 (-1122))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *4 *5 *3 *3 *4 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *5 (-112)) - (-5 *2 (-1057)) (-5 *1 (-766))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) - (-5 *4 (-702 (-1194 *8))) (-4 *5 (-1071)) (-4 *8 (-1071)) - (-4 *6 (-1265 *5)) (-5 *2 (-702 *6)) (-5 *1 (-513 *5 *6 *7 *8)) - (-4 *7 (-1265 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1280 *4)) - (-4 *4 (-38 (-419 (-576)))) (-5 *2 (-1 (-1179 *4) (-1179 *4))) - (-5 *1 (-1282 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-541))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-1198)) (-5 *6 (-112)) + (-4 *7 (-13 (-317) (-148) (-1060 (-576)) (-652 (-576)))) + (-4 *3 (-13 (-1224) (-979) (-29 *7))) + (-5 *2 + (-3 (|:| |f1| (-856 *3)) (|:| |f2| (-657 (-856 *3))) + (|:| |fail| "failed") (|:| |pole| "potentialPole"))) + (-5 *1 (-221 *7 *3)) (-5 *5 (-856 *3))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-657 *3)) (-4 *3 (-1122)) (-5 *1 (-103 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-700 *3 *4 *5)) (-4 *3 (-1071)) (-4 *4 (-384 *3)) + (-4 *5 (-384 *3)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1075 *3 *4 *5 *6 *7)) (-4 *5 (-1071)) + (-4 *6 (-243 *4 *5)) (-4 *7 (-243 *3 *5)) (-5 *2 (-112))))) +(((*1 *2 *3 *2) + (-12 (-4 *2 (-13 (-374) (-861))) (-5 *1 (-183 *2 *3)) + (-4 *3 (-1265 (-171 *2))))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-374) (-861))) (-5 *1 (-183 *2 *3)) + (-4 *3 (-1265 (-171 *2)))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-941)) (-5 *4 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1290))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112))))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4467)) (-4 *1 (-1277 *2)) (-4 *2 (-1239))))) +(((*1 *1 *2) (-12 (-5 *2 (-419 (-576))) (-5 *1 (-108)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-657 (-548))) (-5 *1 (-548))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-908 *3)) (-4 *3 (-1122))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13669,9 +13535,6 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) - (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) ((*1 *2 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3)))) @@ -13687,71 +13550,38 @@ (-12 (-5 *2 (-1294)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-862) - (-10 -8 (-15 -2780 ((-1180) $ (-1198))) (-15 -2011 (*2 $)) - (-15 -2884 (*2 $))))))) + (-10 -8 (-15 -2835 ((-1180) $ (-1198))) (-15 -2041 (*2 $)) + (-15 -1729 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-406)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-576)) (-5 *2 (-1294)) (-5 *1 (-406)))) ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-514)))) ((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-723)))) ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-1219)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-576)) (-5 *2 (-1294)) (-5 *1 (-1219))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-419 (-576))) - (-4 *4 (-13 (-568) (-1060 (-576)) (-652 (-576)))) - (-5 *1 (-286 *4 *2)) (-4 *2 (-13 (-27) (-1224) (-442 *4)))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *6 (-941)) (-4 *5 (-317)) (-4 *3 (-1265 *5)) + (-5 *2 (-2 (|:| |plist| (-657 *3)) (|:| |modulo| *5))) + (-5 *1 (-472 *5 *3)) (-5 *4 (-657 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-657 (-1107))) (-5 *1 (-301))))) (((*1 *1 *1) (-12 (-4 *1 (-1087 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-806)) - (-4 *4 (-862)) (-4 *2 (-568))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 *3)) (-5 *4 (-908 *5)) (-4 *5 (-1122)) - (-4 *3 (-167 *6)) (-4 (-972 *6) (-902 *5)) - (-4 *6 (-13 (-902 *5) (-174))) (-5 *1 (-180 *5 *6 *3)))) - ((*1 *2 *1 *3 *2) - (-12 (-5 *2 (-905 *4 *1)) (-5 *3 (-908 *4)) (-4 *1 (-902 *4)) - (-4 *4 (-1122)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 *6)) (-5 *4 (-908 *5)) (-4 *5 (-1122)) - (-4 *6 (-13 (-1122) (-1060 *3))) (-4 *3 (-902 *5)) - (-5 *1 (-951 *5 *3 *6)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 *3)) (-4 *5 (-1122)) - (-4 *3 (-13 (-442 *6) (-626 *4) (-902 *5) (-1060 (-624 $)))) - (-5 *4 (-908 *5)) (-4 *6 (-13 (-568) (-902 *5))) - (-5 *1 (-952 *5 *6 *3)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 (-576) *3)) (-5 *4 (-908 (-576))) (-4 *3 (-557)) - (-5 *1 (-953 *3)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 *6)) (-5 *3 (-624 *6)) (-4 *5 (-1122)) - (-4 *6 (-13 (-1122) (-1060 (-624 $)) (-626 *4) (-902 *5))) - (-5 *4 (-908 *5)) (-5 *1 (-954 *5 *6)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-901 *5 *6 *3)) (-5 *4 (-908 *5)) (-4 *5 (-1122)) - (-4 *6 (-902 *5)) (-4 *3 (-679 *6)) (-5 *1 (-955 *5 *6 *3)))) - ((*1 *2 *3 *4 *2 *5) - (-12 (-5 *5 (-1 (-905 *6 *3) *8 (-908 *6) (-905 *6 *3))) - (-4 *8 (-862)) (-5 *2 (-905 *6 *3)) (-5 *4 (-908 *6)) - (-4 *6 (-1122)) (-4 *3 (-13 (-969 *9 *7 *8) (-626 *4))) - (-4 *7 (-806)) (-4 *9 (-13 (-1071) (-902 *6))) - (-5 *1 (-956 *6 *7 *8 *9 *3)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 *3)) (-4 *5 (-1122)) - (-4 *3 (-13 (-969 *8 *6 *7) (-626 *4))) (-5 *4 (-908 *5)) - (-4 *7 (-902 *5)) (-4 *6 (-806)) (-4 *7 (-862)) - (-4 *8 (-13 (-1071) (-902 *5))) (-5 *1 (-956 *5 *6 *7 *8 *3)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 *3)) (-4 *5 (-1122)) (-4 *3 (-1014 *6)) - (-4 *6 (-13 (-568) (-902 *5) (-626 *4))) (-5 *4 (-908 *5)) - (-5 *1 (-959 *5 *6 *3)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-905 *5 (-1198))) (-5 *3 (-1198)) (-5 *4 (-908 *5)) - (-4 *5 (-1122)) (-5 *1 (-960 *5)))) - ((*1 *2 *3 *4 *5 *2 *6) - (-12 (-5 *4 (-657 (-908 *7))) (-5 *5 (-1 *9 (-657 *9))) - (-5 *6 (-1 (-905 *7 *9) *9 (-908 *7) (-905 *7 *9))) (-4 *7 (-1122)) - (-4 *9 (-13 (-1071) (-626 (-908 *7)) (-1060 *8))) - (-5 *2 (-905 *7 *9)) (-5 *3 (-657 *9)) (-4 *8 (-1071)) - (-5 *1 (-961 *7 *8 *9))))) + (-4 *4 (-862))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1198)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-715 *4 *5 *6 *7)) + (-4 *4 (-626 (-548))) (-4 *5 (-1239)) (-4 *6 (-1239)) + (-4 *7 (-1239))))) +(((*1 *2 *3) + (-12 (-4 *1 (-913)) + (-5 *3 + (-2 (|:| |pde| (-657 (-326 (-227)))) + (|:| |constraints| + (-657 + (-2 (|:| |start| (-227)) (|:| |finish| (-227)) + (|:| |grid| (-784)) (|:| |boundaryType| (-576)) + (|:| |dStart| (-702 (-227))) (|:| |dFinish| (-702 (-227)))))) + (|:| |f| (-657 (-657 (-326 (-227))))) (|:| |st| (-1180)) + (|:| |tol| (-227)))) + (-5 *2 (-1057))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4466)) (-4 *1 (-152 *3)) (-4 *3 (-1239)))) @@ -13764,25 +13594,25 @@ (-4 *5 (-806)) (-4 *3 (-862)) (-4 *2 (-1087 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-784)) (-5 *1 (-1236 *2)) (-4 *2 (-1239))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1179 (-657 (-576)))) (-5 *1 (-899)) - (-5 *3 (-657 (-576)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1060 (-576))) (-4 *3 (-568)) (-5 *1 (-32 *3 *2)) - (-4 *2 (-442 *3)))) - ((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-1194 *4)) (-5 *1 (-166 *3 *4)) - (-4 *3 (-167 *4)))) - ((*1 *1 *1) (-12 (-4 *1 (-1071)) (-4 *1 (-312)))) - ((*1 *2) (-12 (-4 *1 (-339 *3)) (-4 *3 (-374)) (-5 *2 (-1194 *3)))) - ((*1 *2) (-12 (-4 *1 (-737 *3 *2)) (-4 *3 (-174)) (-4 *2 (-1265 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1090 *3 *2)) (-4 *3 (-13 (-861) (-374))) - (-4 *2 (-1265 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) -(((*1 *2 *3) - (-12 (-5 *3 (-326 (-227))) (-5 *2 (-326 (-419 (-576)))) - (-5 *1 (-315))))) +(((*1 *2 *1) (-12 (-4 *1 (-317)) (-5 *2 (-784))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) + (-4 *3 (-1087 *5 *6 *7)) + (-5 *2 (-657 (-2 (|:| |val| *3) (|:| -3946 *4)))) + (-5 *1 (-1094 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-377 *3 *4)) + (-4 *3 (-378 *4)))) + ((*1 *2) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-657 *2)) (-4 *2 (-969 *4 *5 *6)) (-4 *4 (-374)) + (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862)) + (-5 *1 (-462 *4 *5 *6 *2)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-374)) + (-5 *2 + (-2 (|:| R (-702 *6)) (|:| A (-702 *6)) (|:| |Ainv| (-702 *6)))) + (-5 *1 (-1000 *6)) (-5 *3 (-702 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13792,7 +13622,6 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) - ((*1 *1 *2) (-12 (-5 *1 (-341 *2)) (-4 *2 (-862)))) ((*1 *1 *1) (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) @@ -13803,16 +13632,10 @@ (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1184 *3)))) ((*1 *1 *1) (-4 *1 (-1227)))) -(((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-934 *3)) (-4 *3 (-317))))) -(((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-537)))) - ((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-1173))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1289 *5)) (-4 *5 (-805)) (-5 *2 (-112)) - (-5 *1 (-858 *4 *5)) (-14 *4 (-784))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-657 (-326 (-227)))) (|:| -1679 (-657 (-227))))) + (-2 (|:| |lfn| (-657 (-326 (-227)))) (|:| -1706 (-657 (-227))))) (-5 *2 (-657 (-1198))) (-5 *1 (-276)))) ((*1 *2 *3) (-12 (-5 *3 (-1194 *7)) (-4 *7 (-969 *6 *4 *5)) (-4 *4 (-806)) @@ -13834,7 +13657,7 @@ (-5 *1 (-970 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-374) - (-10 -8 (-15 -3515 ($ *7)) (-15 -1590 (*7 $)) (-15 -1602 (*7 $))))))) + (-10 -8 (-15 -3501 ($ *7)) (-15 -1621 (*7 $)) (-15 -1635 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-995 *3 *4 *5)) (-4 *3 (-1071)) (-4 *4 (-805)) (-4 *5 (-862)) (-5 *2 (-657 *5)))) @@ -13844,38 +13667,51 @@ ((*1 *2 *3) (-12 (-5 *3 (-419 (-972 *4))) (-4 *4 (-568)) (-5 *2 (-657 (-1198))) (-5 *1 (-1065 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1179 (-576))) (-5 *1 (-1026 *3)) (-14 *3 (-576))))) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -1701 *4))) + (-5 *1 (-991 *4 *3)) (-4 *3 (-1265 *4))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-374)) (-5 *2 (-2 (|:| -2335 *3) (|:| -3644 *3))) + (-5 *1 (-779 *3 *4)) (-4 *3 (-721 *4)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-374)) (-4 *3 (-1071)) + (-5 *2 (-2 (|:| -2335 *1) (|:| -3644 *1))) (-4 *1 (-867 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-374)) (-4 *5 (-1071)) + (-5 *2 (-2 (|:| -2335 *3) (|:| -3644 *3))) (-5 *1 (-868 *5 *3)) + (-4 *3 (-867 *5))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-784)) (-4 *4 (-1071)) + (-5 *2 (-2 (|:| -2335 *1) (|:| -3644 *1))) (-4 *1 (-1265 *4))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1239)) (-5 *1 (-613 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1239)) (-5 *1 (-1179 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1180)) (-5 *3 (-657 (-270))) (-5 *1 (-268)))) - ((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-270))))) +(((*1 *1) + (|partial| -12 (-4 *1 (-378 *2)) (-4 *2 (-568)) (-4 *2 (-174))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-784)) (-5 *2 (-1 (-390))) (-5 *1 (-1062))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-566 *3)) (-4 *3 (-13 (-416) (-1224))) (-5 *2 (-112))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1289 *1)) (-4 *1 (-652 *4)) (-4 *4 (-1071)) - (-5 *2 (-2 (|:| -3962 (-702 *4)) (|:| |vec| (-1289 *4)))))) - ((*1 *2 *3) - (-12 (-5 *3 (-1289 *1)) (-4 *1 (-652 *4)) (-4 *4 (-1071)) - (-5 *2 (-702 *4))))) -(((*1 *2) - (|partial| -12 (-4 *3 (-568)) (-4 *3 (-174)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -2469 (-657 *1)))) - (-4 *1 (-378 *3)))) - ((*1 *2) - (|partial| -12 - (-5 *2 - (-2 (|:| |particular| (-465 *3 *4 *5 *6)) - (|:| -2469 (-657 (-465 *3 *4 *5 *6))))) - (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-174)) (-14 *4 (-941)) - (-14 *5 (-657 (-1198))) (-14 *6 (-1289 (-702 *3)))))) (((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -3519 (-576)) (|:| -1502 (-657 *3)))) - (-5 *1 (-454 *3)) (-4 *3 (-1265 (-576)))))) -(((*1 *2 *3 *2) (-12 (-5 *2 (-1180)) (-5 *3 (-576)) (-5 *1 (-246))))) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1289 (-326 (-227)))) (|:| |yinit| (-657 (-227))) + (|:| |intvals| (-657 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-390)) (-5 *1 (-207))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1306 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1071)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1312 *3 *4)) (-4 *3 (-1071)) + (-4 *4 (-859))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1186 3 *3)) (-4 *3 (-1071)) (-4 *1 (-1156 *3)))) + ((*1 *1) (-12 (-4 *1 (-1156 *2)) (-4 *2 (-1071))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-795 *2)) (-4 *2 (-1071))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1024))))) @@ -13899,7 +13735,10 @@ (((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-173)))) ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-1290)))) ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-1291))))) -(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-835))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-464)) (-4 *6 (-806)) (-4 *7 (-862)) + (-4 *3 (-1087 *5 *6 *7)) (-5 *2 (-657 *4)) + (-5 *1 (-1130 *5 *6 *7 *3 *4)) (-4 *4 (-1093 *5 *6 *7 *3))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1194 (-419 (-1194 *2)))) (-5 *4 (-624 *2)) (-4 *2 (-13 (-442 *5) (-27) (-1224))) @@ -13916,53 +13755,72 @@ (-4 *6 (-1071)) (-4 *2 (-13 (-374) - (-10 -8 (-15 -3515 ($ *7)) (-15 -1590 (*7 $)) (-15 -1602 (*7 $))))) + (-10 -8 (-15 -3501 ($ *7)) (-15 -1621 (*7 $)) (-15 -1635 (*7 $))))) (-5 *1 (-970 *5 *4 *6 *7 *2)) (-4 *7 (-969 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-419 (-1194 (-419 (-972 *5))))) (-5 *4 (-1198)) (-5 *2 (-419 (-972 *5))) (-5 *1 (-1065 *5)) (-4 *5 (-568))))) -(((*1 *2) (-12 (-5 *2 (-941)) (-5 *1 (-714)))) - ((*1 *2 *2) (-12 (-5 *2 (-941)) (-5 *1 (-714))))) -(((*1 *2 *3) (-12 (-5 *2 (-657 (-576))) (-5 *1 (-573)) (-5 *3 (-576))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) + (-4 *4 (-1122))))) +(((*1 *1 *1 *1) (-5 *1 (-877))) ((*1 *1 *1) (-5 *1 (-877))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1194 (-576))) (-5 *3 (-576)) (-4 *1 (-884 *4))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1239)) (-5 *1 (-613 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1239)) (-5 *1 (-1179 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-1289 *4)) (-5 *3 (-784)) (-4 *4 (-360)) - (-5 *1 (-540 *4))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-657 *7)) (-4 *7 (-1087 *4 *5 *6)) (-4 *4 (-464)) - (-4 *5 (-806)) (-4 *6 (-862)) (-5 *2 (-112)) - (-5 *1 (-1010 *4 *5 *6 *7 *8)) (-4 *8 (-1093 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-657 *7)) (-4 *7 (-1087 *4 *5 *6)) (-4 *4 (-464)) - (-4 *5 (-806)) (-4 *6 (-862)) (-5 *2 (-112)) - (-5 *1 (-1129 *4 *5 *6 *7 *8)) (-4 *8 (-1093 *4 *5 *6 *7))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-419 (-972 (-171 (-576))))) (-5 *2 (-657 (-171 *4))) - (-5 *1 (-389 *4)) (-4 *4 (-13 (-374) (-861))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-657 (-419 (-972 (-171 (-576)))))) - (-5 *4 (-657 (-1198))) (-5 *2 (-657 (-657 (-171 *5)))) - (-5 *1 (-389 *5)) (-4 *5 (-13 (-374) (-861)))))) -(((*1 *2 *2 *1) - (-12 (-4 *1 (-1232 *3 *4 *5 *2)) (-4 *3 (-568)) (-4 *4 (-806)) - (-4 *5 (-862)) (-4 *2 (-1087 *3 *4 *5))))) -(((*1 *2 *1) - (-12 (-4 *1 (-998 *3 *4 *5 *6)) (-4 *3 (-1071)) (-4 *4 (-806)) - (-4 *5 (-862)) (-4 *6 (-1087 *3 *4 *5)) (-4 *3 (-568)) - (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-4 *4 (-568)) (-5 *2 (-784)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-429 *4))))) -(((*1 *1 *1) (-4 *1 (-641))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-702 *3)) (-4 *3 (-317)) (-5 *1 (-713 *3))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-337 *3)) (-4 *3 (-1239)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-576)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1239)) (-14 *4 *2)))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-576))) (-4 *3 (-1071)) (-5 *1 (-607 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-576))) (-4 *1 (-1249 *3)) (-4 *3 (-1071)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-576))) (-4 *1 (-1280 *3)) (-4 *3 (-1071))))) +(((*1 *2 *2) + (-12 + (-5 *2 + (-1009 (-419 (-576)) (-879 *3) (-245 *4 (-784)) + (-253 *3 (-419 (-576))))) + (-14 *3 (-657 (-1198))) (-14 *4 (-784)) (-5 *1 (-1008 *3 *4))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-657 (-1116 (-390)))) (-5 *3 (-657 (-270))) + (-5 *1 (-268)))) + ((*1 *1 *2) (-12 (-5 *2 (-657 (-1116 (-390)))) (-5 *1 (-270)))) + ((*1 *2 *1 *2) (-12 (-5 *2 (-657 (-1116 (-390)))) (-5 *1 (-480)))) + ((*1 *2 *1) (-12 (-5 *2 (-657 (-1116 (-390)))) (-5 *1 (-480))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-289)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-908 *3)) (-4 *3 (-1122)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1306 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1071)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1312 *3 *4)) (-4 *3 (-1071)) + (-4 *4 (-859))))) +(((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1024))))) ((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-642 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1024) (-1224)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-657 (-493 *4 *5))) (-14 *4 (-657 (-1198))) - (-4 *5 (-464)) (-5 *2 (-657 (-253 *4 *5))) (-5 *1 (-643 *4 *5))))) + (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1280 *3)) + (-5 *1 (-287 *3 *4 *2)) (-4 *2 (-1251 *3 *4)))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) + (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) + ((*1 *1 *2) (-12 (-5 *1 (-341 *2)) (-4 *2 (-862)))) + ((*1 *1 *1) + (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-657 (-1198))) + (-14 *3 (-657 (-1198))) (-4 *4 (-399)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) + (-5 *1 (-1183 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) + (-5 *1 (-1184 *3)))) + ((*1 *1 *1) (-4 *1 (-1227)))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1071)) (-4 *3 (-805)))) ((*1 *1 *2 *3) @@ -13970,10 +13828,10 @@ (-4 *2 (-374)) (-14 *5 (-1015 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-726 *5 *6 *7)) (-4 *5 (-862)) - (-4 *6 (-243 (-3437 *4) (-784))) + (-4 *6 (-243 (-3440 *4) (-784))) (-14 *7 - (-1 (-112) (-2 (|:| -3146 *5) (|:| -2128 *6)) - (-2 (|:| -3146 *5) (|:| -2128 *6)))) + (-1 (-112) (-2 (|:| -3178 *5) (|:| -1801 *6)) + (-2 (|:| -3178 *5) (|:| -1801 *6)))) (-14 *4 (-657 (-1198))) (-4 *2 (-174)) (-5 *1 (-473 *4 *2 *5 *6 *7 *8)) (-4 *8 (-969 *2 *6 (-879 *4))))) ((*1 *1 *2 *3) @@ -14003,13 +13861,16 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-995 *4 *3 *2)) (-4 *4 (-1071)) (-4 *3 (-805)) (-4 *2 (-862))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-607 *2)) (-4 *2 (-1071))))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-1243)) (-4 *5 (-1265 *3)) (-4 *6 (-1265 (-419 *5))) - (-5 *2 (-112)) (-5 *1 (-352 *4 *3 *5 *6)) (-4 *4 (-353 *3 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1243)) (-4 *4 (-1265 *3)) - (-4 *5 (-1265 (-419 *4))) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-4 *4 (-360)) (-5 *2 (-112)) (-5 *1 (-218 *4 *3)) + (-4 *3 (-1265 *4))))) +(((*1 *2 *3) + (-12 (-4 *2 (-374)) (-4 *2 (-861)) (-5 *1 (-965 *2 *3)) + (-4 *3 (-1265 *2))))) +(((*1 *2 *3) (-12 (-5 *3 (-854)) (-5 *2 (-1057)) (-5 *1 (-853)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-657 (-326 (-390)))) (-5 *4 (-657 (-390))) + (-5 *2 (-1057)) (-5 *1 (-853))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-941)) (-4 *6 (-568)) (-5 *2 (-657 (-326 *6))) (-5 *1 (-223 *5 *6)) (-5 *3 (-326 *6)) (-4 *5 (-1071)))) @@ -14035,63 +13896,90 @@ ((*1 *2 *1) (-12 (-5 *2 (-1304 *3 *4)) (-5 *1 (-1313 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1071))))) -(((*1 *2 *3) - (-12 (-5 *3 (-941)) - (-5 *2 - (-3 (-1194 *4) - (-1289 (-657 (-2 (|:| -3037 *4) (|:| -3146 (-1142))))))) - (-5 *1 (-357 *4)) (-4 *4 (-360))))) -(((*1 *2) - (-12 (-5 *2 (-1294)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) - (-4 *4 (-1122))))) +(((*1 *1 *1) (-12 (-5 *1 (-304 *2)) (-4 *2 (-21)) (-4 *2 (-1239))))) +(((*1 *1) (-5 *1 (-142)))) (((*1 *2 *3) (-12 (-5 *3 (-657 (-576))) (-5 *2 (-924 (-576))) (-5 *1 (-937)))) ((*1 *2) (-12 (-5 *2 (-924 (-576))) (-5 *1 (-937))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-806)) (-4 *4 (-862)) (-4 *6 (-317)) (-5 *2 (-430 *3)) - (-5 *1 (-755 *5 *4 *6 *3)) (-4 *3 (-969 *6 *5 *4))))) +(((*1 *2 *3 *4 *3 *5) + (-12 (-5 *3 (-1180)) (-5 *4 (-171 (-227))) (-5 *5 (-576)) + (-5 *2 (-1057)) (-5 *1 (-771))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-446))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-963 *3) (-963 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-374) (-1224) (-1024)))))) -(((*1 *2) - (-12 (-5 *2 (-784)) (-5 *1 (-121 *3)) (-4 *3 (-1265 (-576))))) + (-12 + (-5 *3 + (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) + (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (-5 *2 + (-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 (-194))))) +(((*1 *1 *1) (-4 *1 (-641))) ((*1 *2 *2) - (-12 (-5 *2 (-784)) (-5 *1 (-121 *3)) (-4 *3 (-1265 (-576)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-657 (-326 (-227)))) (-5 *2 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(-419 (-576)))) (-4 *4 (-1280 *3)) - (-5 *1 (-287 *3 *4 *2)) (-4 *2 (-1251 *3 *4)))) - ((*1 *2 *2) - (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1249 *3)) - (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1272 *3 *4)) (-4 *5 (-1005 *4)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) - (-5 *1 (-1183 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1179 *3)) (-4 *3 (-38 (-419 (-576)))) - (-5 *1 (-1184 *3))))) -(((*1 *2 *1) - (-12 (-4 *2 (-969 *3 *5 *4)) (-5 *1 (-1009 *3 *4 *5 *2)) - (-4 *3 (-464)) (-4 *4 (-862)) (-4 *5 (-806))))) -(((*1 *1 *1 *1) (-4 *1 (-989)))) -(((*1 *2 *3) (-12 (-5 *3 (-1289 *1)) (-4 *1 (-378 *2)) (-4 *2 (-174)))) - ((*1 *2) (-12 (-4 *2 (-174)) (-5 *1 (-428 *3 *2)) (-4 *3 (-429 *2)))) - ((*1 *2) (-12 (-4 *1 (-429 *2)) (-4 *2 (-174))))) -(((*1 *1 *1 *1) (-5 *1 (-877)))) -(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-97))))) -(((*1 *1) (-5 *1 (-142))) ((*1 *1 *1) (-5 *1 (-145))) - ((*1 *1 *1) (-4 *1 (-1166)))) -(((*1 *1 *1) (-5 *1 (-877)))) + (-12 (-5 *4 (-1198)) + (-4 *5 (-13 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*5 (-806)) (-4 *7 (-568)) (-5 *2 (-430 *3)) (-5 *1 (-468 *4 *5 *6 *7 *3)) (-4 *6 (-568)) (-4 *3 (-969 *7 *5 *4)))) @@ -14697,13 +14539,13 @@ (-12 (-4 *4 (-806)) (-4 *5 (-13 (-862) - (-10 -8 (-15 -4136 ((-1198) $)) - (-15 -2993 ((-3 $ "failed") (-1198)))))) + (-10 -8 (-15 -4148 ((-1198) $)) + (-15 -3032 ((-3 $ "failed") (-1198)))))) (-4 *6 (-317)) (-5 *2 (-430 *3)) (-5 *1 (-743 *4 *5 *6 *3)) (-4 *3 (-969 (-972 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-806)) - (-4 *5 (-13 (-862) (-10 -8 (-15 -4136 ((-1198) $))))) (-4 *6 (-568)) + (-4 *5 (-13 (-862) (-10 -8 (-15 -4148 ((-1198) $))))) (-4 *6 (-568)) (-5 *2 (-430 *3)) (-5 *1 (-745 *4 *5 *6 *3)) (-4 *3 (-969 (-419 (-972 *6)) *4 *5)))) ((*1 *2 *3) @@ -14739,13 +14581,42 @@ ((*1 *2 *1) (-12 (-5 *2 (-430 *1)) (-4 *1 (-1243)))) ((*1 *2 *3) (-12 (-5 *2 (-430 *3)) (-5 *1 (-1254 *3)) (-4 *3 (-1265 (-576)))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1120 *2)) (-4 *2 (-1122))))) -(((*1 *2 *1) (-12 (-4 *1 (-437 *3)) (-4 *3 (-1122)) (-5 *2 (-784))))) -(((*1 *2 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(-1122)) - (-4 *2 (-862))))) + (|partial| -12 (-4 *1 (-1251 *3 *2)) (-4 *3 (-1071)) + (-4 *2 (-1280 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1203))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-702 *4)) (-5 *3 (-941)) (|has| *4 (-6 (-4468 "*"))) + (-4 *4 (-1071)) (-5 *1 (-1050 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-657 (-702 *4))) (-5 *3 (-941)) + (|has| *4 (-6 (-4468 "*"))) (-4 *4 (-1071)) (-5 *1 (-1050 *4))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1294)) (-5 *1 (-835))))) (((*1 *1 *1) (-12 (-4 *1 (-384 *2)) (-4 *2 (-1239)) (-4 *2 (-862)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-384 *3)) (-4 *3 (-1239)))) @@ -14838,25 +14720,8 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1071)) (-4 *5 (-806)) (-4 *3 (-862)) (-4 *6 (-1087 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -2681 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3427 *1) (|:| |upper| *1))) (-4 *1 (-998 *4 *5 *3 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1198)) (-5 *2 (-1 (-1194 (-972 *4)) (-972 *4))) - (-5 *1 (-1297 *4)) (-4 *4 (-374))))) -(((*1 *1 *1 *1) (-5 *1 (-877)))) -(((*1 *1 *1) (-12 (-4 *1 (-1280 *2)) (-4 *2 (-1071))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1194 *1)) (-4 *1 (-464)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-1194 *6)) (-4 *6 (-969 *5 *3 *4)) (-4 *3 (-806)) - (-4 *4 (-862)) (-4 *5 (-929)) (-5 *1 (-469 *3 *4 *5 *6)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-1194 *1)) (-4 *1 (-929))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1071)) (-4 *7 (-1071)) - (-4 *6 (-1265 *5)) (-5 *2 (-1194 (-1194 *7))) - (-5 *1 (-513 *5 *6 *4 *7)) (-4 *4 (-1265 *6))))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-374)) (-5 *1 (-914 *2 *3)) - (-4 *2 (-1265 *3))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-624 *1)) (-4 *1 (-442 *4)) (-4 *4 (-1122)) (-4 *4 (-568)) (-5 *2 (-419 (-1194 *1))))) @@ -14880,113 +14745,71 @@ (-5 *1 (-970 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-374) - (-10 -8 (-15 -3515 ($ *7)) (-15 -1590 (*7 $)) (-15 -1602 (*7 $))))))) + (-10 -8 (-15 -3501 ($ *7)) (-15 -1621 (*7 $)) (-15 -1635 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1194 *3)) (-4 *3 (-13 (-374) - (-10 -8 (-15 -3515 ($ *7)) (-15 -1590 (*7 $)) (-15 -1602 (*7 $))))) + (-10 -8 (-15 -3501 ($ *7)) (-15 -1621 (*7 $)) (-15 -1635 (*7 $))))) (-4 *7 (-969 *6 *5 *4)) (-4 *5 (-806)) (-4 *4 (-862)) (-4 *6 (-1071)) (-5 *1 (-970 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1198)) (-4 *5 (-568)) (-5 *2 (-419 (-1194 (-419 (-972 *5))))) (-5 *1 (-1065 *5)) (-5 *3 (-419 (-972 *5)))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -4228 *6) (|:| |sol?| (-112))) (-576) - *6)) - (-4 *6 (-374)) (-4 *7 (-1265 *6)) - (-5 *2 - (-3 (-2 (|:| |answer| (-419 *7)) (|:| |a0| *6)) - (-2 (|:| -3579 (-419 *7)) (|:| |coeff| (-419 *7))) "failed")) - (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-657 *3)) (-4 *3 (-1265 *5)) (-4 *5 (-317)) - (-5 *2 (-784)) (-5 *1 (-467 *5 *3))))) -(((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-1194 (-972 *4))) (-5 *1 (-428 *3 *4)) - (-4 *3 (-429 *4)))) - ((*1 *2) - (-12 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(-374)) - (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862)) - (-5 *1 (-462 *4 *5 *6 *2)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-374)) - (-5 *2 - (-2 (|:| R (-702 *6)) (|:| A (-702 *6)) (|:| |Ainv| (-702 *6)))) - (-5 *1 (-1000 *6)) (-5 *3 (-702 *6))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-795 *2)) (-4 *2 (-1071))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-289)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-908 *3)) (-4 *3 (-1122)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1306 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1071)) - (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1312 *3 *4)) (-4 *3 (-1071)) - (-4 *4 (-859))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) - (|:| -3936 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (-5 *2 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| 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23262) (-4328 . 23070) (-4329 . 22865) (-4330 . 22692) + (-4331 . 22560) (-4332 . 22439) (-4333 . 22360) (-4334 . 22081) + (-4335 . 22011) (-4336 . 21983) (-4337 . 21896) (-4338 . 21769) + (-4339 . 21706) (-4340 . 21564) (-4341 . 21469) (-4342 . 21127) + (-4343 . 19946) (-4344 . 19727) (-4345 . 19412) (-4346 . 19341) + (-4347 . 19196) (-4348 . 19144) (-4349 . 19050) (-4350 . 19022) + (-4351 . 18939) (-4352 . 18887) (-4353 . 18676) (-4354 . 18593) + (-4355 . 18329) (-4356 . 18269) (-4357 . 18161) (-4358 . 18076) + (-4359 . 17542) (-4360 . 17471) (-4361 . 17374) (-4362 . 17317) + (-4363 . 17209) (-4364 . 17092) (-4365 . 16565) (-4366 . 16477) + (-4367 . 16424) (-4368 . 16393) (-4369 . 16183) (-4370 . 16124) + (-4371 . 16056) (-4372 . 15982) (-4373 . 15911) (-4374 . 15720) + (-4375 . 15511) (-4376 . 15407) (-4377 . 15348) (-4378 . 15262) + (-4379 . 15159) (-4380 . 15127) (-4381 . 15031) (-4382 . 14894) + (-4383 . 14833) (-4384 . 14732) (-4385 . 14592) (-4386 . 14539) + (-4387 . 14490) 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