diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1332 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9090 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29401 |
5 files changed, 21016 insertions, 21017 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 20032c16..47c3fa92 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2296269 . 3487271630) +(2296269 . 3487768761) (-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 -2163) +(-32 R -2189) ((|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 -1063) (QUOTE (-577))))) @@ -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 -2163 UP UPUP -1876) +(-40 -2189 UP UPUP -4349) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-3777 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-3777 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-3777 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-3777 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-3777 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -654) (QUOTE (-577)))) (-3777 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) -(-41 R -2163) +((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-3700 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-3700 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-3700 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-3700 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-3700 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -654) (QUOTE (-577)))) (-3700 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) +(-41 R -2189) ((|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 (-465))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -443) (|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."))) ((-4470 . T) (-4471 . T)) -((-3777 (-12 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#2|))))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-865))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#2|))))))) +((-3700 (-12 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2909) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2909) (|devaluate| |#2|))))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-865))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2909) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2163) +(-54 |Base| R -2189) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -4138) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4103) ((|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 -4138) +(-62 -4103) ((|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 -4138) +(-63 -4103) ((|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 -4138) +(-64 -4103) ((|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 -4138) +(-65 -4103) ((|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 -4138) +(-66 -4103) ((|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 -4138) +(-67 -4103) ((|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 -4138) +(-68 -4103) ((|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 -4138) +(-69 -4103) ((|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 -4138) +(-70 -4103) ((|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 -4138) +(-71 -4103) ((|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 -4138) +(-72 -4103) ((|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 -4138) +(-73 -4103) ((|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 -4138) +(-74 -4103) ((|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 -4138) +(-77 -4103) ((|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 -4138) +(-78 -4103) ((|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 -4138) +(-79 -4103) ((|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 -4138) +(-80 -4103) ((|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 -4138) +(-81 -4103) ((|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 -4138) +(-82 -4103) ((|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 -4138) +(-83 -4103) ((|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 -4138) +(-84 -4103) ((|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 -4138) +(-85 -4103) ((|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 -4138) +(-86 -4103) ((|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 -4138) +(-87 -4103) ((|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 -4138) +(-88 -4103) ((|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 -4138) +(-89 -4103) ((|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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-3777 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) +((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-3700 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (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 -2163 UP) +(-116 -2189 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}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-932))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-117 |#1|) (QUOTE (-1047))) (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865))) (-3777 (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-1177))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-318))) (|HasCategory| (-117 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-932))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-117 |#1|) (QUOTE (-1047))) (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865))) (-3700 (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-1177))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-318))) (|HasCategory| (-117 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (|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"))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|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."))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) (-3777 (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-130) (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-130) (QUOTE (-865))) (-3777 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) +((-3700 (-12 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) (-3700 (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-130) (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-130) (QUOTE (-865))) (-3700 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4472 "*") . T)) NIL -(-136 |minix| -1388 S T$) +(-136 |minix| -2608 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -1388 R) +(-137 |minix| -2608 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) ((-4470 . T) (-4460 . T) (-4471 . T)) -((-3777 (-12 (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) +((-3700 (-12 (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (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."))) ((-4467 . T)) NIL -(-149 -2163 UP UPUP) +(-149 -2189 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 -2163) +(-159 R -2189) ((|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 (-932))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4466)) (|HasAttribute| |#2| (QUOTE -4469)) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569)))) (-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})"))) -((-4463 -3777 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-2667 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4463 -3700 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-2684 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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}."))) -((-4463 -3777 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-2667 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-3700 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-361)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-932))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-932)))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-932))))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-569)))) (-3700 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1085))) (-12 (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-238)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasAttribute| |#1| (QUOTE -4466)) (|HasAttribute| |#1| (QUOTE -4469)) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-361))))) (-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| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -2163) +(-190 R -2189) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -800,23 +800,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-218 -2163 UP UPUP R) +(-218 -2189 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 -(-219 -2163 FP) +(-219 -2189 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 (-220) ((|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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-3777 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) +((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-3700 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) (-221) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-222 R -2163) +(-222 R -2189) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -831,18 +831,18 @@ NIL (-225 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-226 |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}."))) ((-4467 . T)) NIL -(-227 R -2163) +(-227 R -2189) ((|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 (-228) ((|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}."))) -((-2659 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-2676 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-229) ((|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)}.}"))) @@ -851,7 +851,7 @@ NIL (-230 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}"))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-231 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 @@ -900,22 +900,22 @@ 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 -(-243 S -1388 R) +(-243 S -2608 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 (-375))) (|HasCategory| |#3| (QUOTE (-809))) (|HasCategory| |#3| (QUOTE (-865))) (|HasAttribute| |#3| (QUOTE -4467)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (QUOTE (-742))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (QUOTE (-1125)))) -(-244 -1388 R) +(-244 -2608 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"))) ((-4464 |has| |#2| (-1074)) (-4465 |has| |#2| (-1074)) (-4467 |has| |#2| (-6 -4467)) (-4470 . T)) NIL -(-245 -1388 A B) +(-245 -2608 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 -(-246 -1388 R) +(-246 -2608 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."))) ((-4464 |has| |#2| (-1074)) (-4465 |has| |#2| (-1074)) (-4467 |has| |#2| (-6 -4467)) (-4470 . 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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 @@ -935,7 +935,7 @@ NIL (-251 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}"))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-252 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 @@ -947,7 +947,7 @@ NIL (-254 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall| (|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 @@ -1027,7 +1027,7 @@ NIL (-274 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"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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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 @@ -1072,11 +1072,11 @@ 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 -(-286 R -2163) +(-286 R -2189) ((|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 -(-287 R -2163) +(-287 R -2189) ((|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 @@ -1128,7 +1128,7 @@ 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 -(-300 S R |Mod| -1941 -3572 |exactQuo|) +(-300 S R |Mod| -3714 -4428 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL @@ -1150,21 +1150,21 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4470 . T) (-4471 . 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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 -(-308 -2163 S) +(-308 -2189 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 -(-309 E -2163) +(-309 E -2189) ((|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 @@ -1212,7 +1212,7 @@ 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 -(-321 -2163) +(-321 -2189) ((|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 @@ -1227,7 +1227,7 @@ NIL (-324 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))}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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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 @@ -1238,9 +1238,9 @@ NIL NIL (-327 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."))) -((-4467 -3777 (-12 (|has| |#1| (-569)) (-3777 (|has| |#1| (-1074)) (|has| |#1| (-486)))) (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) ((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-569)) (-4462 |has| |#1| (-569))) -((-3777 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) 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(QUOTE -654) (QUOTE (-577)))))) (-3700 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1137)))) (-3700 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))))) (-3700 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-1074)))) (-3700 (-12 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1137))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) +(-328 R -2189) ((|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 @@ -1251,7 +1251,7 @@ NIL (-330 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."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . 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(|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 @@ -1283,12 +1283,12 @@ NIL (-338 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."))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-339 S -2163) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-339 S -2189) ((|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 (-380)))) -(-340 -2163) +(-340 -2189) ((|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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL @@ -1312,15 +1312,15 @@ 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 -(-346 S -2163 UP UPUP R) +(-346 S -2189 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 -(-347 -2163 UP UPUP R) +(-347 -2189 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 -(-348 -2163 UP UPUP R) +(-348 -2189 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 @@ -1340,26 +1340,26 @@ 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 -(-353 S -2163 UP UPUP) +(-353 S -2189 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 (-380))) (|HasCategory| |#2| (QUOTE (-375)))) -(-354 -2163 UP UPUP) +(-354 -2189 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."))) ((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-355 |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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) +((-3700 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) (-356 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3700 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3700 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-358 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 @@ -1376,31 +1376,31 @@ 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL -(-362 R UP -2163) +(-362 R UP -2189) ((|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 (-363 |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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) +((-3700 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) (-364 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3700 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3700 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-366 |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}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) +((-3700 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) (-367 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) -(-368 -2163 GF) +((-3700 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +(-368 -2189 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 @@ -1408,14 +1408,14 @@ 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 -(-370 -2163 FP FPP) +(-370 -2189 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 (-371 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}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3700 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-372 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 @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4453 . T) (-4461 . T) (-2659 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4453 . T) (-4461 . T) (-2676 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-392 |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}."))) @@ -1548,7 +1548,7 @@ 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 -(-405 -2163 UP UPUP R) +(-405 -2189 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 @@ -1572,11 +1572,11 @@ 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 -(-411 -4138 |returnType| -3189 |symbols|) +(-411 -4103 |returnType| -3175 |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 -(-412 -2163 UP) +(-412 -2189 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1598,7 +1598,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4453)) (|HasAttribute| |#1| (QUOTE -4461))) (-417) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-2659 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-2676 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-418 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."))) @@ -1611,7 +1611,7 @@ NIL (-420 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."))) ((-4457 -12 (|has| |#1| (-6 -4468)) (|has| |#1| (-465)) (|has| |#1| (-6 -4457))) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-865)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844))))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-558))) (-12 (|HasAttribute| |#1| (QUOTE -4468)) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-465)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-865)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844))))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-558))) (-12 (|HasAttribute| |#1| (QUOTE -4468)) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-465)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) (-421 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1632,11 +1632,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-426 R -2163 UP A) +(-426 R -2189 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4467 . T)) NIL -(-427 R -2163 UP A |ibasis|) +(-427 R -2189 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 -1063) (|devaluate| |#2|)))) @@ -1655,7 +1655,7 @@ NIL (-431 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."))) ((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -320) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -297) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1246))) (-3777 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1246)))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-465)))) +((|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -320) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -297) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1246))) (-3700 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1246)))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-465)))) (-432 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 @@ -1684,7 +1684,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4470 . T) (-4460 . T) (-4471 . T)) NIL -(-439 R -2163) +(-439 R -2189) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1692,7 +1692,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4457 -12 (|has| |#1| (-6 -4457)) (|has| |#2| (-6 -4457))) (-4464 . T) (-4465 . T) (-4467 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4457)) (|HasAttribute| |#2| (QUOTE -4457)))) -(-441 R -2163) +(-441 R -2189) ((|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 @@ -1702,17 +1702,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-1137))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (-443 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}."))) -((-4467 -3777 (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) ((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-569)) (-4462 |has| |#1| (-569))) +((-4467 -3700 (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) ((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-569)) (-4462 |has| |#1| (-569))) NIL -(-444 R -2163) +(-444 R -2189) ((|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 -(-445 R -2163) +(-445 R -2189) ((|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)))) -(-446 R -2163) +(-446 R -2189) ((|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 @@ -1720,7 +1720,7 @@ 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 -(-448 R -2163 UP) +(-448 R -2189 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 -1063) (QUOTE (-48))))) @@ -1752,7 +1752,7 @@ 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 -(-456 R UP -2163) +(-456 R UP -2189) ((|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 @@ -1799,7 +1799,7 @@ NIL (-467 |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"))) (((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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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 @@ -1864,7 +1864,7 @@ 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 -(-484 |lv| -2163 R) +(-484 |lv| -2189 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 @@ -1879,11 +1879,11 @@ NIL (-487 |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.") 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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)}"))) ((-4471 . T) (-4470 . T)) @@ -1899,7 +1899,7 @@ NIL (-492 |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."))) ((-4470 . T) (-4471 . 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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 @@ -1907,11 +1907,11 @@ NIL (-494 |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 @@ -1919,8 +1919,8 @@ NIL (-497 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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-498 -2163 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-498 -2189 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 @@ -1931,7 +1931,7 @@ NIL (-500) ((|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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1956,7 +1956,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-507 -2163 UP |AlExt| |AlPol|) +(-507 -2189 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 @@ -1967,16 +1967,16 @@ NIL (-509 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-510 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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-511 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 -(-512 R UP -2163) +(-512 R UP -2189) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1996,7 +1996,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-517 -2163 |Expon| |VarSet| |DPoly|) +(-517 -2189 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -627) (QUOTE (-1201))))) @@ -2047,7 +2047,7 @@ NIL (-529 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-530) ((|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 @@ -2055,15 +2055,15 @@ NIL (-531 |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}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-3777 (|HasCategory| (-594 |#1|) (QUOTE (-146))) (|HasCategory| (-594 |#1|) (QUOTE (-380)))) (|HasCategory| (-594 |#1|) (QUOTE (-148))) (|HasCategory| (-594 |#1|) (QUOTE (-380))) (|HasCategory| (-594 |#1|) (QUOTE (-146)))) +((-3700 (|HasCategory| (-594 |#1|) (QUOTE (-146))) (|HasCategory| (-594 |#1|) (QUOTE (-380)))) (|HasCategory| (-594 |#1|) (QUOTE (-148))) (|HasCategory| (-594 |#1|) (QUOTE (-380))) (|HasCategory| (-594 |#1|) (QUOTE (-146)))) (-532 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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-533 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."))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-534 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 @@ -2075,7 +2075,7 @@ NIL (-536 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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-537) ((|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 @@ -2108,7 +2108,7 @@ 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| (-787) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125))))) -(-545 K -2163 |Par|) +(-545 K -2189 |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 @@ -2132,7 +2132,7 @@ 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 -(-551 K -2163 |Par|) +(-551 K -2189 |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 @@ -2183,12 +2183,12 @@ NIL (-563 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#2|)))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102)))) -(-564 R -2163) +((-12 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2909) (|devaluate| |#2|)))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102)))) +(-564 R -2189) ((|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 -(-565 R0 -2163 UP UPUP R) +(-565 R0 -2189 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 @@ -2198,7 +2198,7 @@ NIL NIL (-567 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."))) -((-2659 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-2676 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-568 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."))) @@ -2208,7 +2208,7 @@ 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."))) ((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL -(-570 R -2163) +(-570 R -2189) ((|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 @@ -2220,7 +2220,7 @@ 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 -(-573 R -2163 L) +(-573 R -2189 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 -672) (|devaluate| |#2|)))) @@ -2228,11 +2228,11 @@ 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 -(-575 -2163 UP UPUP R) +(-575 -2189 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 -(-576 -2163 UP) +(-576 -2189 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 @@ -2244,15 +2244,15 @@ 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 -(-579 R -2163 L) +(-579 R -2189 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 -672) (|devaluate| |#2|)))) -(-580 R -2163) +(-580 R -2189) ((|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 -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1164)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-642))))) -(-581 -2163 UP) +(-581 -2189 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 @@ -2260,27 +2260,27 @@ 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 -(-583 -2163) +(-583 -2189) ((|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 (-584 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."))) -((-2659 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-2676 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-585) ((|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 -(-586 R -2163) +(-586 R -2189) ((|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 -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-295))) (|HasCategory| |#2| (QUOTE (-642))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-295)))) (|HasCategory| |#1| (QUOTE (-569)))) -(-587 -2163 UP) +(-587 -2189 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 -(-588 R -2163) +(-588 R -2189) ((|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 @@ -2312,11 +2312,11 @@ 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 -(-596 R -2163) +(-596 R -2189) ((|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 -(-597 E -2163) +(-597 E -2189) ((|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 @@ -2324,7 +2324,7 @@ 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 -(-599 -2163) +(-599 -2189) ((|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}."))) ((-4465 . T) (-4464 . T)) ((|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-1201))))) @@ -2355,7 +2355,7 @@ NIL (-606 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-3777 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-3777 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) +((-3700 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-3700 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-3700 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-607 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 @@ -2363,7 +2363,7 @@ NIL (-608 |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}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|)))) (|HasCategory| (-577) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|)))) (|HasCategory| (-577) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4070) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577)))))) (-609 |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.}"))) (((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) @@ -2380,7 +2380,7 @@ 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 -(-613 R -2163 FG) +(-613 R -2189 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 @@ -2391,7 +2391,7 @@ NIL (-615 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-616 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,12 +2410,12 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4467 -3777 (-2342 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) -((-3777 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) +((-4467 -3700 (-2361 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) +((-3700 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-621 |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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| (-1183) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2909) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| (-1183) (QUOTE (-865))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (QUOTE (-102)))) (-622 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 @@ -2440,7 +2440,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-628 -2163 UP) +(-628 -2189 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2468,7 +2468,7 @@ 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}."))) ((-4464 . T) (-4465 . T) (-4467 . T)) ((|HasCategory| |#1| (QUOTE (-864)))) -(-635 R -2163) +(-635 R -2189) ((|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 @@ -2500,18 +2500,18 @@ 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 -(-643 R -2163) +(-643 R -2189) ((|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 -(-644 |lv| -2163) +(-644 |lv| -2189) ((|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 (-645) ((|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."))) ((-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2328) (QUOTE (-52))))))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-1183) (QUOTE (-865))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (QUOTE (-1125)))) +((-12 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2909) (QUOTE (-52))))))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-1183) (QUOTE (-865))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (QUOTE (-1125)))) (-646 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2522,8 +2522,8 @@ NIL NIL (-648 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4467 -3777 (-2342 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) -((-3777 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) +((-4467 -3700 (-2361 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) +((-3700 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-649 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 @@ -2539,7 +2539,7 @@ NIL (-652 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 -((-2332 (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-375)))) +((-2352 (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-375)))) (-653 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) ((-4465 . T) (-4464 . T)) @@ -2571,7 +2571,7 @@ NIL (-660 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."))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-661 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2583,7 +2583,7 @@ NIL (-663 S) ((|substitute| (($ |#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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-664 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 @@ -2600,7 +2600,7 @@ 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 -(-668 R -2163 L) +(-668 R -2189 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 @@ -2620,11 +2620,11 @@ 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}."))) ((-4464 . T) (-4465 . T) (-4467 . T)) NIL -(-673 -2163 UP) +(-673 -2189 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)))) -(-674 A -1571) +(-674 A -4367) ((|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}}"))) ((-4464 . T) (-4465 . T) (-4467 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) @@ -2660,11 +2660,11 @@ 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}."))) ((-4471 . T) (-4470 . T)) NIL -(-683 -2163) +(-683 -2189) ((|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 -(-684 -2163 |Row| |Col| M) +(-684 -2189 |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 @@ -2675,7 +2675,7 @@ NIL (-686 |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."))) ((-4467 . T) (-4470 . T) (-4464 . T) (-4465 . T)) -((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569))) (-3777 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569))) (-3700 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-687) ((|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 @@ -2695,7 +2695,7 @@ NIL (-691 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 -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-692) ((|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 @@ -2751,7 +2751,7 @@ NIL (-705 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."))) ((-4470 . T) (-4471 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-706 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 @@ -2760,7 +2760,7 @@ 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 -(-708 S -2163 FLAF FLAS) +(-708 S -2189 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}.")) 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T) (-4469 |has| (-715) (-6 -4469)) (-4466 |has| (-715) (-6 -4466)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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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}."))) ((-4471 . T)) @@ -2784,13 +2784,13 @@ 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 (-715) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2659 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-2676 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-716 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."))) @@ -2816,7 +2816,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-722 S -2562 I) +(-722 S -2620 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2836,14 +2836,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-727 R |Mod| -1941 -3572 |exactQuo|) +(-727 R |Mod| -3714 -4428 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-728 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4466 |has| |#1| (-375)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) (-729 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2852,7 +2852,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-731 R |Mod| -1941 -3572 |exactQuo|) +(-731 R |Mod| -3714 -4428 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4467 . T)) NIL @@ -2864,7 +2864,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4465 . T) (-4464 . T)) NIL -(-734 -2163) +(-734 -2189) ((|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]]}."))) ((-4467 . T)) NIL @@ -2900,7 +2900,7 @@ 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 -(-743 -2163 UP) +(-743 -2189 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 @@ -2919,7 +2919,7 @@ NIL (-747 |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."))) (((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-932))) (-3777 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-3777 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-3777 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-3777 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-932))) (-3700 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-3700 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-3700 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-3700 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) (-748 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 @@ -3052,11 +3052,11 @@ 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 -(-781 -2163) +(-781 -2189) ((|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 -(-782 P -2163) +(-782 P -2189) ((|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 @@ -3064,7 +3064,7 @@ NIL NIL NIL NIL -(-784 UP -2163) +(-784 UP -2189) ((|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 @@ -3080,7 +3080,7 @@ 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."))) (((-4472 "*") . T)) NIL -(-788 R -2163) +(-788 R -2189) ((|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 @@ -3100,7 +3100,7 @@ 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 -(-793 -2163 |ExtF| |SUEx| |ExtP| |n|) +(-793 -2189 |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 @@ -3115,7 +3115,7 @@ NIL (-796 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."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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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 @@ -3123,7 +3123,7 @@ NIL (-798 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| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4466 |has| |#1| (-375)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3184,23 +3184,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4464 . T) (-4465 . T) (-4467 . T)) NIL -(-814 -3777 R OS S) +(-814 -3700 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-815 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-3777 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (-3777 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-3700 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (-3700 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (-816) ((|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 -(-817 R -2163 L) +(-817 R -2189 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 -(-818 R -2163) +(-818 R -2189) ((|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 @@ -3208,7 +3208,7 @@ 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 -(-820 R -2163) +(-820 R -2189) ((|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 @@ -3216,11 +3216,11 @@ 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 -(-822 -2163 UP UPUP R) +(-822 -2189 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 -(-823 -2163 UP L LQ) +(-823 -2189 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 @@ -3228,38 +3228,38 @@ 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 -(-825 -2163 UP L LQ) +(-825 -2189 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 -(-826 -2163 UP) +(-826 -2189 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 -(-827 -2163 L UP A LO) +(-827 -2189 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 -(-828 -2163 UP) +(-828 -2189 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)))) -(-829 -2163 LO) +(-829 -2189 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}.") 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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(((-4472 "*") |has| |#2| (-375)) (-4463 |has| |#2| (-375)) (-4468 |has| |#2| (-375)) (-4462 |has| |#2| (-375)) (-4467 . T) (-4465 . T) (-4464 . T)) @@ -3327,7 +3327,7 @@ NIL (-849 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."))) ((-4467 |has| |#1| (-864))) -((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-3777 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-3777 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) +((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-3700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-3700 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) (-850 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 @@ -3367,12 +3367,12 @@ NIL (-859 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4467 |has| |#1| (-864))) -((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-3777 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-3777 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) +((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-3700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-3700 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) (-860) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-861 -1388 S) +(-861 -2608 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 @@ -3416,11 +3416,11 @@ 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 (-375))) (|HasCategory| |#1| (QUOTE (-569)))) -(-872 R |sigma| -2028) +(-872 R |sigma| -1847) ((|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."))) ((-4464 . T) (-4465 . T) (-4467 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) -(-873 |x| R |sigma| -2028) +(-873 |x| R |sigma| -1847) ((|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}."))) ((-4464 . T) (-4465 . T) (-4467 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-375)))) @@ -3487,15 +3487,15 @@ NIL (-889 |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)."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-888 |#1|) (QUOTE (-932))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-148))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-888 |#1|) (QUOTE (-1047))) (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865))) (-3777 (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-1177))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-238))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-239))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -888) (|devaluate| |#1|)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (QUOTE (-318))) (|HasCategory| (-888 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))))) +((|HasCategory| (-888 |#1|) (QUOTE (-932))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-148))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-888 |#1|) (QUOTE (-1047))) (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865))) (-3700 (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-1177))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-238))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-239))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -888) (|devaluate| |#1|)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (QUOTE (-318))) (|HasCategory| (-888 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))))) (-890 |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)}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865))) (-3777 (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865))) (-3700 (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) (-891 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 (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) (-892) ((|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 @@ -3555,7 +3555,7 @@ NIL (-906 |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 (-2332 (|HasCategory| |#2| (QUOTE (-1074)))) (-2332 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (-2332 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) +((-12 (-2352 (|HasCategory| |#2| (QUOTE (-1074)))) (-2352 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (-2352 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) (-907 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 @@ -3564,7 +3564,7 @@ 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 -(-909 R -2562) +(-909 R -2620) ((|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 @@ -3596,7 +3596,7 @@ 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 -(-917 UP -2163) +(-917 UP -2189) ((|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 @@ -3627,7 +3627,7 @@ NIL (-924 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 (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-925 |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 @@ -3643,7 +3643,7 @@ NIL (-928 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."))) ((-4467 . T)) -((-3777 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) +((-3700 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) (-929 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 @@ -3664,7 +3664,7 @@ 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."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-380)))) -(-934 R0 -2163 UP UPUP R) +(-934 R0 -2189 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 @@ -3692,7 +3692,7 @@ 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 -(-941 -2163) +(-941 -2189) ((|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 @@ -3708,11 +3708,11 @@ 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}."))) (((-4472 "*") . T)) NIL -(-945 -2163 P) +(-945 -2189 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-946 |xx| -2163) +(-946 |xx| -2189) ((|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 @@ -3736,7 +3736,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-952 R -2163) +(-952 R -2189) ((|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 @@ -3748,7 +3748,7 @@ 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 -(-955 S R -2163) +(-955 S R -2189) ((|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 @@ -3768,11 +3768,11 @@ 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 -905) (|devaluate| |#1|)))) -(-960 R -2163 -2562) +(-960 R -2189 -2620) ((|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 -(-961 -2562) +(-961 -2620) ((|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 @@ -3795,7 +3795,7 @@ NIL (-966 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-967 |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 @@ -3820,7 +3820,7 @@ 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}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) NIL -(-973 E V R P -2163) +(-973 E V R P -2189) ((|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 @@ -3831,8 +3831,8 @@ NIL (-975 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-976 E V R P -2163) +((|HasCategory| |#1| (QUOTE (-932))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-976 E V R P -2189) ((|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 (-465)))) @@ -3855,12 +3855,12 @@ NIL (-981 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"))) ((-4471 . T) (-4470 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-982) ((|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 -(-983 -2163) +(-983 -2189) ((|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 @@ -3875,11 +3875,11 @@ NIL (-986 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}"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4468))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4468))) (-987 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"))) ((-4467 -12 (|has| |#2| (-486)) (|has| |#1| (-486)))) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-809))) (|HasCategory| |#2| (QUOTE (-809)))) (-12 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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 @@ -3968,7 +3968,7 @@ 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 -(-1010 K R UP -2163) +(-1010 K R UP -2189) ((|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 @@ -4027,11 +4027,11 @@ NIL (-1024 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.}"))) ((-4463 |has| |#1| (-301)) (-4464 . T) (-4465 . T) (-4467 . 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((-4470 . T) (-4471 . 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(** (($ $ (|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4040,14 +4040,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1028 -2163 UP UPUP |radicnd| |n|) +(-1028 -2189 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . 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(|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-3777 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) +((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-3700 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) (-1030) ((|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 @@ -4080,19 +4080,19 @@ 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}}"))) ((-4463 . T) (-4468 . T) (-4462 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4467 . T)) NIL -(-1038 R -2163) +(-1038 R -2189) ((|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 -(-1039 R -2163) +(-1039 R -2189) ((|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 -(-1040 -2163 UP) +(-1040 -2189 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 -(-1041 -2163 UP) +(-1041 -2189 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 @@ -4127,8 +4127,8 @@ NIL (-1049 |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"))) ((-4463 . T) (-4468 . T) (-4462 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4467 . T)) -((-3777 (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577))))) -(-1050 -2163 L) +((-3700 (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577))))) +(-1050 -2189 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 @@ -4164,14 +4164,14 @@ 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 -(-1059 -2163 |Expon| |VarSet| |FPol| |LFPol|) +(-1059 -2189 |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"))) (((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL (-1060) ((|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.}"))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -2328) (QUOTE (-52))))))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -2909) (QUOTE (-52))))))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-102)))) (-1061) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4228,7 +4228,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4467 . T)) NIL -(-1075 |xx| -2163) +(-1075 |xx| -2189) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4247,7 +4247,7 @@ NIL (-1079 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4470 . T) (-4465 . T) (-4464 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-3777 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375)))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-880))))) +((|HasCategory| |#3| (QUOTE (-174))) (-3700 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375)))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-880))))) (-1080 |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 @@ -4283,7 +4283,7 @@ NIL (-1088) ((|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}"))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -2328) (QUOTE (-52))))))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-3777 (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -2909) (QUOTE (-52))))))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-3700 (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (QUOTE (-102)))) (-1089 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 @@ -4332,11 +4332,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1101 |Base| R -2163) +(-1101 |Base| R -2189) ((|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 -(-1102 |Base| R -2163) +(-1102 |Base| R -2189) ((|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 @@ -4351,7 +4351,7 @@ NIL (-1105 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."))) ((-4463 |has| |#1| (-375)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-3777 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (-1106 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 @@ -4379,7 +4379,7 @@ NIL (-1112 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"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4439,7 +4439,7 @@ NIL (-1127 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)}}"))) ((-4470 . T) (-4460 . T) (-4471 . T)) -((-3777 (-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-3700 (-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-1128 |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 ().")) 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(-577))))) (-12 (|HasCategory| |#3| (QUOTE (-865))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))))) (|HasCategory| (-577) (QUOTE (-865))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1074)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -923) (QUOTE (-1201))))) (-3700 (|HasCategory| |#3| (QUOTE (-1074))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-1125)))) (|HasAttribute| |#3| (QUOTE -4467)) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1074)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -921) (QUOTE (-1201))))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) (-1139 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 @@ -4492,7 +4492,7 @@ 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 -(-1141 R -2163) +(-1141 R -2189) ((|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 @@ -4531,16 +4531,16 @@ NIL (-1150 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."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3777 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-932))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-3700 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1151 |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}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) (-1152 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}"))) ((-4471 . T) (-4470 . T)) NIL -(-1153 UP -2163) +(-1153 UP -2189) ((|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 @@ -4595,11 +4595,11 @@ NIL (-1166 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."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))) (-3777 (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (-3777 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))))) (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))) (-3700 (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (-3700 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))))) (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102)))) (-1167 |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}."))) ((-4467 . T) (-4459 |has| |#2| (-6 (-4472 "*"))) (-4470 . T) (-4464 . T) (-4465 . T)) -((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3777 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (-3777 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-3700 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (-3700 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1168 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4619,7 +4619,7 @@ NIL (-1172 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1173 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 @@ -4631,7 +4631,7 @@ NIL (-1175 |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."))) ((-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#2|)))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-865))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125)))) +((-12 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2909) (|devaluate| |#2|)))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-865))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125)))) (-1176) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4659,15 +4659,15 @@ NIL (-1182 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) ((-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1183) ((|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"))) ((-4471 . 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T)) -((-3777 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-3777 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-3777 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-3777 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) +((-3700 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-3700 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-3700 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-3700 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-1184 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 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 @@ -4698,9 +4698,9 @@ NIL NIL (-1192 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4719,15 +4719,15 @@ NIL (-1197 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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We may integrate a series when we can divide coefficients by integers."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . 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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}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-3777 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4230) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -4181) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -4070) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-3700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4439) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2240) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) (-1200) ((|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 @@ -4743,7 +4743,7 @@ NIL (-1203 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3777 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| (-996) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasAttribute| |#1| (QUOTE -4468))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| (-996) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasAttribute| |#1| (QUOTE -4468))) (-1204) ((|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 @@ -4787,7 +4787,7 @@ NIL (-1214 |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}"))) ((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2284) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2328) (|devaluate| |#2|)))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-3777 (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2909) (|devaluate| |#2|)))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-3700 (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (QUOTE (-102)))) (-1215 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 @@ -4843,7 +4843,7 @@ NIL (-1228 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3777 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3777 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-3700 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-3700 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1229 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4852,7 +4852,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1231 R -2163) +(-1231 R -2189) ((|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 @@ -4860,7 +4860,7 @@ 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 -(-1233 R -2163) +(-1233 R -2189) ((|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 -627) (LIST (QUOTE -911) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -905) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -905) (|devaluate| |#1|))))) @@ -4875,7 +4875,7 @@ NIL (-1236 |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}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) (-1237 |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 @@ -4888,7 +4888,7 @@ 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 (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) -(-1240 -2163) +(-1240 -2189) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4951,11 +4951,11 @@ NIL (-1255 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4991,7 +4991,7 @@ NIL (-1265 |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}"))) (((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4466 |has| |#2| (-375)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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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 @@ -5007,7 +5007,7 @@ NIL (-1269 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 -921) (QUOTE (-1201)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1137))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4100) (LIST (|devaluate| |#2|) (QUOTE (-1201)))))) +((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1137))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4070) (LIST (|devaluate| |#2|) (QUOTE (-1201)))))) (-1270 |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."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) @@ -5035,15 +5035,15 @@ NIL (-1276 |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)}."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-3777 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-3777 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4230) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -4181) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) +((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -4070) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-3700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4439) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2240) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-1277 |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."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-3777 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-3777 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4230) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -4181) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-3700 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -4070) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-3700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4439) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2240) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) (-1278 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))}."))) (((-4472 "*") |has| (-1277 |#2| |#3| |#4|) (-174)) (-4463 |has| (-1277 |#2| |#3| |#4|) (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-174))) (-3777 (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-375))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-465))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-569)))) +((|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-174))) (-3700 (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-375))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-465))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-569)))) (-1279 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5059,7 +5059,7 @@ NIL (-1282 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-577)))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasSignature| |#2| (LIST (QUOTE -4181) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4230) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1201))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasSignature| |#2| (LIST (QUOTE -2240) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4439) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1201))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375)))) (-1283 |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."))) (((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) @@ -5067,12 +5067,12 @@ NIL (-1284 |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}."))) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3777 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-3777 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4230) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -4181) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-3700 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -4070) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-3700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4439) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2240) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) (-1285 |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 -(-1286 -2163 UP L UTS) +(-1286 -2189 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 (-569)))) @@ -5099,7 +5099,7 @@ NIL (-1292 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."))) ((-4471 . T) (-4470 . 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(|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 @@ -5132,7 +5132,7 @@ 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 -(-1301 K R UP -2163) +(-1301 K R UP -2189) ((|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 @@ -5168,11 +5168,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) NIL -(-1310 S -2163) +(-1310 S -2189) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1311 -2163) +(-1311 -2189) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 0a3c7632..088b86e8 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205510 . 3487271636) -(((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((#0=(-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) #0#) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))))) -((((-577)) . T) (($) -3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T)) +(205510 . 3487768768) +(((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((#0=(-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) #0#) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))))) +((((-577)) . T) (($) -3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-577)) . T)) -((($ $) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2| |#2|) . T) ((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577))))) +((($ $) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2| |#2|) . T) ((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-577)) |has| |#1| (-654 (-577))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#2|) . T)) -((($) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2|) . T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) +((($) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2|) . T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) (|has| |#1| (-932)) ((((-880)) . T)) ((((-880)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1183)) . T) (((-228)) . T) (((-391)) . T) (((-911 (-391))) . T)) (((|#1|) . T)) ((((-228)) . T) (((-880)) . T)) -(-3777 (|has| |#2| (-809)) (|has| |#2| (-865))) -(-3777 (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) (-12 (|has| |#1| (-865)) (|has| |#2| (-865)))) +(-3700 (|has| |#2| (-809)) (|has| |#2| (-865))) +(-3700 (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) (-12 (|has| |#1| (-865)) (|has| |#2| (-865)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) -((($ $) . T) ((#0=(-420 (-577)) #0#) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1| |#1|) . 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T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1206)) . T)) (((|#1|) . T) (((-577)) |has| |#1| (-1063 (-577))) (((-420 (-577))) |has| |#1| (-1063 (-420 (-577))))) -(-3777 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) -(((|#2| (-495 (-2021 |#1|) (-787))) . T)) -((((-1201)) -3777 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) +(-3700 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(((|#2| (-495 (-2014 |#1|) (-787))) . T)) +((((-1201)) -3700 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) (((|#1| (-544 (-1201))) . T)) ((((-1183)) . T) (((-981 (-130))) . T) (((-880)) . T)) ((((-880)) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((#0=(-888 |#1|) #0#) . T) ((#1=(-420 (-577)) #1#) . T) (($ $) . T)) (|has| |#4| (-380)) (|has| |#3| (-380)) @@ -75,14 +75,14 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-569)) -((((-577)) . T) (((-420 (-577))) -3777 (|has| |#2| (-38 (-420 (-577)))) (|has| |#2| (-1063 (-420 (-577))))) ((|#2|) . T) (($) -3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((-882 |#1|)) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) -((((-2 (|:| -2433 |#1|) (|:| -3163 |#2|))) . T)) +((((-577)) . T) (((-420 (-577))) -3700 (|has| |#2| (-38 (-420 (-577)))) (|has| |#2| (-1063 (-420 (-577))))) ((|#2|) . T) (($) -3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((-882 |#1|)) . T)) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) +((((-2 (|:| -2493 |#1|) (|:| -2844 |#2|))) . T)) ((($) . T)) ((((-880)) |has| |#1| (-626 (-880))) ((|#1|) . T)) -((((-577)) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T) (($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (((-1201)) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) +((((-577)) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T) (($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (((-1201)) . T)) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) ((((-549)) |has| |#1| (-627 (-549)))) ((((-1201)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-880)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577)))) ((|#2| |#2|) . T) (($ $) -3777 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) +(((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577)))) ((|#2| |#2|) . 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T) (($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) +((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) +(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . T) (($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) ((($ $) . T)) ((($) . T)) ((((-577)) . T) (($) . T) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) @@ -132,30 +132,30 @@ (|has| |#1| (-380)) (((|#1|) . T)) ((((-880)) . T)) -((((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) (($) . T) ((|#1|) . T)) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) -(((|#1|) . 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T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) (|has| |#1| (-1125)) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) (|has| |#1| (-1125)) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) (|has| |#1| (-864)) (((|#1| |#1|) . T)) ((($) . T) (((-420 (-577))) . T)) @@ -170,12 +170,12 @@ (|has| |#3| (-809)) (|has| |#3| (-809)) (((|#1| |#2|) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((((-1206)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) (((-1201) |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-527 (-1201) |#2|)))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) ((((-577)) . T) (((-420 (-577))) . T)) (((|#1| (-1201) (-1113 (-1201)) (-544 (-1113 (-1201)))) . T)) ((((-577) |#1|) . T)) @@ -195,29 +195,29 @@ ((((-1183) |#1|) . T)) ((((-1259 (-577)) $) . T) (((-577) (-130)) . T)) (((|#1|) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) (((|#3| (-787)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) ((($) . T) (((-420 (-577))) . T)) ((($) . T)) ((($) . 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T)) ((((-420 (-577))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-375)) ((((-1259 (-577)) $) . T) (((-577) |#1|) . T)) -((($) -3777 (|has| (-420 |#2|) (-239)) (|has| (-420 |#2|) (-238)))) +((($) -3700 (|has| (-420 |#2|) (-239)) (|has| (-420 |#2|) (-238)))) ((($) . T) (((-577)) . T) (((-420 (-577))) . T)) (((|#1| |#2|) . T)) ((((-880)) . T)) @@ -241,13 +241,13 @@ ((((-880)) . T)) ((((-880)) . T)) (((|#1| |#1|) . T)) -(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . T) (($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) -((($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) +(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . 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T) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074))) (($) |has| |#2| (-1074)) (((-577)) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) ((((-880)) . T)) ((((-880)) . T)) ((((-880)) . T)) @@ -258,10 +258,10 @@ ((((-171 (-228))) |has| |#1| (-1047)) (((-171 (-391))) |has| |#1| (-1047)) (((-549)) |has| |#1| (-627 (-549))) (((-1197 |#1|)) . T) (((-911 (-577))) |has| |#1| (-627 (-911 (-577)))) (((-911 (-391))) |has| |#1| (-627 (-911 (-391))))) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#1|) . T)) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) -((((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#2|) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569)))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-864))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-864))) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#2|) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569)))) (|has| |#1| (-375)) ((((-880)) . T)) ((($) . T)) @@ -269,7 +269,7 @@ ((((-130)) . T)) (-12 (|has| |#4| (-239)) (|has| |#4| (-1074))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) -((($) -3777 (|has| |#2| (-239)) (|has| |#2| (-238)))) +((($) -3700 (|has| |#2| (-239)) (|has| |#2| (-238)))) (|has| |#4| (-1074)) (|has| |#3| (-1074)) ((((-880)) . T) (((-1206)) . T)) @@ -280,45 +280,45 @@ (((|#1|) . T)) ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) |has| |#1| (-1063 (-577))) ((|#1|) . T)) (((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) -(((|#2|) . T) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) (|has| |#1| (-569)) -((((-577)) -3777 (-12 (|has| |#4| (-1063 (-577))) (|has| |#4| (-1125))) (|has| |#4| (-1074))) ((|#4|) |has| |#4| (-1125)) (((-420 (-577))) -12 (|has| |#4| (-1063 (-420 (-577)))) (|has| |#4| (-1125)))) -((((-577)) -3777 (-12 (|has| |#3| (-1063 (-577))) (|has| |#3| (-1125))) (|has| |#3| (-1074))) ((|#3|) |has| |#3| (-1125)) (((-420 (-577))) -12 (|has| |#3| (-1063 (-420 (-577)))) (|has| |#3| (-1125)))) +((((-577)) -3700 (-12 (|has| |#4| (-1063 (-577))) (|has| |#4| (-1125))) (|has| |#4| (-1074))) ((|#4|) |has| |#4| (-1125)) (((-420 (-577))) -12 (|has| |#4| (-1063 (-420 (-577)))) (|has| |#4| (-1125)))) +((((-577)) -3700 (-12 (|has| |#3| (-1063 (-577))) (|has| |#3| (-1125))) (|has| |#3| (-1074))) ((|#3|) |has| |#3| (-1125)) (((-420 (-577))) -12 (|has| |#3| (-1063 (-420 (-577)))) (|has| |#3| (-1125)))) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (|has| |#1| (-569)) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) (((|#1|) . 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T)) -(((|#1|) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) . T)) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1199 |#1| |#2| |#3|)) |has| |#1| (-375)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) . T)) (((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) (($) . T)) -(((|#4| |#4|) -3777 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-1074)))) -(((|#3| |#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074)))) +(((|#4| |#4|) -3700 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-1074)))) +(((|#3| |#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074)))) (((|#2|) . T)) (((|#1|) . T)) ((((-549)) |has| |#2| (-627 (-549))) (((-911 (-391))) |has| |#2| (-627 (-911 (-391)))) (((-911 (-577))) |has| |#2| (-627 (-911 (-577))))) ((((-880)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2433 |#1|) (|:| -3163 |#2|))) . T) (((-880)) . T)) +((((-2 (|:| -2493 |#1|) (|:| -2844 |#2|))) . T) (((-880)) . T)) ((((-549)) |has| |#1| (-627 (-549))) (((-911 (-391))) |has| |#1| (-627 (-911 (-391)))) (((-911 (-577))) |has| |#1| (-627 (-911 (-577))))) -(((|#4|) -3777 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-1074)))) -(((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074)))) -((((-2 (|:| -2433 |#1|) (|:| -3163 |#2|))) . T)) +(((|#4|) -3700 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-1074)))) +(((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074)))) +((((-2 (|:| -2493 |#1|) (|:| -2844 |#2|))) . T)) ((((-880)) . T)) ((((-880)) . T)) ((((-549)) . T) (((-577)) . T) (((-911 (-577))) . T) (((-391)) . T) (((-228)) . T)) @@ -326,15 +326,15 @@ (((|#1|) . T) (((-577)) |has| |#1| (-1063 (-577))) (((-420 (-577))) |has| |#1| (-1063 (-420 (-577))))) ((($) . 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T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1125)) ((((-933 |#1|)) . T) (($) . T) (((-420 (-577))) . T)) (((|#1|) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) ((((-549)) |has| |#1| (-627 (-549)))) ((((-880)) . T) (((-1206)) . T)) -((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) +((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) ((((-1206)) . T)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (|has| |#1| (-239)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#1| (-544 (-834 (-1201)))) . T)) (((|#1| (-996)) . T)) ((((-577)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1177)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) +((((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) (|has| (-1278 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1278 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-577)) |has| |#2| (-654 (-577)))) -((((-1150 |#1| (-1201))) . T) (((-577)) . T) (((-834 (-1201))) . T) (($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-1201)) . T)) +((((-1150 |#1| (-1201))) . T) (((-577)) . T) (((-834 (-1201))) . T) (($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-1201)) . 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T)) +(((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) ((#0=(-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) #0#) |has| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (-320 (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))))) ((((-880)) . T)) ((((-577) |#1|) . T)) ((((-549)) -12 (|has| |#1| (-627 (-549))) (|has| |#2| (-627 (-549)))) (((-911 (-391))) -12 (|has| |#1| (-627 (-911 (-391)))) (|has| |#2| (-627 (-911 (-391))))) (((-911 (-577))) -12 (|has| |#1| (-627 (-911 (-577)))) (|has| |#2| (-627 (-911 (-577)))))) ((($) . T)) ((((-880)) . T)) -((($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) +((($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) ((((-880)) . T)) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((((-880)) . T)) ((((-880)) . T)) (|has| (-1277 |#2| |#3| |#4|) (-148)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) (((|#1|) . T)) ((($) . T)) ((((-577) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-864))) ((((-880)) |has| |#1| (-1125))) -((($) -3777 (|has| |#1| (-239)) (|has| |#1| (-238)))) -(-3777 (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)) (|has| |#1| (-1137))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) +((($) -3700 (|has| |#1| (-239)) (|has| |#1| (-238)))) +(-3700 (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)) (|has| |#1| (-1137))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((((-933 |#1|)) . T)) ((((-420 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-577) |#1|))) @@ -437,7 +437,7 @@ ((((-880)) . T)) ((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569))) (|has| |#1| (-375)) -(-3777 (-12 (|has| (-1284 |#1| |#2| |#3|) (-239)) (|has| |#1| (-375))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) +(-3700 (-12 (|has| (-1284 |#1| |#2| |#3|) (-239)) (|has| |#1| (-375))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-375)) (|has| |#1| (-15 * (|#1| (-787) |#1|))) @@ -451,23 +451,23 @@ ((((-1259 (-577)) $) . T) (((-577) |#1|) . T)) ((((-880)) . T)) (((|#2|) . T)) -(-3777 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((((-577)) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569))) ((($) |has| |#1| (-569)) (((-577)) . T)) (|has| |#2| (-809)) (|has| |#2| (-809)) -((((-1284 |#1| |#2| |#3|)) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-577)) . T) ((|#1|) |has| |#1| (-174))) -((((-1288 |#2|)) . T) (((-1284 |#1| |#2| |#3|)) . T) (((-1256 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-577)) . T) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569)))) +((((-1284 |#1| |#2| |#3|)) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-577)) . T) ((|#1|) |has| |#1| (-174))) +((((-1288 |#2|)) . T) (((-1284 |#1| |#2| |#3|)) . T) (((-1256 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-577)) . T) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569)))) ((($) |has| |#1| (-569)) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) (((-577)) . T)) (((|#1|) . T)) ((((-1201)) -12 (|has| |#3| (-921 (-1201))) (|has| |#3| (-1074)))) (((|#1|) . T)) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-836))) -(-3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) -(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . T) (($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-569)))) +(-3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) +(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . T) (($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-569)))) ((($ $) |has| |#1| (-569)) ((|#1| |#1|) . T)) -((($ (-1201)) -3777 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) +((($ (-1201)) -3700 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) (((#0=(-715) (-1197 #0#)) . T)) ((((-594 |#1|)) . T) (((-420 (-577))) . T) (($) . T)) ((((-420 (-577))) . T) (($) . T)) @@ -475,18 +475,18 @@ ((((-880)) . T) (((-1292 |#3|)) . T)) ((((-594 |#1|)) . T) (($) . T) (((-420 (-577))) . T)) ((($) . T) (((-420 (-577))) . T)) -((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (($) -3777 (|has| |#1| (-174)) (|has| |#1| (-569)))) +((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-569)))) ((($) |has| |#1| (-569)) ((|#1|) . T)) ((((-880)) . T)) ((($) . T) (((-577)) . T) (((-420 (-577))) . T)) ((($) . T)) -((($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((#0=(-420 (-577)) #0#) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((#1=(-1284 |#1| |#2| |#3|) #1#) |has| |#1| (-375)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((#0=(-420 (-577)) #0#) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375)))) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) . T)) -(((|#1|) . T) (($) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375)))) +((($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((#0=(-420 (-577)) #0#) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((#1=(-1284 |#1| |#2| |#3|) #1#) |has| |#1| (-375)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . T) (($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((#0=(-420 (-577)) #0#) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375)))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) . T)) +(((|#1|) . T) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375)))) (((|#3|) |has| |#3| (-1074))) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-569))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-569))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-569))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-569))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) (|has| (-1119 |#1|) (-1125)) (((|#2| (-835 |#1|)) . T)) ((($) . T) (((-577)) . T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) . T)) @@ -494,20 +494,20 @@ (((|#1|) . T) (((-420 (-577))) . T) (((-577)) . T) (($) . T)) (((|#1|) . T) (((-420 (-577))) . T) (((-577)) . T) (($) . T)) (((|#1|) . 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T)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#1|) . T)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((((-420 $) (-420 $)) |has| |#1| (-569)) (($ $) . T) ((|#1| |#1|) . T)) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((#0=(-1107) |#2|) . T) ((#0# $) . T) (($ $) . T)) ((((-880)) . T)) ((((-933 |#1|)) . T)) @@ -516,22 +516,22 @@ ((((-246 |#1| |#2|) |#2|) . T)) ((((-880)) . T)) (((|#3|) |has| |#3| (-1125)) (((-577)) -12 (|has| |#3| (-1063 (-577))) (|has| |#3| (-1125))) (((-420 (-577))) -12 (|has| |#3| (-1063 (-420 (-577)))) (|has| |#3| (-1125)))) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#1|) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) ((((-549)) |has| |#1| (-627 (-549)))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) (|has| |#1| (-375)) ((((-1206)) . T)) (((|#1|) . T)) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-864))) ((($) . T)) ((((-1201) |#1|) |has| |#1| (-527 (-1201) |#1|)) ((|#1| |#1|) |has| |#1| (-320 |#1|))) (|has| |#2| (-836)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-864)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-544 |#3|)) . T)) ((((-880)) . T)) @@ -540,15 +540,15 @@ (|has| |#1| (-380)) ((((-420 (-577))) . T)) (((|#1|) . T)) -(-3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((((-420 (-577))) . T)) ((((-1183) |#1|) . T)) (|has| |#1| (-380)) ((((-577)) . T)) ((((-577)) . T)) (((|#1|) . T) (((-577)) . T)) -(-3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) ((((-880)) . T)) (((|#1|) . T) (((-420 (-577))) . T) (((-577)) . T) (($) . T)) ((((-1201)) -12 (|has| |#1| (-375)) (|has| |#1| (-921 (-1201))))) @@ -562,12 +562,12 @@ ((((-577) |#3|) . T)) (((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) (|has| |#2| (-1074)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) -(-3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) +(-3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((((-880)) . T)) ((((-1278 |#1| |#2| |#3| |#4|)) . T)) ((((-420 (-577))) . T) (((-577)) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) @@ -576,9 +576,9 @@ ((($) . T) (((-577)) . T) (((-420 (-577))) . T)) ((((-577)) . T)) ((((-577)) . T)) -((($) . T) (((-577)) . 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T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) (((|#2|) . T)) @@ -942,7 +942,7 @@ ((((-660 |#1|)) . T)) ((((-880)) . T)) ((((-549)) |has| |#1| (-627 (-549)))) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) (((|#2|) |has| |#2| (-320 |#2|))) (((#0=(-577) #0#) . T) ((#1=(-420 (-577)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -953,14 +953,14 @@ ((($) . T) (((-577)) . T) (((-420 (-577))) . T)) (|has| |#2| (-380)) (((#0=(-577) #0#) . T) ((#1=(-420 (-577)) #1#) . T) (($ $) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-865)) (|has| |#1| (-1125))) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) (((|#1|) . T) (((-420 (-577))) . T) (($) . 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T)) ((((-549)) |has| |#1| (-627 (-549)))) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) -((($) . T) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((($) . T) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) ((((-880)) . T)) ((((-1199 |#1| |#2| |#3|) $) -12 (|has| (-1199 |#1| |#2| |#3|) (-297 (-1199 |#1| |#2| |#3|) (-1199 |#1| |#2| |#3|))) (|has| |#1| (-375))) (($ $) . T) (((-577) |#1|) . T)) ((($ $) . T) (((-420 (-577)) |#1|) . T)) @@ -981,7 +981,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-577)) . T) (($) . T)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((($) . T) (((-577)) . T) ((|#2|) . T)) ((((-577)) . T) (($) . T) ((|#2|) . T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) ((((-420 (-577))) . T) (((-577)) . T)) @@ -990,29 +990,29 @@ (((|#1|) . T)) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-569)) (|has| |#1| (-1074))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-569)) (|has| |#1| (-1074))) ((((-112)) . T)) ((((-549)) |has| |#1| (-627 (-549))) (((-228)) . #0=(|has| |#1| (-1047))) (((-391)) . #0#)) ((((-880)) . T)) (((|#1|) . 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T)) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#2|) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-569))) (|has| |#1| (-569)) -(((|#1|) . T) (($) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375)))) -((($) . T) (((-577)) . T) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) +(((|#1|) . T) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375)))) +((($) . T) (((-577)) . T) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) ((|#1|) . T) (((-577)) . T)) (|has| |#1| (-932)) -(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569)))) +(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569)))) (((|#1|) . T)) (|has| |#1| (-1125)) ((((-880)) . T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-569))) ((((-880)) . T)) ((((-880)) . T)) ((((-880)) . T)) @@ -1025,7 +1025,7 @@ ((((-1206)) . T) (((-880)) . T)) ((((-1206)) . T)) ((((-880)) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) (((|#1| (-996)) . T)) (((|#1| |#1|) . T)) ((($) . T)) @@ -1041,23 +1041,23 @@ (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) -(-3777 (-12 (|has| |#1| (-486)) (|has| |#2| (-486))) (-12 (|has| |#1| (-742)) (|has| |#2| (-742)))) +(-3700 (-12 (|has| |#1| (-486)) (|has| |#2| (-486))) (-12 (|has| |#1| (-742)) (|has| |#2| (-742)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-577)) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) ((((-880)) . T)) -(-3777 (|has| |#1| (-239)) (|has| |#1| (-238))) +(-3700 (|has| |#1| (-239)) (|has| |#1| (-238))) (|has| |#1| (-361)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-420 (-577))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-420 (-577))) . T)) -((($) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#1|) . T)) +((($) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#1|) . T)) (|has| |#1| (-844)) ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) |has| |#1| (-1063 (-577))) ((|#1|) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) (((|#1| $) |has| |#1| (-297 |#1| |#1|))) ((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569))) ((($) |has| |#1| (-569))) @@ -1065,49 +1065,49 @@ (((|#4|) |has| |#4| (-1125))) (((|#3|) |has| |#3| (-1125))) (|has| |#3| (-380)) -((($) |has| |#1| (-569)) ((|#1|) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-577)) . T)) +((($) |has| |#1| (-569)) ((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-577)) . T)) ((((-880)) . 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T)) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-569)) (|has| |#1| (-1074))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-569)) (|has| |#1| (-1074))) (((|#1|) |has| |#1| (-174))) (|has| $ (-148)) (|has| $ (-148)) ((((-1206)) . T)) (((|#1|) |has| |#1| (-174))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) ((((-880)) . T)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-486)) (|has| |#1| (-569)) (|has| |#1| (-1074)) (|has| |#1| (-1137))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-486)) (|has| |#1| (-569)) (|has| |#1| (-1074)) (|has| |#1| (-1137))) ((($ $) |has| |#1| (-297 $ $)) ((|#1| $) |has| |#1| (-297 |#1| |#1|))) (((|#1| (-420 (-577))) . T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1201)) . T)) (|has| |#1| (-569)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (|has| |#1| (-569)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-148)) -(((|#2| (-246 (-2021 |#1|) (-787)) (-882 |#1|)) . T)) +(((|#2| (-246 (-2014 |#1|) (-787)) (-882 |#1|)) . T)) (((|#1| (-544 |#3|) |#3|) . T)) (|has| |#1| (-146)) (((#0=(-420 (-577)) #0#) |has| |#2| (-375)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-146)) ((((-420 (-577))) |has| |#2| (-375)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) -(-3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) -(-3777 (|has| |#1| (-361)) (|has| |#1| (-380))) +(-3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#1| (-361)) (|has| |#1| (-380))) ((((-1167 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) -(((|#2|) . T) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (|has| |#3| (-809)) (|has| |#3| (-809)) ((((-880)) . T)) @@ -1176,18 +1176,18 @@ ((((-880)) . T)) ((((-880)) . T)) (((|#1| |#2|) . T)) -((((-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201)))) (((-1107)) . T)) +((((-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201)))) (((-1107)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-625 $)) . T)) (((|#1| (-420 (-577))) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) ((($ (-1288 |#2|)) . T) (($ (-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201))))) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) -((((-577)) -3777 (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) (|has| |#2| (-1074))) ((|#2|) |has| |#2| (-1125)) (((-420 (-577))) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) +((((-577)) -3700 (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) (|has| |#2| (-1074))) ((|#2|) |has| |#2| (-1125)) (((-420 (-577))) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) @@ -1195,15 +1195,15 @@ ((((-880)) . T)) ((((-880)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))))) -(((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) (((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) |has| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (-320 (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))))) +(((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))))) +(((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) (((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) |has| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (-320 (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))))) ((((-880)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-577)) |has| |#2| (-654 (-577)))) ((((-1201) (-52)) . T)) -((((-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) +((((-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-882 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-844)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-577)) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T)) ((((-577)) . T) (($) . T) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (|has| (-1119 |#1|) (-1125)) -(((|#2| |#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074)))) -(((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)))) -((((-577) (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074)))) +(((|#2| |#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074)))) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)))) +((((-577) (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074)))) ((((-577)) . T)) ((((-1206)) . T)) ((((-787)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-420 (-577))) . T) (($) . T)) ((($) . T) (((-420 (-577))) . T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-569))) ((((-1206)) . T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((((-577)) . T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-569))) (|has| |#1| (-146)) ((((-577)) . 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T)) -(-3777 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((|#1|) . T) (($) . T)) (((|#2|) |has| |#2| (-174))) -((($) -3777 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2|) |has| |#2| (-174)) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) +((($) -3700 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2|) |has| |#2| (-174)) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) ((((-888 |#1|)) . T)) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-380)) (|has| |#2| (-742)) (|has| |#2| (-809)) (|has| |#2| (-865)) (|has| |#2| (-1074)) (|has| |#2| (-1125))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-380)) (|has| |#2| (-742)) (|has| |#2| (-809)) (|has| |#2| (-865)) (|has| |#2| (-1074)) (|has| |#2| (-1125))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (|has| |#2| (-1177)) -(((#0=(-52)) . T) (((-2 (|:| -2284 (-1201)) (|:| -2328 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2327 (-1201)) (|:| -2909 #0#))) . T)) (((|#1| |#2|) . T)) (((|#1| (-651 |#2|)) . T)) (|has| |#3| (-1074)) @@ -1269,10 +1269,10 @@ (((|#1| (-577) (-1107)) . T)) (((|#1| (-420 (-577)) (-1107)) . T)) ((((-1201)) . T)) -((($) -3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) -((($) -3777 (|has| (-420 |#2|) (-239)) (|has| (-420 |#2|) (-238)))) +((($) -3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) +((($) -3700 (|has| (-420 |#2|) (-239)) (|has| (-420 |#2|) (-238)))) ((((-577) |#2|) . T)) -((($ (-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) +((($ (-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-380)) @@ -1280,43 +1280,43 @@ ((((-880)) . 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T)) (((|#1|) |has| |#1| (-320 |#1|))) @@ -1326,21 +1326,21 @@ (|has| |#1| (-380)) ((((-1201) $) |has| |#1| (-527 (-1201) $)) (($ $) |has| |#1| (-320 $)) ((|#1| |#1|) |has| |#1| (-320 |#1|)) (((-1201) |#1|) |has| |#1| (-527 (-1201) |#1|))) ((((-1201)) |has| |#1| (-921 (-1201)))) -(-3777 (-12 (|has| |#1| (-239)) (|has| |#1| (-375))) (|has| |#1| (-361))) +(-3700 (-12 (|has| |#1| (-239)) (|has| |#1| (-375))) (|has| |#1| (-361))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-401) |#1|) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) (((|#2|) . T) (((-880)) . T)) ((((-880)) . T)) (((|#2|) . T)) ((((-933 |#1|)) . T)) ((((-880)) . T) (((-1206)) . T)) ((((-1206)) . T)) -((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) -((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) +((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) +((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) @@ -1349,7 +1349,7 @@ (((|#1|) . T) (((-420 (-577))) . T) (($) . T) (((-577)) . T)) (((|#1| |#1|) . T)) (((#0=(-888 |#1|)) |has| #0# (-320 #0#))) -((((-577)) . T) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T)) +((((-577)) . T) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-809)) (|has| |#2| (-809)) @@ -1358,7 +1358,7 @@ (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) (|has| |#2| (-1074)) ((($) . T) (((-577)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1227)) (((#0=(-577) #0#) . T) ((#1=(-420 (-577)) #1#) . T) (($ $) . T)) @@ -1372,7 +1372,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-420 (-577)) #0#) . T)) (|has| |#1| (-375)) ((((-577)) . T) (((-420 (-577))) . T) (($) . 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T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) +((($) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2|) . T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577))))) ((((-577)) |has| #0=(-420 |#2|) (-654 (-577))) ((#0#) . T)) ((($) . T) (((-577)) . T)) ((((-577) (-145)) . T)) -((((-577) (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T) ((|#1| |#2|) . T)) +((((-577) (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T) ((|#1| |#2|) . T)) ((((-420 (-577))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((((-880)) . T)) ((((-933 |#1|)) . T)) (|has| |#1| (-375)) @@ -1420,11 +1420,11 @@ (|has| |#1| (-375)) (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-864)) -((($) -3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) +((($) -3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) (|has| |#1| (-375)) (((|#1|) . T) (($) . T)) (|has| |#1| (-864)) -((($) . T) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) +((($) . T) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) ((((-1201)) |has| |#1| (-921 (-1201)))) (|has| |#1| (-864)) ((((-519)) . T)) @@ -1440,7 +1440,7 @@ ((((-549)) . T)) ((((-880)) . T)) ((($) . T)) -((((-577) (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T) (((-1259 (-577)) $) . T) ((|#1| |#2|) . T)) +((((-577) (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T) (((-1259 (-577)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-174))) @@ -1450,22 +1450,22 @@ (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#3|) . 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T)) -(((#0=(-420 (-577)) #0#) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#1| |#1|) . T)) +(((#0=(-420 (-577)) #0#) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#1| |#1|) . T)) ((((-420 (-577))) |has| |#1| (-1063 (-577))) (((-577)) |has| |#1| (-1063 (-577))) (((-1201)) |has| |#1| (-1063 (-1201))) ((|#1|) . T)) ((($) . T)) ((($) . T)) @@ -1482,7 +1482,7 @@ ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) |has| |#1| (-1063 (-577))) ((|#1|) . T)) ((($) . T) (((-577)) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T)) ((((-577)) |has| |#1| (-905 (-577))) (((-391)) |has| |#1| (-905 (-391)))) -((((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#1|) . 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T)) -(((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074)))) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074)))) (|has| $ (-148)) ((((-420 |#2|)) . T)) ((((-420 (-577))) |has| #0=(-420 |#2|) (-1063 (-420 (-577)))) (((-577)) |has| #0# (-1063 (-577))) ((#0#) . T)) @@ -1567,11 +1567,11 @@ (|has| |#2| (-148)) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) (|has| |#1| (-148)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) (|has| |#1| (-148)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) (|has| |#1| (-148)) (((|#1|) . T)) (|has| |#2| (-239)) @@ -1608,9 +1608,9 @@ ((((-880)) . T)) ((((-880)) . T)) ((((-1024 |#1|)) . T) ((|#1|) . T)) -((((-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (((-834 (-1201))) . T)) +((((-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (((-834 (-1201))) . T)) ((((-880)) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((((-420 (-577))) . T) (((-420 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1197 |#1|)) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) @@ -1619,8 +1619,8 @@ (((|#1|) . T) (((-577)) . T) (($) . T)) (((|#2|) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) ((((-577) |#2|) . T)) (((|#1|) . T) (((-420 (-577))) . T) (((-577)) . T) (($) . T)) ((($) . T) (((-577)) . T) (((-420 (-577))) . T)) @@ -1631,9 +1631,9 @@ ((((-880)) . T)) (((|#4|) -12 (|has| |#4| (-320 |#4|)) (|has| |#4| (-1125)))) (((|#3|) -12 (|has| |#3| (-320 |#3|)) (|has| |#3| (-1125)))) -(-3777 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (-12 (|has| |#1| (-375)) (|has| |#2| (-238)))) +(-3700 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (-12 (|has| |#1| (-375)) (|has| |#2| (-238)))) (|has| |#1| (-38 (-420 (-577)))) -(((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((#0=(-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) #0#) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((#0=(-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) #0#) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#2| (-375)) @@ -1642,21 +1642,21 @@ (((|#2|) . T)) ((((-1284 |#1| |#2| |#3|)) |has| |#1| (-375))) (((|#1|) |has| |#1| (-174))) -((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932)))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (|has| |#1| (-1125)) (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-38 (-420 (-577)))) ((((-1183) (-52)) . T)) (((|#1|) . T)) -((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . 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T)) -((((-577)) -3777 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074))) ((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-742)) (|has| |#2| (-1074))) (($) |has| |#2| (-1074))) +((((-577)) -3700 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074))) ((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-742)) (|has| |#2| (-1074))) (($) |has| |#2| (-1074))) (((|#1|) . T)) ((((-577) |#3|) . T)) ((((-577) (-145)) . T)) @@ -1672,7 +1672,7 @@ ((((-577)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#1|) . T)) -((($ (-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) +((($ (-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) (((|#2|) . T) (((-577)) |has| |#2| (-654 (-577)))) ((((-145)) . T)) ((((-880)) . T)) @@ -1683,26 +1683,26 @@ (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#1| |#2|) . T)) -(-3777 (|has| |#2| (-239)) (|has| |#2| (-238))) +(-3700 (|has| |#2| (-239)) (|has| |#2| (-238))) ((((-577) (-145)) . T) (((-1259 (-577)) $) . T)) -(((#0=(-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) #0#) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +(((#0=(-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) #0#) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (|has| |#1| (-865)) (((|#2| (-787) (-1107)) . T)) (((|#1| |#2|) . T)) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) (|has| |#1| (-807)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-569))) -((((-1201)) -3777 (-12 (|has| (-1284 |#1| |#2| |#3|) (-921 (-1201))) (|has| |#1| (-375))) (-12 (|has| (-1284 |#1| |#2| |#3|) (-923 (-1201))) (|has| |#1| (-375))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-569))) +((((-1201)) -3700 (-12 (|has| (-1284 |#1| |#2| |#3|) (-921 (-1201))) (|has| |#1| (-375))) (-12 (|has| (-1284 |#1| |#2| |#3|) (-923 (-1201))) (|has| |#1| (-375))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))))) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201))))) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-787) |#1|))) (|has| |#1| (-921 (-1201))))) (((|#1|) |has| |#1| (-174))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3777 (|has| |#1| (-148)) (-12 (|has| |#1| (-375)) (|has| |#2| (-148)))) +(-3700 (|has| |#1| (-148)) (-12 (|has| |#1| (-375)) (|has| |#2| (-148)))) (((|#4|) . T)) -(-3777 (|has| |#1| (-146)) (-12 (|has| |#1| (-375)) (|has| |#2| (-146)))) +(-3700 (|has| |#1| (-146)) (-12 (|has| |#1| (-375)) (|has| |#2| (-146)))) ((((-1183) |#1|) . T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1716,24 +1716,24 @@ (((|#3|) . T)) ((((-1284 |#1| |#2| |#3|)) |has| |#1| (-375))) ((($) . T) (((-577)) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T)) -((((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1199 |#1| |#2| |#3|)) |has| |#1| (-375)) (((-577)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-577)) . T) (($) . T)) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1199 |#1| |#2| |#3|)) |has| |#1| (-375)) (((-577)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-577)) . T) (($) . T)) ((((-880)) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-865)) (|has| |#1| (-1125))) (((|#1|) . T)) (((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) (((-577)) . T) (($) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125))) (((-981 |#1|)) . T)) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125))) (((-981 |#1|)) . T)) (|has| |#1| (-864)) (|has| |#1| (-864)) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) ((((-981 |#1|)) . T)) -(((|#4|) -3777 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-742)))) -(((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-742)))) +(((|#4|) -3700 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-742)))) +(((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-742)))) (|has| |#2| (-375)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -3777 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-742)) (|has| |#4| (-1074)))) -(((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-742)) (|has| |#3| (-1074)))) +(((|#4|) -3700 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-742)) (|has| |#4| (-1074)))) +(((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-742)) (|has| |#3| (-1074)))) (((|#2|) |has| |#2| (-1074))) (((|#2|) |has| |#2| (-1074))) ((((-1183) |#1|) . T)) @@ -1745,8 +1745,8 @@ ((((-401) (-1183)) . T)) ((($ (-1201)) . T)) ((($) |has| |#1| (-569)) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((((-880)) -3777 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-626 (-880))) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-380)) (|has| |#2| (-742)) (|has| |#2| (-809)) (|has| |#2| (-865)) (|has| |#2| (-1074)) (|has| |#2| (-1125))) (((-1292 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2284 (-1183)) (|:| -2328 #0#))) . T)) +((((-880)) -3700 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-626 (-880))) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-380)) (|has| |#2| (-742)) (|has| |#2| (-809)) (|has| |#2| (-865)) (|has| |#2| (-1074)) (|has| |#2| (-1125))) (((-1292 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2327 (-1183)) (|:| -2909 #0#))) . T)) (((|#1|) . T)) ((((-880)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) @@ -1755,7 +1755,7 @@ ((((-577)) . T)) (|has| |#2| (-148)) (|has| |#1| (-486)) -(-3777 (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) +(-3700 (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) (|has| |#1| (-375)) ((((-880)) . T)) (|has| |#1| (-38 (-420 (-577)))) @@ -1766,8 +1766,8 @@ (|has| |#1| (-864)) ((((-880)) . T)) (((|#2|) . T)) -((((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569)))) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569)))) ((($) |has| |#1| (-569)) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#2|) . T) (((-577)) . T) (((-835 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1776,8 +1776,8 @@ ((((-933 |#1|)) . T) (((-420 (-577))) . T) (($) . T)) ((((-880)) . T)) ((((-880)) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) -(((|#2| (-495 (-2021 |#1|) (-787)) (-882 |#1|)) . T)) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(((|#2| (-495 (-2014 |#1|) (-787)) (-882 |#1|)) . T)) ((((-420 (-577))) . #0=(|has| |#2| (-375))) (($) . #0#)) (((|#1| (-544 (-1201)) (-1201)) . T)) (((|#1|) . T)) @@ -1798,19 +1798,19 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((((-1201) (-52)) . 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T) (((-577)) |has| |#1| (-1063 (-577))) (((-420 (-577))) |has| |#1| (-1063 (-420 (-577))))) (|has| |#1| (-865)) (|has| |#1| (-865)) @@ -1831,15 +1831,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-320 |#4|)) (|has| |#4| (-1125)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-320 |#4|)) (|has| |#4| (-1125)))) -(((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)))) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -(-3777 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-932))) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +(((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +(-3700 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-932))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((($ |#2|) . T)) -((($ (-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (($ (-1107)) . T)) +((($ (-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (($ (-1107)) . T)) ((($ $) . T) ((#0=(-420 (-577)) #0#) . T)) ((((-577) |#2|) . T)) -(((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)))) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)))) (|has| |#1| (-361)) (((|#3| |#3|) -12 (|has| |#3| (-320 |#3|)) (|has| |#3| (-1125)))) (((|#2|) . T) (((-577)) . T)) @@ -1848,7 +1848,7 @@ (|has| |#1| (-836)) (|has| |#1| (-836)) (((|#1|) . T)) -(-3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361))) (|has| |#1| (-864)) (|has| |#1| (-864)) (|has| |#1| (-864)) @@ -1857,14 +1857,14 @@ ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((((-1201)) |has| |#1| (-921 (-1201))) (((-1107)) . T)) (((|#1|) . T)) (|has| |#1| (-864)) -(((#0=(-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) #0#) |has| (-2 (|:| -2284 (-1183)) (|:| -2328 (-52))) (-320 (-2 (|:| -2284 (-1183)) (|:| -2328 (-52)))))) +(((#0=(-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) #0#) |has| (-2 (|:| -2327 (-1183)) (|:| -2909 (-52))) (-320 (-2 (|:| -2327 (-1183)) (|:| -2909 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (|has| |#1| (-1125)) ((((-880)) . T) (((-1206)) . T)) @@ -1888,14 +1888,14 @@ (((|#3|) . T)) (((|#1| (-787) (-1107)) . T)) ((((-145)) . T)) -((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) -3777 (|has| |#1| (-864)) (|has| |#1| (-1063 (-577)))) ((|#1|) . T)) +((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) -3700 (|has| |#1| (-864)) (|has| |#1| (-1063 (-577)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-145)) . 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T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1914,31 +1914,31 @@ ((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569))) ((($) |has| |#1| (-569))) (((|#2|) . T)) -((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (($) -3777 (|has| |#1| (-174)) (|has| |#1| (-569)))) +((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-569)))) ((($) |has| |#1| (-569)) ((|#1|) . T)) ((($) |has| |#1| (-864))) ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) (|has| |#1| (-932)) ((((-1201)) . T)) ((((-880)) . T)) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (((-1284 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) . 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T)) -(-3777 (|has| |#2| (-465)) (|has| |#2| (-932))) -(((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) ((#0=(-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) #0#) |has| (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|)) (-320 (-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))))) -(-3777 (|has| |#1| (-465)) (|has| |#1| (-932))) +(-3700 (|has| |#2| (-465)) (|has| |#2| (-932))) +(((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) ((#0=(-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) #0#) |has| (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|)) (-320 (-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))))) +(-3700 (|has| |#1| (-465)) (|has| |#1| (-932))) (((|#1|) . T)) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) @@ -1947,23 +1947,23 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)))) +(((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)))) (|has| |#1| (-865)) (|has| |#1| (-569)) ((((-594 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3777 (-12 (|has| |#1| (-375)) (|has| |#2| (-836))) (-12 (|has| |#1| (-375)) (|has| |#2| (-865)))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-836))) (-12 (|has| |#1| (-375)) (|has| |#2| (-865)))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) ((((-933 |#1|)) . T)) (((|#1| (-509 |#1| |#3|) (-509 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-787)) . T)) ((((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569))) -((((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-1199 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569)))) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-1199 |#1| |#2| |#3|)) |has| |#1| (-375)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569)))) ((($) |has| |#1| (-569)) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) ((((-577)) |has| #0=(-420 |#2|) (-654 (-577))) ((#0#) . T) (((-420 (-577))) . T) (($) . T)) ((((-688 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1972,7 +1972,7 @@ ((((-880)) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) ((((-880)) . T)) -((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) +((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) ((((-1206)) . T)) ((((-420 (-577))) . T) (($) . T) (((-420 |#1|)) . T) ((|#1|) . T) (((-577)) . T)) (((|#3|) . T) (((-577)) . T) (((-625 $)) . T)) @@ -1980,12 +1980,12 @@ ((((-880)) . T)) ((((-880)) . T)) (((|#2|) . 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T)) @@ -2156,8 +2156,8 @@ (|has| |#1| (-864)) (|has| |#1| (-864)) (((|#1| (-577) (-1107)) . T)) -(-3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +(-3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#1| (-420 (-577)) (-1107)) . T)) (((|#1| (-787) (-1107)) . T)) (|has| |#1| (-865)) @@ -2171,41 +2171,41 @@ ((((-933 |#1|)) . T) (($) . T) (((-420 (-577))) . T)) (|has| |#1| (-1125)) ((((-420 (-577))) |has| |#2| (-375)) (($) . T) (((-577)) . T)) -((((-577)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)))) +((((-577)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)))) (((|#1|) . 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T)) ((($) |has| |#1| (-239))) @@ -2240,12 +2240,12 @@ (|has| |#1| (-146)) ((($) |has| |#1| (-569)) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#1|) |has| |#1| (-174))) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-569))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-569))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((((-577)) . T) ((|#1|) . T) (($) . T) (((-420 (-577))) . T) (((-1201)) |has| |#1| (-1063 (-1201)))) (((|#1| |#2|) . T)) -((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) -3777 (|has| |#1| (-864)) (|has| |#1| (-1063 (-577)))) ((|#1|) . T)) -(-3777 (-12 (|has| |#4| (-239)) (|has| |#4| (-1074))) (-12 (|has| |#4| (-238)) (|has| |#4| (-1074)))) -(-3777 (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1074)))) +((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) -3700 (|has| |#1| (-864)) (|has| |#1| (-1063 (-577)))) ((|#1|) . T)) +(-3700 (-12 (|has| |#4| (-239)) (|has| |#4| (-1074))) (-12 (|has| |#4| (-238)) (|has| |#4| (-1074)))) +(-3700 (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1074)))) ((((-145)) . T)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) @@ -2256,13 +2256,13 @@ ((((-880)) . T)) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) ((($) . T) (((-577)) |has| |#1| (-654 (-577))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) (|has| |#1| (-375)) (|has| |#1| (-375)) ((($ |#2|) . T)) (|has| (-420 |#2|) (-239)) ((((-660 |#1|)) . T)) -((($ (-1288 |#2|)) . T) (($ (-1201)) -3777 (-12 (|has| (-1199 |#1| |#2| |#3|) (-921 (-1201))) (|has| |#1| (-375))) (-12 (|has| (-1199 |#1| |#2| |#3|) (-923 (-1201))) (|has| |#1| (-375))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))))) +((($ (-1288 |#2|)) . T) (($ (-1201)) -3700 (-12 (|has| (-1199 |#1| |#2| |#3|) (-921 (-1201))) (|has| |#1| (-375))) (-12 (|has| (-1199 |#1| |#2| |#3|) (-923 (-1201))) (|has| |#1| (-375))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))))) ((($ (-1288 |#2|)) . T) (($ (-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201))))) ((($ (-1288 |#2|)) . T) (($ (-1201)) -12 (|has| |#1| (-15 * (|#1| (-787) |#1|))) (|has| |#1| (-921 (-1201))))) (|has| |#1| (-932)) @@ -2270,7 +2270,7 @@ (((|#2|) |has| |#2| (-1074))) (|has| |#1| (-375)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))))) +(((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))))) (((|#1|) |has| |#1| (-174))) ((($ (-882 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2281,7 +2281,7 @@ (((|#1|) . T)) ((((-420 |#2|)) . T) (((-420 (-577))) . T) (($) . T) (((-577)) . T)) ((((-660 $)) . T) (((-1183)) . T) (((-1201)) . T) (((-577)) . T) (((-228)) . T) (((-880)) . T)) -((((-577)) -3777 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074))) ((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-742)) (|has| |#3| (-1074))) (($) |has| |#3| (-1074))) +((((-577)) -3700 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074))) ((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-742)) (|has| |#3| (-1074))) (($) |has| |#3| (-1074))) ((((-420 (-577))) . T) (((-577)) . T) (((-625 $)) . T)) (((|#1|) . T)) ((((-880)) . T)) @@ -2297,7 +2297,7 @@ (((|#1| (-787) (-1107)) . T)) ((((-880)) . T)) (((#0=(-420 |#2|) #0#) . T) ((#1=(-420 (-577)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-577)) -3777 (|has| (-420 (-577)) (-1063 (-577))) (|has| |#1| (-1063 (-577)))) (((-420 (-577))) . T)) +(((|#1|) . T) (((-577)) -3700 (|has| (-420 (-577)) (-1063 (-577))) (|has| |#1| (-1063 (-577)))) (((-420 (-577))) . T)) (((|#1| (-615 |#1| |#3|) (-615 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2317,37 +2317,37 @@ ((((-715)) . T)) ((((-715)) . T)) (((|#2|) |has| |#2| (-174))) -(-3777 (|has| |#1| (-239)) (|has| |#1| (-238))) +(-3700 (|has| |#1| (-239)) (|has| |#1| (-238))) ((((-577)) . T) ((|#2|) . T) (((-420 (-577))) |has| |#2| (-1063 (-420 (-577))))) -((((-112)) |has| |#1| (-1125)) (((-880)) -3777 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)) (|has| |#1| (-1137)) (|has| |#1| (-1125)))) +((((-112)) |has| |#1| (-1125)) (((-880)) -3700 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)) (|has| |#1| (-1137)) (|has| |#1| (-1125)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-577)) . T) (((-420 (-577))) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . 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T) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) ((((-577) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|))))) +(((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|))))) ((((-391)) . T)) ((((-715)) . T)) ((((-420 (-577))) . #0=(|has| |#2| (-375))) (($) . #0#)) (((|#1|) |has| |#1| (-174))) ((((-420 (-975 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) -(-3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1074))) @@ -2359,7 +2359,7 @@ ((((-1201)) |has| |#2| (-921 (-1201)))) (|has| |#1| (-865)) ((((-880)) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (|has| |#1| (-807)) ((((-420 (-577))) . T) (($) . T)) (|has| |#1| (-486)) @@ -2367,8 +2367,8 @@ (|has| |#1| (-380)) (|has| |#1| (-380)) (|has| |#1| (-375)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-486)) (|has| |#1| (-569)) (|has| |#1| (-1074)) (|has| |#1| (-1137))) -((($) -3777 (|has| |#1| (-239)) (|has| |#1| (-238)) (|has| |#1| (-361)))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-486)) (|has| |#1| (-569)) (|has| |#1| (-1074)) (|has| |#1| (-1137))) +((($) -3700 (|has| |#1| (-239)) (|has| |#1| (-238)) (|has| |#1| (-361)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-361)) @@ -2379,7 +2379,7 @@ (|has| |#1| (-38 (-420 (-577)))) (((|#2|) . T) (((-880)) . T)) (((|#2|) . T) (((-880)) . T)) -((($ (-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) +((($ (-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) @@ -2390,18 +2390,18 @@ (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-865)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) +((((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-577)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) |has| (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)) (-320 (-2 (|:| -2284 |#1|) (|:| -2328 |#2|)))) ((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) |has| (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)) (-320 (-2 (|:| -2327 |#1|) (|:| -2909 |#2|)))) ((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) (((|#2|) . 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T)) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#1|) |has| |#1| (-174))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#1|) |has| |#1| (-174))) (|has| |#1| (-146)) (|has| |#1| (-148)) -(-3777 (-12 (|has| (-1199 |#1| |#2| |#3|) (-148)) (|has| |#1| (-375))) (|has| |#1| (-148))) -(-3777 (-12 (|has| (-1199 |#1| |#2| |#3|) (-146)) (|has| |#1| (-375))) (|has| |#1| (-146))) +(-3700 (-12 (|has| (-1199 |#1| |#2| |#3|) (-148)) (|has| |#1| (-375))) (|has| |#1| (-148))) +(-3700 (-12 (|has| (-1199 |#1| |#2| |#3|) (-146)) (|has| |#1| (-375))) (|has| |#1| (-146))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) ((((-1284 |#1| |#2| |#3|)) |has| |#1| (-375))) (|has| |#1| (-864)) (((|#1| |#2|) . T)) @@ -2639,13 +2639,13 @@ ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) ((|#1|) . T) (((-577)) . T)) (|has| |#2| (-146)) (|has| |#2| (-148)) -(-3777 (|has| |#2| (-836)) (|has| |#2| (-865))) +(-3700 (|has| |#2| (-836)) (|has| |#2| (-865))) ((((-933 |#1|)) . T) (((-420 (-577))) . T) (($) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) ((((-577)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-577)) . T)) (((|#2|) . T)) -((((-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) +((((-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-375))) ((((-420 |#2|)) . T)) @@ -2654,10 +2654,10 @@ ((((-880)) . T)) ((((-880)) . T)) ((((-549)) |has| |#1| (-627 (-549)))) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((((-577)) . T) (($) . T) (((-420 (-577))) . T)) ((((-1201) |#1|) |has| |#1| (-527 (-1201) |#1|)) ((|#1| |#1|) |has| |#1| (-320 |#1|))) -(((|#1|) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)))) +(((|#1|) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)))) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) ((((-577)) . T) (((-420 (-577))) . T) (($) . T)) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) @@ -2667,14 +2667,14 @@ (((|#1|) . T) (($) . T) (((-420 (-577))) . T)) (((|#1|) . T) (($) . T) (((-420 (-577))) . T)) (((|#2|) |has| |#2| (-375))) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) (((|#2|) . T)) ((((-420 (-577))) . T) (((-715)) . T) (($) . T)) -((($) . T) (((-420 (-577))) -3777 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) +((($) . T) (((-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) -(-3777 (|has| |#1| (-239)) (|has| |#1| (-238))) +(-3700 (|has| |#1| (-239)) (|has| |#1| (-238))) (((#0=(-796 |#1| (-882 |#2|)) #0#) |has| (-796 |#1| (-882 |#2|)) (-320 (-796 |#1| (-882 |#2|))))) -((($) -3777 (|has| |#1| (-239)) (|has| |#1| (-238)))) +((($) -3700 (|has| |#1| (-239)) (|has| |#1| (-238)))) ((((-577)) . T) (($) . T)) ((((-882 |#1|)) . T)) (((|#2|) |has| |#2| (-174))) @@ -2683,7 +2683,7 @@ ((((-1201)) |has| |#1| (-921 (-1201))) (((-1107)) . T)) ((((-1201)) |has| |#1| (-921 (-1201))) (((-1113 (-1201))) . T)) (((|#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125)))) -((($ (-1201)) -3777 (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))))) +((($ (-1201)) -3700 (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))))) ((((-420 (-577))) . T) (((-577)) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (|has| |#1| (-38 (-420 (-577)))) @@ -2692,13 +2692,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . 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T)) +((((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-569))) ((|#1|) . T)) (|has| |#1| (-375)) -((($) |has| |#1| (-864)) (((-577)) -3777 (|has| |#1| (-21)) (|has| |#1| (-864)))) -((($) -3777 (-12 (|has| (-1284 |#1| |#2| |#3|) (-239)) (|has| |#1| (-375))) (-12 (|has| (-1284 |#1| |#2| |#3|) (-238)) (|has| |#1| (-375))) (|has| |#1| (-15 * (|#1| (-577) |#1|))))) +((($) |has| |#1| (-864)) (((-577)) -3700 (|has| |#1| (-21)) (|has| |#1| (-864)))) +((($) -3700 (-12 (|has| (-1284 |#1| |#2| |#3|) (-239)) (|has| |#1| (-375))) (-12 (|has| (-1284 |#1| |#2| |#3|) (-238)) (|has| |#1| (-375))) (|has| |#1| (-15 * (|#1| (-577) |#1|))))) ((($) |has| |#1| (-15 * (|#1| (-420 (-577)) |#1|)))) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -2766,16 +2766,16 @@ (((|#2| |#3|) . T)) (((|#1| (-544 |#2|)) . T)) (((|#1| (-787)) . T)) -(-3777 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((|#1| (-544 (-1113 (-1201)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-932)) -(-3777 (|has| |#2| (-809)) (|has| |#2| (-865))) +(-3700 (|has| |#2| (-809)) (|has| |#2| (-865))) ((((-880)) . T)) -(((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-742)))) -(((|#2|) -3777 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-742)) (|has| |#2| (-1074)))) -((($ (-1201)) -3777 (-12 (|has| |#3| (-921 (-1201))) (|has| |#3| (-1074))) (-12 (|has| |#3| (-923 (-1201))) (|has| |#3| (-1074))))) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-742)))) +(((|#2|) -3700 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-742)) (|has| |#2| (-1074)))) +((($ (-1201)) -3700 (-12 (|has| |#3| (-921 (-1201))) (|has| |#3| (-1074))) (-12 (|has| |#3| (-923 (-1201))) (|has| |#3| (-1074))))) ((($ $) . T) ((#0=(-1277 |#2| |#3| |#4|) #0#) . T) ((#1=(-420 (-577)) #1#) |has| #0# (-38 (-420 (-577))))) ((((-933 |#1|)) . T)) (-12 (|has| |#1| (-375)) (|has| |#2| (-836))) @@ -2783,14 +2783,14 @@ ((((-880)) . T)) ((($) . T) (((-577)) . T)) ((($) . T)) -(-3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (|has| |#1| (-375)) (|has| |#1| (-375)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1277 |#2| |#3| |#4|)) . T) (((-420 (-577))) |has| #0# (-38 (-420 (-577))))) ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) -(-3777 (-12 (|has| |#1| (-318)) (|has| |#1| (-932))) (|has| |#1| (-375)) (|has| |#1| (-361))) -(-3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) +(-3700 (-12 (|has| |#1| (-318)) (|has| |#1| (-932))) (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) ((((-577)) |has| |#1| (-654 (-577))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-880)) . T)) @@ -2828,7 +2828,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1201)) -3777 (-12 (|has| |#1| (-375)) (|has| |#1| (-921 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#1| (-923 (-1201)))))) +((($ (-1201)) -3700 (-12 (|has| |#1| (-375)) (|has| |#1| (-921 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#1| (-923 (-1201)))))) ((((-880)) . T)) (((|#1| (-544 (-1201))) . T)) ((($ $) . T)) @@ -2838,29 +2838,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-320 |#4|)) (|has| |#4| (-1125)))) (((|#2|) . 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T) (((-577)) . T)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1183)) (|:| -2909 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((((-880)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-577)) . T)) (((|#1| (-420 (-577))) . T)) (((|#1|) . T)) -(-3777 (|has| |#1| (-301)) (|has| |#1| (-375))) +(-3700 (|has| |#1| (-301)) (|has| |#1| (-375))) ((((-145)) . T)) ((((-577)) |has| #0=(-420 |#2|) (-654 (-577))) ((#0#) . T) (((-420 (-577))) . T) (($) . T)) (|has| |#1| (-864)) @@ -2876,7 +2876,7 @@ ((((-880)) . T)) ((((-880)) . T)) ((((-189)) . T) (((-880)) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-880)) . T)) ((((-880)) . T)) @@ -2893,8 +2893,8 @@ (|has| |#1| (-865)) ((((-880)) . T)) ((((-549)) |has| |#1| (-627 (-549)))) -((((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) -((($) -3777 (-12 (|has| (-1199 |#1| |#2| |#3|) (-239)) (|has| |#1| (-375))) (-12 (|has| (-1199 |#1| |#2| |#3|) (-238)) (|has| |#1| (-375))) (|has| |#1| (-15 * (|#1| (-577) |#1|))))) +((((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) +((($) -3700 (-12 (|has| (-1199 |#1| |#2| |#3|) (-239)) (|has| |#1| (-375))) (-12 (|has| (-1199 |#1| |#2| |#3|) (-238)) (|has| |#1| (-375))) (|has| |#1| (-15 * (|#1| (-577) |#1|))))) ((((-880)) . T)) (((|#2|) |has| |#2| (-375))) ((((-880)) . T)) @@ -2909,19 +2909,19 @@ (|has| |#3| (-1074)) (|has| |#1| (-1125)) ((((-1201) (-52)) . T)) -(-3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-577)) . T)) (((|#1|) . T)) @@ -2933,12 +2933,12 @@ (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (|has| |#1| (-836)) (((#0=(-933 |#1|) #0#) . T) (($ $) . T) ((#1=(-420 (-577)) #1#) . T)) ((((-420 |#2|)) . T)) (|has| |#1| (-864)) -((((-1228 |#1|)) . T) (((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-1228 |#1|)) . T) (((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) (((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) . T) ((#1=(-577) #1#) . T) (($ $) . T)) ((((-933 |#1|)) . T) (($) . T) (((-420 (-577))) . T)) (((|#2|) |has| |#2| (-1074)) (((-577)) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) @@ -2955,36 +2955,36 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) ((((-577) |#3|) . T)) (((|#1|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2284 (-1201)) (|:| -2328 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2327 (-1201)) (|:| -2909 #0#))) . T)) (|has| |#1| (-361)) ((((-577)) . T)) ((((-880)) . T)) (((|#1|) . T)) (((#0=(-1278 |#1| |#2| |#3| |#4|) $) |has| #0# (-297 #0# #0#))) (|has| |#1| (-375)) -(-3777 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074)))) -(((|#1|) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-1074))) (($) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) (((-577)) -3777 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)))) +(-3700 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074)))) +(((|#1|) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-1074))) (($) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074))) (((-577)) -3700 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)))) (((#0=(-1107) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) (((#0=(-420 (-577)) #0#) . T) ((#1=(-715) #1#) . T) (($ $) . T)) ((((-327 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-420 (-577))) |has| |#1| (-375))) ((((-880)) . T)) (|has| |#1| (-1125)) (((|#1|) . T)) -(((|#1|) -3777 (|has| |#2| (-379 |#1|)) (|has| |#2| (-430 |#1|)))) -(((|#1|) -3777 (|has| |#2| (-379 |#1|)) (|has| |#2| (-430 |#1|)))) +(((|#1|) -3700 (|has| |#2| (-379 |#1|)) (|has| |#2| (-430 |#1|)))) +(((|#1|) -3700 (|has| |#2| (-379 |#1|)) (|has| |#2| (-430 |#1|)))) (((|#2|) . T)) ((((-420 (-577))) . T) (((-715)) . T) (($) . T)) ((((-592)) . T)) (((|#3| |#3|) . T)) -((($ (-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) +((($ (-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) (|has| |#1| (-865)) (|has| |#2| (-239)) ((((-882 |#1|)) . T)) @@ -3005,10 +3005,10 @@ (|has| |#1| (-1125)) (((|#2|) . T)) (((|#1|) . T)) -((($) -3777 (|has| |#1| (-239)) (|has| |#1| (-238)))) +((($) -3700 (|has| |#1| (-239)) (|has| |#1| (-238)))) ((((-577)) . T)) (((|#2|) . T) (((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) ((|#1|) . T) (($) . T) (((-577)) . T)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (((|#2|) . T) (((-577)) |has| |#2| (-654 (-577)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3051,7 +3051,7 @@ (|has| |#2| (-1047)) ((($) . T)) (|has| |#1| (-932)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3061,32 +3061,32 @@ (|has| |#1| (-375)) ((((-933 |#1|)) . T)) ((($) . T) (((-577)) . T) ((|#1|) . T) (((-420 (-577))) . T)) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) -((($) |has| |#1| (-864)) (((-577)) -3777 (|has| |#1| (-21)) (|has| |#1| (-864)))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) |has| |#1| (-864)) (((-577)) -3700 (|has| |#1| (-21)) (|has| |#1| (-864)))) ((($ $) . T) ((#0=(-420 (-577)) #0#) . T)) -(-3777 (|has| |#1| (-380)) (|has| |#1| (-865))) +(-3700 (|has| |#1| (-380)) (|has| |#1| (-865))) (((|#1|) . T)) ((((-787)) . T)) ((((-880)) . T)) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201))))) ((((-420 |#2|) |#3|) . T)) -(-3777 (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1074)))) +(-3700 (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1074)))) ((($) . T) (((-420 (-577))) . T)) ((($) . T) (((-577)) . T) (((-420 (-577))) . T) (((-625 $)) . T)) ((((-577)) . T) (($) . T)) ((((-577)) . T) (($) . T)) ((((-787) |#1|) . T)) -(((|#2| (-246 (-2021 |#1|) (-787))) . T)) +(((|#2| (-246 (-2014 |#1|) (-787))) . T)) (((|#1| (-544 |#3|)) . T)) ((((-420 (-577))) . T)) -(-3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((((-1183)) . T) (((-880)) . T)) -(((#0=(-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) #0#) |has| (-2 (|:| -2284 (-1201)) (|:| -2328 (-52))) (-320 (-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))))) +(((#0=(-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) #0#) |has| (-2 (|:| -2327 (-1201)) (|:| -2909 (-52))) (-320 (-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))))) ((((-1183)) . T)) (|has| |#1| (-932)) (|has| |#2| (-375)) (((|#1|) . T) (($) . T) (((-577)) . T)) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) ((((-171 (-391))) . T) (((-228)) . T) (((-391)) . T)) ((((-880)) . T)) (((|#1|) . T)) @@ -3103,11 +3103,11 @@ (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) -(-3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361))) (|has| |#1| (-38 (-420 (-577)))) (-12 (|has| |#1| (-558)) (|has| |#1| (-844))) ((((-880)) . T)) -((((-1201)) -3777 (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))))) +((((-1201)) -3700 (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))))) (|has| |#1| (-375)) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201))))) (|has| |#1| (-375)) @@ -3120,13 +3120,13 @@ ((((-577) |#1|) . T)) ((((-1201)) |has| |#1| (-921 (-1201)))) (((|#1|) . T)) -(-3777 (-12 (|has| |#1| (-239)) (|has| |#1| (-375))) (-12 (|has| |#1| (-238)) (|has| |#1| (-375))) (|has| |#1| (-361))) +(-3700 (-12 (|has| |#1| (-239)) (|has| |#1| (-375))) (-12 (|has| |#1| (-238)) (|has| |#1| (-375))) (|has| |#1| (-361))) (((|#2|) |has| |#1| (-375))) (((|#2|) |has| |#1| (-375))) -(-3777 (|has| |#4| (-809)) (|has| |#4| (-865))) -(-3777 (|has| |#3| (-809)) (|has| |#3| (-865))) +(-3700 (|has| |#4| (-809)) (|has| |#4| (-865))) +(-3700 (|has| |#3| (-809)) (|has| |#3| (-865))) ((((-577)) . T) (($) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) @@ -3161,32 +3161,32 @@ ((((-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-905 (-391)))) (((-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-905 (-577))))) (((|#1|) . T)) ((($) . T) (((-577)) . T) ((|#2|) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (((|#3|) . T)) ((((-1183)) . T) (((-519)) . T) (((-228)) . T) (((-577)) . T)) (((|#1|) . T)) (|has| |#1| (-375)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (|has| |#1| (-375)) (|has| |#1| (-569)) (((|#4| |#4|) -12 (|has| |#4| (-320 |#4|)) (|has| |#4| (-1125)))) ((((-420 |#2|)) . T) (((-420 (-577))) . T) (($) . T) (((-577)) . T)) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1074)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) +((((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (|has| |#1| (-38 (-420 (-577)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-420 (-577)))) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) ((($) . T)) (|has| |#1| (-148)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) (|has| |#1| (-148)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-380))) (|has| |#1| (-148)) ((($) . T)) ((((-594 |#1|)) . T)) @@ -3202,7 +3202,7 @@ ((((-420 (-577))) |has| |#2| (-1063 (-577))) (((-577)) |has| |#2| (-1063 (-577))) (((-1201)) |has| |#2| (-1063 (-1201))) ((|#2|) . T)) (((#0=(-420 |#2|) #0#) . T) ((#1=(-420 (-577)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-3777 (|has| |#1| (-146)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-361))) (|has| |#1| (-148)) ((((-880)) . T)) ((($) . T)) @@ -3222,15 +3222,15 @@ ((((-420 |#2|)) . T)) ((((-880)) . T)) (((|#1|) . T)) -((((-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +((((-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201))))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) (|has| |#1| (-807)) (|has| |#1| (-807)) ((((-880)) . T)) ((((-933 |#1|)) . T) (((-420 (-577))) . T) (($) . T) (((-577)) . T)) ((((-880)) . T)) ((((-549)) |has| |#1| (-627 (-549)))) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3239,7 +3239,7 @@ ((((-1278 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-420 (-577))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569)) (((-420 (-577))) |has| |#1| (-569))) ((((-880)) . T)) -(-3777 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074)))) +(-3700 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074)))) ((((-880)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3252,10 +3252,10 @@ ((((-880)) . T)) (((|#2|) . T)) ((((-577)) . T)) -((((-1201)) -3777 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) +((((-1201)) -3700 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) ((((-880)) . T)) ((((-577)) . T)) -(-3777 (|has| |#2| (-809)) (|has| |#2| (-865))) +(-3700 (|has| |#2| (-809)) (|has| |#2| (-865))) ((((-171 (-391))) . T) (((-228)) . T) (((-391)) . T)) ((((-880)) . T)) ((((-880)) . T)) @@ -3267,11 +3267,11 @@ (((|#1|) . T) (($) . T) (((-420 (-577))) . T)) (|has| |#1| (-375)) (|has| |#1| (-375)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) ((((-880)) . T)) ((((-577) $) . T) (((-660 (-577)) $) . T)) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)) (|has| |#1| (-1137)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-486)) (|has| |#1| (-742)) (|has| |#1| (-921 (-1201))) (|has| |#1| (-1074)) (|has| |#1| (-1137)) (|has| |#1| (-1125))) (|has| |#1| (-1177)) ((((-933 |#1|)) . T) (((-420 (-577))) . T) (($) . T)) ((($) . T)) @@ -3281,22 +3281,22 @@ (((#0=(-117 |#1|) $) |has| #0# (-297 #0# #0#))) (((|#1|) |has| |#1| (-174))) ((((-327 |#1|)) . T) (((-577)) . T)) -(-3777 (|has| |#2| (-239)) (|has| |#2| (-238))) +(-3700 (|has| |#2| (-239)) (|has| |#2| (-238))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-880)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-880)) . T)) -((((-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) +((((-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) (((|#1|) |has| |#1| (-320 |#1|))) ((((-577) |#1|) . T) (((-1259 (-577)) $) . T)) (((|#1| |#2|) . T)) ((((-1201) |#1|) . T)) -(((|#1|) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)))) +(((|#1|) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)))) (((|#1|) . T)) ((($ (-1201)) . T)) -(((|#1|) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-1074)))) +(((|#1|) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-1074)))) ((((-577)) . T) (((-420 (-577))) . T)) (((|#1|) . T)) (|has| |#1| (-569)) @@ -3305,15 +3305,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-420 |#2|)) . T) (((-420 (-577))) . T) (($) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (|has| |#1| (-375)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) (|has| |#1| (-375)) (|has| |#1| (-569)) ((($) . T)) (|has| |#1| (-1125)) ((((-796 |#1| (-882 |#2|))) |has| (-796 |#1| (-882 |#2|)) (-320 (-796 |#1| (-882 |#2|))))) -(-3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3322,17 +3322,17 @@ (((|#1| (-787)) . T)) (|has| |#1| (-239)) (((|#1| (-544 (-1113 (-1201)))) . T)) -((($) -3777 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))))) +((($) -3700 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))))) ((((-594 |#1|)) . T) (((-420 (-577))) . T) (($) . T) (((-577)) . T)) ((((-577)) . T) (((-420 (-577))) . T) (($) . T)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1183)) (|:| -2909 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-577)) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (|has| |#2| (-375)) ((((-880)) . T)) ((((-880)) . T)) -(-3777 (|has| |#3| (-809)) (|has| |#3| (-865))) +(-3700 (|has| |#3| (-809)) (|has| |#3| (-865))) ((((-880)) . T)) ((((-1145)) . T) (((-880)) . T)) ((((-549)) . T) (((-880)) . T)) @@ -3343,14 +3343,14 @@ ((((-577)) . T)) (((|#3|) . T)) ((((-880)) . T)) -(-3777 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361))) -((((-577)) . 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T) (($) -3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((-882 |#1|)) . T)) +((((-1150 |#1| |#2|)) . T) ((|#2|) . T) (($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-577)) . T)) +((((-1197 |#1|)) . T) (((-577)) . T) (($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) (((-1107)) . T) ((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577)))))) +(-3700 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-569)) (|has| |#1| (-1074))) (((#0=(-594 |#1|) #0#) . T) (($ $) . T) ((#1=(-420 (-577)) #1#) . T)) ((($ $) . T) ((#0=(-420 (-577)) #0#) . T)) -((((-1150 |#1| (-1201))) . T) (((-577)) . T) (((-1113 (-1201))) . T) (($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-1201)) . T)) +((((-1150 |#1| (-1201))) . T) (((-577)) . T) (((-1113 (-1201))) . T) (($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577))))) (((-1201)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1| (-1292 |#1|) (-1292 |#1|)) . T)) ((((-594 |#1|)) . T) (($) . T) (((-420 (-577))) . T)) @@ -3365,7 +3365,7 @@ ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) ((|#1|) . T) (((-577)) . T)) (((|#1|) . T)) ((((-880)) . T)) -(((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577)))) ((|#2| |#2|) . T) (($ $) -3777 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) +(((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577)))) ((|#2| |#2|) . T) (($ $) -3700 (|has| |#2| (-174)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3374,30 +3374,30 @@ (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) (((|#1|) . T) (((-420 (-577))) . T) (($) . T)) -((($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) -((($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) +((($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) +((($ $) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1| |#1|) . T) ((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577))))) (((|#2|) . 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T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (|has| |#2| (-932)) (|has| |#1| (-932)) -((($) -3777 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-174)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((((-880)) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -2284 (-1183)) (|:| -2328 |#1|))) . T)) +((((-2 (|:| -2327 (-1183)) (|:| -2909 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3777 (|has| |#2| (-809)) (|has| |#2| (-865))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#2| (-809)) (|has| |#2| (-865))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-420 (-577))) . T)) ((((-1201)) . T) ((|#1|) . T)) @@ -3409,15 +3409,15 @@ (((#0=(-420 (-577)) #0#) . T)) ((((-420 (-577))) . T)) (((|#1|) |has| |#1| (-174))) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-1074))) (((|#1|) . T)) (((|#1|) . T)) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) (((|#1|) . T)) ((((-420 (-577))) . T) (((-577)) . T) (($) . T)) ((((-549)) . T)) ((((-880)) . T)) -((($) -3777 (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1074))))) +((($) -3700 (-12 (|has| |#3| (-239)) (|has| |#3| (-1074))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1074))))) (|has| |#1| (-865)) ((((-880)) . T)) ((((-577)) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-569))) @@ -3433,21 +3433,21 @@ ((($ $) . T) ((#0=(-420 (-577)) #0#) . T)) ((((-1201)) |has| |#1| (-921 (-1201)))) ((((-933 |#1|)) . T) (((-420 (-577))) . T) (($) . T)) -((($) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#1|) . T)) -(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . T) (($ $) -3777 (|has| |#1| (-174)) (|has| |#1| (-569)))) +((($) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#1|) . T)) +(((#0=(-420 (-577)) #0#) |has| |#1| (-38 (-420 (-577)))) ((|#1| |#1|) . 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T) (((-577)) |has| |#2| (-1063 (-577))) (((-420 (-577))) |has| |#2| (-1063 (-420 (-577))))) ((((-1107)) . T) ((|#2|) . T) (((-577)) |has| |#2| (-1063 (-577))) (((-420 (-577))) |has| |#2| (-1063 (-420 (-577))))) (((|#1|) . T)) @@ -3467,11 +3467,11 @@ ((($) |has| |#1| (-380))) (|has| |#2| (-836)) (|has| |#2| (-836)) -((((-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#2|) |has| |#1| (-375)) (($) . T) ((|#1|) . T)) +((((-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) ((|#2|) |has| |#1| (-375)) (($) . T) ((|#1|) . T)) ((($ (-1201)) |has| |#1| (-921 (-1201)))) (((|#1|) . T) (((-577)) |has| |#1| (-1063 (-577))) (((-420 (-577))) |has| |#1| (-1063 (-420 (-577))))) -((($) -3777 (-12 (|has| |#1| (-239)) (|has| |#1| (-375))) (-12 (|has| |#1| (-238)) (|has| |#1| (-375))) (|has| |#1| (-361)))) -(((|#1|) . T) (((-420 (-577))) -3777 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) . T)) +((($) -3700 (-12 (|has| |#1| (-239)) (|has| |#1| (-375))) (-12 (|has| |#1| (-238)) (|has| |#1| (-375))) (|has| |#1| (-361)))) +(((|#1|) . T) (((-420 (-577))) -3700 (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-375))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) ((((-577)) |has| |#1| (-905 (-577))) (((-391)) |has| |#1| (-905 (-391)))) (((|#1|) . T)) @@ -3486,7 +3486,7 @@ (|has| |#1| (-375)) (|has| |#1| (-375)) (((|#4|) -12 (|has| |#4| (-320 |#4|)) (|has| |#4| (-1125)))) -(((|#2|) -3777 (|has| |#2| (-6 (-4472 "*"))) (|has| |#2| (-174)))) +(((|#2|) -3700 (|has| |#2| (-6 (-4472 "*"))) (|has| |#2| (-174)))) (((|#2|) . T)) (|has| |#1| (-375)) (((|#2|) . T)) @@ -3500,12 +3500,12 @@ (((|#2| (-787)) . T)) ((((-1201)) . T)) ((((-888 |#1|)) . T)) -(-3777 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074))) -(-3777 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-809)) (|has| |#3| (-1074))) +(-3700 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074))) +(-3700 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-809)) (|has| |#3| (-1074))) ((((-880)) . T)) (((|#1|) . T)) -(-3777 (|has| |#2| (-809)) (|has| |#2| (-865))) -(-3777 (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) (-12 (|has| |#1| (-865)) (|has| |#2| (-865)))) +(-3700 (|has| |#2| (-809)) (|has| |#2| (-865))) +(-3700 (-12 (|has| |#1| (-809)) (|has| |#2| (-809))) (-12 (|has| |#1| (-865)) (|has| |#2| (-865)))) ((((-888 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-380)) @@ -3523,7 +3523,7 @@ (((|#1|) . T)) ((((-880)) . T)) ((($) . T) ((|#2|) . T) (((-420 (-577))) . T) (((-577)) |has| |#2| (-654 (-577)))) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) @@ -3532,7 +3532,7 @@ (((|#1|) . T)) ((((-880)) . T)) (|has| |#2| (-932)) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) ((((-549)) |has| |#2| (-627 (-549))) (((-911 (-391))) |has| |#2| (-627 (-911 (-391)))) (((-911 (-577))) |has| |#2| (-627 (-911 (-577))))) ((((-880)) . T)) ((((-880)) . T)) @@ -3543,7 +3543,7 @@ ((((-1197 |#1|)) . T) (((-880)) . T)) ((((-880)) . T)) ((((-420 (-577))) |has| |#2| (-1063 (-420 (-577)))) (((-577)) |has| |#2| (-1063 (-577))) ((|#2|) . T) (((-882 |#1|)) . T)) -((((-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (((-1107)) . T)) +((((-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (((-1107)) . T)) ((((-117 |#1|)) . T) (($) . T) (((-420 (-577))) . T)) ((((-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) (((-577)) |has| |#1| (-1063 (-577))) ((|#1|) . T) (((-1201)) . T)) ((((-880)) . T)) @@ -3563,10 +3563,10 @@ ((((-660 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-420 (-577)) |#1|)))) ((($) . T) (((-577)) . T) (((-1278 |#1| |#2| |#3| |#4|)) . T) (((-420 (-577))) . 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T)) @@ -3581,16 +3581,16 @@ ((((-420 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-880)) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) -(((|#2| (-495 (-2021 |#1|) (-787))) . T)) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(((|#2| (-495 (-2014 |#1|) (-787))) . T)) ((((-577) |#1|) . T)) ((((-1183)) . T) (((-880)) . T)) (((|#2| |#2|) . T)) (((|#1| (-544 (-1201))) . T)) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) ((((-577)) . T)) (((|#2|) . T)) -((($) -3777 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))))) +((($) -3700 (-12 (|has| |#2| (-239)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))))) (((|#2|) . T)) ((((-1201)) |has| |#1| (-921 (-1201))) (((-1107)) . T)) (((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) @@ -3599,9 +3599,9 @@ ((($) . T) (((-420 (-577))) . T)) ((($) . T)) ((($) . T)) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) (((|#1|) . T)) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((((-880)) . T)) ((((-145)) . T)) (((|#1|) . T) (((-420 (-577))) . T)) @@ -3610,7 +3610,7 @@ ((((-880)) . T)) (((|#1|) . T)) (|has| |#1| (-1177)) -((($ (-1201)) -3777 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) +((($ (-1201)) -3700 (|has| (-420 |#2|) (-921 (-1201))) (|has| (-420 |#2|) (-923 (-1201))))) (((|#1|) . T)) (((|#1| (-544 (-882 |#2|)) (-882 |#2|) (-796 |#1| (-882 |#2|))) . T)) ((((-420 $) (-420 $)) |has| |#1| (-569)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3635,44 +3635,44 @@ (|has| |#1| (-1125)) (|has| |#1| (-1125)) (|has| |#2| (-375)) -(((|#1|) . T) (($) -3777 (|has| |#1| (-301)) (|has| |#1| (-375))) (((-420 (-577))) |has| |#1| (-375))) +(((|#1|) . T) (($) -3700 (|has| |#1| (-301)) (|has| |#1| (-375))) (((-420 (-577))) |has| |#1| (-375))) (|has| |#1| (-375)) (|has| |#1| (-375)) -((($) -3777 (|has| |#2| (-239)) (|has| |#2| (-238)))) +((($) -3700 (|has| |#2| (-239)) (|has| |#2| (-238)))) ((((-577)) . T)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-1125)) -((($ (-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) +((($ (-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) ((((-1201)) -12 (|has| |#4| (-921 (-1201))) (|has| |#4| (-1074)))) ((((-1201)) -12 (|has| |#3| (-921 (-1201))) (|has| |#3| (-1074)))) (((|#1|) . T)) (|has| |#1| (-239)) -(((|#2| (-246 (-2021 |#1|) (-787))) . T)) +(((|#2| (-246 (-2014 |#1|) (-787))) . 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T)) (((|#2| |#2|) . T) ((#0=(-420 (-577)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-420 (-577))) . T) (($) . T)) @@ -3876,7 +3876,7 @@ ((((-880)) . T)) ((((-880)) . T)) ((((-880)) . T)) -(-3777 (|has| |#1| (-239)) (|has| |#1| (-238))) +(-3700 (|has| |#1| (-239)) (|has| |#1| (-238))) (((|#1|) . T) (((-880)) . T) (((-1206)) . T)) ((((-1206)) . T)) ((((-880)) . T)) @@ -3885,23 +3885,23 @@ ((($) . T) (((-577)) . T) (((-117 |#1|)) . T) (((-420 (-577))) . T)) ((((-651 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) -((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) +((((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) |has| |#2| (-174)) (($) -3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-420 (-577))) |has| |#2| (-38 (-420 (-577)))) ((|#2|) . T) (((-577)) |has| |#2| (-654 (-577)))) ((($) . T) (((-577)) . T)) (((|#1| (-544 (-882 |#2|)) (-882 |#2|) (-796 |#1| (-882 |#2|))) . T)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((((-1129)) . T)) ((((-880)) . T)) ((((-1206)) . T) (((-880)) . T)) ((((-1206)) . T) (((-880)) . T)) ((((-1206)) . T)) ((((-1206)) . T)) -((($) -3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) ((($) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) ((($) . T) (((-577)) . T)) (|has| |#2| (-932)) -((($) -3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) +((($) -3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((|#1|) |has| |#1| (-174)) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#1| |#2| (-246 |#1| |#2|) (-246 |#1| |#2|)) . T)) ((((-880)) . T)) (((|#1|) . T)) @@ -3916,9 +3916,9 @@ (((|#1| |#1|) |has| |#1| (-174))) ((((-715)) . T)) ((((-715)) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) ((((-1206)) . T)) -(-3777 (|has| |#2| (-809)) (|has| |#2| (-865))) +(-3700 (|has| |#2| (-809)) (|has| |#2| (-865))) (((|#1|) |has| |#1| (-174))) ((((-1206)) . T)) (((|#1| |#1|) . T)) @@ -3931,19 +3931,19 @@ (((|#1| (-577)) . T)) (((|#1|) . T)) ((((-420 (-577))) . T) (((-577)) . T) (($) . T)) -((($ (-1201)) -3777 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (($ (-1107)) . T)) +((($ (-1201)) -3700 (|has| |#1| (-921 (-1201))) (|has| |#1| (-923 (-1201)))) (($ (-1107)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1206)) . T)) ((((-1206)) . T)) ((((-1206)) . T)) ((((-1206)) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((((-1206)) . T)) ((((-1206)) . T)) (|has| |#1| (-375)) (|has| |#1| (-375)) -(-3777 (|has| |#1| (-174)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-174)) (|has| |#1| (-569))) (((|#1| (-577)) . T)) (((|#1| (-420 (-577))) . T)) (((|#1| (-787)) . T)) @@ -3951,24 +3951,24 @@ (((|#1| (-544 |#2|) |#2|) . T)) ((((-577) |#1|) . T)) ((((-577) |#1|) . T)) -(-3777 (|has| |#1| (-102)) (|has| |#1| (-1125))) -(-3777 (|has| (-420 |#2|) (-239)) (|has| (-420 |#2|) (-238))) +(-3700 (|has| |#1| (-102)) (|has| |#1| (-1125))) +(-3700 (|has| (-420 |#2|) (-239)) (|has| (-420 |#2|) (-238))) ((((-577) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-911 (-391))) . T) (((-911 (-577))) . T) (((-1201)) . T) (((-549)) . T)) -(-3777 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) -(-3777 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-809)) (|has| |#2| (-809)))) +(-3700 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-809)) (|has| |#2| (-1074))) +(-3700 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-809)) (|has| |#2| (-809)))) ((((-880)) . T)) ((((-577)) . T)) ((((-577)) . T)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1201)) -12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) (|has| |#2| (-1074)) -(-3777 (-12 (|has| |#1| (-486)) (|has| |#2| (-486))) (-12 (|has| |#1| (-742)) (|has| |#2| (-742)))) +(-3700 (-12 (|has| |#1| (-486)) (|has| |#2| (-486))) (-12 (|has| |#1| (-742)) (|has| |#2| (-742)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-375)) @@ -4001,7 +4001,7 @@ (((|#1| |#2|) . T)) ((((-577)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-577)) . T)) -(-3777 (|has| |#1| (-361)) (|has| |#1| (-380))) +(-3700 (|has| |#1| (-361)) (|has| |#1| (-380))) (((|#1| |#2|) . T)) ((((-228)) . T)) ((((-420 (-577))) . T) (($) . T) (((-577)) . T)) @@ -4010,11 +4010,11 @@ ((($) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((|#1|) . T) (((-577)) |has| |#1| (-654 (-577)))) ((($) . T) (((-577)) |has| |#1| (-654 (-577))) ((|#1|) . T) (((-420 (-577))) |has| |#1| (-38 (-420 (-577))))) (((|#2|) |has| |#2| (-1125)) (((-577)) -12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) (((-420 (-577))) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) -(-3777 (|has| |#2| (-239)) (|has| |#2| (-238))) +(-3700 (|has| |#2| (-239)) (|has| |#2| (-238))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-627 (-549)))) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-865)) (|has| |#1| (-1125)))) ((((-577) $) . T) (((-660 (-577)) $) . T)) ((($) . T) (((-420 (-577))) . T)) (|has| |#1| (-932)) @@ -4026,14 +4026,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-577)) . T)) ((((-1206)) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-569))) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-569))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-864))) (((|#2|) . T)) -(-3777 (|has| |#1| (-21)) (|has| |#1| (-864))) +(-3700 (|has| |#1| (-21)) (|has| |#1| (-864))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-880)) -3777 (-12 (|has| |#1| (-626 (-880))) (|has| |#2| (-626 (-880)))) (-12 (|has| |#1| (-1125)) (|has| |#2| (-1125))))) +((((-880)) -3700 (-12 (|has| |#1| (-626 (-880))) (|has| |#2| (-626 (-880)))) (-12 (|has| |#1| (-1125)) (|has| |#2| (-1125))))) ((((-420 |#2|) |#3|) . T)) ((((-420 (-577))) . T) (($) . T)) (|has| |#1| (-38 (-420 (-577)))) @@ -4042,7 +4042,7 @@ ((($) . T) (((-577)) . T)) (|has| (-420 |#2|) (-148)) (|has| (-420 |#2|) (-146)) -(-3777 (|has| |#3| (-809)) (|has| |#3| (-865))) +(-3700 (|has| |#3| (-809)) (|has| |#3| (-865))) ((($) . T)) ((((-715)) . T)) (((|#1|) . T) (((-420 (-577))) . T) (((-577)) . T) (($) . T)) @@ -4058,7 +4058,7 @@ ((((-1206)) . T)) ((((-577)) . T)) (((|#2|) . T)) -((((-1201)) -3777 (-12 (|has| (-1199 |#1| |#2| |#3|) (-921 (-1201))) (|has| |#1| (-375))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))))) +((((-1201)) -3700 (-12 (|has| (-1199 |#1| |#2| |#3|) (-921 (-1201))) (|has| |#1| (-375))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201)))))) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201))))) ((((-1201)) -12 (|has| |#1| (-15 * (|#1| (-787) |#1|))) (|has| |#1| (-921 (-1201))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4074,11 +4074,11 @@ ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) ((((-1165 |#1| |#2|)) . T)) ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) -(((|#2|) . T) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1047)) -(((|#2|) . T) (((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) ((($) . T)) ((((-880)) . T)) ((((-549)) |has| |#2| (-627 (-549))) (((-911 (-577))) |has| |#2| (-627 (-911 (-577)))) (((-911 (-391))) |has| |#2| (-627 (-911 (-391)))) (((-391)) . #0=(|has| |#2| (-1047))) (((-228)) . #0#)) @@ -4087,7 +4087,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577)))) -((((-1201)) -3777 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) +((((-1201)) -3700 (|has| |#2| (-921 (-1201))) (|has| |#2| (-923 (-1201))))) ((((-880)) . T)) (((|#2|) . T)) ((((-880)) . T)) @@ -4097,15 +4097,15 @@ ((((-1199 |#1| |#2| |#3|)) . T)) ((((-1199 |#1| |#2| |#3|)) . T) (((-1192 |#1| |#2| |#3|)) . T)) ((((-880)) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) ((((-577) |#1|) . T)) ((((-1199 |#1| |#2| |#3|)) |has| |#1| (-375))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-375)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -3777 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-1074))) (($) |has| |#4| (-1074)) (((-577)) -12 (|has| |#4| (-654 (-577))) (|has| |#4| (-1074)))) -(((|#2|) . T) ((|#3|) -3777 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074))) (($) |has| |#3| (-1074)) (((-577)) -12 (|has| |#3| (-654 (-577))) (|has| |#3| (-1074)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -3700 (|has| |#4| (-174)) (|has| |#4| (-375)) (|has| |#4| (-1074))) (($) |has| |#4| (-1074)) (((-577)) -12 (|has| |#4| (-654 (-577))) (|has| |#4| (-1074)))) +(((|#2|) . T) ((|#3|) -3700 (|has| |#3| (-174)) (|has| |#3| (-375)) (|has| |#3| (-1074))) (($) |has| |#3| (-1074)) (((-577)) -12 (|has| |#3| (-654 (-577))) (|has| |#3| (-1074)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -4119,7 +4119,7 @@ ((((-189)) . T) (((-880)) . T)) ((((-880)) . T)) (((|#1|) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) ((((-130)) . T) (((-880)) . T)) ((((-577) |#1|) . T) (((-1259 (-577)) $) . T)) ((((-880)) . T)) @@ -4129,14 +4129,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-375)) (|has| |#2| (-297 |#2| |#2|))) (($ $) . T) (((-577) |#1|) . T)) ((($ $) . T) (((-420 (-577)) |#1|) . T)) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-932))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-465)) (|has| |#1| (-932))) ((($ (-1201)) |has| |#1| (-1074))) -(-3777 (|has| |#1| (-865)) (|has| |#1| (-1125))) +(-3700 (|has| |#1| (-865)) (|has| |#1| (-1125))) ((((-880)) . T)) ((((-880)) . T)) ((((-880)) . T)) (((|#1| (-544 |#2|)) . T)) -((((-2 (|:| -2284 (-1201)) (|:| -2328 (-52)))) . T)) +((((-2 (|:| -2327 (-1201)) (|:| -2909 (-52)))) . T)) ((((-577) (-130)) . T)) (((|#1| (-577)) . T)) (((|#1| (-420 (-577))) . T)) @@ -4151,8 +4151,8 @@ ((((-1206)) . T)) ((((-880)) . T) (((-1206)) . T)) ((((-880)) . T) (((-1206)) . T)) -(-3777 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) -(-3777 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) +(-3700 (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) +(-3700 (|has| |#1| (-465)) (|has| |#1| (-569)) (|has| |#1| (-932))) ((($) . T)) (((|#2| (-544 (-882 |#1|))) . T)) ((((-1206)) . T)) @@ -4167,7 +4167,7 @@ ((((-1206)) . T)) ((((-880)) . T) (((-1206)) . T)) ((((-1206)) . T)) -((((-880)) -3777 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) +((((-880)) -3700 (|has| |#1| (-626 (-880))) (|has| |#1| (-1125)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1183) |#1|) . T)) @@ -4175,7 +4175,7 @@ ((((-420 |#2|)) . T)) (|has| |#1| (-569)) (|has| |#1| (-569)) -((((-2 (|:| -2284 |#1|) (|:| -2328 |#2|))) . T)) +((((-2 (|:| -2327 |#1|) (|:| -2909 |#2|))) . T)) (((|#2| (-787)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-420 (-577))) . T)) @@ -4185,14 +4185,14 @@ ((((-577)) . T) (($) . T)) (((|#2| $) |has| |#2| (-297 |#2| |#2|))) (((|#1| (-660 |#1|)) |has| |#1| (-864))) -(-3777 (|has| |#1| (-239)) (|has| |#1| (-361))) -(-3777 (|has| |#1| (-375)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-239)) (|has| |#1| (-361))) +(-3700 (|has| |#1| (-375)) (|has| |#1| (-361))) ((((-1288 |#1|)) . T) (((-577)) . T) ((|#2|) . T) (((-420 (-577))) |has| |#2| (-1063 (-420 (-577))))) (|has| |#1| (-1125)) (((|#1|) . T)) ((((-420 (-577))) . T) (($) . T)) -((((-1288 |#1|)) . T) (((-577)) . T) (($) -3777 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((-1107)) . T) ((|#2|) . T) (((-420 (-577))) -3777 (|has| |#2| (-38 (-420 (-577)))) (|has| |#2| (-1063 (-420 (-577)))))) -((((-1024 |#1|)) . T) ((|#1|) . T) (((-577)) -3777 (|has| (-1024 |#1|) (-1063 (-577))) (|has| |#1| (-1063 (-577)))) (((-420 (-577))) -3777 (|has| (-1024 |#1|) (-1063 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577)))))) +((((-1288 |#1|)) . T) (((-577)) . T) (($) -3700 (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) (((-1107)) . T) ((|#2|) . T) (((-420 (-577))) -3700 (|has| |#2| (-38 (-420 (-577)))) (|has| |#2| (-1063 (-420 (-577)))))) +((((-1024 |#1|)) . T) ((|#1|) . T) (((-577)) -3700 (|has| (-1024 |#1|) (-1063 (-577))) (|has| |#1| (-1063 (-577)))) (((-420 (-577))) -3700 (|has| (-1024 |#1|) (-1063 (-420 (-577)))) (|has| |#1| (-1063 (-420 (-577)))))) ((((-933 |#1|)) . T) (((-420 (-577))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) (((|#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125)))) @@ -4209,11 +4209,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1165 |#1| |#2|) #0#) |has| (-1165 |#1| |#2|) (-320 (-1165 |#1| |#2|)))) (((|#1|) . 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. -1125) T) ((-529 . -19) 194248) ((-509 . -19) 194232) ((-59 . -617) 194209) ((-1028 . -238) 194146) ((-924 . -102) 194096) ((-872 . -742) T) ((-798 . -1125) T) ((-529 . -617) 194073) ((-509 . -617) 194050) ((-796 . -1125) T) ((-796 . -1090) 194017) ((-474 . -1125) T) ((-467 . -1125) T) ((-599 . -733) 193992) ((-665 . -1125) T) ((-1284 . -47) 193969) ((-1278 . -102) T) ((-1277 . -47) 193939) ((-1256 . -47) 193916) ((-1236 . -174) 193867) ((-1198 . -318) 193846) ((-1192 . -318) 193825) ((-1121 . -629) 193806) ((-1115 . -629) 193787) ((-1105 . -569) 193738) ((-1105 . -1246) 193689) ((-1098 . -629) 193670) ((-1029 . -921) NIL) ((-1091 . -629) 193651) ((-686 . -132) T) ((-640 . -1137) T) ((-1061 . -629) 193632) ((-1044 . -629) 193613) ((-730 . -1081) 193583) ((-728 . -915) 193486) ((-715 . -662) 193436) ((-285 . -1125) T) ((-85 . -454) T) ((-85 . -408) T) ((-727 . -174) T) ((-653 . -1081) 193420) ((-50 . -1125) T) ((-608 . -47) 193397) ((-228 . -664) 193362) ((-594 . -1125) T) ((-531 . 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192544) ((-1256 . -1063) 192510) ((-1236 . -527) 192477) ((-1214 . -627) NIL) ((-528 . -629) 192461) ((-1214 . -626) 192443) ((-1167 . -1148) 192388) ((-1112 . -733) 192237) ((-494 . -932) 192216) ((-1102 . -102) T) ((-1087 . -664) 192188) ((-975 . -664) 192077) ((-834 . -868) T) ((-798 . -733) 191906) ((-610 . -503) 191887) ((-598 . -503) 191868) ((-610 . -626) 191834) ((-598 . -626) 191800) ((-549 . -626) 191782) ((-592 . -1242) T) ((-549 . -627) 191763) ((-796 . -733) 191612) ((-1071 . -1235) 191541) ((-636 . -662) 191513) ((-393 . -25) T) ((-393 . -21) T) ((-494 . -664) 191402) ((-474 . -733) 191373) ((-467 . -733) 191222) ((-1012 . -102) T) ((-924 . -320) 191160) ((-894 . -93) T) ((-753 . -102) T) ((-653 . -629) 191137) ((-118 . -662) 191067) ((-618 . -629) 191049) ((-730 . -629) 191003) ((-697 . -93) T) ((-544 . -25) T) ((-692 . -93) T) ((-680 . -626) 190985) ((-661 . -503) 190966) ((-661 . -626) 190919) ((-142 . -102) T) ((-44 . -132) T) ((-609 . -1242) T) ((-608 . -1242) T) 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-742) T) ((-529 . -627) 189818) ((-529 . -626) 189730) ((-510 . -626) 189662) ((-509 . -627) 189623) ((-509 . -626) 189535) ((-1105 . -375) 189486) ((-40 . -424) 189463) ((-77 . -1242) T) ((-889 . -932) NIL) ((-371 . -340) 189447) ((-371 . -375) T) ((-365 . -340) 189431) ((-365 . -375) T) ((-357 . -340) 189415) ((-357 . -375) T) ((-327 . -295) 189394) ((-108 . -375) T) ((-70 . -1242) T) ((-655 . -1125) T) ((-1256 . -350) 189346) ((-889 . -664) 189291) ((-1256 . -389) 189243) ((-987 . -132) 189098) ((-831 . -132) 188969) ((-45 . -868) NIL) ((-981 . -667) 188953) ((-1112 . -174) 188864) ((-981 . -385) 188848) ((-1087 . -810) T) ((-1087 . -807) T) ((-890 . -629) 188746) ((-798 . -174) 188637) ((-796 . -174) 188548) ((-832 . -47) 188510) ((-1087 . -742) T) ((-338 . -502) 188494) ((-975 . -742) T) ((-1305 . -320) 188432) ((-1284 . -921) 188345) ((-467 . -174) 188256) ((-251 . -297) 188208) ((-1277 . -921) 188114) ((-1276 . -1081) 187949) ((-1256 . -921) 187782) ((-494 . -742) T) ((-1255 . -1081) 187590) ((-1236 . -301) 187569) ((-1211 . -1242) T) ((-1208 . -380) T) ((-1207 . -380) T) ((-1171 . -152) 187553) ((-1145 . -102) T) ((-1143 . -1125) T) ((-1105 . -23) T) ((-1105 . -1137) T) ((-1100 . -102) T) ((-1082 . -626) 187520) ((-1028 . -422) 187492) ((-950 . -978) T) ((-753 . -320) 187430) ((-75 . -1242) T) ((-680 . -394) 187402) ((-171 . -932) 187355) ((-30 . -978) T) ((-112 . -860) T) ((-1 . -626) 187337) ((-1024 . -915) 187258) ((-129 . -667) 187240) ((-50 . -633) 187224) ((-710 . -662) 187159) ((-608 . -921) 187072) ((-451 . -102) T) ((-129 . -385) 187054) ((-142 . -320) NIL) ((-890 . -1074) T) ((-849 . -865) 187033) ((-81 . -1242) T) ((-727 . -301) T) ((-40 . -1083) T) ((-594 . -174) T) ((-531 . -174) T) ((-524 . -626) 187015) ((-171 . -664) 186889) ((-520 . -626) 186871) ((-363 . -148) 186853) ((-363 . -146) T) ((-371 . -1137) T) ((-365 . -1137) T) ((-357 . -1137) T) ((-1029 . -318) T) ((-937 . -318) T) ((-890 . -249) T) ((-108 . -1137) T) ((-890 . -239) 186832) ((-1276 . -111) 186653) ((-1255 . -111) 186442) ((-251 . -1280) 186426) ((-577 . -864) T) ((-371 . -23) T) ((-366 . -361) T) ((-327 . -320) 186413) ((-324 . -320) 186354) ((-365 . -23) T) ((-330 . -132) T) ((-357 . -23) T) ((-1029 . -1047) T) ((-31 . -629) 186335) ((-108 . -23) T) ((-670 . -1076) 186319) ((-251 . -617) 186296) ((-655 . -733) 186280) ((-344 . -1125) T) ((-670 . -656) 186250) ((-1278 . -38) 186142) ((-1265 . -932) 186121) ((-112 . -1125) T) ((-832 . -1242) T) ((-426 . -1242) T) ((-1060 . -102) T) ((-1265 . -664) 186010) ((-889 . -810) NIL) ((-873 . -664) 185984) ((-889 . -807) NIL) ((-832 . -905) NIL) ((-889 . -742) T) ((-1112 . -527) 185857) ((-798 . -527) 185804) ((-796 . -527) 185756) ((-584 . -664) 185743) ((-832 . -1063) 185571) ((-467 . -527) 185514) ((-401 . -402) T) ((-1276 . -629) 185327) ((-1255 . -629) 185075) ((-60 . -1242) T) ((-634 . -865) 185054) ((-513 . -677) T) ((-1171 . -1001) 185023) ((-1049 . -662) 184960) ((-1028 . -465) T) ((-715 . -864) T) ((-523 . -808) T) ((-487 . -1081) 184795) ((-513 . -113) T) ((-355 . -1125) T) ((-324 . -1177) NIL) ((-300 . -132) T) ((-407 . -1125) T) ((-888 . -1083) T) ((-710 . -382) 184762) ((-366 . -662) 184692) ((-226 . -633) 184669) ((-338 . -297) 184621) ((-487 . -111) 184442) ((-1276 . -1074) T) ((-1255 . -1074) T) ((-832 . -389) 184426) ((-840 . -1242) T) ((-171 . -742) T) ((-1307 . -1242) T) ((-670 . -102) T) ((-1276 . -249) 184405) ((-1276 . -239) 184357) ((-1255 . -239) 184262) ((-1255 . -249) 184241) ((-1028 . -415) NIL) ((-686 . -654) 184189) ((-327 . -38) 184099) ((-324 . -38) 184028) ((-69 . -626) 184010) ((-330 . -506) 183976) ((-48 . -662) 183926) ((-1214 . -299) 183905) ((-1250 . -865) T) ((-1138 . -1137) 183883) ((-83 . -1242) T) ((-61 . -626) 183865) ((-882 . -868) T) ((-492 . -299) 183844) ((-1307 . -1063) 183821) ((-1189 . -1125) T) ((-1138 . -23) 183673) ((-832 . -921) 183609) ((-1265 . -742) T) ((-1127 . -1242) T) ((-487 . -629) 183435) ((-363 . -238) T) ((-1112 . -301) 183366) ((-989 . -1125) T) ((-912 . -102) T) ((-798 . -301) 183277) ((-338 . -19) 183261) ((-59 . -299) 183238) ((-796 . -301) 183169) ((-873 . -742) T) ((-118 . -864) NIL) ((-529 . -299) 183146) ((-338 . -617) 183123) ((-509 . -299) 183100) ((-467 . -301) 183031) ((-1060 . -320) 182882) ((-894 . -503) 182863) ((-894 . -626) 182829) ((-697 . -503) 182810) ((-584 . -742) T) ((-692 . -503) 182791) ((-697 . -626) 182741) ((-692 . -626) 182707) ((-678 . -626) 182689) ((-491 . -503) 182670) ((-491 . -626) 182636) ((-251 . -627) 182597) ((-251 . -503) 182574) ((-139 . -503) 182555) ((-138 . -503) 182536) ((-134 . -503) 182517) ((-251 . -626) 182409) ((-215 . -102) T) ((-139 . -626) 182375) ((-138 . -626) 182341) ((-134 . -626) 182307) ((-1172 . -34) T) ((-966 . -1242) T) ((-355 . -733) 182252) ((-686 . -25) T) ((-686 . -21) T) ((-1201 . -629) 182233) ((-342 . -1242) T) ((-487 . -1074) T) ((-648 . -430) 182198) ((-620 . -430) 182163) ((-1145 . -1177) T) ((-1277 . -318) 182142) ((-728 . -1076) 181965) ((-594 . -301) T) ((-531 . -301) T) ((-1256 . -318) 181944) ((-487 . -239) 181896) ((-487 . -249) 181875) ((-452 . -1242) T) ((-728 . -656) 181704) ((-1256 . -1047) NIL) ((-1105 . -132) T) ((-890 . -811) 181683) ((-145 . -102) T) ((-40 . -1125) T) ((-890 . -808) 181662) ((-660 . -1035) 181646) ((-593 . -1083) T) ((-577 . -1083) T) ((-508 . -1083) T) ((-420 . -465) T) ((-371 . -132) T) ((-327 . -413) 181630) ((-324 . -413) 181591) ((-365 . -132) T) ((-357 . -132) T) ((-1206 . -1125) T) ((-1145 . -38) 181578) ((-1119 . -626) 181545) ((-108 . -132) T) ((-977 . -1125) T) ((-944 . -1125) T) ((-787 . -1125) T) ((-688 . -1125) T) ((-717 . -148) T) ((-117 . -148) T) ((-1314 . -21) T) ((-1314 . -25) T) ((-1312 . -21) T) ((-1312 . -25) T) ((-680 . -1081) 181529) ((-544 . -865) T) ((-513 . -865) T) ((-377 . -1242) T) ((-367 . -1081) 181481) ((-364 . -1081) 181433) ((-356 . -1081) 181385) ((-259 . -1242) T) ((-258 . -1242) T) ((-274 . -1081) 181228) ((-254 . -1081) 181071) ((-680 . -111) 181050) ((-833 . -1246) 181029) ((-560 . -860) T) ((-327 . -923) 180995) ((-367 . -111) 180933) ((-364 . -111) 180871) ((-356 . -111) 180809) ((-274 . -111) 180638) ((-254 . -111) 180467) ((-324 . -923) NIL) ((-636 . -424) 180451) ((-44 . -21) T) ((-44 . -25) T) ((-928 . -868) 180402) ((-831 . -654) 180308) ((-833 . -569) 180287) ((-500 . -868) T) ((-259 . -1063) 180114) ((-258 . -1063) 179941) ((-127 . -120) 179925) ((-220 . -868) T) ((-933 . -1081) 179890) ((-728 . -102) T) ((-715 . -1083) T) ((-610 . -629) 179871) ((-598 . -629) 179852) ((-549 . -631) 179755) ((-355 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -626) 179737) ((-933 . -111) 179693) ((-40 . -733) 179638) ((-888 . -1125) T) ((-680 . -629) 179615) ((-661 . -629) 179596) ((-367 . -629) 179533) ((-364 . -629) 179470) ((-356 . -629) 179407) ((-560 . -1125) T) ((-338 . -627) 179368) ((-338 . -626) 179280) ((-274 . -629) 179033) ((-254 . -629) 178818) ((-188 . -1242) T) ((-1255 . -808) 178771) ((-1255 . -811) 178724) ((-259 . -389) 178693) ((-258 . -389) 178662) ((-562 . -868) T) ((-670 . -38) 178632) ((-621 . -34) T) ((-495 . -1137) 178610) ((-488 . -34) T) ((-1138 . -132) 178481) ((-987 . -25) 178292) ((-933 . -629) 178242) ((-892 . -626) 178224) ((-217 . -860) T) ((-987 . -21) 178179) ((-831 . -25) 178012) ((-831 . -21) 177923) ((-1248 . -380) T) ((-636 . -1083) T) ((-1203 . -569) 177902) ((-1197 . -47) 177879) ((-367 . -1074) T) ((-364 . -1074) T) ((-495 . -23) 177731) ((-356 . -1074) T) ((-274 . -1074) T) ((-254 . -1074) T) ((-1150 . -47) 177703) ((-118 . -1083) T) ((-1059 . -664) 177677) ((-981 . -34) T) ((-367 . -239) 177656) ((-367 . -249) T) ((-364 . -239) 177635) ((-364 . -249) T) ((-356 . -239) 177614) ((-356 . -249) T) ((-274 . -337) 177586) ((-254 . -337) 177543) ((-274 . -239) 177522) ((-1182 . -152) 177506) ((-259 . -921) 177438) ((-258 . -921) 177370) ((-1167 . -915) 177291) ((-1107 . -865) T) ((-1259 . -1242) 177269) ((-427 . -1137) T) ((-1236 . -1027) 177235) ((-1079 . -23) T) ((-1049 . -864) T) ((-933 . -1074) T) ((-333 . -664) 177217) ((-717 . -238) T) ((-686 . -235) 177162) ((-1198 . -943) 177141) ((-1192 . -943) 177120) ((-1192 . -836) NIL) ((-1024 . -1076) 177016) ((-990 . -1242) T) ((-933 . -249) T) ((-833 . -375) 176995) ((-217 . -1125) T) ((-397 . -23) T) ((-128 . -1125) 176973) ((-122 . -1125) 176951) ((-933 . -239) T) ((-129 . -34) T) ((-391 . -664) 176916) ((-1024 . -656) 176864) ((-888 . -733) 176851) ((-1321 . -662) 176823) ((-1071 . -152) 176788) ((-1018 . -1242) T) ((-880 . -1242) T) ((-40 . -174) T) ((-710 . -424) 176770) ((-728 . -320) 176757) ((-852 . -664) 176717) ((-843 . -664) 176691) ((-330 . -25) T) ((-330 . -21) T) ((-674 . -297) 176670) ((-593 . -1125) T) ((-577 . -1125) T) ((-508 . -1125) T) ((-1197 . -1242) T) ((-251 . -299) 176647) ((-1150 . -1242) T) ((-872 . -1242) T) ((-324 . -273) 176608) ((-324 . -233) 176569) ((-1247 . -868) T) ((-1197 . -905) NIL) ((-55 . -1125) T) ((-1150 . -905) 176428) ((-130 . -865) T) ((-1197 . -1063) 176308) ((-1150 . -1063) 176191) ((-185 . -626) 176173) ((-872 . -1063) 176069) ((-798 . -297) 175996) ((-833 . -1137) T) ((-1059 . -742) T) ((-1071 . -1001) 175925) ((-615 . -667) 175909) ((-1028 . -915) 175816) ((-1024 . -102) T) ((-833 . -23) T) ((-728 . -1177) 175794) ((-710 . -1083) T) ((-615 . -385) 175778) ((-363 . -465) T) ((-355 . -301) T) ((-1293 . -1125) T) ((-255 . -1125) T) ((-412 . -102) T) ((-300 . -21) T) ((-300 . -25) T) ((-373 . -742) T) ((-726 . -1125) T) ((-715 . -1125) T) ((-373 . -486) T) ((-1236 . -626) 175760) ((-1197 . -389) 175744) ((-1150 . -389) 175728) ((-1049 . -424) 175690) ((-142 . -232) 175672) ((-391 . -810) T) ((-391 . -807) T) ((-888 . -174) T) ((-391 . -742) T) ((-727 . -626) 175654) ((-728 . -38) 175483) ((-1292 . -1290) 175467) ((-363 . -415) T) ((-1292 . -1125) 175417) ((-1215 . -1125) T) ((-593 . -733) 175404) ((-577 . -733) 175391) ((-508 . -733) 175356) ((-1278 . -662) 175246) ((-327 . -642) 175225) ((-852 . -742) T) ((-843 . -742) T) ((-1140 . -1242) T) ((-660 . -1242) T) ((-1105 . -654) 175173) ((-1197 . -921) 175116) ((-1150 . -921) 175100) ((-831 . -235) 174991) ((-678 . -1081) 174975) ((-108 . -654) 174957) ((-495 . -132) 174828) ((-1203 . -1137) T) ((-835 . -1242) T) ((-975 . -47) 174797) ((-636 . -1125) T) ((-678 . -111) 174776) ((-504 . -626) 174742) ((-338 . -299) 174719) ((-399 . -1242) T) ((-335 . -1242) T) ((-494 . -47) 174676) ((-1203 . -23) T) ((-118 . -1125) T) ((-103 . -102) 174626) ((-1304 . -1137) T) ((-561 . -865) T) ((-228 . -1242) T) ((-1079 . -132) T) ((-1049 . -1083) T) ((-1304 . -23) T) ((-1222 . -626) 174608) ((-835 . -1063) 174592) ((-1145 . -844) T) ((-1028 . -740) 174564) ((-1130 . -1125) T) ((-715 . -733) 174529) ((-599 . -626) 174511) ((-399 . -1063) 174495) ((-366 . -1083) T) ((-397 . -132) T) ((-335 . -1063) 174479) ((-1105 . -21) T) ((-1105 . -25) T) ((-1029 . -836) T) ((-228 . -905) 174461) ((-1029 . -943) T) ((-91 . -34) T) ((-1024 . -320) 174426) ((-937 . -943) T) ((-894 . -629) 174407) ((-730 . -664) 174367) ((-500 . -1246) T) ((-697 . -629) 174348) ((-692 . -629) 174329) ((-653 . -664) 174313) ((-220 . -1246) T) ((-420 . -915) 174234) ((-228 . -1063) 174194) ((-40 . -301) T) ((-500 . -569) T) ((-491 . -629) 174175) ((-371 . -25) T) ((-327 . -662) 173830) ((-324 . -662) 173744) ((-371 . -21) T) ((-365 . -25) T) ((-365 . -21) T) ((-220 . -569) T) ((-357 . -25) T) ((-357 . -21) T) ((-330 . -235) 173690) ((-251 . -629) 173667) ((-139 . -629) 173648) ((-138 . -629) 173629) ((-134 . -629) 173610) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1083) T) ((-593 . -174) T) ((-577 . -174) T) ((-508 . -174) T) ((-1087 . -1242) T) ((-975 . -1242) T) ((-729 . -1242) T) ((-655 . -297) 173577) ((-674 . -626) 173559) ((-494 . -1242) T) ((-753 . -752) 173543) ((-348 . -626) 173525) ((-68 . -395) T) ((-68 . -408) T) ((-1127 . -107) 173509) ((-1087 . -905) 173491) ((-975 . -905) 173416) ((-669 . -1137) T) ((-636 . -733) 173403) ((-494 . -905) NIL) ((-1171 . -102) T) ((-1119 . -631) 173387) ((-1087 . -1063) 173369) ((-97 . -626) 173351) ((-490 . -148) T) ((-975 . -1063) 173231) ((-118 . -733) 173176) ((-728 . -923) 173083) ((-669 . -23) T) ((-494 . -1063) 172959) ((-1112 . -627) NIL) ((-1112 . -626) 172941) ((-798 . -627) NIL) ((-798 . -626) 172902) ((-796 . -627) 172536) ((-796 . -626) 172450) ((-1138 . -654) 172356) ((-815 . -868) 172335) ((-474 . -626) 172317) ((-467 . -626) 172299) ((-467 . -627) 172160) ((-1060 . -232) 172106) ((-890 . -932) 172085) ((-127 . -34) T) ((-833 . -132) T) ((-665 . -626) 172067) ((-591 . -102) T) ((-367 . -1311) 172051) ((-364 . -1311) 172035) ((-356 . -1311) 172019) ((-122 . -527) 171952) ((-128 . -527) 171885) ((-524 . -808) T) ((-524 . -811) T) ((-523 . -810) T) ((-103 . -320) 171823) ((-225 . -102) 171773) ((-715 . -174) T) ((-710 . -1125) T) ((-890 . -664) 171689) ((-65 . -396) T) ((-285 . -626) 171671) ((-65 . -408) T) ((-975 . -389) 171655) ((-888 . -301) T) ((-50 . -626) 171637) ((-1024 . -38) 171585) ((-1145 . -662) 171557) ((-594 . -626) 171539) ((-494 . -389) 171523) ((-594 . -627) 171505) ((-531 . -626) 171487) ((-933 . -1311) 171474) ((-889 . -1242) T) ((-717 . -465) T) ((-508 . -527) 171440) ((-1303 . -1242) T) ((-1302 . -1242) T) ((-500 . -375) T) ((-367 . -380) 171419) ((-364 . -380) 171398) ((-356 . -380) 171377) ((-730 . -742) T) ((-220 . -375) T) ((-117 . -465) T) ((-1315 . -1306) 171361) ((-889 . -903) 171338) ((-889 . -905) NIL) ((-987 . -865) 171237) ((-831 . -865) 171188) ((-1249 . -102) T) ((-670 . -672) 171172) ((-1228 . -34) T) ((-173 . -626) 171154) ((-1138 . -25) 170987) ((-1138 . -21) 170898) ((-889 . -1063) 170875) ((-975 . -921) 170856) ((-1265 . -47) 170833) ((-933 . -380) T) ((-606 . -868) T) ((-59 . -667) 170817) ((-529 . -667) 170801) ((-494 . -921) 170778) ((-71 . -454) T) ((-71 . -408) T) ((-509 . -667) 170762) ((-59 . -385) 170746) ((-636 . -174) T) ((-529 . -385) 170730) ((-509 . -385) 170714) ((-559 . -1242) T) ((-843 . -724) 170698) ((-1197 . -318) 170677) ((-1203 . -132) T) ((-1167 . -1076) 170661) ((-118 . -174) T) ((-1167 . -656) 170593) ((-1171 . -320) 170531) ((-171 . -1242) T) ((-1304 . -132) T) ((-1277 . -943) 170510) ((-1256 . -943) 170489) ((-1256 . -836) NIL) ((-884 . -1076) 170459) ((-648 . -760) 170443) ((-620 . -760) 170427) ((-1255 . -932) 170380) ((-1049 . -1125) T) ((-928 . -1137) T) ((-884 . -656) 170350) ((-710 . -733) 170300) ((-919 . -1242) T) ((-889 . -389) 170277) ((-889 . -350) 170254) ((-857 . -1242) T) ((-824 . -1242) T) ((-171 . -903) 170238) ((-171 . -905) 170163) ((-785 . -1242) T) ((-693 . -1242) T) ((-1292 . -527) 170096) ((-1276 . -664) 169993) ((-1105 . -235) 169866) ((-500 . -1137) T) ((-366 . -1125) T) ((-220 . -1137) T) ((-76 . -454) T) ((-76 . -408) T) ((-171 . -1063) 169762) ((-305 . -915) 169719) ((-330 . -865) T) ((-1255 . -664) 169527) ((-890 . -810) 169506) ((-890 . -807) 169485) ((-890 . -742) T) ((-500 . -23) T) ((-371 . -235) 169458) ((-365 . -235) 169431) ((-357 . -235) 169404) ((-176 . -465) T) ((-86 . -454) T) ((-225 . -320) 169342) ((-86 . -408) T) ((-226 . -626) 169324) ((-108 . -235) 169311) ((-220 . -23) T) ((-1316 . -1309) 169290) ((-693 . -1063) 169274) ((-593 . -301) T) ((-577 . -301) T) ((-508 . -301) T) ((-1265 . -1242) T) ((-137 . -483) 169229) ((-873 . -1242) T) ((-670 . -662) 169188) ((-48 . -1125) T) ((-728 . -273) 169172) ((-728 . -233) 169156) ((-889 . -921) NIL) ((-584 . -1242) T) ((-1265 . -905) NIL) ((-908 . -102) T) ((-904 . -102) T) ((-655 . -626) 169138) ((-401 . -1125) T) ((-171 . -389) 169122) ((-171 . -350) 169106) ((-1265 . -1063) 168986) ((-873 . -1063) 168882) ((-1167 . -102) T) ((-1024 . -923) 168805) ((-678 . -808) 168784) ((-669 . -132) T) ((-678 . -811) 168763) ((-118 . -527) 168671) ((-584 . -1063) 168653) ((-305 . -1299) 168623) ((-1192 . -868) NIL) ((-884 . -102) T) ((-986 . -569) 168602) ((-1236 . -1081) 168485) ((-1028 . -1076) 168430) ((-495 . -654) 168336) ((-927 . -1125) T) ((-1049 . -733) 168273) ((-727 . -1081) 168238) ((-1028 . -656) 168183) ((-630 . -102) T) 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-102) T) ((-599 . -111) 166767) ((-1236 . -1074) T) ((-1167 . -320) 166705) ((-1087 . -1047) T) ((-1079 . -25) T) ((-66 . -1242) T) ((-911 . -1242) T) ((-1079 . -21) T) ((-727 . -1074) T) ((-397 . -21) T) ((-397 . -25) T) ((-710 . -527) NIL) ((-1049 . -174) T) ((-727 . -249) T) ((-1087 . -558) T) ((-728 . -662) 166615) ((-519 . -102) T) ((-515 . -102) T) ((-366 . -174) T) ((-355 . -626) 166597) ((-420 . -1076) 166549) ((-407 . -626) 166531) ((-1145 . -864) T) ((-487 . -742) T) ((-911 . -1063) 166499) ((-420 . -656) 166451) ((-108 . -865) T) ((-674 . -1081) 166435) ((-500 . -132) T) ((-1278 . -1083) T) ((-220 . -132) T) ((-1182 . -102) 166385) ((-99 . -1125) T) ((-246 . -868) 166336) ((-251 . -682) 166320) ((-251 . -667) 166304) ((-674 . -111) 166283) ((-599 . -629) 166267) ((-327 . -424) 166251) ((-251 . -385) 166235) ((-1184 . -241) 166182) ((-1024 . -273) 166166) ((-1024 . -233) 166150) ((-74 . -1242) T) ((-48 . -174) T) ((-717 . -400) T) ((-717 . -144) T) ((-1315 . -102) T) ((-1223 . -1242) T) ((-1222 . -629) 166132) ((-1113 . -1242) T) ((-1112 . -1081) 165975) ((-1101 . -1242) T) ((-274 . -932) 165954) ((-254 . -932) 165933) ((-798 . -1081) 165756) ((-796 . -1081) 165599) ((-621 . -1242) T) ((-1189 . -626) 165581) ((-1112 . -111) 165410) ((-1071 . -102) T) ((-488 . -1242) T) ((-474 . -1081) 165381) ((-467 . -1081) 165224) ((-680 . -664) 165208) ((-889 . -318) T) ((-798 . -111) 165017) ((-796 . -111) 164846) ((-367 . -664) 164798) ((-364 . -664) 164750) ((-356 . -664) 164702) ((-274 . -664) 164591) ((-254 . -664) 164480) ((-1183 . -865) T) ((-1113 . -1063) 164464) ((-1101 . -1063) 164441) ((-1029 . -868) T) ((-1025 . -34) T) ((-474 . -111) 164402) ((-467 . -111) 164231) ((-996 . -868) T) ((-989 . -626) 164213) ((-986 . -1137) T) ((-981 . -1242) T) ((-127 . -1035) 164197) ((-866 . -1242) T) ((-889 . -1047) NIL) ((-751 . -1137) T) ((-731 . -1137) T) ((-674 . -629) 164115) ((-1292 . -502) 164099) ((-1209 . -1242) T) ((-1208 . -1242) T) ((-1167 . -38) 164059) ((-986 . -23) T) ((-933 . -664) 164024) ((-883 . -1125) T) ((-859 . -102) T) ((-833 . -21) T) ((-648 . -1076) 164008) ((-620 . -1076) 163992) ((-833 . -25) T) ((-751 . -23) T) ((-731 . -23) T) ((-648 . -656) 163976) ((-110 . -677) T) ((-620 . -656) 163960) ((-594 . -1081) 163925) ((-531 . -1081) 163870) ((-230 . -57) 163828) ((-466 . -23) T) ((-420 . -102) T) ((-1207 . -1242) T) ((-271 . -102) T) ((-110 . -113) T) ((-710 . -301) T) ((-884 . -38) 163798) ((-1112 . -629) 163534) ((-594 . -111) 163490) ((-531 . -111) 163419) ((-431 . -1137) T) ((-327 . -1083) 163309) ((-324 . -1083) T) ((-129 . -1242) T) ((-131 . -1242) T) ((-798 . -629) 163057) ((-796 . -629) 162823) ((-674 . -1074) T) ((-1321 . -1125) T) ((-467 . -629) 162608) ((-171 . -318) 162539) ((-431 . -23) T) ((-40 . -626) 162521) ((-40 . -627) 162505) ((-108 . -1017) 162487) ((-117 . -887) 162471) ((-665 . -629) 162455) ((-48 . -527) 162421) ((-1228 . -1035) 162405) ((-1206 . -626) 162372) ((-1214 . -34) T) ((-977 . -626) 162338) 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-1063) 160593) ((-655 . -1081) 160577) ((-205 . -803) T) ((-204 . -803) T) ((-203 . -803) T) ((-202 . -803) T) ((-201 . -803) T) ((-200 . -803) T) ((-199 . -803) T) ((-198 . -803) T) ((-197 . -803) T) ((-196 . -803) T) ((-560 . -626) 160559) ((-508 . -1027) T) ((-284 . -855) T) ((-283 . -855) T) ((-282 . -855) T) ((-281 . -855) T) ((-48 . -301) T) ((-280 . -855) T) ((-279 . -855) T) ((-278 . -855) T) ((-195 . -803) T) ((-655 . -111) 160538) ((-625 . -865) T) ((-670 . -424) 160522) ((-686 . -238) 160473) ((-226 . -629) 160435) ((-110 . -865) T) ((-669 . -21) T) ((-669 . -25) T) ((-1315 . -38) 160405) ((-118 . -297) 160356) ((-1292 . -19) 160340) ((-1256 . -868) NIL) ((-1292 . -617) 160317) ((-1305 . -1125) T) ((-363 . -1076) 160262) ((-1102 . -1125) T) ((-1012 . -1125) T) ((-986 . -132) T) ((-833 . -235) 160249) ((-753 . -1125) T) ((-363 . -656) 160194) ((-751 . -132) T) ((-731 . -132) T) ((-524 . -809) T) ((-524 . -810) T) ((-466 . -132) T) ((-420 . -1177) 160172) ((-226 . -1074) T) 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159078) ((-1197 . -943) 159057) ((-747 . -1137) T) ((-651 . -102) T) ((-528 . -1242) T) ((-523 . -1242) T) ((-521 . -1242) T) ((-363 . -102) T) ((-1241 . -1108) T) ((-1145 . -860) T) ((-834 . -865) T) ((-747 . -23) T) ((-355 . -1081) 159002) ((-1172 . -107) 158986) ((-1293 . -626) 158968) ((-653 . -1242) T) ((-1199 . -23) T) ((-1199 . -1137) T) ((-1198 . -1137) T) ((-1198 . -23) T) ((-528 . -1063) 158952) ((-1192 . -1137) T) ((-1151 . -1137) T) ((-355 . -111) 158881) ((-1029 . -1246) T) ((-127 . -1242) T) ((-937 . -1246) T) ((-1192 . -23) T) ((-1167 . -273) 158865) ((-710 . -297) NIL) ((-730 . -1242) T) ((-1167 . -233) 158849) ((-1151 . -23) T) ((-1100 . -1125) T) ((-1029 . -569) T) ((-937 . -569) T) ((-256 . -1242) T) ((-189 . -1242) T) ((-163 . -1242) T) ((-158 . -1242) T) ((-255 . -626) 158831) ((-831 . -238) 158728) ((-815 . -132) T) ((-726 . -626) 158710) ((-327 . -733) 158620) ((-324 . -733) 158549) ((-715 . -626) 158531) ((-715 . -627) 158476) ((-420 . -413) 158460) ((-451 . -1125) T) ((-500 . -25) T) ((-500 . -21) T) ((-1145 . -1125) T) ((-220 . -25) T) ((-220 . -21) T) ((-728 . -424) 158444) ((-730 . -1063) 158413) ((-1292 . -626) 158325) ((-1292 . -627) 158286) ((-1278 . -174) T) ((-1215 . -626) 158268) ((-251 . -34) T) ((-355 . -629) 158198) ((-407 . -629) 158180) ((-949 . -999) T) ((-1228 . -1242) T) ((-678 . -807) 158159) ((-678 . -810) 158138) ((-411 . -408) T) ((-536 . -102) 158088) ((-1248 . -1242) T) ((-1060 . -1125) T) ((-420 . -923) 158011) ((-225 . -1020) 157995) ((-854 . -1242) T) ((-517 . -102) T) ((-636 . -626) 157977) ((-45 . -865) NIL) ((-636 . -627) 157954) ((-1060 . -623) 157929) ((-924 . -527) 157862) ((-330 . -238) 157814) ((-355 . -1074) T) ((-118 . -627) NIL) ((-118 . -626) 157796) ((-890 . -1242) T) ((-686 . -430) 157780) ((-686 . -1148) 157725) ((-513 . -152) 157707) ((-355 . -239) T) ((-355 . -249) T) ((-40 . -1081) 157652) ((-890 . -903) 157636) ((-890 . -905) 157561) ((-728 . -1083) T) ((-710 . -1027) NIL) ((-1276 . -47) 157531) ((-1255 . -47) 157508) ((-1166 . -1035) 157479) ((-1145 . -733) 157466) ((-3 . |UnionCategory|) T) ((-1130 . -626) 157448) ((-1105 . -148) 157427) ((-1105 . -146) 157378) ((-1029 . -375) T) ((-989 . -629) 157362) ((-228 . -943) T) ((-40 . -111) 157291) ((-890 . -1063) 157155) ((-1028 . -233) 157132) ((-1028 . -273) 157109) ((-717 . -1076) 157096) ((-937 . -375) T) ((-717 . -656) 157083) ((-330 . -1230) 157049) ((-391 . -318) T) ((-330 . -1227) 157015) ((-327 . -174) 156994) ((-324 . -174) T) ((-621 . -1218) 156970) ((-594 . -1311) 156957) ((-531 . -1311) 156934) ((-117 . -1076) 156921) ((-371 . -148) 156900) ((-371 . -146) 156851) ((-365 . -148) 156830) ((-365 . -146) 156781) ((-357 . -148) 156760) ((-117 . -656) 156747) ((-357 . -146) 156698) ((-330 . -35) 156664) ((-488 . -1218) 156643) ((0 . |EnumerationCategory|) T) ((-330 . -95) 156609) ((-391 . -1047) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -241) 156559) ((-670 . -1125) T) ((-621 . -107) 156506) ((-498 . -132) T) 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-662) 155423) ((-937 . -1137) T) ((-937 . -23) T) ((-890 . -921) 155382) ((-363 . -38) 155347) ((-888 . -1081) 155334) ((-342 . -868) T) ((-82 . -626) 155316) ((-40 . -1074) T) ((-888 . -111) 155301) ((-734 . -1242) T) ((-717 . -102) T) ((-710 . -626) 155283) ((-615 . -1242) T) ((-609 . -569) 155262) ((-440 . -1137) T) ((-351 . -1076) 155246) ((-215 . -1125) T) ((-176 . -1076) 155178) ((-487 . -47) 155148) ((-40 . -239) 155120) ((-40 . -249) T) ((-135 . -102) T) ((-117 . -102) T) ((-608 . -569) 155099) ((-351 . -656) 155083) ((-710 . -627) 154991) ((-327 . -527) 154957) ((-176 . -656) 154889) ((-324 . -527) 154781) ((-500 . -235) 154768) ((-1276 . -1063) 154752) ((-1255 . -1063) 154538) ((-1024 . -424) 154522) ((-220 . -235) 154509) ((-440 . -23) T) ((-1145 . -174) T) ((-1278 . -301) T) ((-670 . -733) 154479) ((-145 . -1125) T) ((-48 . -1027) T) ((-420 . -273) 154463) ((-420 . -233) 154447) ((-306 . -241) 154397) ((-889 . -943) T) ((-889 . -836) NIL) ((-888 . -629) 154369) ((-259 . -868) 154320) ((-258 . -868) 154271) ((-882 . -865) T) ((-1255 . -350) 154241) ((-1255 . -389) 154211) ((-1105 . -238) 154090) ((-225 . -1146) 154074) ((-305 . -923) 154033) ((-1292 . -299) 154010) ((-371 . -238) 153989) ((-365 . -238) 153968) ((-487 . -1242) T) ((-357 . -238) 153947) ((-108 . -238) T) ((-1236 . -664) 153872) ((-1028 . -662) 153802) ((-986 . -21) T) ((-986 . -25) T) ((-751 . -21) T) ((-751 . -25) T) ((-731 . -21) T) ((-731 . -25) T) ((-727 . -664) 153767) ((-466 . -21) T) ((-466 . -25) T) ((-351 . -102) T) ((-176 . -102) T) ((-1024 . -1083) T) ((-888 . -1074) T) ((-790 . -102) T) ((-1277 . -375) 153746) ((-1276 . -921) 153652) ((-1256 . -375) 153631) ((-1255 . -921) 153482) ((-1201 . -1242) T) ((-1049 . -626) 153464) ((-420 . -844) 153417) ((-1199 . -506) 153383) ((-171 . -943) 153314) ((-1198 . -506) 153280) ((-1192 . -506) 153246) ((-728 . -1125) T) ((-1151 . -506) 153212) ((-593 . -1081) 153199) ((-577 . -1081) 153186) ((-508 . -1081) 153151) ((-327 . -301) 153130) 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-107) 151851) ((-937 . -132) T) ((-928 . -865) 151802) ((-717 . -1177) T) ((-715 . -111) 151758) ((-859 . -662) 151675) ((-609 . -1137) T) ((-608 . -1137) T) ((-728 . -733) 151504) ((-727 . -742) T) ((-815 . -25) T) ((-815 . -21) T) ((-500 . -865) T) ((-610 . -1242) T) ((-609 . -23) T) ((-598 . -1242) T) ((-220 . -865) T) ((-420 . -662) 151441) ((-593 . -1074) T) ((-577 . -1074) T) ((-549 . -1242) T) ((-508 . -1074) T) ((-355 . -1311) 151418) ((-330 . -465) 151397) ((-351 . -320) 151384) ((-608 . -23) T) ((-440 . -132) T) ((-674 . -664) 151358) ((-251 . -1035) 151342) ((-890 . -318) T) ((-1316 . -1306) 151326) ((-787 . -808) T) ((-787 . -811) T) ((-717 . -38) 151313) ((-577 . -239) T) ((-508 . -249) T) ((-508 . -239) T) ((-1305 . -502) 151297) ((-1288 . -1242) T) ((-1175 . -241) 151247) ((-1112 . -932) 151226) ((-117 . -38) 151213) ((-211 . -816) T) ((-210 . -816) T) ((-209 . -816) T) ((-208 . -816) T) ((-890 . -1047) 151191) ((-680 . -1242) T) ((-661 . -1242) T) ((-798 . -932) 151170) 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148543) ((-254 . -921) 148520) ((-118 . -1074) T) ((-1112 . -742) T) ((-832 . -1137) T) ((-835 . -868) T) ((-636 . -239) 148499) ((-634 . -102) T) ((-524 . -1242) T) ((-520 . -1242) T) ((-798 . -742) T) ((-796 . -742) T) ((-1247 . -865) T) ((-426 . -1137) T) ((-118 . -249) T) ((-40 . -380) NIL) ((-118 . -239) NIL) ((-399 . -868) 148478) ((-467 . -742) T) ((-832 . -23) T) ((-747 . -25) T) ((-747 . -21) T) ((-686 . -915) 148399) ((-1102 . -297) 148378) ((-78 . -409) T) ((-78 . -408) T) ((-546 . -783) 148360) ((-228 . -868) T) ((-710 . -1081) 148310) ((-1317 . -102) T) ((-1284 . -132) T) ((-1277 . -132) T) ((-1256 . -132) T) ((-1199 . -25) T) ((-1167 . -424) 148294) ((-648 . -379) 148226) ((-620 . -379) 148158) ((-1182 . -1174) 148142) ((-103 . -1125) 148120) ((-1199 . -21) T) ((-1198 . -21) T) ((-883 . -626) 148102) ((-1024 . -733) 148050) ((-226 . -664) 148017) ((-710 . -111) 147951) ((-50 . -742) T) ((-1198 . -25) T) ((-363 . -361) T) ((-1192 . -21) T) ((-1105 . -465) 147902) ((-1192 . 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146803) ((-1203 . -146) 146782) ((-1203 . -148) 146761) ((-1171 . -1125) T) ((-1171 . -1096) 146730) ((-69 . -1242) T) ((-1049 . -1081) 146667) ((-363 . -662) 146597) ((-884 . -1083) T) ((-246 . -654) 146503) ((-710 . -1074) T) ((-366 . -1081) 146448) ((-61 . -1242) T) ((-1049 . -111) 146364) ((-924 . -626) 146275) ((-710 . -249) T) ((-710 . -239) NIL) ((-859 . -864) 146254) ((-715 . -811) T) ((-715 . -808) T) ((-1028 . -424) 146231) ((-366 . -111) 146160) ((-391 . -943) T) ((-420 . -864) 146139) ((-728 . -301) 146050) ((-226 . -742) T) ((-1284 . -506) 146016) ((-1277 . -506) 145982) ((-1256 . -506) 145948) ((-591 . -1125) T) ((-327 . -1027) 145927) ((-225 . -1125) 145905) ((-1249 . -860) T) ((-330 . -998) 145867) ((-105 . -102) T) ((-48 . -1081) 145832) ((-889 . -868) NIL) ((-1316 . -102) T) ((-393 . -102) T) ((-1278 . -626) 145814) ((-1158 . -1159) 145798) ((-1029 . -654) 145780) ((-894 . -1242) T) ((-48 . -111) 145736) ((-697 . -1242) T) ((-692 . -1242) T) ((-678 . -1242) T) ((-831 . -915) 145603) ((-491 . -1242) T) ((-251 . -1242) T) ((-544 . -102) T) ((-513 . -102) T) ((-153 . -1299) 145587) ((-139 . -1242) T) ((-138 . -1242) T) ((-134 . -1242) T) ((-1241 . -102) T) ((-1049 . -629) 145524) ((-833 . -238) T) ((-1197 . -1246) 145503) ((-217 . -380) T) ((-366 . -629) 145433) ((-1150 . -1246) 145412) ((-246 . -25) 145245) ((-246 . -21) 145156) ((-128 . -120) 145140) ((-122 . -120) 145124) ((-44 . -760) 145108) ((-1197 . -569) 145019) ((-1150 . -569) 144950) ((-1249 . -1125) T) ((-559 . -868) T) ((-1060 . -297) 144925) ((-1191 . -1108) T) ((-1019 . -1108) T) ((-832 . -132) T) ((-118 . -811) NIL) ((-118 . -808) NIL) ((-367 . -318) T) ((-364 . -318) T) ((-356 . -318) T) ((-1119 . -1242) 144903) ((-259 . -1137) 144881) ((-258 . -1137) 144859) ((-1049 . -1074) T) ((-1028 . -1083) T) ((-48 . -629) 144792) ((-355 . -664) 144737) ((-1305 . -626) 144699) ((-1305 . -627) 144660) ((-634 . -38) 144644) ((-1199 . -235) 144597) ((-1198 . -235) 144543) ((-1102 . -626) 144525) 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T) ((-1107 . -102) T) ((-88 . -1242) T) ((-513 . -320) NIL) ((-1025 . -107) 143423) ((-908 . -1125) T) ((-904 . -1125) T) ((-1292 . -667) 143407) ((-1292 . -385) 143391) ((-338 . -1242) T) ((-606 . -865) T) ((-1167 . -1125) T) ((-1167 . -1078) 143331) ((-103 . -527) 143264) ((-950 . -626) 143246) ((-355 . -742) T) ((-30 . -626) 143228) ((-884 . -1125) T) ((-859 . -1083) 143207) ((-40 . -664) 143114) ((-228 . -1246) T) ((-420 . -1083) T) ((-1183 . -152) 143096) ((-1024 . -301) 143047) ((-892 . -1242) T) ((-630 . -1125) T) ((-228 . -569) T) ((-330 . -1273) 143031) ((-330 . -1270) 143001) ((-717 . -662) 142973) ((-1214 . -1218) 142952) ((-1100 . -626) 142934) ((-1214 . -107) 142884) ((-663 . -152) 142868) ((-645 . -152) 142814) ((-117 . -662) 142786) ((-492 . -1218) 142765) ((-500 . -148) T) ((-500 . -146) NIL) ((-1145 . -627) 142680) ((-451 . -626) 142662) ((-220 . -148) T) ((-220 . -146) NIL) ((-1145 . -626) 142644) ((-130 . -102) T) ((-52 . -102) T) ((-1256 . -654) 142596) ((-492 . -107) 142546) ((-1018 . -23) T) ((-1316 . -38) 142516) ((-1197 . -1137) T) ((-1150 . -1137) T) ((-1087 . -1246) T) ((-246 . -235) 142407) ((-322 . -102) T) ((-872 . -1137) T) ((-975 . -1246) 142386) ((-494 . -1246) 142365) ((-1087 . -569) T) ((-975 . -569) 142296) ((-1197 . -23) T) ((-1176 . -1108) T) ((-1150 . -23) T) ((-872 . -23) T) ((-494 . -569) 142227) ((-1167 . -733) 142159) ((-686 . -1076) 142143) ((-1171 . -527) 142076) ((-686 . -656) 142060) ((-1060 . -627) NIL) ((-1060 . -626) 142042) ((-96 . -1108) T) ((-1321 . -1081) 142029) ((-884 . -733) 141999) ((-1321 . -111) 141984) ((-1236 . -47) 141953) ((-1192 . -865) NIL) ((-259 . -132) T) ((-258 . -132) T) ((-1129 . -1125) T) ((-1028 . -1125) T) ((-62 . -626) 141935) ((-1105 . -915) 141804) ((-1049 . -808) T) ((-1049 . -811) T) ((-1284 . -25) T) ((-1284 . -21) T) ((-1277 . -21) T) ((-1277 . -25) T) ((-888 . -664) 141791) ((-1256 . -21) T) ((-1256 . -25) T) ((-1052 . -152) 141775) ((-1029 . -235) 141762) ((-890 . -836) 141741) 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T) ((-833 . -465) 141152) ((-153 . -1076) 141136) ((-1071 . -1096) 141065) ((-1052 . -1001) 141034) ((-835 . -1137) T) ((-1028 . -733) 140979) ((-153 . -656) 140963) ((-399 . -1137) T) ((-489 . -1001) 140932) ((-476 . -1001) 140901) ((-1208 . -868) T) ((-110 . -152) 140883) ((-73 . -626) 140865) ((-912 . -626) 140847) ((-1207 . -868) T) ((-1105 . -740) 140826) ((-1321 . -1074) T) ((-832 . -654) 140774) ((-305 . -1083) 140716) ((-171 . -1246) 140621) ((-228 . -1137) T) ((-335 . -23) T) ((-1192 . -1017) 140573) ((-1278 . -1081) 140478) ((-859 . -1125) T) ((-129 . -868) T) ((-1151 . -756) 140457) ((-1276 . -943) 140436) ((-1255 . -943) 140415) ((-888 . -742) T) ((-171 . -569) 140326) ((-593 . -664) 140313) ((-577 . -664) 140285) ((-420 . -1125) T) ((-271 . -1125) T) ((-215 . -626) 140267) ((-508 . -664) 140217) ((-228 . -23) T) ((-1255 . -836) 140170) ((-1314 . -102) T) ((-504 . -1242) T) ((-366 . -1311) 140147) ((-1312 . -102) T) ((-1278 . -111) 140039) ((-1138 . -915) 139906) ((-831 . 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137153) ((-665 . -1242) T) ((-798 . -905) NIL) ((-796 . -905) 137012) ((-1307 . -25) T) ((-1307 . -21) T) ((-1239 . -102) 136990) ((-1131 . -408) T) ((-636 . -664) 136977) ((-467 . -905) NIL) ((-691 . -102) 136927) ((-1112 . -1063) 136754) ((-889 . -23) T) ((-798 . -1063) 136613) ((-796 . -1063) 136470) ((-118 . -664) 136415) ((-467 . -1063) 136291) ((-285 . -1242) T) ((-327 . -629) 135855) ((-324 . -629) 135738) ((-50 . -1242) T) ((-403 . -662) 135707) ((-665 . -1063) 135691) ((-640 . -102) T) ((-594 . -1242) T) ((-531 . -1242) T) ((-225 . -502) 135675) ((-1292 . -34) T) ((-634 . -662) 135634) ((-300 . -1076) 135621) ((-137 . -629) 135605) ((-300 . -656) 135592) ((-648 . -733) 135576) ((-620 . -733) 135560) ((-686 . -38) 135520) ((-330 . -102) T) ((-1145 . -1081) 135507) ((-85 . -626) 135489) ((-50 . -1063) 135473) ((-1112 . -389) 135457) ((-798 . -389) 135441) ((-715 . -742) T) ((-715 . -810) T) ((-715 . -807) T) ((-60 . -57) 135403) ((-594 . -1063) 135390) ((-531 . -1063) 135367) ((-173 . -1242) T) ((-335 . -132) T) ((-327 . -1074) 135257) ((-324 . -1074) T) ((-171 . -1137) T) ((-796 . -389) 135241) ((-45 . -152) 135191) ((-1029 . -1017) 135173) ((-467 . -389) 135157) ((-420 . -174) T) ((-327 . -249) 135136) ((-324 . -249) T) ((-324 . -239) NIL) ((-305 . -1125) 134918) ((-228 . -132) T) ((-1145 . -111) 134903) ((-171 . -23) T) ((-815 . -148) 134882) ((-815 . -146) 134861) ((-259 . -654) 134767) ((-258 . -654) 134673) ((-330 . -295) 134639) ((-1182 . -527) 134572) ((-490 . -662) 134522) ((-651 . -860) T) ((-495 . -915) 134389) ((-1158 . -1125) T) ((-228 . -1085) T) ((-831 . -320) 134327) ((-1112 . -921) 134262) ((-798 . -921) 134205) ((-796 . -921) 134189) ((-1314 . -38) 134159) ((-1312 . -38) 134129) ((-1265 . -1137) T) ((-873 . -1137) T) ((-467 . -921) 134106) ((-876 . -1125) T) ((-1265 . -23) T) ((-1145 . -629) 134078) ((-1087 . -132) T) ((-873 . -23) T) ((-584 . -1137) T) ((-636 . -742) T) ((-523 . -868) T) ((-367 . -943) T) ((-364 . -943) T) ((-300 . -102) T) ((-356 . -943) T) ((-995 . -1108) T) ((-975 . -132) T) ((-832 . -235) 134023) ((-118 . -810) NIL) ((-118 . -807) NIL) ((-118 . -742) T) ((-1071 . -527) 133924) ((-710 . -932) NIL) ((-584 . -23) T) ((-494 . -132) T) ((-431 . -238) 133875) ((-691 . -320) 133813) ((-226 . -1242) T) ((-651 . -1125) T) ((-648 . -777) T) ((-620 . -777) T) ((-1256 . -865) NIL) ((-1105 . -1076) 133723) ((-1028 . -301) T) ((-710 . -664) 133673) ((-259 . -25) T) ((-363 . -1125) T) ((-259 . -21) T) ((-258 . -25) T) ((-258 . -21) T) ((-153 . -38) 133657) ((-2 . -102) T) ((-933 . -943) T) ((-1105 . -656) 133525) ((-495 . -1299) 133495) ((-1145 . -1074) T) ((-727 . -318) T) ((-717 . -1083) T) ((-371 . -1076) 133447) ((-365 . -1076) 133399) ((-357 . -1076) 133351) ((-371 . -656) 133303) ((-226 . -1063) 133280) ((-365 . -656) 133232) ((-108 . -1076) 133182) ((-357 . -656) 133134) ((-305 . -733) 133076) ((-655 . -1242) T) ((-500 . -465) T) ((-420 . -527) 132988) ((-108 . -656) 132938) ((-220 . -465) T) ((-1145 . -239) T) ((-306 . -152) 132888) ((-1024 . -627) 132849) ((-1024 . -626) 132831) ((-1014 . -626) 132813) ((-117 . -1083) T) ((-670 . -1081) 132797) ((-228 . -506) T) ((-412 . -626) 132779) ((-412 . -627) 132756) ((-1079 . -1299) 132726) ((-670 . -111) 132705) ((-686 . -923) 132628) ((-1167 . -502) 132612) ((-1316 . -662) 132571) ((-393 . -662) 132540) ((-63 . -454) T) ((-63 . -408) T) ((-1184 . -102) T) ((-889 . -132) T) ((-497 . -102) 132490) ((-1143 . -1242) T) ((-1248 . -868) T) ((-1321 . -380) T) ((-1105 . -102) T) ((-1086 . -102) T) ((-363 . -733) 132435) ((-890 . -868) 132386) ((-747 . -148) 132365) ((-747 . -146) 132344) ((-670 . -629) 132262) ((-1049 . -664) 132199) ((-536 . -1125) 132177) ((-371 . -102) T) ((-365 . -102) T) ((-357 . -102) T) ((-108 . -102) T) ((-517 . -1125) T) ((-366 . -664) 132122) ((-1197 . -654) 132070) ((-1150 . -654) 132018) ((-397 . -522) 131997) ((-849 . -864) 131976) ((-710 . -742) T) ((-391 . -1246) T) ((-344 . -1242) T) ((-1256 . -1017) 131928) ((-351 . -1083) T) ((-112 . -1242) T) ((-176 . -1083) T) ((-103 . -626) 131860) ((-1199 . -146) 131839) ((-1199 . -148) 131818) ((-391 . -569) T) ((-1198 . -148) 131797) ((-1198 . -146) 131776) ((-1192 . -146) 131683) ((-420 . -301) T) ((-1192 . -148) 131590) ((-1151 . -148) 131569) ((-1151 . -146) 131548) ((-330 . -38) 131389) ((-171 . -132) T) ((-324 . -811) NIL) ((-324 . -808) NIL) ((-670 . -1074) T) ((-48 . -664) 131339) ((-1138 . -1076) 131240) ((-912 . -629) 131217) ((-1138 . -656) 131139) ((-1191 . -102) T) ((-1019 . -102) T) ((-1018 . -21) T) ((-128 . -1035) 131123) ((-122 . -1035) 131107) ((-1018 . -25) T) ((-924 . -120) 131091) ((-1183 . -102) T) ((-1265 . -132) T) ((-1255 . -868) 130990) ((-1197 . -25) T) ((-1197 . -21) T) ((-1184 . -320) 130785) ((-355 . -1242) T) ((-1150 . -25) T) ((-873 . -132) T) ((-407 . -1242) T) ((-1150 . -21) T) ((-872 . -25) T) ((-872 . -21) T) ((-798 . -318) 130764) ((-1182 . -502) 130748) ((-1175 . -152) 130698) ((-1171 . -626) 130660) ((-663 . -102) 130610) ((-645 . -102) T) ((-1171 . -627) 130571) ((-584 . -132) T) ((-634 . -864) 130550) ((-1049 . -807) T) ((-1049 . -810) T) ((-1049 . -742) T) ((-831 . -923) 130419) ((-728 . -1081) 130242) ((-615 . -868) 130221) ((-497 . -320) 130159) ((-466 . -430) 130129) ((-363 . -174) T) ((-300 . -38) 130116) ((-259 . -235) 130007) ((-258 . -235) 129898) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-355 . -1063) 129875) ((-278 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-728 . -111) 129684) ((-366 . -742) T) ((-686 . -273) 129668) ((-686 . -233) 129652) ((-594 . -318) T) ((-531 . -318) T) ((-305 . -527) 129601) ((-1189 . -1242) T) ((-108 . -320) NIL) ((-72 . -408) T) ((-1138 . -102) 129333) ((-849 . -424) 129317) ((-1145 . -811) T) ((-1145 . -808) T) ((-717 . -1125) T) ((-591 . -626) 129299) ((-391 . -375) T) ((-171 . -506) 129277) ((-225 . -626) 129209) ((-135 . -1125) T) ((-117 . -1125) T) ((-989 . -1242) T) ((-48 . -742) T) ((-1071 . -502) 129174) ((-142 . -438) 129156) ((-142 . -380) T) ((-1052 . -102) T) ((-525 . -522) 129135) ((-728 . -629) 128891) ((-1249 . -626) 128873) ((-1206 . -1242) T) ((-1206 . -1063) 128809) ((-1199 . -238) 128768) ((-489 . -102) T) ((-476 . -102) T) ((-1198 . -238) 128720) ((-1192 . -238) 128543) ((-1059 . -1137) T) ((-330 . -923) 128449) ((-1201 . -868) T) ((-1199 . -35) 128415) ((-1199 . -95) 128381) ((-1199 . -1230) 128347) ((-1199 . -1227) 128313) ((-1198 . -1227) 128279) ((-1198 . -1230) 128245) ((-1198 . -95) 128211) ((-1198 . -35) 128177) ((-1192 . -1227) 128143) ((-1192 . -1230) 128109) ((-1183 . -320) NIL) ((-89 . -409) T) ((-89 . -408) T) ((-1105 . -1177) 128088) ((-40 . -1242) T) ((-1192 . -95) 128054) ((-1059 . -23) T) ((-1192 . -35) 128020) ((-584 . -506) T) ((-1151 . -35) 127986) ((-1151 . -95) 127952) ((-1151 . -1230) 127918) ((-1151 . -1227) 127884) ((-373 . -1137) T) ((-371 . -1177) 127863) ((-365 . -1177) 127842) ((-357 . -1177) 127821) ((-1129 . -297) 127777) ((-977 . -1242) T) ((-944 . -1242) T) ((-108 . -1177) T) ((-849 . -1083) 127756) ((-787 . -1242) T) ((-663 . -320) 127694) ((-645 . -320) 127545) ((-688 . -1242) T) ((-728 . -1074) T) ((-1087 . -654) 127527) ((-1105 . -38) 127395) ((-975 . -654) 127343) ((-1029 . -148) T) ((-1029 . -146) NIL) ((-391 . -1137) T) ((-335 . -25) T) ((-333 . -23) T) ((-966 . -865) 127322) ((-728 . -337) 127299) ((-494 . -654) 127247) ((-40 . -1063) 127135) ((-728 . -239) T) ((-717 . -733) 127122) ((-351 . -1125) T) ((-176 . -1125) T) ((-342 . -865) T) ((-431 . -465) 127072) ((-391 . -23) T) ((-371 . -38) 127037) ((-365 . -38) 127002) ((-357 . -38) 126967) ((-80 . -454) T) ((-80 . -408) T) ((-228 . -25) T) ((-228 . -21) T) ((-852 . -1137) T) ((-108 . -38) 126917) ((-843 . -1137) T) ((-790 . -1125) T) ((-117 . -733) 126904) ((-688 . -1063) 126888) ((-625 . -102) T) ((-852 . -23) T) ((-843 . -23) T) ((-1182 . -297) 126840) ((-1138 . -320) 126778) ((-495 . -1076) 126679) ((-1127 . -241) 126663) ((-64 . -409) T) ((-64 . -408) T) ((-1176 . -102) T) ((-110 . -102) T) ((-495 . -656) 126585) ((-40 . -389) 126562) ((-96 . -102) T) ((-669 . -870) 126546) ((-1197 . -235) 126533) ((-1160 . -1108) T) ((-1087 . -21) T) ((-1087 . -25) T) ((-1079 . -1076) 126517) ((-831 . -273) 126486) ((-831 . -233) 126455) ((-975 . -25) T) ((-975 . -21) T) ((-1145 . -380) T) ((-1079 . -656) 126397) ((-634 . -1083) T) ((-1052 . -320) 126335) ((-908 . -626) 126317) ((-686 . -662) 126276) ((-494 . -25) T) ((-494 . -21) T) ((-397 . -1076) 126260) ((-904 . -626) 126242) ((-888 . -1242) T) ((-536 . -527) 126175) ((-259 . -865) 126126) ((-258 . -865) 126077) ((-397 . -656) 126047) ((-889 . -654) 126024) ((-489 . -320) 125962) ((-560 . -1242) T) 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((-217 . -1242) T) ((-128 . -1242) T) ((-122 . -1242) T) ((-108 . -923) NIL) ((-833 . -1076) 124303) ((-59 . -868) 124282) ((-833 . -656) 124224) ((-529 . -868) 124203) ((-509 . -868) 124182) ((-1059 . -132) T) ((-686 . -379) 124166) ((-153 . -662) 124125) ((-1321 . -742) T) ((-648 . -297) 124083) ((-620 . -297) 124041) ((-1284 . -146) 124020) ((-1265 . -654) 123968) ((-1024 . -1074) T) ((-1129 . -626) 123950) ((-1028 . -626) 123932) ((-593 . -1242) T) ((-577 . -1242) T) ((-508 . -1242) T) ((-528 . -23) T) ((-523 . -23) T) ((-355 . -318) T) ((-521 . -23) T) ((-333 . -132) T) ((-3 . -1125) T) ((-1028 . -627) 123916) ((-1024 . -249) 123895) ((-1024 . -239) 123874) ((-1284 . -148) 123853) ((-1277 . -148) 123832) ((-849 . -1125) T) ((-1277 . -146) 123811) ((-1276 . -1246) 123790) ((-1256 . -146) 123697) ((-1256 . -148) 123604) ((-1255 . -1246) 123583) ((-391 . -132) T) ((-228 . -235) 123570) ((-176 . -174) T) ((-577 . -905) 123552) ((0 . -1125) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1242) T) ((-49 . -1125) T) ((-1278 . -664) 123457) ((-1276 . -569) 123408) ((-1255 . -569) 123359) ((-730 . -1137) T) ((-653 . -23) T) ((-577 . -1063) 123341) ((-608 . -148) 123320) ((-608 . -146) 123299) ((-508 . -1063) 123242) ((-1160 . -1162) T) ((-87 . -396) T) ((-87 . -408) T) ((-890 . -375) T) ((-852 . -132) T) ((-843 . -132) T) ((-987 . -662) 123186) ((-730 . -23) T) ((-519 . -626) 123152) ((-515 . -626) 123134) ((-831 . -662) 122913) ((-1316 . -1083) T) ((-391 . -1085) T) ((-1051 . -1125) 122891) ((-55 . -1063) 122873) ((-924 . -34) T) ((-495 . -320) 122811) ((-605 . -102) T) ((-1182 . -627) 122772) ((-1182 . -626) 122704) ((-1203 . -1076) 122587) ((-45 . -102) T) ((-833 . -102) T) ((-1203 . -656) 122484) ((-1293 . -1242) T) ((-1265 . -25) T) ((-1265 . -21) T) ((-1087 . -235) 122471) ((-873 . -25) T) ((-524 . -868) T) ((-255 . -1242) T) ((-44 . -379) 122455) ((-873 . -21) T) ((-747 . -465) 122406) ((-1315 . -626) 122388) ((-726 . -1242) T) ((-715 . -1242) T) ((-1304 . -1076) 122358) ((-1079 . -320) 122296) ((-687 . -1108) T) ((-619 . -1108) T) ((-403 . -1125) T) ((-584 . -25) T) ((-584 . -21) T) ((-182 . -1108) T) ((-162 . -1108) T) ((-157 . -1108) T) ((-155 . -1108) T) ((-1304 . -656) 122266) ((-634 . -1125) T) ((-715 . -905) 122248) ((-1292 . -1242) T) ((-230 . -320) 122186) ((-145 . -380) T) ((-1215 . -1242) T) ((-1071 . -627) 122128) ((-1071 . -626) 122071) ((-324 . -932) NIL) ((-1250 . -860) T) ((-1138 . -923) 121940) ((-715 . -1063) 121885) ((-727 . -943) T) ((-487 . -1246) 121864) ((-1198 . -465) 121843) ((-1192 . -465) 121822) ((-341 . -102) T) ((-890 . -1137) T) ((-330 . -662) 121704) ((-327 . -664) 121433) ((-324 . -664) 121362) ((-487 . -569) 121313) ((-351 . -527) 121279) ((-563 . -152) 121229) ((-40 . -318) T) ((-859 . -626) 121211) ((-717 . -301) T) ((-890 . -23) T) ((-391 . -506) T) ((-1105 . -273) 121181) ((-1105 . -233) 121151) ((-525 . -102) T) ((-420 . -627) 120958) ((-420 . -626) 120940) ((-271 . -626) 120922) ((-117 . -301) T) ((-1278 . -742) T) ((-636 . -1242) T) ((-1317 . -1125) T) ((-1276 . -375) 120901) ((-1255 . -375) 120880) ((-1305 . -34) T) ((-1250 . -1125) T) ((-118 . -1242) T) ((-108 . -273) 120862) ((-108 . -233) 120844) ((-1203 . -102) T) ((-490 . -1125) T) ((-536 . -502) 120828) ((-753 . -34) T) ((-669 . -1076) 120812) ((-669 . -656) 120782) ((-889 . -235) NIL) ((-142 . -34) T) ((-118 . -903) 120759) ((-118 . -905) NIL) ((-636 . -1063) 120642) ((-1304 . -102) T) ((-1284 . -238) 120601) ((-660 . -865) 120580) ((-1277 . -238) 120532) ((-1256 . -238) 120355) ((-306 . -102) T) ((-728 . -380) 120334) ((-118 . -1063) 120311) ((-403 . -733) 120295) ((-608 . -238) 120254) ((-634 . -733) 120238) ((-1130 . -1242) T) ((-45 . -320) 120042) ((-832 . -146) 120021) ((-832 . -148) 120000) ((-300 . -662) 119972) ((-1315 . -394) 119951) ((-835 . -865) T) ((-1294 . -1125) T) ((-1184 . -232) 119898) ((-399 . -865) 119877) ((-1284 . -35) 119843) ((-1284 . -1230) 119809) ((-1284 . -1227) 119775) ((-1277 . -1227) 119741) ((-528 . -132) T) ((-1277 . -1230) 119707) ((-1256 . -1227) 119673) ((-1256 . -1230) 119639) ((-1284 . -95) 119605) ((-1277 . -95) 119571) ((-431 . -915) 119492) ((-648 . -626) 119461) ((-620 . -626) 119430) ((-228 . -865) T) ((-1277 . -35) 119396) ((-1276 . -1137) T) ((-1256 . -95) 119362) ((-1145 . -664) 119334) ((-1256 . -35) 119300) ((-1255 . -1137) T) ((-606 . -152) 119282) ((-1105 . -361) 119261) ((-176 . -301) T) ((-118 . -389) 119238) ((-118 . -350) 119215) ((-171 . -235) 119140) ((-888 . -318) T) ((-324 . -810) NIL) ((-324 . -807) NIL) ((-327 . -742) 118989) ((-324 . -742) T) ((-653 . -132) T) ((-487 . -375) 118968) ((-371 . -361) 118947) ((-365 . -361) 118926) ((-357 . -361) 118905) ((-327 . -486) 118884) ((-1276 . -23) T) ((-1255 . -23) T) ((-734 . -1137) T) ((-730 . -132) T) ((-669 . -102) T) ((-490 . -733) 118849) ((-678 . -868) 118828) ((-45 . -293) 118778) ((-105 . -1125) T) ((-68 . -626) 118760) ((-251 . -868) 118739) ((-995 . -102) T) ((-882 . -102) T) ((-636 . -921) 118698) ((-1316 . -1125) T) ((-393 . -1125) T) ((-1265 . -235) 118685) ((-1241 . -1125) T) ((-82 . -1242) T) ((-1138 . -273) 118654) ((-1087 . -865) T) ((-118 . -921) NIL) ((-798 . -943) 118633) ((-729 . -865) T) ((-544 . -1125) T) ((-513 . -1125) T) ((-367 . -1246) T) ((-364 . -1246) T) ((-356 . -1246) T) ((-274 . -1246) 118612) ((-254 . -1246) 118591) ((-546 . -878) T) ((-1138 . -233) 118560) ((-1183 . -844) T) ((-1167 . -1081) 118544) ((-403 . -777) T) ((-710 . -1242) T) ((-707 . -1063) 118528) ((-367 . -569) T) ((-364 . -569) T) ((-356 . -569) T) ((-274 . -569) 118459) ((-254 . -569) 118390) ((-538 . -1108) T) ((-1167 . -111) 118369) ((-466 . -760) 118339) ((-884 . -1081) 118309) ((-833 . -38) 118251) ((-710 . -903) 118233) ((-710 . -905) 118215) ((-306 . -320) 118019) ((-1182 . -299) 117996) ((-933 . -1246) T) ((-1105 . -662) 117891) ((-1029 . -465) T) ((-686 . -424) 117875) ((-884 . -111) 117840) ((-937 . -465) T) ((-710 . -1063) 117785) ((-933 . -569) T) ((-546 . -626) 117767) 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. -1083) T) ((-747 . -972) 116302) ((-1167 . -239) 116281) ((-366 . -1242) T) ((-1107 . -1125) T) ((-1059 . -25) T) ((-1059 . -21) T) ((-1028 . -1081) 116226) ((-338 . -868) 116205) ((-928 . -102) T) ((-884 . -1074) T) ((-710 . -921) NIL) ((-367 . -340) 116189) ((-367 . -375) T) ((-364 . -340) 116173) ((-364 . -375) T) ((-356 . -340) 116157) ((-356 . -375) T) ((-500 . -102) T) ((-1304 . -38) 116127) ((-559 . -865) T) ((-536 . -703) 116077) ((-220 . -102) T) ((-1049 . -1063) 115957) ((-1028 . -111) 115886) ((-651 . -626) 115868) ((-1199 . -998) 115837) ((-1198 . -998) 115799) ((-533 . -152) 115783) ((-1105 . -382) 115762) ((-363 . -626) 115744) ((-333 . -21) T) ((-366 . -1063) 115721) ((-333 . -25) T) ((-1192 . -998) 115690) ((-48 . -1242) T) ((-76 . -626) 115672) ((-1151 . -998) 115639) ((-715 . -318) T) ((-130 . -860) T) ((-933 . -375) T) ((-391 . -25) T) ((-391 . -21) T) ((-933 . -340) 115626) ((-86 . -626) 115608) ((-715 . -1047) T) ((-693 . -865) T) ((-401 . -1242) T) ((-1276 . 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. -569) T) ((-608 . -915) 106249) ((-327 . -903) 106233) ((-327 . -905) 106158) ((-324 . -903) 106119) ((-140 . -1242) T) ((-137 . -1242) T) ((-115 . -1242) T) ((-324 . -905) NIL) ((-815 . -320) 106084) ((-330 . -733) 105925) ((-399 . -398) 105909) ((-335 . -334) 105886) ((-498 . -102) T) ((-487 . -25) T) ((-487 . -21) T) ((-431 . -38) 105860) ((-327 . -1063) 105523) ((-228 . -1227) T) ((-228 . -1230) T) ((-3 . -626) 105505) ((-324 . -1063) 105435) ((-890 . -235) 105380) ((-2 . -1125) T) ((-2 . |RecordCategory|) T) ((-1138 . -1083) 105358) ((-849 . -626) 105340) ((-1087 . -238) T) ((-593 . -943) T) ((-577 . -836) T) ((-577 . -943) T) ((-508 . -943) T) ((-137 . -1063) 105324) ((-228 . -95) T) ((-171 . -148) 105303) ((-75 . -454) T) ((0 . -626) 105285) ((-75 . -408) T) ((-171 . -146) 105236) ((-228 . -35) T) ((-49 . -626) 105218) ((-490 . -1083) T) ((-500 . -273) 105200) ((-500 . -233) 105182) ((-497 . -993) 105166) ((-220 . -273) 105148) ((-220 . -233) 105130) ((-81 . -454) T) ((-81 . 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. -1227) 100829) ((-211 . -1125) T) ((-210 . -1125) T) ((-117 . -1074) T) ((-209 . -1125) T) ((-208 . -1125) T) ((-205 . -1125) T) ((-204 . -1125) T) ((-203 . -1125) T) ((-202 . -1125) T) ((-201 . -1125) T) ((-200 . -1125) T) ((-199 . -1125) T) ((-198 . -1125) T) ((-197 . -1125) T) ((-196 . -1125) T) ((-195 . -1125) T) ((-246 . -102) 100561) ((-171 . -35) 100539) ((-171 . -95) 100517) ((-670 . -1063) 100413) ((-495 . -1083) 100391) ((-1138 . -1125) 100143) ((-1167 . -34) T) ((-686 . -502) 100127) ((-73 . -1242) T) ((-105 . -626) 100109) ((-912 . -1242) T) ((-1316 . -626) 100091) ((-393 . -626) 100073) ((-351 . -629) 100025) ((-176 . -629) 99942) ((-1241 . -503) 99923) ((-747 . -38) 99772) ((-584 . -1230) T) ((-584 . -1227) T) ((-544 . -626) 99754) ((-533 . -320) 99692) ((-513 . -626) 99674) ((-513 . -627) 99656) ((-1241 . -626) 99622) ((-1192 . -1177) NIL) ((-215 . -1242) T) ((-1052 . -1096) 99591) ((-1052 . -1125) T) ((-1029 . -102) T) ((-996 . -102) T) ((-937 . -102) T) ((-912 . -1063) 99568) ((-1167 . -742) T) ((-1028 . -664) 99475) ((-489 . -1125) T) ((-476 . -1125) T) ((-599 . -23) T) ((-584 . -35) T) ((-584 . -95) T) ((-440 . -102) T) ((-1088 . -232) 99421) ((-1199 . -38) 99318) ((-1198 . -38) 99159) ((-944 . -868) T) ((-884 . -742) T) ((-787 . -868) T) ((-710 . -943) T) ((-688 . -868) T) ((-524 . -25) T) ((-520 . -21) T) ((-520 . -25) T) ((-1192 . -38) 98955) ((-351 . -1074) T) ((-145 . -1242) T) ((-1105 . -174) T) ((-176 . -1074) T) ((-1151 . -38) 98852) ((-728 . -47) 98829) ((-371 . -174) T) ((-365 . -174) T) ((-532 . -57) 98803) ((-510 . -57) 98753) ((-363 . -1311) 98730) ((-228 . -465) T) ((-330 . -301) 98681) ((-357 . -174) T) ((-176 . -249) T) ((-1255 . -865) 98580) ((-108 . -174) T) ((-890 . -1017) 98564) ((-674 . -1137) T) ((-594 . -375) T) ((-594 . -340) 98551) ((-531 . -340) 98528) ((-531 . -375) T) ((-327 . -318) 98507) ((-324 . -318) T) ((-615 . -865) 98486) ((-1138 . -733) 98428) ((-533 . -293) 98412) ((-674 . -23) T) ((-431 . -233) 98396) 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96435) ((-560 . -868) T) ((-1107 . -627) 96416) ((-420 . -932) 96395) ((-1236 . -132) T) ((-50 . -1137) T) ((-1192 . -413) 96347) ((-1049 . -943) T) ((-1028 . -742) T) ((-859 . -664) 96320) ((-728 . -905) NIL) ((-609 . -1076) 96280) ((-594 . -1137) T) ((-531 . -1137) T) ((-608 . -1076) 96163) ((-1182 . -34) T) ((-1029 . -320) NIL) ((-831 . -502) 96147) ((-609 . -656) 96120) ((-366 . -943) T) ((-608 . -656) 96017) ((-933 . -235) 96004) ((-420 . -664) 95920) ((-50 . -23) T) ((-727 . -132) T) ((-728 . -1063) 95800) ((-594 . -23) T) ((-108 . -527) NIL) ((-531 . -23) T) ((-171 . -422) 95771) ((-1165 . -1125) T) ((-1307 . -1306) 95755) ((-747 . -923) 95732) ((-717 . -811) T) ((-717 . -808) T) ((-1145 . -318) T) ((-391 . -148) T) ((-291 . -626) 95714) ((-290 . -626) 95696) ((-1255 . -1017) 95666) ((-48 . -943) T) ((-691 . -502) 95650) ((-259 . -1299) 95620) ((-258 . -1299) 95590) ((-1113 . -238) T) ((-1201 . -865) T) ((-1145 . -1047) T) ((-1071 . -34) T) ((-852 . -148) 95569) ((-852 . -146) 95548) ((-753 . -107) 95532) ((-625 . -133) T) ((-1203 . -1083) T) ((-495 . -1125) 95284) ((-1199 . -923) 95197) ((-1198 . -923) 95103) ((-1192 . -923) 94864) ((-889 . -465) T) ((-85 . -1242) T) ((-142 . -107) 94846) ((-1151 . -923) 94830) ((-728 . -389) 94814) ((-849 . -629) 94682) ((-1315 . -742) T) ((-1304 . -1083) T) ((-1284 . -102) T) ((-1277 . -102) T) ((-1145 . -558) T) ((-592 . -102) T) ((-130 . -503) 94664) ((-1197 . -972) 94633) ((-403 . -1081) 94617) ((-1150 . -972) 94584) ((-44 . -297) 94561) ((-130 . -626) 94528) ((-52 . -626) 94510) ((-217 . -868) T) ((-669 . -424) 94494) ((-1256 . -102) T) ((-1183 . -527) NIL) ((-678 . -25) T) ((-634 . -1081) 94478) ((-678 . -21) T) ((-986 . -662) 94388) ((-751 . -662) 94333) ((-731 . -662) 94305) ((-403 . -111) 94284) ((-225 . -262) 94268) ((-1079 . -1078) 94208) ((-1079 . -1125) T) ((-1029 . -1177) T) ((-834 . -1125) T) ((-466 . -662) 94123) ((-648 . -664) 94107) ((-634 . -111) 94086) ((-620 . -664) 94070) ((-355 . -1246) T) ((-609 . -102) T) ((-322 . -503) 94051) ((-599 . -132) T) ((-608 . -102) T) ((-427 . -1125) T) ((-397 . -1125) T) ((-322 . -626) 94017) ((-230 . -1125) 93995) ((-663 . -527) 93928) ((-645 . -527) 93772) ((-849 . -1074) 93751) ((-660 . -152) 93735) ((-355 . -569) T) ((-728 . -921) 93678) ((-563 . -232) 93628) ((-1284 . -295) 93594) ((-1277 . -295) 93560) ((-1105 . -301) 93511) ((-577 . -868) T) ((-500 . -864) T) ((-226 . -1137) T) ((-1256 . -295) 93477) ((-1236 . -506) 93443) ((-1029 . -38) 93393) ((-220 . -864) T) ((-431 . -662) 93352) ((-937 . -38) 93304) ((-859 . -810) 93283) ((-859 . -807) 93262) ((-859 . -742) 93241) ((-371 . -301) T) ((-365 . -301) T) ((-357 . -301) T) ((-171 . -465) 93172) ((-440 . -38) 93156) ((-226 . -23) T) ((-108 . -301) T) ((-420 . -810) 93135) ((-420 . -807) 93114) ((-420 . -742) T) ((-513 . -299) 93089) ((-490 . -1081) 93054) ((-674 . -132) T) ((-634 . -629) 93023) ((-1138 . -527) 92956) ((-348 . -132) T) ((-171 . -415) 92935) ((-495 . -733) 92877) ((-831 . -297) 92854) ((-490 . -111) 92810) ((-669 . -1083) T) ((-655 . -23) T) ((-1197 . -915) 92713) ((-1150 . -915) 92695) ((-832 . -1076) 92538) ((-1303 . -1108) T) ((-1265 . -465) 92469) ((-832 . -656) 92318) ((-1302 . -1108) T) ((-1112 . -132) T) ((-1079 . -733) 92260) ((-1052 . -527) 92193) ((-798 . -132) T) ((-796 . -132) T) ((-715 . -868) T) ((-584 . -465) T) ((-634 . -1074) T) ((-605 . -1125) T) ((-546 . -175) T) ((-474 . -132) T) ((-467 . -132) T) ((-391 . -238) T) ((-1024 . -1242) T) ((-45 . -1125) T) ((-397 . -733) 92163) ((-833 . -1125) T) ((-489 . -527) 92096) ((-476 . -527) 92029) ((-1317 . -629) 92011) ((-466 . -379) 91981) ((-45 . -623) 91960) ((-412 . -1242) T) ((-327 . -313) T) ((-1292 . -868) 91939) ((-843 . -238) 91918) ((-490 . -629) 91868) ((-1256 . -320) 91753) ((-686 . -626) 91715) ((-59 . -865) 91694) ((-1029 . -413) 91676) ((-561 . -626) 91658) ((-815 . -662) 91617) ((-831 . -617) 91594) ((-529 . -865) 91573) ((-509 . -865) 91552) ((-1024 . -1063) 91448) ((-40 . -1246) T) 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-742) T) ((-879 . -626) 87147) ((-1198 . -662) 87029) ((-1192 . -662) 86866) ((-1151 . -662) 86776) ((-1256 . -413) 86728) ((-1138 . -502) 86712) ((-60 . -320) 86650) ((-342 . -102) T) ((-1236 . -21) T) ((-1236 . -25) T) ((-40 . -1137) T) ((-727 . -21) T) ((-640 . -626) 86632) ((-528 . -334) 86611) ((-727 . -25) T) ((-452 . -102) T) ((-108 . -297) NIL) ((-944 . -1137) T) ((-40 . -23) T) ((-787 . -1137) T) ((-577 . -1246) T) ((-508 . -1246) T) ((-1029 . -273) 86593) ((-330 . -626) 86575) ((-1029 . -233) 86557) ((-171 . -167) 86541) ((-593 . -569) T) ((-577 . -569) T) ((-508 . -569) T) ((-787 . -23) T) ((-1276 . -148) 86520) ((-1276 . -146) 86499) ((-1184 . -617) 86475) ((-1255 . -146) 86400) ((-1052 . -502) 86384) ((-1249 . -1242) T) ((-1255 . -148) 86309) ((-1307 . -1313) 86288) ((-889 . -915) NIL) ((-489 . -502) 86272) ((-476 . -502) 86256) ((-536 . -34) T) ((-669 . -733) 86226) ((-1284 . -923) 86139) ((-1277 . -923) 86045) ((-1256 . -923) 85806) ((-112 . -992) T) ((-1203 . -174) 85757) ((-678 . -865) 85736) ((-377 . -102) T) ((-608 . -923) 85649) ((-246 . -244) 85628) ((-259 . -102) T) ((-258 . -102) T) ((-1265 . -972) 85597) ((-251 . -865) 85576) ((-1049 . -868) T) ((-832 . -38) 85425) ((-45 . -527) 85217) ((-1183 . -297) 85167) ((-216 . -1125) T) ((-1175 . -1125) T) ((-890 . -238) 85118) ((-1175 . -623) 85097) ((-599 . -25) T) ((-599 . -21) T) ((-1127 . -320) 85035) ((-986 . -424) 85019) ((-715 . -1246) T) ((-645 . -297) 84972) ((-1112 . -654) 84920) ((-928 . -1125) T) ((-798 . -654) 84868) ((-796 . -654) 84816) ((-355 . -132) T) ((-300 . -626) 84798) ((-888 . -1137) T) ((-715 . -569) T) ((-130 . -629) 84780) ((-467 . -654) 84728) ((-171 . -915) 84649) ((-928 . -926) 84633) ((-391 . -465) T) ((-500 . -1125) T) ((-966 . -320) 84571) ((-717 . -664) 84543) ((-562 . -860) T) ((-220 . -1125) T) ((-327 . -943) 84522) ((-324 . -943) T) ((-324 . -836) NIL) ((-403 . -736) T) ((-888 . -23) T) ((-117 . -664) 84509) ((-487 . -146) 84488) ((-431 . -424) 84472) ((-487 . -148) 84451) ((-110 . -502) 84433) ((-322 . -629) 84414) ((-2 . -626) 84396) ((-188 . -102) T) ((-1183 . -19) 84378) ((-1183 . -617) 84353) ((-674 . -21) T) ((-674 . -25) T) ((-606 . -1169) T) ((-1138 . -297) 84330) ((-348 . -25) T) ((-348 . -21) T) ((-908 . -1242) T) ((-904 . -1242) T) ((-1314 . -1081) 84314) ((-246 . -662) 84093) ((-508 . -375) T) ((-1312 . -1081) 84077) ((-1307 . -38) 84047) ((-1276 . -1227) 84013) ((-1276 . -1230) 83979) ((-1265 . -915) 83882) ((-1197 . -1076) 83705) ((-1167 . -1242) T) ((-1150 . -1076) 83548) ((-872 . -1076) 83532) ((-645 . -617) 83507) ((-1276 . -95) 83473) ((-1276 . -238) 83425) ((-1259 . -102) 83403) ((-1197 . -656) 83232) ((-1150 . -656) 83081) ((-872 . -656) 83051) ((-1256 . -233) 83003) ((-1112 . -25) T) ((-562 . -1125) T) ((-1112 . -21) T) ((-986 . -1083) T) ((-544 . -808) T) ((-544 . -811) T) ((-118 . -1246) T) ((-884 . -1242) T) ((-636 . -569) T) ((-798 . -25) T) ((-798 . -21) T) ((-796 . -21) T) ((-796 . -25) T) ((-751 . -1083) T) ((-731 . -1083) T) ((-686 . -1081) 82987) ((-530 . -1108) T) ((-474 . -25) T) ((-118 . -569) T) ((-474 . -21) T) ((-467 . -25) T) ((-467 . -21) T) ((-1256 . -273) 82939) ((-1176 . -93) T) ((-1167 . -1063) 82835) ((-833 . -301) 82814) ((-1255 . -1227) 82780) ((-839 . -1125) T) ((-989 . -992) T) ((-686 . -111) 82759) ((-630 . -1242) T) ((-306 . -527) 82551) ((-1255 . -1230) 82517) ((-1255 . -238) 82376) ((-1250 . -380) T) ((-259 . -320) 82314) ((-258 . -320) 82252) ((-1247 . -860) T) ((-1184 . -627) NIL) ((-1184 . -626) 82234) ((-1167 . -389) 82218) ((-1145 . -836) T) ((-1145 . -943) T) ((-96 . -93) T) ((-1138 . -617) 82195) ((-1105 . -627) 82179) ((-1105 . -626) 82161) ((-1029 . -662) 82111) ((-937 . -662) 82048) ((-831 . -299) 82025) ((-497 . -626) 81957) ((-621 . -152) 81904) ((-500 . -733) 81854) ((-431 . -1083) T) ((-495 . -502) 81838) ((-440 . -662) 81797) ((-338 . -865) 81776) ((-351 . -664) 81750) ((-50 . -21) T) ((-50 . -25) T) ((-220 . -733) 81700) ((-171 . -740) 81671) ((-176 . -664) 81603) ((-594 . -21) T) ((-594 . -25) T) ((-531 . -25) T) ((-531 . -21) T) ((-488 . -152) 81553) ((-1086 . -626) 81535) ((-1018 . -102) T) ((-880 . -102) T) ((-832 . -923) 81435) ((-815 . -424) 81398) ((-40 . -132) T) ((-715 . -375) T) ((-717 . -742) T) ((-717 . -810) T) ((-717 . -807) T) ((-214 . -916) T) ((-593 . -1137) T) ((-577 . -1137) T) ((-508 . -1137) T) ((-371 . -626) 81380) ((-365 . -626) 81362) ((-357 . -626) 81344) ((-66 . -409) T) ((-66 . -408) T) ((-108 . -627) 81274) ((-108 . -626) 81216) ((-213 . -916) T) ((-981 . -152) 81200) ((-787 . -132) T) ((-686 . -629) 81118) ((-135 . -742) T) ((-117 . -742) T) ((-1276 . -35) 81084) ((-1079 . -502) 81068) ((-593 . -23) T) ((-577 . -23) T) ((-508 . -23) T) ((-1255 . -95) 81034) ((-1255 . -35) 81000) ((-1197 . -102) T) ((-1150 . -102) T) ((-872 . -102) T) ((-230 . -502) 80984) ((-1314 . -111) 80963) ((-1312 . -111) 80942) ((-44 . -1081) 80926) ((-1315 . -1242) T) ((-1314 . -629) 80872) ((-1314 . -1074) T) ((-1312 . -629) 80801) 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. -465) T) ((-928 . -297) 65638) ((-831 . -380) 65617) ((-523 . -522) 65596) ((-521 . -522) 65575) ((-890 . -915) 65496) ((-500 . -297) NIL) ((-495 . -299) 65473) ((-431 . -301) T) ((-366 . -132) T) ((-220 . -297) NIL) ((-710 . -506) NIL) ((-99 . -1137) T) ((-40 . -235) 65404) ((-171 . -38) 65232) ((-975 . -923) 65213) ((-1276 . -998) 65175) ((-1255 . -998) 65144) ((-1172 . -320) 65082) ((-494 . -923) 65059) ((-1138 . -1074) 65037) ((-933 . -415) T) ((-653 . -522) 65009) ((-1278 . -569) T) ((-1175 . -617) 64988) ((-112 . -865) T) ((-1088 . -502) 64919) ((-593 . -21) T) ((-593 . -25) T) ((-577 . -21) T) ((-577 . -25) T) ((-508 . -25) T) ((-508 . -21) T) ((-1265 . -1177) 64897) ((-1138 . -239) 64849) ((-48 . -132) T) ((-1223 . -102) T) ((-246 . -1125) 64601) ((-889 . -413) 64578) ((-1113 . -102) T) ((-1101 . -102) T) ((-912 . -868) T) ((-621 . -102) T) ((-488 . -102) T) ((-1265 . -38) 64407) ((-873 . -38) 64377) ((-1059 . -1076) 64351) ((-747 . -174) 64262) ((-669 . -626) 64244) ((-661 . 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. -320) 52471) ((-411 . -1242) T) ((-110 . -385) 52453) ((-324 . -132) T) ((-69 . -408) T) ((-110 . -124) T) ((-533 . -502) 52437) ((-670 . -1137) T) ((-606 . -19) 52419) ((-61 . -454) T) ((-61 . -408) T) ((-840 . -1125) T) ((-606 . -617) 52394) ((-490 . -1063) 52354) ((-669 . -1074) T) ((-670 . -23) T) ((-1307 . -1125) T) ((-31 . -102) T) ((-1265 . -662) 52264) ((-873 . -662) 52223) ((-832 . -733) 52072) ((-1294 . -1242) T) ((-590 . -878) T) ((-584 . -662) 52044) ((-118 . -865) NIL) ((-1197 . -424) 52028) ((-1150 . -424) 52012) ((-872 . -424) 51996) ((-891 . -102) 51947) ((-1276 . -102) T) ((-1256 . -527) 51716) ((-1255 . -102) T) ((-1228 . -320) 51654) ((-1199 . -297) 51619) ((-1198 . -297) 51577) ((-538 . -93) T) ((-1192 . -297) 51405) ((-323 . -626) 51387) ((-1127 . -1125) T) ((-1105 . -664) 51261) ((-727 . -465) T) ((-705 . -626) 51193) ((-300 . -742) T) ((-108 . -932) NIL) ((-705 . -627) 51154) ((-614 . -626) 51136) ((-590 . -626) 51118) ((-563 . -627) NIL) ((-563 . -626) 51100) 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. -320) 20349) ((-496 . -1125) T) ((-1150 . -627) 20097) ((-1059 . -174) T) ((-966 . -299) 20074) ((-221 . -1125) T) ((-872 . -626) 20056) ((-621 . -527) 19839) ((-81 . -629) 19780) ((-834 . -1063) 19764) ((-488 . -527) 19556) ((-849 . -868) 19535) ((-986 . -742) T) ((-751 . -742) T) ((-731 . -742) T) ((-363 . -1137) T) ((-1204 . -626) 19517) ((-226 . -102) T) ((-495 . -389) 19486) ((-528 . -1125) T) ((-523 . -1125) T) ((-521 . -1125) T) ((-815 . -664) 19460) ((-1049 . -465) T) ((-981 . -527) 19393) ((-363 . -23) T) ((-648 . -132) T) ((-620 . -132) T) ((-366 . -465) T) ((-246 . -380) 19372) ((-391 . -174) T) ((-1276 . -1083) T) ((-1255 . -1083) T) ((-228 . -1027) T) ((-832 . -629) 19109) ((-715 . -400) T) ((-431 . -742) T) ((-717 . -1246) T) ((-1167 . -654) 19057) ((-653 . -1125) T) ((-655 . -102) T) ((-593 . -887) 19041) ((-1307 . -1081) 19025) ((-1184 . -1218) 19001) ((-717 . -569) T) ((-127 . -1125) 18979) ((-730 . -1125) T) ((-674 . -38) 18949) ((-495 . -921) 18881) ((-256 . -1125) 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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 a46a630a..7c63d799 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3487271628) +(30 . 3487768760) (4473 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,668 +488,668 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |symmetricPower| |bat| |f02awf| |alphanumeric?| - |iiacoth| FG2F |lowerBound| |quadratic?| |cothIfCan| |fortranDouble| - |exponential| |mapSolve| |mapBivariate| |palglimint0| |imagI| |nary?| - |countable?| |symmetricRemainder| |surface| |predicate| - |divideExponents| |elliptic| |setScreenResolution| |Lazard| - 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|size| |bernoulliB| |leviCivitaSymbol| |hasSolution?| |systemCommand| - |dual| |reduce| |characteristicSet| |integralCoordinates| - |numberOfComposites| |f01qef| |quote| |evenInfiniteProduct| - |operators| |componentUpperBound| |trailingCoefficient| |leader| - |tableForDiscreteLogarithm| |coerceS| |determinant| |sorted?| - |setleaves!| |acosIfCan| |makeSketch| |expextendedint| |algDsolve| - |OMputApp| |tanQ| |input| |iteratedInitials| |showSummary| - |OMlistSymbols| |byteBuffer| |direction| |linearPolynomials| - |vectorise| |node?| |symbol| |linearlyDependent?| |setOrder| |swap!| - |library| |move| |curryRight| |realRoots| |complexElementary| - |sayLength| |LyndonCoordinates| |slex| |expression| |infRittWu?| - |skewSFunction| |radicalEigenvalues| |round| |iiperm| |initial| - |numericalOptimization| |computeCycleEntry| |fortranCarriageReturn| - |physicalLength| |rename!| |next| |integer| |iicosh| |henselFact| - |optimize| |unrankImproperPartitions1| |biRank| |credPol| - |linearlyDependentOverZ?| |dimensionsOf| |setClosed| |shufflein| - 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|toseInvertible?| |reduceBasisAtInfinity| |child?| |linearDependence| - |e04jaf| |perspective| |setelt!| |inHallBasis?| |changeThreshhold| - |trigs| |viewWriteAvailable| |cfirst| |constantCoefficientRicDE| - |getCurve| |eigenMatrix| |iitanh| |subresultantSequence| |maxColIndex| - |iipow| |linearDependenceOverZ| |wrregime| |logGamma| - |generalizedEigenvector| |LyndonBasis| |hasHi| |returns| |BasicMethod| - |setfirst!| |finiteBound| |redPol| |in?| |varselect| |indices| - |mainValue| |resetAttributeButtons| |constructor| |makeSeries| - |semiDiscriminantEuclidean| |top!| |modularGcd| |e01bgf| - |screenResolution3D| |removeRedundantFactors| |wholeRagits| |tube| - |intermediateResultsIF| |front| |root?| |pol| |even?| |makeprod| - |s19adf| |hostPlatform| |divisorCascade| |alternating| |idealiser| - |factors| |removeCoshSq| |pToDmp| |prepareDecompose| |cyclicParents| - |UP2ifCan| |setValue!| |makeGraphImage| UTS2UP |polar| |regime| |box| - |blankSeparate| |characteristicPolynomial| |euclideanSize| - |rootOfIrreduciblePoly| |overlap| |multMonom| |modulus| |nothing| - |lexGroebner| |s17aff| |genericRightTrace| |maxint| - |internalZeroSetSplit| |equation| |cCsch| |compdegd| |whatInfinity| - |OMgetAttr| |map| |f04atf| |compactFraction| |reduceLODE| - |create3Space| |factorPolynomial| |prem| - |rightCharacteristicPolynomial| |say| |copy!| |acotIfCan| |makeMulti| - |toseInvertibleSet| |simpson| |contractSolve| |lexTriangular| - |getButtonValue| |e04mbf| |zoom| |OMUnknownSymbol?| |bigEndian| - |selectMultiDimensionalRoutines| |solveRetract| |sts2stst| - |normalizeAtInfinity| |powern| |sizeMultiplication| |iicoth| - |SturmHabichtSequence| |identityMatrix| |real?| |reset| - |solveLinearlyOverQ| |generalizedEigenvectors| |var1StepsDefault| - |divisor| |changeVar| |OMputAttr| SEGMENT |bezoutMatrix| - |PollardSmallFactor| |minColIndex| |iidsum| |sortConstraints| - |hypergeometric0F1| |kmax| |zeroDimensional?| |octon| |solveLinear| - |call| |chainSubResultants| |doubleRank| |gbasis| |reduction| |write| - 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|clearTable!| |complexEigenvalues| |weakBiRank| + |splitConstant| |cTanh| |pow| |lazyPquo| |sizeMultiplication| |s19acf| + |nextPartition| |besselY| |symmetricDifference| |insertTop!| + |positive?| |wronskianMatrix| |lazyGintegrate| |And| |left| + |headReduce| |iicoth| |rightOne| |fractRagits| |newReduc| + |tryFunctionalDecomposition?| |beauzamyBound| |s17akf| |laplacian| + |outputList| |imagI| |opeval| |tensorProduct| |Or| |isExpt| |right| + |gcdcofactprim| |SturmHabichtSequence| |close| |ideal| + |OMencodingUnknown| |forLoop| |nary?| |iibinom| + |initializeGroupForWordProblem| |symmetricSquare| + |mainCharacterization| |bandedJacobian| |Not| |cTan| |identityMatrix| + |rationalApproximation| |rombergo| |semiResultantReduitEuclidean| + |calcRanges| |exptMod| |f02agf| |getDatabase| |cot2trig| |leader| + |linears| |display| |real?| |internalSubQuasiComponent?| |twoFactor| + |findCycle| |lex| |mapUnivariate| |generators| |iroot| |computeInt| + |dmpToP| |solveLinearlyOverQ| |useEisensteinCriterion| + |purelyAlgebraic?| |generalizedContinuumHypothesisAssumed| + |computeCycleLength| |fTable| |lowerCase| |integralLastSubResultant| + |tableau| |generalizedEigenvectors| |quasiRegular| |parametersOf| + |rationalPower| |selectPDERoutines| |alphabetic?| |e04ycf| + |printInfo!| |indicialEquation| |addiag| |rootPoly| |var1StepsDefault| + |vedf2vef| |elRow2!| |cyclotomicFactorization| |specialTrigs| + |singular?| |explicitlyFinite?| |factorOfDegree| |factorSquareFree| + |df2mf| |divisor| |doubleFloatFormat| |enterPointData| |upperCase| + |integral?| |localAbs| |irVar| |vector| |conditionP| |lift| |input| + |changeVar| |unprotectedRemoveRedundantFactors| |balancedBinaryTree| + |parametric?| |init| |transcendent?| |tanintegrate| |readable?| |mdeg| + |differentiate| |resultant| |reduce| |hitherPlane| |testDim| |library| + |OMputAttr| |setCondition!| |box| |squareTop| |clipSurface| |Beta| + |rightExactQuotient| |position| |roughEqualIdeals?| |sinhIfCan| |rule| + |readByte!| |showAll?| |stirling1| |bezoutMatrix| UP2UTS |SFunction| + |explicitlyEmpty?| |jokerMode| |cycle| |imaginary| + |removeConstantTerm| |viewThetaDefault| |patternVariable| |symbol| + |showSummary| |hasTopPredicate?| |parent| |subscript| |belong?| + |jordanAlgebra?| |swapRows!| |normal01| |indicialEquationAtInfinity| + |expression| |setelt!| |optimize| |unary?| |expandLog| |outputGeneral| + |pointPlot| |groebnerFactorize| |diophantineSystem| + |resetVariableOrder| |LazardQuotient2| |integer| |inHallBasis?| + |differentialVariables| |conjug| |linearPart| |initials| |numFunEvals| + |exactQuotient!| |processTemplate| |d02gaf| |changeThreshhold| |subst| + |nextNormalPoly| |c06gcf| |simplify| |permutationRepresentation| + |zeroDim?| |distFact| |trigs| |showAttributes| |duplicates?| + |var2StepsDefault| |heap| |validExponential| |completeSmith| + |getVariableOrder| |branchPointAtInfinity?| |dimension| + |viewWriteAvailable| |totalfract| |getExplanations| + |numberOfIrreduciblePoly| |iicsch| |monic?| |separateFactors| |assert| + |lSpaceBasis| |inR?| |cfirst| |iiacot| |leaves| |externalList| + |minimize| |revert| |moduleSum| |coleman| |expenseOfEvaluationIF| + |zag| |constantCoefficientRicDE| |imagK| |divergence| |OMgetSymbol| + |gcdPolynomial| |iisinh| |makeViewport3D| |simplifyExp| |getCurve| + |pointColorPalette| |nextLatticePermutation| |OMserve| |e02aef| + |possiblyInfinite?| |initTable!| |byte| |heapSort| + |unrankImproperPartitions0| |dioSolve| |eigenMatrix| + |eisensteinIrreducible?| |irreducibleRepresentation| |quasiComponent| + |multinomial| |fortranLinkerArgs| |lprop| |llprop| |minGbasis| + |d01alf| |delta| |iitanh| |innerint| |nullSpace| |OMputEndAtp| + |contract| |univariatePolynomials| |noLinearFactor?| |conjunction| + |subresultantSequence| |log2| |roughBase?| |submod| + |factorGroebnerBasis| |baseRDE| |irCtor| |acscIfCan| + |indicialEquations| |qelt| |maxColIndex| |cAcsch| |trapezoidal| |dark| + |cycleElt| |qsetelt| |factorAndSplit| |palgLODE| |degreePartition| + |d02ejf| |iipow| |pushdterm| |singRicDE| |OMputObject| |quotient| + |monicDecomposeIfCan| |uniform01| |viewPhiDefault| |head| |xRange| + |constructor| |linearDependenceOverZ| |OMconnectTCP| |plotPolar| + |rationalPoints| |explogs2trigs| |f07adf| |internalLastSubResultant| + |initiallyReduce| |yRange| |wrregime| |rootPower| |meshFun2Var| + |integralMatrix| |domainTemplate| |dimensions| |clearTheFTable| + |refine| |generalInfiniteProduct| |zRange| |logGamma| + |createLowComplexityTable| |solveLinearPolynomialEquationByRecursion| + |s18def| |polarCoordinates| |option?| |LagrangeInterpolation| + |inconsistent?| |systemSizeIF| |map!| |lambda| + |generalizedEigenvector| |weights| |createNormalElement| |moebiusMu| + |exprHasWeightCosWXorSinWX| |qsetelt!| |mainSquareFreePart| |nothing| + |e04ucf| |jacobian| |charthRoot| |LyndonBasis| |printStats!| + |lighting| |completeHermite| |stoseIntegralLastSubResultant| |pomopo!| + |rightNorm| |OMgetEndObject| |showRegion| |hasHi| |perfectNthRoot| + |resetBadValues| |rroot| |subtractIfCan| |extractSplittingLeaf| + |tower| |extendedSubResultantGcd| |normFactors| |maxrow| |type| + |returns| |evaluate| |rem| |cosIfCan| |elaborate| |tab| + |modularFactor| |mapdiv| |polCase| |setTopPredicate| |groebnerIdeal| + |BasicMethod| |quo| |cotIfCan| |iisin| |drawToScale| |vark| + |numberOfComputedEntries| |quoted?| |coerceImages| SEGMENT |setfirst!| + |purelyTranscendental?| |compound?| |c06ecf| |upperCase?| + |exprToGenUPS| |yCoord| |shiftLeft| |algebraicSort| |acsch| + |finiteBound| |horizConcat| |div| |typeList| |upperCase!| |iiacsch| + |constDsolve| |subResultantGcd| |setAdaptive3D| |subspace| |someBasis| + |redPol| |squareFreeLexTriangular| |elRow1!| |exquo| + |leadingCoefficientRicDE| |tracePowMod| |queue| |s17ahf| + |complexNumeric| |quickSort| |tubeRadiusDefault| |in?| |intcompBasis| + |OMopenFile| ~= |infLex?| |basis| |resultantReduit| |roughUnitIdeal?| + |imagE| |bubbleSort!| |iiatan| |varselect| + 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|getOrder| |divideExponents| |top!| |getProperties| |bringDown| + |subset?| |chvar| |elliptic| |palgLODE0| |key?| |factor| |s18aef| + |lllip| |modularGcd| |nextPrimitivePoly| |minPoints| |extract!| + |realElementary| |message| |repeatUntilLoop| |zeroSetSplit| |sqrt| + |setEpilogue!| |positiveSolve| |setScreenResolution| |e01bgf| + |recoverAfterFail| |deleteRoutine!| |palgextint| |scopes| + |sumOfKthPowerDivisors| |minimumDegree| |outputAsTex| |real| |over| + |Lazard| |screenResolution3D| |transform| |ReduceOrder| |delay| + |optAttributes| |argscript| |imag| |stronglyReduced?| + |OMsupportsSymbol?| |empty| |removeRedundantFactors| + |linearAssociatedOrder| |unitNormal| |permutationGroup| |paraboloidal| + |cAcot| |directProduct| |mappingAst| |reorder| |fractionFreeGauss!| + |wholeRagits| |quasiAlgebraicSet| |colorDef| |semiResultantEuclidean2| + |OMgetEndBind| |knownInfBasis| |ipow| |integralAtInfinity?| |overset?| + |tube| |extractBottom!| |optpair| |OMgetVariable| |conjugates| + |pureLex| |redpps| |brace| |printCode| |wordInStrongGenerators| + |intermediateResultsIF| |laguerre| |setOfMinN| |inGroundField?| + |iicot| |zeroDimPrimary?| |f02bbf| |fortran| |destruct| |lfinfieldint| + |points| |bright| |front| |limitedint| |endOfFile?| |abs| + |basisOfCenter| |associative?| |reducedDiscriminant| |bumptab| + |permutations| |Lazard2| |root?| |startTable!| |pseudoRemainder| + |rewriteIdealWithHeadRemainder| |c06fqf| F |setMaxPoints| |green| + |ptree| |reseed| |incrementKthElement| |iterationVar| F2FG |eval| + |pol| |flatten| |subHeight| |cyclicEntries| |currentSubProgram| + |Aleph| |tubeRadius| |plus| |check| |getMultiplicationTable| + |baseRDEsys| |listLoops| |convert| |even?| |OMputFloat| |typeLists| + |outputSpacing| |traceMatrix| |infinityNorm| |nextsousResultant2| + |positiveRemainder| |monomial| |removeSuperfluousQuasiComponents| + |airyAi| |makeprod| |stFunc2| |fixedPointExquo| |e02bcf| + |fillPascalTriangle| |lazyPseudoRemainder| |voidMode| |multivariate| + |radicalOfLeftTraceForm| |derivative| |error| |s19adf| |wreath| + |iiasin| |defineProperty| |makeSin| |bit?| |times| |variables| + |minRowIndex| |fibonacci| |infieldIntegrate| |hostPlatform| |size| + |readInt16!| |cRationalPower| |singularitiesOf| + |solveLinearPolynomialEquationByFractions| |critM| |listBranches| + |constantRight| |changeMeasure| |divisorCascade| |c06gbf| |deref| + |lyndon| |cschIfCan| |innerEigenvectors| |leftScalarTimes!| |s17acf| + |rdregime| |alternating| |normalizedAssociate| + |lastSubResultantEuclidean| |primitive?| |c02aff| |digit| + |fortranDoubleComplex| |iExquo| |se2rfi| |idealiser| |clipParametric| + |tan2cot| |exprToXXP| |monom| |cubic| |s13acf| |setMinPoints3D| + |iisqrt3| |semiSubResultantGcdEuclidean2| |factors| + |createPrimitiveNormalPoly| |mindegTerm| |autoReduced?| |bfKeys| + |s17dhf| |qinterval| |taylor| |e02akf| |errorInfo| + |basisOfLeftAnnihilator| |removeCoshSq| |d01gaf| |outerProduct| + |OMsend| |leftUnits| |script| |OMputBVar| |intersect| |laurent| + |c05pbf| |trunc| |pToDmp| |normalDenom| |collect| + |fullPartialFraction| |common| |symbolTableOf| |pile| + |multiplyExponents| |puiseux| |neglist| |truncate| |prepareDecompose| + |oblateSpheroidal| |triangSolve| |stoseInvertibleSet| |enqueue!| + |less?| |dualSignature| |innerSolve| |cyclicParents| |associates?| + |pointSizeDefault| |expintfldpoly| |key| |tex| |inv| |badValues| + |cycleTail| |ldf2lst| |nextPrimitiveNormalPoly| |node| |UP2ifCan| + |bipolarCylindrical| |definingEquations| |uniform| |ground?| |null| + |optional?| |coerceListOfPairs| |f01ref| |mainVariables| |lfunc| + |setValue!| |retract| |member?| |OMputError| |filename| |ground| |not| + |vspace| |selectFiniteRoutines| |pdct| |ode| |numberOfVariables| + |taylorIfCan| |cardinality| |s21baf| |and| |leadingMonomial| + |showTheSymbolTable| |wholePart| |components| |modularGcdPrimitive| + |numer| |partialQuotients| |safetyMargin| |dihedralGroup| |assign| + |parse| |or| |light| |principalIdeal| |leadingCoefficient| + |palginfieldint| |numerator| |odd?| |denom| |iiasech| |atom?| + |shallowCopy| |setsubMatrix!| |groebgen| |primitiveMonomials| |nthr| + |xor| |stoseInvertible?reg| |child| |pointLists| |edf2df| + |OMputEndObject| |eq?| |setprevious!| |edf2efi| |delete| |f02fjf| |pi| + |dmpToHdmp| |purelyAlgebraicLeadingMonomial?| |roughBasicSet| |hclf| + |pole?| |matrixDimensions| |bounds| |infinity| |redmat| |zeroOf| + |numberOfHues| |binary| |leftReducedSystem| |critT| |headReduced?| + |branchPoint?| |appendPoint| ** |back| |var2Steps| |plenaryPower| + |degreeSubResultantEuclidean| |Vectorise| |maxPoints3D| |froot| + |integerBound| |cAtanh| |symmetricPower| |internal?| + |integralDerivationMatrix| |vconcat| |polygon| |bumprow| |bat| + |primes| |diagonalMatrix| |exprHasLogarithmicWeights| + |minimalPolynomial| |kernel| |symmetric?| |pop!| |screenResolution| + |rischDE| |inf| RF2UTS |f02awf| |OMputSymbol| |returnType!| + |clipWithRanges| |selectfirst| |list| |setClipValue| |iicsc| + |rightUnits| |norm| |currentEnv| |mainForm| |sec2cos| |alphanumeric?| + |super| |triangularSystems| |lambert| |draw| |cExp| + |removeSuperfluousCases| |equation| |null?| |symFunc| + |coercePreimagesImages| |regularRepresentation| |sequence| |map| + |currentScope| |iiacoth| |constantOpIfCan| |putProperties| + |alternative?| |sort!| |isImplies| |constantIfCan| |linearElement| + |difference| |besselK| |ode2| FG2F |li| |hostByteOrder| |c06fuf| + |OMputInteger| |isAtom| |tanAn| |quadraticNorm| |categoryMode| |index| + |basisOfCentroid| |representationType| |lowerBound| |f04asf| + |argument| |monomRDEsys| |simplifyLog| |squareFreePart| + |taylorQuoByVar| |s19abf| |concat!| |semiResultantEuclideannaif| + |linear| |quadratic?| |makeObject| |aLinear| |setProperty| + |shiftRoots| |pushNewContour| |pleskenSplit| |makeCos| + |subResultantGcdEuclidean| |fractionPart| |cothIfCan| |s17aef| |coef| + |safeFloor| |semiDegreeSubResultantEuclidean| |whitePoint| |unmakeSUP| + |iisqrt2| |finite?| |clearTheSymbolTable| |pair| |rowEchelon| + |polynomial| |fortranDouble| |irreducibleFactor| |rationalIfCan| + |point| |createNormalPrimitivePoly| |tanh2trigh| |extensionDegree| + |expint| |ScanRoman| |cyclePartition| |stoseInvertibleSetsqfreg| + |LiePolyIfCan| |exponential| |log10| |numberOfNormalPoly| + |removeSinSq| |splitSquarefree| |cycleEntry| |powerSum| |s17dgf| + |solid?| |fortranCharacter| |flexibleArray| |innerSolve1| |mapSolve| + |eulerE| |sumSquares| |unparse| |getlo| |leftRegularRepresentation| + |genus| |s20adf| |cAcoth| |c05nbf| |lookup| |extendedEuclidean| + |series| |any?| |youngDiagram| |isMult| |doubleDisc| |dmp2rfi| + |indiceSubResultant| |putColorInfo| |OMputString| |just| |inc| + |createThreeSpace| |unit?| |extendedint| |rewriteIdealWithRemainder| + |OMreadStr| |test| |cyclotomic| |cosSinInfo| |f07fdf| |mainVariable?| + |stosePrepareSubResAlgo| |comment| |reducedQPowers| |failed| + |leftPower| |definingInequation| |stirling2| |twist| |gramschmidt| + |algebraic?| |conical| |f2st| |rightUnit| |qfactor| |OMencodingBinary| + |rational| |size?| |primitivePart| |f01rdf| |commaSeparate| + |hasPredicate?| |dim| |OMclose| |debug| |primintegrate| |youngGroup| + |min| |reducedForm| |latex| |newLine| |stoseInvertible?| |dequeue!| + |setStatus!| D |denominator| |printHeader| |firstSubsetGray| + |yCoordinates| |sparsityIF| |generic?| |traverse| |changeWeightLevel| + |recolor| |createIrreduciblePoly| |children| |oddlambert| + |rightFactorIfCan| |zerosOf| |nil| |overlabel| |numberOfComponents| + |ListOfTerms| |deepCopy| |kovacic| |log| |dihedral| |rspace| |rules| + |rootSimp| |normalDeriv| |mapBivariate| |signatureAst| |cartesian| + |prefix| |mix| |setRealSteps| |OMputEndError| |ranges| |Gamma| + |minus!| |repeating?| |numberOfOperations| |palgintegrate| + |palglimint0| |controlPanel| |outputBinaryFile| |solveInField| + |invertibleElseSplit?| |setleft!| |f01qcf| |e01daf| |OMcloseConn| + |patternMatch| |prevPrime| |content| |var1Steps| |apply| |isPlus| + |integral| |approximate| |rarrow| |overbar| |fprindINFO| + |continuedFraction| |cscIfCan| |coordinates| |tubePlot| |complex| + |leadingTerm| |first| |leftFactor| |factorset| |curry| + |rewriteSetWithReduction| |empty?| |modifyPoint| |makeUnit| + |mathieu23| |selectIntegrationRoutines| |cAsinh| |rest| + |degreeSubResultant| |collectUpper| |clearFortranOutputStack| + |ceiling| |f2df| |leadingIndex| |mesh?| |solve| |OMgetEndAtp| + |OMgetAtp| |lastSubResultant| |sinh2csch| |mapCoef| |redPo| + |comparison| |float| |f07aef| |complexEigenvectors| |solveid| + |numeric| |quasiMonicPolynomials| |unknown| |moduloP| |schwerpunkt| + |frst| |minPoly| |polyPart| |measure2Result| |radical| |complexLimit| + |commonDenominator| |mapExpon| |print| |cyclicGroup| |radicalRoots| + |trueEqual| |monomial?| |shrinkable| |primintfldpoly| |primeFactor| + |makeFloatFunction| |rightPower| |resolve| |diagonal| + |uncouplingMatrices| |denomLODE| |unit| |d01fcf| |terms| |setvalue!| + |directSum| |d01aqf| |expandTrigProducts| |curveColor| |cot2tan| + |oneDimensionalArray| |sort| |factorsOfCyclicGroupSize| + |virtualDegree| |d02kef| |setUnion| |rubiksGroup| |dAndcExp| + |OMputEndAttr| |elem?| |cAsin| |zeroVector| |bfEntry| + |genericRightNorm| |Ei| |level| |exprex| |pseudoDivide| |outputFixed| + |selectSumOfSquaresRoutines| |implies| |split!| |subResultantsChain| + |normalizedDivide| |perfectSquare?| |rightRecip| |arbitrary| |push!| + |f02axf| |computeBasis| |startTableGcd!| |setLength!| + |restorePrecision| |cAcsc| |goodnessOfFit| |d03edf| + |numericalIntegration| |UnVectorise| |rectangularMatrix| |any| |read!| + |discreteLog| |sign| |Hausdorff| |scan| |random| |atanIfCan| |s14aaf| + |getOperator| |univariatePolynomial| GE |consnewpol| |e02bef| + |complex?| |f02wef| |nthExpon| |convergents| |unitsColorDefault| + |cCot| GT |groebSolve| |monomialIntPoly| + |standardBasisOfCyclicSubmodule| |scanOneDimSubspaces| + |squareFreePrim| |nextSubsetGray| |addPoint| |leftRemainder| LE + |gcdPrimitive| |lowerCase!| |getIdentifier| |numberOfFractionalTerms| + |mapDown!| |socf2socdf| |minrank| |reflect| LT |concat| |increase| + |complexExpand| |leftDiscriminant| |radicalEigenvectors| + |normalizeIfCan| |shift| |legendreP| |ridHack1| |interReduce| |remove| + |ravel| |spherical| |exponent| |partialNumerators| |position!| + |OMputAtp| |factorSquareFreeByRecursion| |pair?| |f04arf| |reshape| + |RittWuCompare| |symbol?| |writeInt8!| |atanhIfCan| + |factorSquareFreePolynomial| |OMencodingXML| |subPolSet?| |radPoly| + |last| |sturmSequence| |lastSubResultantElseSplit| |insertBottom!| + |extractClosed| |lp| |pquo| |categoryFrame| + |removeRedundantFactorsInContents| |assoc| |complement| |splitLinear| + |makeop| |distribute| |lazyIrreducibleFactors| |OMReadError?| |color| + |zero?| |relativeApprox| |simplifyPower| |realZeros| |complexSolve| + |trim| |unknownEndian| |internalInfRittWu?| |integers| |arrayStack| + |systemCommand| |OMgetBVar| |monicRightDivide| |aQuadratic| |cyclic?| + |invertIfCan| |totalDifferential| |curve?| |generalizedInverse| + |update| |strongGenerators| |quotedOperators| |minIndex| + |numberOfMonomials| |showScalarValues| |bits| |logical?| + |removeDuplicates!| |jacobiIdentity?| |f02aff| |karatsubaOnce| + |viewSizeDefault| |entry| |toseInvertible?| |critpOrder| + |abelianGroup| |acschIfCan| |central?| |normal| |aromberg| + |rewriteSetByReducingWithParticularGenerators| |presuper| |units| + |reduceBasisAtInfinity| |ratDenom| |ptFunc| |tanSum| + |rightRankPolynomial| |f04qaf| |numericIfCan| |taylorRep| |child?| + |closed| |s14baf| |radicalSolve| |expIfCan| |drawStyle| |droot| + |genericRightTraceForm| |linearDependence| |pdf2ef| |e02dff| + |pascalTriangle| |realEigenvectors| |mindeg| |reindex| |rowEch| + |e04jaf| |lazy?| |unexpand| |infix| |delete!| |f04mcf| |length| + |linkToFortran| |readInt8!| |perspective| |pmintegrate| |usingTable?| + |viewDeltaYDefault| |code| |invmod| |scripts| |definingPolynomial| + |explimitedint| |extractIfCan| |retractIfCan| |df2ef| + |lineColorDefault| |clipBoolean| |cCoth| |swapColumns!| |iifact| + |userOrdered?| |makeSketch| |zeroSquareMatrix| |readLineIfCan!| + |alphanumeric| |declare!| |function| |listOfMonoms| |bsolve| + |inverseIntegralMatrixAtInfinity| |arity| |expextendedint| + |createMultiplicationTable| |leadingIdeal| |subResultantChain| + |f04maf| |weierstrass| |escape| |ignore?| |top| |algDsolve| |e02ddf| + |messagePrint| |musserTrials| |computePowers| |pade| |continue| + |OMputApp| |f02akf| |hermiteH| |associator| |build| |midpoints| + |cycleRagits| |compose| |tanQ| |univariatePolynomialsGcds| |point?| + |before?| |primeFrobenius| |totalGroebner| |has?| |isTimes| + |iteratedInitials| |lazyResidueClass| |laurentRep| |isOp| + |idealiserMatrix| |wordsForStrongGenerators| |e04dgf| + |leftExtendedGcd| |OMlistSymbols| |distdfact| EQ |label| + |genericRightMinimalPolynomial| |monomialIntegrate| + |lazyPremWithDefault| |cosh2sech| |byteBuffer| |iflist2Result| + |close!| |f02adf| |segment| |OMgetString| |supRittWu?| |lieAlgebra?| + |btwFact| |direction| |list?| |integralBasis| |increment| + |realEigenvalues| |nthRootIfCan| |pToHdmp| |bivariatePolynomials| + |linearPolynomials| |rootRadius| |OMputEndBVar| |Is| |cSech| + |integer?| |void| |vectorise| |s14abf| |generalSqFr| |csc2sin| + |yellow| |internalIntegrate0| |setIntersection| |plus!| |hash| + |besselI| |node?| |morphism| |ScanFloatIgnoreSpacesIfCan| |relerror| + |graphs| |lcm| |count| |setPoly| |OMgetBind| |expressIdealMember| + |quasiMonic?| |linearlyDependent?| |createZechTable| |torsionIfCan| + |chebyshevT| |say| |imagi| |toseSquareFreePart| |generalPosition| + |diagonalProduct| |category| |setOrder| |increasePrecision| + |sturmVariationsOf| |append| |f04axf| |setVariableOrder| + |lookupFunction| |padecf| |viewpoint| |domain| |swap!| |prinb| + |approxNthRoot| |asechIfCan| |option| |reset| |monicLeftDivide| + |partialFraction| |gcd| |cAcos| |gderiv| |normal?| |package| + |datalist| |isobaric?| |move| |internalSubPolSet?| + |zeroSetSplitIntoTriangularSystems| |commutator| |sqfree| + |stoseSquareFreePart| |false| |stiffnessAndStabilityOfODEIF| |equiv| + |curryRight| |leftOne| |inputOutputBinaryFile| + |removeRoughlyRedundantFactorsInPol| |write| |lyndon?| + |squareFreePolynomial| |associatorDependence| |maximumExponent| |open| + |realRoots| |dimensionOfIrreducibleRepresentation| |generator| + |OMgetObject| |leftFactorIfCan| |aQuartic| |save| |crushedSet| + |rotate| |e02zaf| |medialSet| |adaptive?| |complexElementary| + |GospersMethod| |RemainderList| |genericPosition| |conjugate| + |brillhartTrials| |internalAugment| |df2st| |normInvertible?| GF2FG + |sayLength| |sncndn| |lazyPseudoQuotient| |curve| |separate| + |asecIfCan| |constant?| |callForm?| |makingStats?| |leftTrace| + |LyndonCoordinates| |iiacosh| |moebius| |postfix| |hconcat| + |selectNonFiniteRoutines| |euclideanGroebner| |supersub| + |generalizedContinuumHypothesisAssumed?| |operations| |slex| |f01brf| + |recip| |lifting1| |mvar| |arguments| |stop| |makeTerm| |allRootsOf| + |simpsono| |adjoint| |nonLinearPart| |infRittWu?| + |halfExtendedResultant1| |OMconnOutDevice| |inputBinaryFile| |f01mcf| + |changeName| |clikeUniv| |pushuconst| |acoshIfCan| |fortranInteger| + |skewSFunction| |pdf2df| |e02dcf| |exportedOperators| |binomThmExpt| + |useNagFunctions| |numFunEvals3D| |extractProperty| |monicDivide| + |radicalEigenvalues| |mkPrim| |rightDivide| |duplicates| |ddFact| + |decomposeFunc| |mainKernel| |attributeData| |hyperelliptic| |round| + |readUInt32!| |phiCoord| |bernoulli| |s17agf| |binomial| + |listConjugateBases| |OMgetEndError| |s17dcf| |iiperm| |factor1| + |squareFreeFactors| |incr| |listOfLists| |iisech| |tanNa| |mapGen| + |factorSFBRlcUnit| |divide| |toScale| |numericalOptimization| + |alternatingGroup| |constant| |inverseIntegralMatrix| |hi| |select!| + |e04naf| |fill!| |lazyPseudoDivide| |imagJ| |computeCycleEntry| + |createMultiplicationMatrix| |sinIfCan| |mkIntegral| |ldf2vmf| + |leftCharacteristicPolynomial| |tryFunctionalDecomposition| + |frobenius| |step| |OMread| |subresultantVector| + |fortranCarriageReturn| |pmComplexintegrate| |nextItem| |localUnquote| + |littleEndian| |composite| |setFormula!| |internalDecompose| + |dictionary| |leadingSupport| |physicalLength| |checkRur| |negative?| + |viewport3D| |sumOfSquares| |viewZoomDefault| |d02cjf| |cos2sec| + |addmod| |rename!| |vertConcat| |readIfCan!| |isPower| |eigenvectors| + |multiplyCoefficients| |primlimitedint| |measure| |htrigs| |iicosh| + |algebraicVariables| |anticoord| |selectOrPolynomials| |makeFR| + |lintgcd| |mainVariable| |setProperties| |linSolve| + |getSyntaxFormsFromFile| |erf| |henselFact| |meshPar2Var| + |exponential1| |LazardQuotient| |complementaryBasis| |cCos| + |cyclicSubmodule| |prepareSubResAlgo| |iFTable| + |unrankImproperPartitions1| |f02ajf| |bivariateSLPEBR| |coth2trigh| + |ODESolve| |halfExtendedSubResultantGcd1| |sup| |wholeRadix| |digamma| + |biRank| |OMbindTCP| |fixedDivisor| |replace| |doublyTransitive?| + |outputAsScript| |nextSublist| |deepestTail| |scripted?| |dilog| + |credPol| |primPartElseUnitCanonical| |startStats!| |macroExpand| + |denomRicDE| |numberOfFactors| |showTheFTable| + |numberOfImproperPartitions| |oddInfiniteProduct| |extendIfCan| |sin| + |int| |linearlyDependentOverZ?| |binarySearchTree| |nextColeman| + |doubleResultant| |goodPoint| |SturmHabichtCoefficients| |mkcomm| + |showClipRegion| |recur| |cos| |dimensionsOf| |rightTrace| + |perfectNthPower?| |factorsOfDegree| |insert| |trace2PowMod| + |OMUnknownCD?| |antiAssociative?| |rightLcm| |permutation| |tan| + |setClosed| |exp1| |roughSubIdeal?| |f02abf| |signAround| |irDef| + |d01ajf| |bivariate?| |isAnd| |cot| |shufflein| |tanIfCan| + |pointColorDefault| |FormatArabic| |palgRDE| |complexForm| |d03faf| + |blue| |gensym| |parts| |sec| |figureUnits| |roman| |untab| + |elaborateFile| |parabolicCylindrical| |rotatez| |supDimElseRittWu?| + |noKaratsuba| |myDegree| |mr| |csc| |accuracyIF| |algebraicOf| + |karatsubaDivide| |noncommutativeJordanAlgebra?| |ksec| |ParCondList| + |fortranTypeOf| |removeZero| |constantKernel| |asin| |block| + |exactQuotient| |csubst| |putGraph| |entries| |pushup| + |modifyPointData| |tubePointsDefault| |numberOfPrimitivePoly| |acos| + |lfextlimint| |choosemon| |listYoungTableaus| |is?| |ratDsolve| + |graphState| |LiePoly| |elColumn2!| |basisOfRightNucleus| |atan| + |evenlambert| |linearAssociatedExp| |useSingleFactorBound| + |identification| |getMultiplicationMatrix| |insertMatch| |signature| + |sylvesterMatrix| |sPol| |module| |acot| |makeVariable| |connectTo| + |intensity| |isList| |routines| |bezoutResultant| |isQuotient| + |BumInSepFFE| |iiasec| |bandedHessian| |diagonal?| |asec| |e01bff| + |po| |rCoord| |jacobi| |sizePascalTriangle| |schema| |inrootof| + |s15aef| |critMTonD1| |acsc| |nand| |elementary| |multisect| + |discriminant| |hermite| |typeForm| |sumOfDivisors| |zeroMatrix| + |gcdcofact| |inverse| |sinhcosh| |decimal| |sinh| |gradient| |c05adf| + |keys| |evaluateInverse| |showAllElements| |checkPrecision| |iidprod| + |xCoord| |digit?| |omError| |tRange| |cosh| |next| |fixPredicate| + |identity| |iiabs| |iilog| |disjunction| |headRemainder| + |rischNormalize| |topPredicate| |currentCategoryFrame| |tanh| + |mathieu22| |fortranLogical| |stFunc1| |lepol| |zeroDimPrime?| + |solve1| |height| |exprToUPS| |subQuasiComponent?| |rational?| |coth| + |leastPower| |algSplitSimple| |prime?| |c06ebf| |hexDigit| + |possiblyNewVariety?| |OMsupportsCD?| |realSolve| |leftRankPolynomial| + |sech| |getRef| |linearAssociatedLog| |setref| |OMgetFloat| + |fglmIfCan| |s13aaf| |nullary?| |e02ajf| |OMputEndApp| |csch| + |discriminantEuclidean| |iiacos| |getPickedPoints| |rename| |iitan| + |randnum| |getProperty| |primitivePart!| |prod| |asinh| + |colorFunction| |cPower| |failed?| |environment| + |stoseInternalLastSubResultant| |functorData| |OMputBind| + |fortranLiteral| |getMeasure| |invmultisect| |acosh| |fixedPoint| + |KrullNumber| |leftUnit| |s18dcf| |goto| |c06fpf| |getCode| |extend| + |shallowExpand| |nthRoot| |atanh| |basisOfCommutingElements| |Si| + |e02adf| |partitions| |cond| |addBadValue| |outputForm| |s18adf| + |composites| |permanent| |generalLambert| |acoth| |find| + |expintegrate| |d01gbf| |shellSort| |maxRowIndex| |setTex!| + |lflimitedint| |eulerPhi| |s21bdf| |linGenPos| |asech| + |clearTheIFTable| |epilogue| |bitCoef| |explicitEntries?| |slash| + |qualifier| |scalarTypeOf| |resetNew| |superHeight| |rationalFunction| + |orbit| |PollardSmallFactor| |hasoln| |curryLeft| |pr2dmp| + |OMreadFile| |normalized?| |mainPrimitivePart| |multiple| + |unitCanonical| |newTypeLists| |lyndonIfCan| |pushdown| |minColIndex| + |s17def| |wordInGenerators| |replaceKthElement| |setDifference| + |applyQuote| |stoseLastSubResultant| |prolateSpheroidal| |setStatus| + |low| |iidsum| |halfExtendedSubResultantGcd2| |set| + |basisOfMiddleNucleus| |tubePoints| |region| |lifting| |aspFilename| + |open?| |sortConstraints| |dflist| |setnext!| |mat| |badNum| + |adaptive| |resultantReduitEuclidean| |inverseColeman| |tail| + |subNode?| |hypergeometric0F1| |listexp| |nextNormalPrimitivePoly| + |sequences| BY |dom| |setImagSteps| |saturate| |ruleset| + |powerAssociative?| |countRealRoots| |palgint| |rangePascalTriangle| + |kmax| |findConstructor| |declare| |internalIntegrate| |e01sff| + |chineseRemainder| |leftNorm| |useSingleFactorBound?| |endSubProgram| + |univariate?| |mkAnswer| |zeroDimensional?| |rightExtendedGcd| + |reduceByQuasiMonic| |setPosition| |triangulate| |clipPointsDefault| + |OMreceive| |complexZeros| |octon| |createLowComplexityNormalBasis| + |showTheRoutinesTable| |leftZero| |range| |suchThat| + |removeDuplicates| |totalLex| |e02bbf| |solveLinear| |s01eaf| + |factorials| |setLabelValue| |nodeOf?| |lowerPolynomial| + |selectPolynomials| |zCoord| |resultantEuclidean| |alphabetic| |call| + |topFortranOutputStack| |c06gsf| |setErrorBound| |irreducible?| + |scale| |shiftRight| |title| |chainSubResultants| |graphStates| + |readUInt16!| |nullity| |symmetricTensors| |shuffle| + |nonSingularModel| |reduced?| |hdmpToP| |getGraph| NOT |doubleRank| + |ratpart| |fi2df| |getBadValues| |f01maf| |squareMatrix| |s17ajf| + |middle| |groebner| |OMgetInteger| OR |gbasis| |preprocess| |show| + |d02bhf| |createRandomElement| |mainMonomial| |e| |mathieu12| + |exprHasAlgebraicWeight| |whileLoop| |e01bef| |makeResult| AND + |reduction| |satisfy?| |putProperty| |nextIrreduciblePoly| + |basisOfLeftNucloid| |mapExponents| |center| |superscript| |nodes| + |moreAlgebraic?| |operation| |element?| |companionBlocks| |trace| + |updatF| |OMputVariable| |bracket| |bindings| |resultantnaif| + |OMwrite| |viewport2D| |eigenvalues| |variationOfParameters| + |separateDegrees| |certainlySubVariety?| |algebraicCoefficients?| + |ode1| |coHeight| |normalElement| |rightScalarTimes!| |OMgetType| + |s18aff| |adaptive3D?| |index?| |smith| |OMopenString| |stFuncN| + |subMatrix| |Nul| |precision| |getMatch| |LowTriBddDenomInv| + |applyRules| |imagk| |completeHensel| |mainDefiningPolynomial| + |lfextendedint| |rightQuotient| |critBonD| |cAtan| |rotatex| + |safeCeiling| |divideIfCan!| |harmonic| |bitand| |normalise| + |polygon?| |iCompose| |weighted| |coefChoose| |leftMinimalPolynomial| + |bumptab1| |prologue| |printStatement| |OMunhandledSymbol| |bitior| + |condition| |iicos| |mappingMode| |rootProduct| |legendre| |isOr| + |iiexp| |c02agf| |iiGamma| |showTheIFTable| |lfintegrate| |printInfo| + |char| |leaf?| |csch2sinh| |enumerate| |elements| |tValues| |f02bjf| + |randomLC| |HermiteIntegrate| |npcoef| |orbits| |rightRank| + |cycleSplit!| |cAsech| |divideIfCan| |linearForm| |ParCond| + |noValueMode| |coefficients| |LyndonWordsList1| |cdr| * |e01bhf| + |changeBase| |bipolar| |stopTable!| |basisOfLeftNucleus| |compBound| + |every?| |nullary| |c06eaf| |fixedPoints| |s19aaf| |property| + |integerIfCan| |lllp| |corrPoly| |rank| |argumentListOf| |factorial| + |iisec| |closed?| |squareFree| |rightTrim| |setMaxPoints3D| + |setPrologue!| |rightMult| |hessian| |mightHaveRoots| |monomials| + |cLog| |selectODEIVPRoutines| |constantOperator| |airyBi| |reductum| = + |leftTrim| |elaboration| |rootDirectory| |toroidal| |e02ahf| |e01sef| + |fortranComplex| |algint| |limitedIntegrate| |rst| |f02aaf| + |updateStatus!| |numberOfDivisors| |radix| |pack!| |normalize| + |s21bcf| |startPolynomial| |OMgetEndBVar| |primaryDecomp| |c06frf| + |powers| |mpsode| < |firstDenom| |unitVector| |psolve| |lquo| |sincos| + |loadNativeModule| |asinhIfCan| |scaleRoots| |symbolIfCan| |getStream| + |constantLeft| |kind| > |absolutelyIrreducible?| |fmecg| |hexDigit?| + |semiLastSubResultantEuclidean| |enterInCache| |eq| |contours| + |retractable?| |sample| |bitLength| |semiSubResultantGcdEuclidean1| + |op| |clearCache| <= |solid| |nilFactor| |localReal?| + |radicalSimplify| |iter| |createGenericMatrix| |mantissa| |quartic| + |paren| |hspace| |e02baf| |upDateBranches| |normDeriv2| >= |contains?| + |rotate!| |fractRadix| |limitPlus| |genericLeftMinimalPolynomial| + |s17adf| |lists| |triangular?| |quatern| |matrix| |red| |degree| + |showIntensityFunctions| |dequeue| |commutative?| + |singularAtInfinity?| |product| |leastMonomial| |leftTraceMatrix| + |ellipticCylindrical| |antisymmetric?| |weight| |high| |depth| + |numberOfCycles| |stripCommentsAndBlanks| |packageCall| |secIfCan| + |extension| |padicFraction| |linearMatrix| |B1solve| |coerceP| + |subCase?| + |singleFactorBound| |cyclicEqual?| |support| + |univariateSolve| |listRepresentation| |bernoulliB| |critB| |interval| + |sdf2lst| |leastAffineMultiple| |compile| - |anfactor| |setEmpty!| + |collectUnder| |mainContent| |subNodeOf?| |leviCivitaSymbol| |pastel| + |idealSimplify| |removeSquaresIfCan| |scalarMatrix| |union| / + |palglimint| |s20acf| |edf2fi| |meatAxe| |localIntegralBasis| |exp| + |hasSolution?| |minPoints3D| |geometric| |multiEuclideanTree| + |argumentList!| |cyclic| |complete| |tablePow| |algebraicDecompose| + |getGoodPrime| |cn| |second| |dual| |seed| |part?| |f07fef| |floor| + |romberg| LODO2FUN |groebner?| |f04mbf| |axes| |third| + |characteristicSet| |combineFeatureCompatibility| |d02gbf| |max| + |quadraticForm| |cons| |decrease| |OMmakeConn| |divisors| |ref| + |monicRightFactorIfCan| |integralCoordinates| |compiledFunction| + |multiple?| |stoseInvertibleSetreg| |birth| |prindINFO| + |semicolonSeparate| |numberOfChildren| |collectQuasiMonic| |qPot| + |comp| |numberOfComposites| |one?| |coefficient| |dfRange| |order| + |semiResultantEuclidean1| |removeSinhSq| |generate| |nextPrime| + |tanh2coth| |rightZero| |f01qef| |printTypes| |cycleLength| + |antiCommutative?| |transcendenceDegree| |outputMeasure| |xn| + |rangeIsFinite| |extractTop!| |reopen!| |quote| |parseString| |mulmod| + |multiEuclidean| |component| |expenseOfEvaluation| |exponentialOrder| + |hcrf| |incrementBy| |predicates| |square?| |stoseInvertible?sqfreg| + |leftLcm| |evenInfiniteProduct| |e01sbf| |s13adf| |setright!| |makeEq| + |bag| |binaryTree| |branchIfCan| |OMgetEndAttr| |expand| |connect| + |stopTableInvSet!| |operators| |coerce| |intChoose| + |semiIndiceSubResultantEuclidean| |getConstant| |OMgetApp| |space| + |swap| |source| |digits| |remainder| |rightAlternative?| |filterWhile| + |associatedSystem| |generic| |construct| |componentUpperBound| + |s21bbf| |sin2csc| |mergeFactors| |nativeModuleExtension| |bytes| + |status| |nlde| |rightGcd| |filterUntil| |buildSyntax| + |balancedFactorisation| |const| |trailingCoefficient| |rootSplit| + |inspect| |HenselLift| |lagrange| |name| |graeffe| |minPol| |select| + |setMinPoints| |substring?| |viewPosDefault| |f01bsf| + |tableForDiscreteLogarithm| |host| |mirror| |shanksDiscLogAlgorithm| + |mesh| |body| |graphImage| |e02bdf| |basisOfRightNucloid| + |padicallyExpand| |lazyVariations| |coerceS| |basisOfRightAnnihilator| + |createNormalPoly| |highCommonTerms| |nthExponent| + |subscriptedVariables| |initial| |closeComponent| + |resultantEuclideannaif| |suffix?| |removeZeroes| + |constantToUnaryFunction| |expr| |determinant| |d01bbf| + |mainCoefficients| |extractPoint| |removeCosSq| |target| |cylindrical| + |polynomialZeros| |partialDenominators| |rk4a| |lowerCase?| |power!| + |reverse| |sorted?| |drawComplexVectorField| |subTriSet?| + |problemPoints| |logpart| |kroneckerDelta| |lieAdmissible?| + |deepExpand| |binaryFunction| |sqfrFactor| |prefix?| |palgRDE0| + |intPatternMatch| |setleaves!| |monomRDE| |create| |errorKind| + |janko2| |generateIrredPoly| |sylvesterSequence| |gcdprim| + |readUInt8!| |critMonD1| |OMgetEndApp| |acosIfCan| |invertible?| + |remove!| |ffactor| |leftMult| |exponents| |sizeLess?| |d01apf| + |iprint| |makeRecord| |charClass| |variable| |firstUncouplingMatrix| + |cross| |cAcosh| |sub| |infinite?| |newSubProgram| |f01rcf| + |writeLine!| |setRow!| |iterators| |infiniteProduct| |maxrank| + |closedCurve| |totalDegree| |selectsecond| |stronglyReduce| |write!| + |initiallyReduced?| |f04faf| |cyclicCopy| |countRealRootsMultiple| + |unravel| |setButtonValue| |numerators| |genericLeftTrace| + |associatedEquations| |nthFactor| |port| |principal?| |univcase| + |leadingBasisTerm| |s18acf| |extendedResultant| |atoms| |addPoint2| + |diagonals| |fracPart| |firstNumer| |doubleComplex?| |infix?| + |returnTypeOf| |directory| |cSinh| |factorFraction| |ocf2ocdf| + |expPot| |rationalPoint?| |cSec| |t| |makeGraphImage| + |rowEchelonLocal| |mask| |rk4f| |mapmult| |selectOptimizationRoutines| + |findBinding| |curveColorPalette| |output| |laurentIfCan| |push| + |thenBranch| |row| UTS2UP |deleteProperty!| |raisePolynomial| + |changeNameToObjf| |symmetricProduct| |integralRepresents| + |bezoutDiscriminant| |PDESolve| |primlimintfrac| |isOpen?| |polar| + |interpretString| |formula| |genericRightDiscriminant| |algintegrate| + |sechIfCan| |selectAndPolynomials| |ramified?| |setelt| + |matrixConcat3D| |f04adf| |gethi| |regime| |writeUInt8!| + |structuralConstants| |mapMatrixIfCan| |closedCurve?| |besselJ| |case| + |magnitude| |cup| |normalForm| |value| |rootBound| |blankSeparate| + |iiatanh| |hdmpToDmp| |transpose| |rightTraceMatrix| |reducedSystem| + |id| |Zero| |indiceSubResultantEuclidean| |copy| |quotientByP| + |isAbsolutelyIrreducible?| |mergeDifference| + |characteristicPolynomial| |rightDiscriminant| |irreducibleFactors| + |sin?| |unaryFunction| |polyred| |lo| |One| |sech2cosh| |universe| + |showArrayValues| |euclideanSize| |viewWriteDefault| |nrows| + |upperBound| |copyInto!| |separant| |fintegrate| |An| |atrapezoidal| + |rootOfIrreduciblePoly| |lazyIntegrate| |homogeneous?| |tan2trig| + |tanhIfCan| |ncols| |rootsOf| |drawComplex| |sh| |clip| |lexico| + |overlap| |totolex| |flexible?| |nil?| |plusInfinity| |dot| + |setAttributeButtonStep| |simpleBounds?| |att2Result| |properties| + |genericLeftTraceForm| |leftExactQuotient| |multMonom| |e04gcf| |true| + |match?| |rk4qc| |rquo| |minusInfinity| |chiSquare1| + |createPrimitivePoly| |expandPower| |e01saf| |autoCoerce| |translate| + |modulus| |lazyPrem| |stiffnessAndStabilityFactor| |d02raf| |modTree| + |bat1| |nsqfree| |characteristicSerie| |d01asf| |elt| |ran| |objects| + |leftRank| |lexGroebner| |flagFactor| |shape| |particularSolution| + |createPrimitiveElement| |diff| |derivationCoordinates| |splitNodeOf!| + |base| |merge!| |bombieriNorm| |s17aff| |interactiveEnv| + |conditionsForIdempotents| |palgextint0| |edf2ef| + |reciprocalPolynomial| |f04jgf| |nthFlag| |elseBranch| + |genericRightTrace| |approxSqrt| |ip4Address| |leftRecip| |f01qdf| + |ScanFloatIgnoreSpaces| |rdHack1| |coth2tanh| |Frobenius| |chiSquare| + |maxint| |setPredicates| |outputArgs| |primitiveElement| + |antisymmetricTensors| |polyRicDE| |parabolic| |insertionSort!| + |notelem| |f02xef| |quadratic| |checkForZero| |internalZeroSetSplit| + |approximants| |euclideanNormalForm| |setColumn!| |coordinate| |prime| + |getZechTable| |orthonormalBasis| |commutativeEquality| |column| + |result| |cCsch| |toseLastSubResultant| |df2fi| |perfectSqrt| |rootOf| + |OMlistCDs| |denominators| |mainMonomials| |mapUp!| |equality| + |finiteBasis| |compdegd| |character?| |merge| |loopPoints| |summation| + |repSq| |addPointLast| |variable?| |asinIfCan| |whatInfinity| + |midpoint| |backOldPos| |rischDEsys| |integrate| |freeOf?| + |cyclotomicDecomposition| |ef2edf| |pointColor| |double?| |OMgetAttr| + |solveLinearPolynomialEquation| |OMencodingSGML| |deriv| + |startTableInvSet!| |pointData| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-235 $) -3777 (|has| |#1| (-361)) (|has| |#1| (-238)) (|has| |#1| (-239))) ((-233 |#1|) . T) ((-239) -3777 (|has| |#1| (-361)) (|has| |#1| (-239))) ((-238) -3777 (|has| |#1| (-361)) (|has| |#1| (-238)) (|has| |#1| (-239))) ((-273 |#1|) . T) ((-249) -3777 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-295) |has| |#1| (-1227)) ((-297 |#1| $) |has| |#1| (-297 |#1| |#1|)) ((-301) -3777 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-318) -3777 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-320 |#1|) |has| |#1| (-320 |#1|)) ((-375) -3777 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-415) |has| |#1| (-361)) ((-380) -3777 (|has| |#1| (-380)) (|has| |#1| (-361))) ((-361) |has| |#1| (-361)) ((-382 |#1| #1#) . T) ((-422 |#1| #1#) . T) ((-350 |#1|) . T) ((-389 |#1|) . T) ((-413 |#1|) . T) ((-424 |#1|) . 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T) ((-915 $ #3=(-1201)) -3777 (|has| |#1| (-923 (-1201))) (|has| |#1| (-921 (-1201)))) ((-921 (-1201)) |has| |#1| (-921 (-1201))) ((-923 #3#) -3777 (|has| |#1| (-923 (-1201))) (|has| |#1| (-921 (-1201)))) ((-905 (-391)) |has| |#1| (-905 (-391))) ((-905 (-577)) |has| |#1| (-905 (-577))) ((-903 |#1|) . T) ((-932) -12 (|has| |#1| (-318)) (|has| |#1| (-932))) ((-943) -3777 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-1027) -12 (|has| |#1| (-1027)) (|has| |#1| (-1227))) ((-1063 (-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) ((-1063 (-577)) |has| |#1| (-1063 (-577))) ((-1063 |#1|) . T) ((-1076 #0#) -3777 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-1076 |#1|) . T) ((-1076 $) . T) ((-1081 #0#) -3777 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-1081 |#1|) . T) ((-1081 $) . T) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) |has| |#1| (-361)) ((-1227) |has| |#1| (-1227)) ((-1230) |has| |#1| (-1227)) ((-1242) . 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(|has| |#2| (-21))) (($ $) 80 (|has| |#2| (-21)))) (-3947 (($ $ $) 73 (|has| |#2| (-25)))) (** (($ $ (-787)) 87 (|has| |#2| (-1074))) (($ $ (-944)) 84 (|has| |#2| (-1074)))) (* (($ $ $) 85 (|has| |#2| (-1074))) (($ $ |#2|) 83 (|has| |#2| (-742))) (($ |#2| $) 82 (|has| |#2| (-742))) (($ (-577) $) 79 (|has| |#2| (-21))) (($ (-787) $) 77 (|has| |#2| (-23))) (($ (-944) $) 74 (|has| |#2| (-25)))) (-2014 (((-787) $) 6 (|has| $ (-6 -4470))))) (((-244 |#1| |#2|) (-141) (-787) (-1242)) (T -244)) -((-4080 (*1 *1 *2) (-12 (-5 *2 (-1292 *4)) (-4 *4 (-1242)) (-4 *1 (-244 *3 *4)))) (-1960 (*1 *1 *2) (-12 (-5 *2 (-944)) (-4 *1 (-244 *3 *4)) (-4 *4 (-1074)) (-4 *4 (-1242)))) (-4362 (*1 *2 *1 *1) (-12 (-4 *1 (-244 *3 *2)) (-4 *2 (-1242)) (-4 *2 (-1074))))) -(-13 (-617 (-577) |t#2|) (-626 (-1292 |t#2|)) (-10 -8 (-6 -4470) (-15 -4080 ($ (-1292 |t#2|))) (IF (|has| |t#2| (-1125)) (-6 (-424 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1074)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-233 |t#2|)) (-6 (-389 |t#2|)) (-15 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(-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -3777 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3777 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-132) -3777 (|has| |#2| (-1074)) (|has| |#2| (-809)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-629 #0=(-420 (-577))) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125))) ((-629 (-577)) -3777 (|has| |#2| (-1074)) (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) ((-629 |#2|) |has| |#2| (-1125)) ((-626 (-880)) -3777 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-626 (-880))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-626 (-1292 |#2|)) . T) ((-235 $) -3777 (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074)))) ((-233 |#2|) |has| |#2| (-1074)) ((-239) -12 (|has| |#2| (-239)) (|has| |#2| (-1074))) ((-238) -3777 (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074)))) ((-273 |#2|) |has| |#2| (-1074)) ((-297 #1=(-577) |#2|) . T) ((-299 #1# |#2|) . T) ((-320 |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((-380) |has| |#2| (-380)) ((-389 |#2|) |has| |#2| (-1074)) ((-424 |#2|) |has| |#2| (-1125)) ((-502 |#2|) . T) ((-617 #1# |#2|) . T) ((-527 |#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((-662 (-577)) -3777 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-662 |#2|) -3777 (|has| |#2| (-1074)) (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-662 $) |has| |#2| (-1074)) ((-664 #2=(-577)) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074))) ((-664 |#2|) -3777 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-664 $) |has| |#2| (-1074)) ((-656 |#2|) -3777 (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-654 #2#) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074))) ((-654 |#2|) |has| |#2| (-1074)) ((-733 |#2|) -3777 (|has| |#2| (-375)) (|has| |#2| (-174))) ((-742) |has| |#2| (-1074)) ((-808) |has| |#2| (-809)) ((-809) |has| |#2| (-809)) ((-810) |has| |#2| (-809)) ((-811) |has| |#2| (-809)) ((-865) -3777 (|has| |#2| (-865)) (|has| |#2| (-809))) ((-868) -3777 (|has| |#2| (-865)) (|has| |#2| (-809))) ((-915 $ #3=(-1201)) -3777 (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) ((-921 (-1201)) -12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074))) ((-923 #3#) -3777 (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) ((-1063 #0#) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125))) ((-1063 (-577)) -12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) ((-1063 |#2|) |has| |#2| (-1125)) ((-1076 |#2|) -3777 (|has| |#2| (-1074)) (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1081 |#2|) -3777 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1074) |has| |#2| (-1074)) ((-1083) |has| |#2| (-1074)) ((-1137) |has| |#2| (-1074)) ((-1125) -3777 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1242) . T) ((-1299 |#2|) |has| |#2| (-375))) -((-4450 (((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 21)) (-1662 ((|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 23)) (-1888 (((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)) 18))) -(((-245 |#1| |#2| |#3|) (-10 -7 (-15 -4450 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -1662 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -1888 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) (-787) (-1242) (-1242)) (T -245)) -((-1888 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-787)) (-4 *6 (-1242)) (-4 *7 (-1242)) (-5 *2 (-246 *5 *7)) (-5 *1 (-245 *5 *6 *7)))) (-1662 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-246 *5 *6)) (-14 *5 (-787)) (-4 *6 (-1242)) (-4 *2 (-1242)) (-5 *1 (-245 *5 *6 *2)))) (-4450 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-246 *6 *7)) (-14 *6 (-787)) (-4 *7 (-1242)) (-4 *5 (-1242)) (-5 *2 (-246 *6 *5)) (-5 *1 (-245 *6 *7 *5))))) -(-10 -7 (-15 -4450 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -1662 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -1888 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) -((-2008 (((-112) $ $) NIL (|has| |#2| (-102)))) (-3473 (((-112) $) NIL (|has| |#2| (-23)))) (-1960 (($ (-944)) 62 (|has| |#2| (-1074)))) (-1696 (((-1297) $ (-577) (-577)) NIL (|has| $ (-6 -4471)))) (-2639 (($ $ $) 68 (|has| |#2| (-809)))) (-2134 (((-3 $ "failed") $ $) 53 (|has| |#2| (-132)))) (-4099 (((-112) $ (-787)) NIL)) (-1656 (((-787)) NIL (|has| |#2| (-380)))) (-4265 ((|#2| $ (-577) |#2|) NIL (|has| $ (-6 -4471)))) (-2267 (($) NIL T CONST)) (-2387 (((-3 (-577) "failed") $) NIL (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) (((-3 (-420 (-577)) "failed") $) NIL (-12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1125)))) (-1766 (((-577) $) NIL (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) (((-420 (-577)) $) NIL (-12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) ((|#2| $) 28 (|has| |#2| (-1125)))) (-2180 (((-705 (-577)) (-705 $)) NIL (-12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) (((-2 (|:| -2675 (-705 (-577))) (|:| |vec| (-1292 (-577)))) (-705 $) (-1292 $)) NIL (-12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) (((-2 (|:| -2675 (-705 |#2|)) (|:| |vec| (-1292 |#2|))) (-705 $) (-1292 $)) NIL (|has| |#2| (-1074))) (((-705 |#2|) (-705 $)) NIL (|has| |#2| (-1074)))) (-3380 (((-3 $ "failed") $) 58 (|has| |#2| (-1074)))) (-3775 (($) NIL (|has| |#2| (-380)))) (-1569 ((|#2| $ (-577) |#2|) NIL (|has| $ (-6 -4471)))) (-1502 ((|#2| $ (-577)) 56)) (-3697 (((-660 |#2|) $) 14 (|has| $ (-6 -4470)))) (-3344 (((-112) $) NIL (|has| |#2| (-1074)))) (-2966 (((-112) $ (-787)) NIL)) (-3809 (((-577) $) 19 (|has| (-577) (-865)))) (-3548 (($ $ $) NIL (|has| |#2| (-865)))) (-2516 (((-660 |#2|) $) NIL (|has| $ (-6 -4470)))) (-3552 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4470)) (|has| |#2| (-1125))))) (-3907 (((-577) $) NIL (|has| (-577) (-865)))) (-3987 (($ $ $) NIL (|has| |#2| (-865)))) (-1556 (($ (-1 |#2| |#2|) $) NIL (|has| $ (-6 -4471)))) (-1888 (($ (-1 |#2| |#2|) $) NIL)) (-4430 (((-944) $) NIL (|has| |#2| (-380)))) (-3234 (((-112) $ (-787)) NIL)) (-4215 (((-705 (-577)) (-1292 $)) NIL (-12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) (((-2 (|:| -2675 (-705 (-577))) (|:| |vec| (-1292 (-577)))) (-1292 $) $) NIL (-12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) (((-2 (|:| -2675 (-705 |#2|)) (|:| |vec| (-1292 |#2|))) (-1292 $) $) NIL (|has| |#2| (-1074))) (((-705 |#2|) (-1292 $)) NIL (|has| |#2| (-1074)))) (-3445 (((-1183) $) NIL (|has| |#2| (-1125)))) (-1834 (((-660 (-577)) $) NIL)) (-1945 (((-112) (-577) $) NIL)) (-2433 (($ (-944)) NIL (|has| |#2| (-380)))) (-3109 (((-1145) $) NIL (|has| |#2| (-1125)))) (-4359 ((|#2| $) NIL (|has| (-577) (-865)))) (-3721 (($ $ |#2|) NIL (|has| $ (-6 -4471)))) (-3326 (((-112) (-1 (-112) |#2|) $) 23 (|has| $ (-6 -4470)))) (-2190 (($ $ 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NIL (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074)))) (($ $ (-1201)) NIL (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1074))) (($ $ (-1 |#2| |#2|) (-787)) NIL (|has| |#2| (-1074)))) (-3121 (((-787) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4470))) (((-787) |#2| $) NIL (-12 (|has| $ (-6 -4470)) (|has| |#2| (-1125))))) (-4288 (($ $) NIL)) (-4100 (((-1292 |#2|) $) 9) (($ (-577)) NIL (-3777 (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) (|has| |#2| (-1074)))) (($ (-420 (-577))) NIL (-12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) (($ |#2|) 12 (|has| |#2| (-1125))) (((-880) $) NIL (|has| |#2| (-626 (-880))))) (-1597 (((-787)) NIL (|has| |#2| (-1074)) CONST)) (-4149 (((-112) $ $) NIL (|has| |#2| (-102)))) (-3440 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4470)))) (-4316 (($) 36 (|has| |#2| (-23)) CONST)) (-4322 (($) 40 (|has| |#2| (-1074)) CONST)) (-2562 (($ $ (-787)) NIL (-12 (|has| |#2| (-238)) (|has| |#2| 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(|has| |#2| (-1074))) (($ $ |#2|) 44 (|has| |#2| (-742))) (($ |#2| $) 45 (|has| |#2| (-742))) (($ (-577) $) NIL (|has| |#2| (-21))) (($ (-787) $) NIL (|has| |#2| (-23))) (($ (-944) $) NIL (|has| |#2| (-25)))) (-2021 (((-787) $) NIL (|has| $ (-6 -4470))))) +((-2139 (*1 *1 *2) (-12 (-5 *2 (-1292 *4)) (-4 *4 (-1242)) (-4 *1 (-244 *3 *4)))) (-3873 (*1 *1 *2) (-12 (-5 *2 (-944)) (-4 *1 (-244 *3 *4)) (-4 *4 (-1074)) (-4 *4 (-1242)))) (-4329 (*1 *2 *1 *1) (-12 (-4 *1 (-244 *3 *2)) (-4 *2 (-1242)) (-4 *2 (-1074))))) +(-13 (-617 (-577) |t#2|) (-626 (-1292 |t#2|)) (-10 -8 (-6 -4470) (-15 -2139 ($ (-1292 |t#2|))) (IF (|has| |t#2| (-1125)) (-6 (-424 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1074)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-233 |t#2|)) (-6 (-389 |t#2|)) (-15 -3873 ($ (-944))) (-15 -4329 (|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| (-742)) (-6 (-656 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-380)) (-6 (-380)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-733 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4467)) (-6 -4467) |%noBranch|) (IF (|has| |t#2| (-865)) (-6 (-865)) |%noBranch|) (IF (|has| |t#2| (-809)) (-6 (-809)) |%noBranch|) (IF (|has| |t#2| (-375)) (-6 (-1299 |t#2|)) |%noBranch|))) +(((-21) -3700 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -3700 (|has| |#2| (-1074)) (|has| |#2| (-809)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -3700 (|has| |#2| (-1074)) (|has| |#2| (-809)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -3700 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3700 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-132) -3700 (|has| |#2| (-1074)) (|has| |#2| (-809)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-629 #0=(-420 (-577))) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125))) ((-629 (-577)) -3700 (|has| |#2| (-1074)) (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) ((-629 |#2|) |has| |#2| (-1125)) ((-626 (-880)) -3700 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-626 (-880))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-626 (-1292 |#2|)) . T) ((-235 $) -3700 (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074)))) ((-233 |#2|) |has| |#2| (-1074)) ((-239) -12 (|has| |#2| (-239)) (|has| |#2| (-1074))) ((-238) -3700 (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074)))) ((-273 |#2|) |has| |#2| (-1074)) ((-297 #1=(-577) |#2|) . T) ((-299 #1# |#2|) . T) ((-320 |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((-380) |has| |#2| (-380)) ((-389 |#2|) |has| |#2| (-1074)) ((-424 |#2|) |has| |#2| (-1125)) ((-502 |#2|) . T) ((-617 #1# |#2|) . T) ((-527 |#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((-662 (-577)) -3700 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-662 |#2|) -3700 (|has| |#2| (-1074)) (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-662 $) |has| |#2| (-1074)) ((-664 #2=(-577)) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074))) ((-664 |#2|) -3700 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-664 $) |has| |#2| (-1074)) ((-656 |#2|) -3700 (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-654 #2#) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074))) ((-654 |#2|) |has| |#2| (-1074)) ((-733 |#2|) -3700 (|has| |#2| (-375)) (|has| |#2| (-174))) ((-742) |has| |#2| (-1074)) ((-808) |has| |#2| (-809)) ((-809) |has| |#2| (-809)) ((-810) |has| |#2| (-809)) ((-811) |has| |#2| (-809)) ((-865) -3700 (|has| |#2| (-865)) (|has| |#2| (-809))) ((-868) -3700 (|has| |#2| (-865)) (|has| |#2| (-809))) ((-915 $ #3=(-1201)) -3700 (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) ((-921 (-1201)) -12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074))) ((-923 #3#) -3700 (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) ((-1063 #0#) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125))) ((-1063 (-577)) -12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) ((-1063 |#2|) |has| |#2| (-1125)) ((-1076 |#2|) -3700 (|has| |#2| (-1074)) (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1081 |#2|) -3700 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1074) |has| |#2| (-1074)) ((-1083) |has| |#2| (-1074)) ((-1137) |has| |#2| (-1074)) ((-1125) -3700 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1242) . T) ((-1299 |#2|) |has| |#2| (-375))) +((-2797 (((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 21)) (-1721 ((|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 23)) (-2471 (((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)) 18))) +(((-245 |#1| |#2| |#3|) (-10 -7 (-15 -2797 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -1721 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -2471 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) (-787) (-1242) (-1242)) (T -245)) +((-2471 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-787)) (-4 *6 (-1242)) (-4 *7 (-1242)) (-5 *2 (-246 *5 *7)) (-5 *1 (-245 *5 *6 *7)))) (-1721 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-246 *5 *6)) (-14 *5 (-787)) (-4 *6 (-1242)) (-4 *2 (-1242)) (-5 *1 (-245 *5 *6 *2)))) (-2797 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-246 *6 *7)) (-14 *6 (-787)) (-4 *7 (-1242)) (-4 *5 (-1242)) (-5 *2 (-246 *6 *5)) (-5 *1 (-245 *6 *7 *5))))) +(-10 -7 (-15 -2797 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -1721 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -2471 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) +((-2004 (((-112) $ $) NIL (|has| |#2| (-102)))) (-2877 (((-112) $) NIL (|has| |#2| (-23)))) (-3873 (($ (-944)) 62 (|has| |#2| (-1074)))) (-3094 (((-1297) $ (-577) (-577)) NIL (|has| $ (-6 -4471)))) (-3305 (($ $ $) 68 (|has| |#2| (-809)))) (-1941 (((-3 $ "failed") $ $) 53 (|has| |#2| (-132)))) (-2603 (((-112) $ (-787)) NIL)) (-2245 (((-787)) NIL (|has| |#2| (-380)))) (-4264 ((|#2| $ (-577) |#2|) NIL (|has| $ (-6 -4471)))) (-3893 (($) NIL T CONST)) (-2963 (((-3 (-577) "failed") $) NIL (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) (((-3 (-420 (-577)) "failed") $) NIL (-12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1125)))) (-2347 (((-577) $) NIL (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) (((-420 (-577)) $) NIL (-12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125)))) ((|#2| $) 28 (|has| |#2| (-1125)))) (-4285 (((-705 (-577)) (-705 $)) NIL (-12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) (((-2 (|:| -3613 (-705 (-577))) (|:| |vec| (-1292 (-577)))) (-705 $) (-1292 $)) NIL (-12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074)))) (((-2 (|:| -3613 (-705 |#2|)) (|:| |vec| (-1292 |#2|))) (-705 $) (-1292 $)) NIL (|has| |#2| (-1074))) (((-705 |#2|) (-705 $)) NIL (|has| |#2| (-1074)))) (-3172 (((-3 $ "failed") $) 58 (|has| |#2| (-1074)))) (-2798 (($) NIL (|has| |#2| (-380)))) (-1922 ((|#2| $ (-577) |#2|) NIL (|has| $ (-6 -4471)))) (-1865 ((|#2| $ (-577)) 56)) (-3370 (((-660 |#2|) $) 14 (|has| $ (-6 -4470)))) (-4024 (((-112) $) NIL (|has| |#2| (-1074)))) (-1420 (((-112) $ (-787)) NIL)) (-2899 (((-577) $) 19 (|has| (-577) (-865)))) (-2613 (($ $ $) NIL (|has| |#2| (-865)))) (-1421 (((-660 |#2|) $) NIL (|has| $ (-6 -4470)))) (-2348 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4470)) (|has| |#2| (-1125))))) 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3700 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-420 (-577)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3700 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-629 #0#) -3700 (|has| |#1| (-1063 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577))))) ((-629 (-577)) . T) ((-629 |#1|) . T) ((-629 |#2|) . T) ((-629 |#3|) . T) ((-629 $) -3700 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465))) ((-626 (-880)) . T) ((-174) -3700 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-174))) ((-627 (-549)) -12 (|has| |#1| (-627 (-549))) (|has| |#3| (-627 (-549)))) ((-627 (-911 (-391))) -12 (|has| |#1| (-627 (-911 (-391)))) (|has| |#3| (-627 (-911 (-391))))) ((-627 (-911 (-577))) -12 (|has| |#1| (-627 (-911 (-577)))) (|has| |#3| (-627 (-911 (-577))))) ((-235 $) -3700 (|has| |#1| (-238)) (|has| |#1| (-239))) ((-233 |#1|) . T) ((-239) |has| |#1| (-239)) ((-238) -3700 (|has| |#1| (-238)) (|has| |#1| (-239))) ((-273 |#1|) . T) ((-301) -3700 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465))) ((-320 $) . T) ((-337 |#1| |#4|) . T) ((-389 |#1|) . T) ((-424 |#1|) . T) ((-465) -3700 (|has| |#1| (-932)) (|has| |#1| (-465))) ((-527 |#2| |#1|) |has| |#1| (-239)) ((-527 |#2| $) |has| |#1| (-239)) ((-527 |#3| |#1|) . T) ((-527 |#3| $) . T) ((-527 $ $) . 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T) ((-313) . T) ((-375) |has| |#1| (-569)) ((-389 |#1|) |has| |#1| (-1074)) ((-413 |#1|) . T) ((-424 |#1|) . T) ((-465) |has| |#1| (-569)) ((-486) |has| |#1| (-486)) ((-527 (-625 $) $) . T) ((-527 $ $) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-420 (-577))) . 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)) ((-629 #0#) . T) ((-629 (-577)) . T) ((-629 #1=(-1201)) |has| |#1| (-1063 (-1201))) ((-629 |#1|) . T) ((-629 $) . T) ((-626 (-880)) . T) ((-174) . T) ((-627 (-228)) |has| |#1| (-1047)) ((-627 (-391)) |has| |#1| (-1047)) ((-627 (-549)) |has| |#1| (-627 (-549))) ((-627 (-911 (-391))) |has| |#1| (-627 (-911 (-391)))) ((-627 (-911 (-577))) |has| |#1| (-627 (-911 (-577)))) ((-235 $) -3700 (|has| |#1| (-238)) (|has| |#1| (-239))) ((-233 |#1|) . T) ((-239) |has| |#1| (-239)) ((-238) -3700 (|has| |#1| (-238)) (|has| |#1| (-239))) ((-273 |#1|) . T) ((-249) . T) ((-297 |#1| $) |has| |#1| (-297 |#1| |#1|)) ((-301) . T) ((-318) . T) ((-320 |#1|) |has| |#1| (-320 |#1|)) ((-375) . T) ((-350 |#1|) . T) ((-389 |#1|) . T) ((-413 |#1|) . T) ((-465) . 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T) ((-174) -3777 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-627 (-228)) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-627 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-627 (-549)) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-549)))) ((-627 (-911 (-391))) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-911 (-391))))) ((-627 (-911 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-911 (-577))))) ((-235 $) -3777 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-233 |#2|) |has| |#1| (-375)) ((-239) -3777 (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-238) -3777 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-273 |#2|) |has| |#1| (-375)) ((-249) |has| |#1| (-375)) ((-295) |has| |#1| (-38 (-420 (-577)))) ((-297 #0# |#1|) . 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T) ((-664 |#2|) |has| |#1| (-375)) ((-664 $) . T) ((-656 #1#) -3777 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-656 |#1|) |has| |#1| (-174)) ((-656 |#2|) |has| |#1| (-375)) ((-656 $) -3777 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-654 #3#) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-654 |#2|) |has| |#1| (-375)) ((-733 #1#) -3777 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-733 |#1|) |has| |#1| (-174)) ((-733 |#2|) |has| |#1| (-375)) ((-733 $) -3777 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-742) . 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T) ((-943) |has| |#1| (-375)) ((-1017 |#2|) |has| |#1| (-375)) ((-1027) |has| |#1| (-38 (-420 (-577)))) ((-1047) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-1063 (-420 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 #2#) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-1201)))) ((-1063 |#2|) . T) ((-1076 #1#) -3777 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1076 |#1|) . T) ((-1076 |#2|) |has| |#1| (-375)) ((-1076 $) -3777 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1081 #1#) -3777 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1081 |#1|) . T) ((-1081 |#2|) |has| |#1| (-375)) ((-1081 $) -3777 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) -12 (|has| |#1| (-375)) (|has| |#2| (-1177))) ((-1227) |has| |#1| (-38 (-420 (-577)))) ((-1230) |has| |#1| (-38 (-420 (-577)))) ((-1242) . T) ((-1246) |has| |#1| (-375)) ((-1252 |#1|) . T) ((-1270 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-577)) . T) ((-25) . T) ((-38 #1=(-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-375)) ((-38 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-35) |has| |#1| (-38 (-420 (-577)))) ((-95) |has| |#1| (-38 (-420 (-577)))) ((-102) . T) ((-111 #1# #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-375)) ((-111 $ $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-132) . T) ((-146) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-629 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-629 (-577)) . T) ((-629 #2=(-1201)) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-1201)))) ((-629 |#1|) |has| |#1| (-174)) ((-629 |#2|) . T) ((-629 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-626 (-880)) . T) ((-174) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-627 (-228)) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-627 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-627 (-549)) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-549)))) ((-627 (-911 (-391))) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-911 (-391))))) ((-627 (-911 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-911 (-577))))) ((-235 $) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-233 |#2|) |has| |#1| (-375)) ((-239) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-238) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-273 |#2|) |has| |#1| (-375)) ((-249) |has| |#1| (-375)) ((-295) |has| |#1| (-38 (-420 (-577)))) ((-297 #0# |#1|) . T) ((-297 |#2| $) -12 (|has| |#1| (-375)) (|has| |#2| (-297 |#2| |#2|))) ((-297 $ $) |has| (-577) (-1137)) ((-301) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-318) |has| |#1| (-375)) ((-320 |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-375) |has| |#1| (-375)) ((-350 |#2|) |has| |#1| (-375)) ((-389 |#2|) |has| |#1| (-375)) ((-413 |#2|) |has| |#1| (-375)) ((-465) |has| |#1| (-375)) ((-506) |has| |#1| (-38 (-420 (-577)))) ((-527 (-1201) |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-527 (-1201) |#2|))) ((-527 |#2| |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-569) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-662 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-662 (-577)) . T) ((-662 |#1|) . T) ((-662 |#2|) |has| |#1| (-375)) ((-662 $) . T) ((-664 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-664 #3=(-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-664 |#1|) . T) ((-664 |#2|) |has| |#1| (-375)) ((-664 $) . T) ((-656 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-656 |#1|) |has| |#1| (-174)) ((-656 |#2|) |has| |#1| (-375)) ((-656 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-654 #3#) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-654 |#2|) |has| |#1| (-375)) ((-733 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-733 |#1|) |has| |#1| (-174)) ((-733 |#2|) |has| |#1| (-375)) ((-733 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-742) . T) ((-807) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-808) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-810) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-811) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-836) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-864) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-865) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-865))) (-12 (|has| |#1| (-375)) (|has| |#2| (-836)))) ((-868) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-865))) (-12 (|has| |#1| (-375)) (|has| |#2| (-836)))) ((-915 $ #4=(-1201)) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-923 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) ((-921 (-1201)) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) ((-923 #4#) -3700 (-12 (|has| |#1| (-375)) (|has| |#2| (-923 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) ((-905 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-905 (-391)))) ((-905 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-905 (-577)))) ((-903 |#2|) |has| |#1| (-375)) ((-932) -12 (|has| |#1| (-375)) (|has| |#2| (-932))) ((-998 |#1| #0# (-1107)) . T) ((-943) |has| |#1| (-375)) ((-1017 |#2|) |has| |#1| (-375)) ((-1027) |has| |#1| (-38 (-420 (-577)))) ((-1047) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-1063 (-420 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 #2#) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-1201)))) ((-1063 |#2|) . T) ((-1076 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1076 |#1|) . T) ((-1076 |#2|) |has| |#1| (-375)) ((-1076 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1081 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1081 |#1|) . T) ((-1081 |#2|) |has| |#1| (-375)) ((-1081 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) -12 (|has| |#1| (-375)) (|has| |#2| (-1177))) ((-1227) |has| |#1| (-38 (-420 (-577)))) ((-1230) |has| |#1| (-38 (-420 (-577)))) ((-1242) . 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T) ((-23) . T) ((-47 |#1| #0=(-420 (-577))) . T) ((-25) . T) ((-38 #1=(-420 (-577))) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-35) |has| |#1| (-38 (-420 (-577)))) ((-95) |has| |#1| (-38 (-420 (-577)))) ((-102) . T) ((-111 #1# #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-629 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-629 (-577)) . T) ((-629 |#1|) |has| |#1| (-174)) ((-629 |#2|) . T) ((-629 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-626 (-880)) . 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T) ((-656 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-656 |#1|) |has| |#1| (-174)) ((-656 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-733 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-733 |#1|) |has| |#1| (-174)) ((-733 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-742) . T) ((-915 $ #2=(-1201)) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201)))) ((-921 #2#) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201)))) ((-923 #2#) -12 (|has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) (|has| |#1| (-921 (-1201)))) ((-998 |#1| #0# (-1107)) . T) ((-943) |has| |#1| (-375)) ((-1027) |has| |#1| (-38 (-420 (-577)))) ((-1063 |#2|) . T) ((-1076 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1076 |#1|) . T) ((-1076 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1081 #1#) -3700 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1081 |#1|) . T) ((-1081 $) -3700 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1227) |has| |#1| (-38 (-420 (-577)))) ((-1230) |has| |#1| (-38 (-420 (-577)))) ((-1242) . T) ((-1246) |has| |#1| (-375)) ((-1270 |#1| #0#) . T) ((-1273 |#1|) . 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3054671 3054857 "UPCDEN" 3055212 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1260 3054078 3054147 3054296 "UP2" 3054484 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1259 3052545 3053282 3053559 "UNISEG" 3053836 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1258 3051760 3051887 3052092 "UNISEG2" 3052388 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1257 3050820 3051000 3051226 "UNIFACT" 3051576 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1256 3033572 3050132 3050374 "ULS" 3050636 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3021202 3033476 3033548 "ULSCONS" 3033553 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1254 3001923 3014283 3014345 "ULSCCAT" 3014983 NIL ULSCCAT (NIL T T) -9 NIL 3015272 NIL) (-1253 3000973 3001218 3001606 "ULSCCAT-" 3001611 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1252 2990037 2996520 2996563 "ULSCAT" 2997426 NIL ULSCAT (NIL T) -9 NIL 2998157 NIL) (-1251 2989467 2989546 2989725 "ULS2" 2989952 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1250 2988586 2989096 2989203 "UINT8" 2989314 T UINT8 (NIL) -8 NIL NIL 2989399) (-1249 2987704 2988214 2988321 "UINT64" 2988432 T UINT64 (NIL) -8 NIL NIL 2988517) (-1248 2986822 2987332 2987439 "UINT32" 2987550 T UINT32 (NIL) -8 NIL NIL 2987635) (-1247 2985940 2986450 2986557 "UINT16" 2986668 T UINT16 (NIL) -8 NIL NIL 2986753) (-1246 2984229 2985186 2985216 "UFD" 2985428 T UFD (NIL) -9 NIL 2985542 NIL) (-1245 2984023 2984069 2984164 "UFD-" 2984169 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1244 2983105 2983288 2983504 "UDVO" 2983829 T UDVO (NIL) -7 NIL NIL NIL) (-1243 2980921 2981330 2981801 "UDPO" 2982669 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1242 2980854 2980859 2980889 "TYPE" 2980894 T TYPE (NIL) -9 NIL NIL NIL) (-1241 2980614 2980809 2980840 "TYPEAST" 2980845 T TYPEAST (NIL) -8 NIL NIL NIL) (-1240 2979585 2979787 2980027 "TWOFACT" 2980408 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1239 2978608 2978994 2979229 "TUPLE" 2979385 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1238 2976299 2976818 2977357 "TUBETOOL" 2978091 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1237 2975148 2975353 2975594 "TUBE" 2976092 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1236 2969877 2974120 2974403 "TS" 2974900 NIL TS (NIL T) -8 NIL NIL NIL) (-1235 2958515 2962634 2962731 "TSETCAT" 2968000 NIL TSETCAT (NIL T T T T) -9 NIL 2969532 NIL) (-1234 2953247 2954847 2956738 "TSETCAT-" 2956743 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1233 2947886 2948733 2949662 "TRMANIP" 2952383 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1232 2947327 2947390 2947553 "TRIMAT" 2947818 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1231 2945193 2945430 2945787 "TRIGMNIP" 2947076 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1230 2944713 2944826 2944856 "TRIGCAT" 2945069 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1229 2944382 2944461 2944602 "TRIGCAT-" 2944607 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1228 2941230 2943240 2943521 "TREE" 2944136 NIL TREE (NIL T) -8 NIL NIL NIL) (-1227 2940504 2941032 2941062 "TRANFUN" 2941097 T TRANFUN (NIL) -9 NIL 2941163 NIL) (-1226 2939783 2939974 2940254 "TRANFUN-" 2940259 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1225 2939587 2939619 2939680 "TOPSP" 2939744 T TOPSP (NIL) -7 NIL NIL NIL) (-1224 2938935 2939050 2939204 "TOOLSIGN" 2939468 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1223 2937569 2938112 2938351 "TEXTFILE" 2938718 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1222 2935481 2936022 2936451 "TEX" 2937162 T TEX (NIL) -8 NIL NIL NIL) (-1221 2935262 2935293 2935365 "TEX1" 2935444 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1220 2934910 2934973 2935063 "TEMUTL" 2935194 T TEMUTL (NIL) -7 NIL NIL NIL) (-1219 2933064 2933344 2933669 "TBCMPPK" 2934633 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1218 2924773 2931150 2931206 "TBAGG" 2931606 NIL TBAGG (NIL T T) -9 NIL 2931817 NIL) (-1217 2919843 2921331 2923085 "TBAGG-" 2923090 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1216 2919227 2919334 2919479 "TANEXP" 2919732 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1215 2918738 2919002 2919092 "TALGOP" 2919172 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1214 2912134 2918595 2918688 "TABLE" 2918693 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1213 2911546 2911645 2911783 "TABLEAU" 2912031 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1212 2906154 2907374 2908622 "TABLBUMP" 2910332 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1211 2905376 2905523 2905704 "SYSTEM" 2905995 T SYSTEM (NIL) -8 NIL NIL NIL) (-1210 2901835 2902534 2903317 "SYSSOLP" 2904627 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1209 2901633 2901790 2901821 "SYSPTR" 2901826 T SYSPTR (NIL) -8 NIL NIL NIL) (-1208 2900669 2901174 2901293 "SYSNNI" 2901479 NIL SYSNNI (NIL NIL) -8 NIL NIL 2901564) (-1207 2899968 2900427 2900506 "SYSINT" 2900566 NIL SYSINT (NIL NIL) -8 NIL NIL 2900611) (-1206 2896300 2897246 2897956 "SYNTAX" 2899280 T SYNTAX (NIL) -8 NIL NIL NIL) (-1205 2893458 2894060 2894692 "SYMTAB" 2895690 T SYMTAB (NIL) -8 NIL NIL NIL) (-1204 2888707 2889609 2890592 "SYMS" 2892497 T SYMS (NIL) -8 NIL NIL NIL) (-1203 2885942 2888165 2888395 "SYMPOLY" 2888512 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1202 2885459 2885534 2885657 "SYMFUNC" 2885854 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1201 2881479 2882771 2883584 "SYMBOL" 2884668 T SYMBOL (NIL) -8 NIL NIL NIL) (-1200 2875018 2876707 2878427 "SWITCH" 2879781 T SWITCH (NIL) -8 NIL NIL NIL) (-1199 2868362 2873974 2874268 "SUTS" 2874782 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1198 2860538 2867744 2868008 "SUPXS" 2868156 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 2852021 2860156 2860282 "SUP" 2860447 NIL SUP (NIL T) -8 NIL NIL NIL) (-1196 2851180 2851307 2851524 "SUPFRACF" 2851889 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1195 2850801 2850860 2850973 "SUP2" 2851115 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1194 2849249 2849523 2849879 "SUMRF" 2850500 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1193 2848584 2848650 2848842 "SUMFS" 2849170 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1192 2831371 2847896 2848138 "SULS" 2848400 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2830973 2831193 2831263 "SUCHTAST" 2831323 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1190 2830268 2830498 2830638 "SUCH" 2830881 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1189 2824135 2825174 2826133 "SUBSPACE" 2829356 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1188 2823565 2823655 2823819 "SUBRESP" 2824023 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1187 2816933 2818230 2819541 "STTF" 2822301 NIL STTF (NIL T) -7 NIL NIL NIL) (-1186 2811106 2812226 2813373 "STTFNC" 2815833 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1185 2802419 2804288 2806082 "STTAYLOR" 2809347 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1184 2795555 2802283 2802366 "STRTBL" 2802371 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1183 2790516 2795264 2795363 "STRING" 2795478 T STRING (NIL) -8 NIL NIL NIL) (-1182 2783272 2788135 2788746 "STREAM" 2789940 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1181 2782782 2782859 2783003 "STREAM3" 2783189 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1180 2781764 2781947 2782182 "STREAM2" 2782595 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1179 2781452 2781504 2781597 "STREAM1" 2781706 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1178 2780468 2780649 2780880 "STINPROD" 2781268 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1177 2780006 2780216 2780246 "STEP" 2780326 T STEP (NIL) -9 NIL 2780404 NIL) (-1176 2779193 2779495 2779643 "STEPAST" 2779880 T STEPAST (NIL) -8 NIL NIL NIL) (-1175 2772631 2779092 2779169 "STBL" 2779174 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1174 2767701 2771794 2771837 "STAGG" 2771990 NIL STAGG (NIL T) -9 NIL 2772079 NIL) (-1173 2765403 2766005 2766877 "STAGG-" 2766882 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1172 2763553 2765173 2765265 "STACK" 2765346 NIL STACK (NIL T) -8 NIL NIL NIL) (-1171 2756248 2761694 2762150 "SREGSET" 2763183 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1170 2748673 2750042 2751555 "SRDCMPK" 2754854 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1169 2741510 2746032 2746062 "SRAGG" 2747365 T SRAGG (NIL) -9 NIL 2747973 NIL) (-1168 2740527 2740782 2741161 "SRAGG-" 2741166 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1167 2734711 2739474 2739895 "SQMATRIX" 2740153 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1166 2728399 2731429 2732156 "SPLTREE" 2734056 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1165 2724362 2725055 2725701 "SPLNODE" 2727825 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1164 2723409 2723642 2723672 "SPFCAT" 2724116 T SPFCAT (NIL) -9 NIL NIL NIL) (-1163 2722146 2722356 2722620 "SPECOUT" 2723167 T SPECOUT (NIL) -7 NIL NIL NIL) (-1162 2713242 2715114 2715144 "SPADXPT" 2719820 T SPADXPT (NIL) -9 NIL 2721984 NIL) (-1161 2713003 2713043 2713112 "SPADPRSR" 2713195 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1160 2711052 2712958 2712989 "SPADAST" 2712994 T SPADAST (NIL) -8 NIL NIL NIL) (-1159 2702983 2704756 2704799 "SPACEC" 2709172 NIL SPACEC (NIL T) -9 NIL 2710988 NIL) (-1158 2701113 2702915 2702964 "SPACE3" 2702969 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1157 2699865 2700036 2700327 "SORTPAK" 2700918 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1156 2697957 2698260 2698672 "SOLVETRA" 2699529 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1155 2697007 2697229 2697490 "SOLVESER" 2697730 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1154 2692311 2693199 2694194 "SOLVERAD" 2696059 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1153 2688126 2688735 2689464 "SOLVEFOR" 2691678 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1152 2682395 2687474 2687571 "SNTSCAT" 2687576 NIL SNTSCAT (NIL T T T T) -9 NIL 2687646 NIL) (-1151 2676501 2680718 2681109 "SMTS" 2682085 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1150 2670910 2676389 2676466 "SMP" 2676471 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1149 2669069 2669370 2669768 "SMITH" 2670607 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1148 2661173 2665648 2665751 "SMATCAT" 2667102 NIL SMATCAT (NIL NIL T T T) -9 NIL 2667652 NIL) (-1147 2658113 2658936 2660114 "SMATCAT-" 2660119 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1146 2655754 2657321 2657364 "SKAGG" 2657625 NIL SKAGG (NIL T) -9 NIL 2657760 NIL) (-1145 2651944 2655227 2655411 "SINT" 2655563 T SINT (NIL) -8 NIL NIL 2655725) (-1144 2651716 2651754 2651820 "SIMPAN" 2651900 T SIMPAN (NIL) -7 NIL NIL NIL) (-1143 2650995 2651251 2651391 "SIG" 2651598 T SIG (NIL) -8 NIL NIL NIL) (-1142 2649833 2650054 2650329 "SIGNRF" 2650754 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1141 2648666 2648817 2649101 "SIGNEF" 2649662 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1140 2647972 2648249 2648373 "SIGAST" 2648564 T SIGAST (NIL) -8 NIL NIL NIL) (-1139 2645662 2646116 2646622 "SHP" 2647513 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1138 2639491 2645563 2645639 "SHDP" 2645644 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1137 2639050 2639242 2639272 "SGROUP" 2639365 T SGROUP (NIL) -9 NIL 2639427 NIL) (-1136 2638908 2638934 2639007 "SGROUP-" 2639012 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1135 2635699 2636397 2637120 "SGCF" 2638207 T SGCF (NIL) -7 NIL NIL NIL) (-1134 2630066 2635145 2635242 "SFRTCAT" 2635247 NIL SFRTCAT (NIL T T T T) -9 NIL 2635286 NIL) (-1133 2623487 2624505 2625641 "SFRGCD" 2629049 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1132 2616613 2617686 2618872 "SFQCMPK" 2622420 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2616233 2616322 2616433 "SFORT" 2616554 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1130 2615351 2616073 2616194 "SEXOF" 2616199 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1129 2614458 2615232 2615300 "SEX" 2615305 T SEX (NIL) -8 NIL NIL NIL) (-1128 2610239 2610954 2611049 "SEXCAT" 2613671 NIL SEXCAT (NIL T T T T T) -9 NIL 2614231 NIL) (-1127 2607392 2610173 2610221 "SET" 2610226 NIL SET (NIL T) -8 NIL NIL NIL) (-1126 2605616 2606105 2606410 "SETMN" 2607133 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1125 2605182 2605334 2605364 "SETCAT" 2605481 T SETCAT (NIL) -9 NIL 2605566 NIL) (-1124 2604962 2605014 2605113 "SETCAT-" 2605118 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1123 2601323 2603423 2603466 "SETAGG" 2604336 NIL SETAGG (NIL T) -9 NIL 2604676 NIL) (-1122 2600781 2600897 2601134 "SETAGG-" 2601139 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1121 2600224 2600477 2600578 "SEQAST" 2600702 T SEQAST (NIL) -8 NIL NIL NIL) (-1120 2599423 2599717 2599778 "SEGXCAT" 2600064 NIL SEGXCAT (NIL T T) -9 NIL 2600184 NIL) (-1119 2598429 2599089 2599271 "SEG" 2599276 NIL SEG (NIL T) -8 NIL NIL NIL) (-1118 2597408 2597622 2597665 "SEGCAT" 2598187 NIL SEGCAT (NIL T) -9 NIL 2598408 NIL) (-1117 2596340 2596771 2596979 "SEGBIND" 2597235 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1116 2595961 2596020 2596133 "SEGBIND2" 2596275 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1115 2595534 2595762 2595839 "SEGAST" 2595906 T SEGAST (NIL) -8 NIL NIL NIL) (-1114 2594753 2594879 2595083 "SEG2" 2595378 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1113 2594124 2594688 2594735 "SDVAR" 2594740 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1112 2586375 2593894 2594024 "SDPOL" 2594029 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1111 2584968 2585234 2585553 "SCPKG" 2586090 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1110 2584132 2584304 2584496 "SCOPE" 2584798 T SCOPE (NIL) -8 NIL NIL NIL) (-1109 2583352 2583486 2583665 "SCACHE" 2583987 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1108 2582984 2583170 2583200 "SASTCAT" 2583205 T SASTCAT (NIL) -9 NIL 2583218 NIL) (-1107 2582471 2582819 2582895 "SAOS" 2582930 T SAOS (NIL) -8 NIL NIL NIL) (-1106 2582036 2582071 2582244 "SAERFFC" 2582430 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1105 2575699 2581933 2582013 "SAE" 2582018 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1104 2575292 2575327 2575486 "SAEFACT" 2575658 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1103 2573613 2573927 2574328 "RURPK" 2574958 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1102 2572250 2572556 2572861 "RULESET" 2573447 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1101 2569473 2570003 2570461 "RULE" 2571931 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1100 2569085 2569267 2569350 "RULECOLD" 2569425 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1099 2568875 2568903 2568974 "RTVALUE" 2569036 T RTVALUE (NIL) -8 NIL NIL NIL) (-1098 2568346 2568592 2568686 "RSTRCAST" 2568803 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1097 2563194 2563989 2564909 "RSETGCD" 2567545 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1096 2552423 2557502 2557599 "RSETCAT" 2561718 NIL RSETCAT (NIL T T T T) -9 NIL 2562815 NIL) (-1095 2550350 2550889 2551713 "RSETCAT-" 2551718 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1094 2542736 2544112 2545632 "RSDCMPK" 2548949 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2540701 2541168 2541242 "RRCC" 2542328 NIL RRCC (NIL T T) -9 NIL 2542672 NIL) (-1092 2540052 2540226 2540505 "RRCC-" 2540510 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1091 2539495 2539748 2539849 "RPTAST" 2539973 T RPTAST (NIL) -8 NIL NIL NIL) (-1090 2512971 2522607 2522674 "RPOLCAT" 2533340 NIL RPOLCAT (NIL T T T) -9 NIL 2536500 NIL) (-1089 2504469 2506809 2509931 "RPOLCAT-" 2509936 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1088 2495406 2502680 2503162 "ROUTINE" 2504009 T ROUTINE (NIL) -8 NIL NIL NIL) (-1087 2492067 2495032 2495172 "ROMAN" 2495288 T ROMAN (NIL) -8 NIL NIL NIL) (-1086 2490311 2490927 2491187 "ROIRC" 2491872 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1085 2486515 2488800 2488830 "RNS" 2489134 T RNS (NIL) -9 NIL 2489408 NIL) (-1084 2485024 2485407 2485941 "RNS-" 2486016 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1083 2484413 2484821 2484851 "RNG" 2484856 T RNG (NIL) -9 NIL 2484877 NIL) (-1082 2483416 2483778 2483980 "RNGBIND" 2484264 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1081 2482801 2483189 2483232 "RMODULE" 2483237 NIL RMODULE (NIL T) -9 NIL 2483264 NIL) (-1080 2481637 2481731 2482067 "RMCAT2" 2482702 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1079 2478487 2480983 2481280 "RMATRIX" 2481399 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1078 2471314 2473574 2473689 "RMATCAT" 2477048 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2478030 NIL) (-1077 2470689 2470836 2471143 "RMATCAT-" 2471148 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1076 2470304 2470476 2470519 "RLINSET" 2470581 NIL RLINSET (NIL T) -9 NIL 2470625 NIL) (-1075 2469871 2469946 2470074 "RINTERP" 2470223 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1074 2468915 2469469 2469499 "RING" 2469555 T RING (NIL) -9 NIL 2469647 NIL) (-1073 2468707 2468751 2468848 "RING-" 2468853 NIL RING- (NIL T) -8 NIL NIL NIL) (-1072 2467548 2467785 2468043 "RIDIST" 2468471 T RIDIST (NIL) -7 NIL NIL NIL) (-1071 2458837 2467016 2467222 "RGCHAIN" 2467396 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1070 2458173 2458579 2458620 "RGBCSPC" 2458678 NIL RGBCSPC (NIL T) -9 NIL 2458730 NIL) (-1069 2457317 2457698 2457739 "RGBCMDL" 2457971 NIL RGBCMDL (NIL T) -9 NIL 2458085 NIL) (-1068 2454311 2454925 2455595 "RF" 2456681 NIL RF (NIL T) -7 NIL NIL NIL) (-1067 2453957 2454020 2454123 "RFFACTOR" 2454242 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1066 2453682 2453717 2453814 "RFFACT" 2453916 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1065 2451799 2452163 2452545 "RFDIST" 2453322 T RFDIST (NIL) -7 NIL NIL NIL) (-1064 2451252 2451344 2451507 "RETSOL" 2451701 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1063 2450888 2450968 2451011 "RETRACT" 2451144 NIL RETRACT (NIL T) -9 NIL 2451231 NIL) (-1062 2450737 2450762 2450849 "RETRACT-" 2450854 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1061 2450339 2450559 2450629 "RETAST" 2450689 T RETAST (NIL) -8 NIL NIL NIL) (-1060 2443083 2449992 2450119 "RESULT" 2450234 T RESULT (NIL) -8 NIL NIL NIL) (-1059 2441674 2442352 2442551 "RESRING" 2442986 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1058 2441310 2441359 2441457 "RESLATC" 2441611 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1057 2441015 2441050 2441157 "REPSQ" 2441269 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1056 2438437 2439017 2439619 "REP" 2440435 T REP (NIL) -7 NIL NIL NIL) (-1055 2438134 2438169 2438280 "REPDB" 2438396 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1054 2432034 2433423 2434646 "REP2" 2436946 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1053 2428411 2429092 2429900 "REP1" 2431261 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1052 2421107 2426552 2427008 "REGSET" 2428041 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1051 2419872 2420255 2420505 "REF" 2420892 NIL REF (NIL T) -8 NIL NIL NIL) (-1050 2419249 2419352 2419519 "REDORDER" 2419756 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1049 2415217 2418462 2418689 "RECLOS" 2419077 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1048 2414269 2414450 2414665 "REALSOLV" 2415024 T REALSOLV (NIL) -7 NIL NIL NIL) (-1047 2414115 2414156 2414186 "REAL" 2414191 T REAL (NIL) -9 NIL 2414226 NIL) (-1046 2410598 2411400 2412284 "REAL0Q" 2413280 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1045 2406199 2407187 2408248 "REAL0" 2409579 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1044 2405670 2405916 2406010 "RDUCEAST" 2406127 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1043 2405075 2405147 2405354 "RDIV" 2405592 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1042 2404143 2404317 2404530 "RDIST" 2404897 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1041 2402740 2403027 2403399 "RDETRS" 2403851 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1040 2400552 2401006 2401544 "RDETR" 2402282 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1039 2399177 2399455 2399852 "RDEEFS" 2400268 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1038 2397686 2397992 2398417 "RDEEF" 2398865 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1037 2391719 2394640 2394670 "RCFIELD" 2395965 T RCFIELD (NIL) -9 NIL 2396696 NIL) (-1036 2389783 2390287 2390983 "RCFIELD-" 2391058 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1035 2386027 2387856 2387899 "RCAGG" 2388983 NIL RCAGG (NIL T) -9 NIL 2389448 NIL) (-1034 2385655 2385749 2385912 "RCAGG-" 2385917 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1033 2384990 2385102 2385267 "RATRET" 2385539 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1032 2384543 2384610 2384731 "RATFACT" 2384918 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1031 2383851 2383971 2384123 "RANDSRC" 2384413 T RANDSRC (NIL) -7 NIL NIL NIL) (-1030 2383585 2383629 2383702 "RADUTIL" 2383800 T RADUTIL (NIL) -7 NIL NIL NIL) (-1029 2376413 2382416 2382727 "RADIX" 2383308 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1028 2366873 2376255 2376385 "RADFF" 2376390 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1027 2366520 2366595 2366625 "RADCAT" 2366785 T RADCAT (NIL) -9 NIL NIL NIL) (-1026 2366302 2366350 2366450 "RADCAT-" 2366455 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1025 2364403 2366072 2366164 "QUEUE" 2366245 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1024 2360664 2364336 2364384 "QUAT" 2364389 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1023 2360295 2360338 2360469 "QUATCT2" 2360615 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2353093 2356718 2356760 "QUATCAT" 2357551 NIL QUATCAT (NIL T) -9 NIL 2358317 NIL) (-1021 2349232 2350269 2351659 "QUATCAT-" 2351755 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2346672 2348280 2348323 "QUAGG" 2348704 NIL QUAGG (NIL T) -9 NIL 2348879 NIL) (-1019 2346274 2346494 2346564 "QQUTAST" 2346624 T QQUTAST (NIL) -8 NIL NIL NIL) (-1018 2345287 2345787 2345952 "QFORM" 2346155 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1017 2335619 2341134 2341176 "QFCAT" 2341844 NIL QFCAT (NIL T) -9 NIL 2342845 NIL) (-1016 2331186 2332387 2333981 "QFCAT-" 2334077 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1015 2330817 2330860 2330991 "QFCAT2" 2331137 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2330272 2330382 2330514 "QEQUAT" 2330707 T QEQUAT (NIL) -8 NIL NIL NIL) (-1013 2323398 2324471 2325657 "QCMPACK" 2329205 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1012 2320936 2321384 2321814 "QALGSET" 2323053 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1011 2320171 2320347 2320583 "QALGSET2" 2320754 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1010 2318856 2319080 2319399 "PWFFINTB" 2319944 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1009 2317031 2317199 2317555 "PUSHVAR" 2318670 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1008 2312920 2313974 2314017 "PTRANFN" 2315928 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1007 2311311 2311602 2311926 "PTPACK" 2312631 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1006 2310940 2310997 2311108 "PTFUNC2" 2311248 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1005 2305335 2309729 2309772 "PTCAT" 2310072 NIL PTCAT (NIL T) -9 NIL 2310225 NIL) (-1004 2304990 2305025 2305151 "PSQFR" 2305294 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1003 2303580 2303878 2304214 "PSEUDLIN" 2304688 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1002 2290304 2292675 2295001 "PSETPK" 2301340 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1001 2283300 2286040 2286138 "PSETCAT" 2289179 NIL PSETCAT (NIL T T T T) -9 NIL 2289993 NIL) (-1000 2281133 2281767 2282591 "PSETCAT-" 2282596 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-999 2280482 2280647 2280675 "PSCURVE" 2280943 T PSCURVE (NIL) -9 NIL 2281110 NIL) (-998 2276466 2277982 2278047 "PSCAT" 2278891 NIL PSCAT (NIL T T T) -9 NIL 2279131 NIL) (-997 2275529 2275745 2276145 "PSCAT-" 2276150 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-996 2273888 2274598 2274861 "PRTITION" 2275286 T PRTITION (NIL) -8 NIL NIL NIL) (-995 2273363 2273609 2273701 "PRTDAST" 2273816 T PRTDAST (NIL) -8 NIL NIL NIL) (-994 2262453 2264667 2266855 "PRS" 2271225 NIL PRS (NIL T T) -7 NIL NIL NIL) (-993 2260239 2261775 2261815 "PRQAGG" 2261998 NIL PRQAGG (NIL T) -9 NIL 2262100 NIL) (-992 2259575 2259880 2259908 "PROPLOG" 2260047 T PROPLOG (NIL) -9 NIL 2260162 NIL) (-991 2259179 2259236 2259359 "PROPFUN2" 2259498 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-990 2258494 2258615 2258787 "PROPFUN1" 2259040 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-989 2256675 2257241 2257538 "PROPFRML" 2258230 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-988 2256144 2256251 2256379 "PROPERTY" 2256567 T PROPERTY (NIL) -8 NIL NIL NIL) (-987 2250202 2254310 2255130 "PRODUCT" 2255370 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-986 2247480 2249660 2249894 "PR" 2250013 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2247276 2247308 2247367 "PRINT" 2247441 T PRINT (NIL) -7 NIL NIL NIL) (-984 2246616 2246733 2246885 "PRIMES" 2247156 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-983 2244681 2245082 2245548 "PRIMELT" 2246195 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-982 2244410 2244459 2244487 "PRIMCAT" 2244611 T PRIMCAT (NIL) -9 NIL NIL NIL) (-981 2240528 2244348 2244393 "PRIMARR" 2244398 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-980 2239535 2239713 2239941 "PRIMARR2" 2240346 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-979 2239178 2239234 2239345 "PREASSOC" 2239473 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-978 2238653 2238786 2238814 "PPCURVE" 2239019 T PPCURVE (NIL) -9 NIL 2239155 NIL) (-977 2238248 2238448 2238531 "PORTNUM" 2238590 T PORTNUM (NIL) -8 NIL NIL NIL) (-976 2235607 2236006 2236598 "POLYROOT" 2237829 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-975 2229513 2235211 2235371 "POLY" 2235480 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2228896 2228954 2229188 "POLYLIFT" 2229449 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-973 2225171 2225620 2226249 "POLYCATQ" 2228441 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-972 2211513 2216918 2216983 "POLYCAT" 2220497 NIL POLYCAT (NIL T T T) -9 NIL 2222375 NIL) (-971 2204962 2206824 2209208 "POLYCAT-" 2209213 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-970 2204549 2204617 2204737 "POLY2UP" 2204888 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-969 2204181 2204238 2204347 "POLY2" 2204486 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-968 2202866 2203105 2203381 "POLUTIL" 2203955 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-967 2201221 2201498 2201829 "POLTOPOL" 2202588 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-966 2196687 2201155 2201202 "POINT" 2201207 NIL POINT (NIL T) -8 NIL NIL NIL) (-965 2194874 2195231 2195606 "PNTHEORY" 2196332 T PNTHEORY (NIL) -7 NIL NIL NIL) (-964 2193332 2193629 2194028 "PMTOOLS" 2194572 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-963 2192925 2193003 2193120 "PMSYM" 2193248 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-962 2192433 2192502 2192677 "PMQFCAT" 2192850 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-961 2191788 2191898 2192054 "PMPRED" 2192310 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-960 2191181 2191267 2191429 "PMPREDFS" 2191689 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-959 2189845 2190053 2190431 "PMPLCAT" 2190943 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-958 2189377 2189456 2189608 "PMLSAGG" 2189760 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-957 2188850 2188926 2189108 "PMKERNEL" 2189295 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-956 2188467 2188542 2188655 "PMINS" 2188769 NIL PMINS (NIL T) -7 NIL NIL NIL) (-955 2187909 2187978 2188187 "PMFS" 2188392 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-954 2187137 2187255 2187460 "PMDOWN" 2187786 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-953 2186304 2186462 2186643 "PMASS" 2186976 T PMASS (NIL) -7 NIL NIL NIL) (-952 2185577 2185687 2185850 "PMASSFS" 2186191 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-951 2185232 2185300 2185394 "PLOTTOOL" 2185503 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-950 2179839 2181043 2182191 "PLOT" 2184104 T PLOT (NIL) -8 NIL NIL NIL) (-949 2175643 2176687 2177608 "PLOT3D" 2178938 T PLOT3D (NIL) -8 NIL NIL NIL) (-948 2174555 2174732 2174967 "PLOT1" 2175447 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-947 2149946 2154621 2159472 "PLEQN" 2169821 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-946 2149264 2149386 2149566 "PINTERP" 2149811 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-945 2148957 2149004 2149107 "PINTERPA" 2149211 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-944 2148173 2148721 2148808 "PI" 2148848 T PI (NIL) -8 NIL NIL 2148915) (-943 2146456 2147431 2147459 "PID" 2147641 T PID (NIL) -9 NIL 2147775 NIL) (-942 2146207 2146244 2146319 "PICOERCE" 2146413 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-941 2145527 2145666 2145842 "PGROEB" 2146063 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-940 2141114 2141928 2142833 "PGE" 2144642 T PGE (NIL) -7 NIL NIL NIL) (-939 2139237 2139484 2139850 "PGCD" 2140831 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-938 2138575 2138678 2138839 "PFRPAC" 2139121 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-937 2135215 2137123 2137476 "PFR" 2138254 NIL PFR (NIL T) -8 NIL NIL NIL) (-936 2133604 2133848 2134173 "PFOTOOLS" 2134962 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-935 2132137 2132376 2132727 "PFOQ" 2133361 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-934 2130638 2130850 2131206 "PFO" 2131921 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-933 2127191 2130527 2130596 "PF" 2130601 NIL PF (NIL NIL) -8 NIL NIL NIL) (-932 2124511 2125782 2125810 "PFECAT" 2126395 T PFECAT (NIL) -9 NIL 2126779 NIL) (-931 2123956 2124110 2124324 "PFECAT-" 2124329 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-930 2122559 2122811 2123112 "PFBRU" 2123705 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-929 2120425 2120777 2121209 "PFBR" 2122210 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-928 2116471 2117937 2118584 "PERM" 2119811 NIL PERM (NIL T) -8 NIL NIL NIL) (-927 2111705 2112678 2113548 "PERMGRP" 2115634 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-926 2109769 2110729 2110770 "PERMCAT" 2111170 NIL PERMCAT (NIL T) -9 NIL 2111468 NIL) (-925 2109422 2109463 2109587 "PERMAN" 2109722 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-924 2106913 2109087 2109209 "PENDTREE" 2109333 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-923 2105842 2106057 2106098 "PDSPC" 2106631 NIL PDSPC (NIL T) -9 NIL 2106876 NIL) (-922 2104945 2105163 2105525 "PDSPC-" 2105530 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-921 2103827 2104595 2104636 "PDRING" 2104641 NIL PDRING (NIL T) -9 NIL 2104669 NIL) (-920 2102714 2103332 2103386 "PDMOD" 2103391 NIL PDMOD (NIL T T) -9 NIL 2103495 NIL) (-919 2099929 2100707 2101375 "PDEPROB" 2102066 T PDEPROB (NIL) -8 NIL NIL NIL) (-918 2097474 2097978 2098533 "PDEPACK" 2099394 T PDEPACK (NIL) -7 NIL NIL NIL) (-917 2096386 2096576 2096827 "PDECOMP" 2097273 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-916 2093951 2094794 2094822 "PDECAT" 2095609 T PDECAT (NIL) -9 NIL 2096322 NIL) (-915 2093580 2093635 2093689 "PDDOM" 2093854 NIL PDDOM (NIL T T) -9 NIL 2093934 NIL) (-914 2093399 2093429 2093536 "PDDOM-" 2093541 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-913 2093150 2093183 2093273 "PCOMP" 2093360 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-912 2091328 2091951 2092248 "PBWLB" 2092879 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-911 2083801 2085401 2086739 "PATTERN" 2090011 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-910 2083433 2083490 2083599 "PATTERN2" 2083738 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-909 2081190 2081578 2082035 "PATTERN1" 2083022 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-908 2078558 2079139 2079620 "PATRES" 2080755 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-907 2078122 2078189 2078321 "PATRES2" 2078485 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-906 2076005 2076410 2076817 "PATMATCH" 2077789 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-905 2075501 2075710 2075751 "PATMAB" 2075858 NIL PATMAB (NIL T) -9 NIL 2075941 NIL) (-904 2074019 2074355 2074613 "PATLRES" 2075306 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-903 2073565 2073688 2073729 "PATAB" 2073734 NIL PATAB (NIL T) -9 NIL 2073906 NIL) (-902 2071747 2072142 2072565 "PARTPERM" 2073162 T PARTPERM (NIL) -7 NIL NIL NIL) (-901 2071368 2071431 2071533 "PARSURF" 2071678 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-900 2071000 2071057 2071166 "PARSU2" 2071305 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-899 2070764 2070804 2070871 "PARSER" 2070953 T PARSER (NIL) -7 NIL NIL NIL) (-898 2070385 2070448 2070550 "PARSCURV" 2070695 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-897 2070017 2070074 2070183 "PARSC2" 2070322 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-896 2069656 2069714 2069811 "PARPCURV" 2069953 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-895 2069288 2069345 2069454 "PARPC2" 2069593 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-894 2068349 2068661 2068843 "PARAMAST" 2069126 T PARAMAST (NIL) -8 NIL NIL NIL) (-893 2067869 2067955 2068074 "PAN2EXPR" 2068250 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-892 2066646 2066990 2067218 "PALETTE" 2067661 T PALETTE (NIL) -8 NIL NIL NIL) (-891 2065039 2065651 2066011 "PAIR" 2066332 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-890 2058631 2064296 2064491 "PADICRC" 2064893 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-889 2051547 2057975 2058160 "PADICRAT" 2058478 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-888 2049862 2051484 2051529 "PADIC" 2051534 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-887 2046958 2048522 2048562 "PADICCT" 2049143 NIL PADICCT (NIL NIL) -9 NIL 2049425 NIL) (-886 2045915 2046115 2046383 "PADEPAC" 2046745 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-885 2045127 2045260 2045466 "PADE" 2045777 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-884 2043514 2044335 2044615 "OWP" 2044931 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-883 2043007 2043220 2043317 "OVERSET" 2043437 T OVERSET (NIL) -8 NIL NIL NIL) (-882 2042053 2042612 2042784 "OVAR" 2042875 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-881 2041317 2041438 2041599 "OUT" 2041912 T OUT (NIL) -7 NIL NIL NIL) (-880 2030189 2032426 2034626 "OUTFORM" 2039137 T OUTFORM (NIL) -8 NIL NIL NIL) (-879 2029525 2029786 2029913 "OUTBFILE" 2030082 T OUTBFILE (NIL) -8 NIL NIL NIL) (-878 2028832 2028997 2029025 "OUTBCON" 2029343 T OUTBCON (NIL) -9 NIL 2029509 NIL) (-877 2028433 2028545 2028702 "OUTBCON-" 2028707 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-876 2027813 2028162 2028251 "OSI" 2028364 T OSI (NIL) -8 NIL NIL NIL) (-875 2027316 2027654 2027682 "OSGROUP" 2027687 T OSGROUP (NIL) -9 NIL 2027709 NIL) (-874 2026061 2026288 2026573 "ORTHPOL" 2027063 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-873 2023612 2025896 2026017 "OREUP" 2026022 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-872 2021015 2023303 2023430 "ORESUP" 2023554 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-871 2018543 2019043 2019604 "OREPCTO" 2020504 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-870 2012215 2014416 2014457 "OREPCAT" 2016805 NIL OREPCAT (NIL T) -9 NIL 2017909 NIL) (-869 2009362 2010144 2011202 "OREPCAT-" 2011207 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-868 2008609 2008832 2008860 "ORDTYPE" 2009169 T ORDTYPE (NIL) -9 NIL 2009332 NIL) (-867 2007952 2008126 2008381 "ORDTYPE-" 2008386 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-866 2007378 2007691 2007849 "ORDSTRCT" 2007854 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-865 2006948 2007246 2007274 "ORDSET" 2007279 T ORDSET (NIL) -9 NIL 2007301 NIL) (-864 2005486 2006277 2006305 "ORDRING" 2006507 T ORDRING (NIL) -9 NIL 2006632 NIL) (-863 2005131 2005225 2005369 "ORDRING-" 2005374 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-862 2004484 2004947 2004975 "ORDMON" 2004980 T ORDMON (NIL) -9 NIL 2005001 NIL) (-861 2003646 2003793 2003988 "ORDFUNS" 2004333 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-860 2002957 2003376 2003404 "ORDFIN" 2003469 T ORDFIN (NIL) -9 NIL 2003543 NIL) (-859 1999516 2001543 2001952 "ORDCOMP" 2002581 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-858 1998782 1998909 1999095 "ORDCOMP2" 1999376 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-857 1995363 1996273 1997087 "OPTPROB" 1997988 T OPTPROB (NIL) -8 NIL NIL NIL) (-856 1992165 1992804 1993508 "OPTPACK" 1994679 T OPTPACK (NIL) -7 NIL NIL NIL) (-855 1989838 1990604 1990632 "OPTCAT" 1991451 T OPTCAT (NIL) -9 NIL 1992101 NIL) (-854 1989222 1989515 1989620 "OPSIG" 1989753 T OPSIG (NIL) -8 NIL NIL NIL) (-853 1988990 1989029 1989095 "OPQUERY" 1989176 T OPQUERY (NIL) -7 NIL NIL NIL) (-852 1986121 1987301 1987805 "OP" 1988519 NIL OP (NIL T) -8 NIL NIL NIL) (-851 1985481 1985707 1985748 "OPERCAT" 1985960 NIL OPERCAT (NIL T) -9 NIL 1986057 NIL) (-850 1985236 1985292 1985409 "OPERCAT-" 1985414 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-849 1982049 1984033 1984402 "ONECOMP" 1984900 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-848 1981354 1981469 1981643 "ONECOMP2" 1981921 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1980773 1980879 1981009 "OMSERVER" 1981244 T OMSERVER (NIL) -7 NIL NIL NIL) (-846 1977635 1980213 1980253 "OMSAGG" 1980314 NIL OMSAGG (NIL T) -9 NIL 1980378 NIL) (-845 1976258 1976521 1976803 "OMPKG" 1977373 T OMPKG (NIL) -7 NIL NIL NIL) (-844 1975688 1975791 1975819 "OM" 1976118 T OM (NIL) -9 NIL NIL NIL) (-843 1974235 1975237 1975406 "OMLO" 1975569 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-842 1973195 1973342 1973562 "OMEXPR" 1974061 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-841 1972486 1972741 1972877 "OMERR" 1973079 T OMERR (NIL) -8 NIL NIL NIL) (-840 1971637 1971907 1972067 "OMERRK" 1972346 T OMERRK (NIL) -8 NIL NIL NIL) (-839 1971088 1971314 1971422 "OMENC" 1971549 T OMENC (NIL) -8 NIL NIL NIL) (-838 1964983 1966168 1967339 "OMDEV" 1969937 T OMDEV (NIL) -8 NIL NIL NIL) (-837 1964052 1964223 1964417 "OMCONN" 1964809 T OMCONN (NIL) -8 NIL NIL NIL) (-836 1962546 1963522 1963550 "OINTDOM" 1963555 T OINTDOM (NIL) -9 NIL 1963576 NIL) (-835 1959884 1961234 1961571 "OFMONOID" 1962241 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-834 1959256 1959821 1959866 "ODVAR" 1959871 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-833 1956679 1959001 1959156 "ODR" 1959161 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-832 1948984 1956455 1956581 "ODPOL" 1956586 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-831 1942783 1948856 1948961 "ODP" 1948966 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-830 1941549 1941764 1942039 "ODETOOLS" 1942557 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-829 1938516 1939174 1939890 "ODESYS" 1940882 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-828 1933398 1934306 1935331 "ODERTRIC" 1937591 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-827 1932824 1932906 1933100 "ODERED" 1933310 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-826 1929712 1930260 1930937 "ODERAT" 1932247 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-825 1926671 1927136 1927733 "ODEPRRIC" 1929241 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-824 1924614 1925210 1925696 "ODEPROB" 1926205 T ODEPROB (NIL) -8 NIL NIL NIL) (-823 1921134 1921619 1922266 "ODEPRIM" 1924093 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-822 1920383 1920485 1920745 "ODEPAL" 1921026 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-821 1916545 1917336 1918200 "ODEPACK" 1919539 T ODEPACK (NIL) -7 NIL NIL NIL) (-820 1915606 1915713 1915935 "ODEINT" 1916434 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-819 1909707 1911132 1912579 "ODEIFTBL" 1914179 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-818 1905105 1905891 1906843 "ODEEF" 1908866 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-817 1904454 1904543 1904766 "ODECONST" 1905010 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-816 1902565 1903226 1903254 "ODECAT" 1903859 T ODECAT (NIL) -9 NIL 1904390 NIL) (-815 1899420 1902270 1902392 "OCT" 1902475 NIL OCT (NIL T) -8 NIL NIL NIL) (-814 1899058 1899101 1899228 "OCTCT2" 1899371 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-813 1893665 1896101 1896141 "OC" 1897238 NIL OC (NIL T) -9 NIL 1898096 NIL) (-812 1890892 1891640 1892630 "OC-" 1892724 NIL OC- (NIL T T) -8 NIL NIL NIL) (-811 1890217 1890685 1890713 "OCAMON" 1890718 T OCAMON (NIL) -9 NIL 1890739 NIL) (-810 1889721 1890062 1890090 "OASGP" 1890095 T OASGP (NIL) -9 NIL 1890115 NIL) (-809 1888955 1889444 1889472 "OAMONS" 1889512 T OAMONS (NIL) -9 NIL 1889555 NIL) (-808 1888342 1888775 1888803 "OAMON" 1888808 T OAMON (NIL) -9 NIL 1888828 NIL) (-807 1887573 1888091 1888119 "OAGROUP" 1888124 T OAGROUP (NIL) -9 NIL 1888144 NIL) (-806 1887263 1887313 1887401 "NUMTUBE" 1887517 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-805 1880836 1882354 1883890 "NUMQUAD" 1885747 T NUMQUAD (NIL) -7 NIL NIL NIL) (-804 1876592 1877580 1878605 "NUMODE" 1879831 T NUMODE (NIL) -7 NIL NIL NIL) (-803 1873933 1874813 1874841 "NUMINT" 1875764 T NUMINT (NIL) -9 NIL 1876528 NIL) (-802 1872881 1873078 1873296 "NUMFMT" 1873735 T NUMFMT (NIL) -7 NIL NIL NIL) (-801 1859240 1862185 1864717 "NUMERIC" 1870388 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-800 1853609 1858688 1858783 "NTSCAT" 1858788 NIL NTSCAT (NIL T T T T) -9 NIL 1858827 NIL) (-799 1852803 1852968 1853161 "NTPOLFN" 1853448 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-798 1840604 1849628 1850440 "NSUP" 1852024 NIL NSUP (NIL T) -8 NIL NIL NIL) (-797 1840236 1840293 1840402 "NSUP2" 1840541 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-796 1830186 1840010 1840143 "NSMP" 1840148 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-795 1828618 1828919 1829276 "NREP" 1829874 NIL NREP (NIL T) -7 NIL NIL NIL) (-794 1827209 1827461 1827819 "NPCOEF" 1828361 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-793 1826275 1826390 1826606 "NORMRETR" 1827090 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-792 1824316 1824606 1825015 "NORMPK" 1825983 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-791 1824001 1824029 1824153 "NORMMA" 1824282 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-790 1823801 1823958 1823987 "NONE" 1823992 T NONE (NIL) -8 NIL NIL NIL) (-789 1823590 1823619 1823688 "NONE1" 1823765 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-788 1823087 1823149 1823328 "NODE1" 1823522 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-787 1821368 1822219 1822474 "NNI" 1822821 T NNI (NIL) -8 NIL NIL 1823056) (-786 1819788 1820101 1820465 "NLINSOL" 1821036 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-785 1816029 1817024 1817923 "NIPROB" 1818909 T NIPROB (NIL) -8 NIL NIL NIL) (-784 1814786 1815020 1815322 "NFINTBAS" 1815791 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-783 1813960 1814436 1814477 "NETCLT" 1814649 NIL NETCLT (NIL T) -9 NIL 1814731 NIL) (-782 1812668 1812899 1813180 "NCODIV" 1813728 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-781 1812430 1812467 1812542 "NCNTFRAC" 1812625 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-780 1810610 1810974 1811394 "NCEP" 1812055 NIL NCEP (NIL T) -7 NIL NIL NIL) (-779 1809447 1810220 1810248 "NASRING" 1810358 T NASRING (NIL) -9 NIL 1810438 NIL) (-778 1809242 1809286 1809380 "NASRING-" 1809385 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-777 1808335 1808860 1808888 "NARNG" 1809005 T NARNG (NIL) -9 NIL 1809096 NIL) (-776 1808027 1808094 1808228 "NARNG-" 1808233 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-775 1806906 1807113 1807348 "NAGSP" 1807812 T NAGSP (NIL) -7 NIL NIL NIL) (-774 1798178 1799862 1801535 "NAGS" 1805253 T NAGS (NIL) -7 NIL NIL NIL) (-773 1796726 1797034 1797365 "NAGF07" 1797867 T NAGF07 (NIL) -7 NIL NIL NIL) (-772 1791264 1792555 1793862 "NAGF04" 1795439 T NAGF04 (NIL) -7 NIL NIL NIL) (-771 1784232 1785846 1787479 "NAGF02" 1789651 T NAGF02 (NIL) -7 NIL NIL NIL) (-770 1779456 1780556 1781673 "NAGF01" 1783135 T NAGF01 (NIL) -7 NIL NIL NIL) (-769 1773084 1774650 1776235 "NAGE04" 1777891 T NAGE04 (NIL) -7 NIL NIL NIL) (-768 1764253 1766374 1768504 "NAGE02" 1770974 T NAGE02 (NIL) -7 NIL NIL NIL) (-767 1760206 1761153 1762117 "NAGE01" 1763309 T NAGE01 (NIL) -7 NIL NIL NIL) (-766 1758001 1758535 1759093 "NAGD03" 1759668 T NAGD03 (NIL) -7 NIL NIL NIL) (-765 1749751 1751679 1753633 "NAGD02" 1756067 T NAGD02 (NIL) -7 NIL NIL NIL) (-764 1743562 1744987 1746427 "NAGD01" 1748331 T NAGD01 (NIL) -7 NIL NIL NIL) (-763 1739771 1740593 1741430 "NAGC06" 1742745 T NAGC06 (NIL) -7 NIL NIL NIL) (-762 1738236 1738568 1738924 "NAGC05" 1739435 T NAGC05 (NIL) -7 NIL NIL NIL) (-761 1737612 1737731 1737875 "NAGC02" 1738112 T NAGC02 (NIL) -7 NIL NIL NIL) (-760 1736557 1737140 1737180 "NAALG" 1737259 NIL NAALG (NIL T) -9 NIL 1737320 NIL) (-759 1736392 1736421 1736511 "NAALG-" 1736516 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-758 1730342 1731450 1732637 "MULTSQFR" 1735288 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-757 1729661 1729736 1729920 "MULTFACT" 1730254 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-756 1722332 1726246 1726299 "MTSCAT" 1727369 NIL MTSCAT (NIL T T) -9 NIL 1727884 NIL) (-755 1722044 1722098 1722190 "MTHING" 1722272 NIL MTHING (NIL T) -7 NIL NIL NIL) (-754 1721836 1721869 1721929 "MSYSCMD" 1722004 T MSYSCMD (NIL) -7 NIL NIL NIL) (-753 1717918 1720591 1720911 "MSET" 1721549 NIL MSET (NIL T) -8 NIL NIL NIL) (-752 1714987 1717479 1717520 "MSETAGG" 1717525 NIL MSETAGG (NIL T) -9 NIL 1717559 NIL) (-751 1710829 1712366 1713111 "MRING" 1714287 NIL MRING (NIL T T) -8 NIL NIL NIL) (-750 1710395 1710462 1710593 "MRF2" 1710756 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-749 1710013 1710048 1710192 "MRATFAC" 1710354 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-748 1707625 1707920 1708351 "MPRFF" 1709718 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-747 1701646 1707479 1707576 "MPOLY" 1707581 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-746 1701136 1701171 1701379 "MPCPF" 1701605 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-745 1700650 1700693 1700877 "MPC3" 1701087 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-744 1699845 1699926 1700147 "MPC2" 1700565 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-743 1698146 1698483 1698873 "MONOTOOL" 1699505 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-742 1697357 1697674 1697702 "MONOID" 1697921 T MONOID (NIL) -9 NIL 1698068 NIL) (-741 1696903 1697022 1697203 "MONOID-" 1697208 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-740 1686493 1692723 1692782 "MONOGEN" 1693456 NIL MONOGEN (NIL T T) -9 NIL 1693912 NIL) (-739 1683711 1684446 1685446 "MONOGEN-" 1685565 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-738 1682530 1682976 1683004 "MONADWU" 1683396 T MONADWU (NIL) -9 NIL 1683634 NIL) (-737 1681902 1682061 1682309 "MONADWU-" 1682314 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-736 1681247 1681491 1681519 "MONAD" 1681726 T MONAD (NIL) -9 NIL 1681838 NIL) (-735 1680932 1681010 1681142 "MONAD-" 1681147 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-734 1679221 1679845 1680124 "MOEBIUS" 1680685 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-733 1678485 1678889 1678929 "MODULE" 1678934 NIL MODULE (NIL T) -9 NIL 1678973 NIL) (-732 1678053 1678149 1678339 "MODULE-" 1678344 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-731 1675733 1676417 1676744 "MODRING" 1677877 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1672677 1673838 1674359 "MODOP" 1675262 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-729 1671265 1671744 1672021 "MODMONOM" 1672540 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-728 1661033 1669556 1669970 "MODMON" 1670902 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-727 1658189 1659877 1660153 "MODFIELD" 1660908 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1657166 1657470 1657660 "MMLFORM" 1658019 T MMLFORM (NIL) -8 NIL NIL NIL) (-725 1656692 1656735 1656914 "MMAP" 1657117 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-724 1654757 1655524 1655565 "MLO" 1655988 NIL MLO (NIL T) -9 NIL 1656230 NIL) (-723 1652123 1652639 1653241 "MLIFT" 1654238 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-722 1651514 1651598 1651752 "MKUCFUNC" 1652034 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-721 1651113 1651183 1651306 "MKRECORD" 1651437 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-720 1650160 1650322 1650550 "MKFUNC" 1650924 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-719 1649548 1649652 1649808 "MKFLCFN" 1650043 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-718 1648825 1648927 1649112 "MKBCFUNC" 1649441 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-717 1645414 1648379 1648515 "MINT" 1648709 T MINT (NIL) -8 NIL NIL NIL) (-716 1644226 1644469 1644746 "MHROWRED" 1645169 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-715 1639606 1642761 1643166 "MFLOAT" 1643841 T MFLOAT (NIL) -8 NIL NIL NIL) (-714 1638963 1639039 1639210 "MFINFACT" 1639518 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-713 1635278 1636126 1637010 "MESH" 1638099 T MESH (NIL) -7 NIL NIL NIL) (-712 1633668 1633980 1634333 "MDDFACT" 1634965 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-711 1630438 1632799 1632840 "MDAGG" 1633095 NIL MDAGG (NIL T) -9 NIL 1633238 NIL) (-710 1619132 1629731 1629938 "MCMPLX" 1630251 T MCMPLX (NIL) -8 NIL NIL NIL) (-709 1618269 1618415 1618616 "MCDEN" 1618981 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-708 1616159 1616429 1616809 "MCALCFN" 1617999 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-707 1615084 1615324 1615557 "MAYBE" 1615965 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-706 1612696 1613219 1613781 "MATSTOR" 1614555 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-705 1608608 1612068 1612316 "MATRIX" 1612481 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-704 1604374 1605081 1605817 "MATLIN" 1607965 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-703 1594200 1597431 1597508 "MATCAT" 1602540 NIL MATCAT (NIL T T T) -9 NIL 1604012 NIL) (-702 1590393 1591463 1592876 "MATCAT-" 1592881 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-701 1588987 1589140 1589473 "MATCAT2" 1590228 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-700 1587099 1587423 1587807 "MAPPKG3" 1588662 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-699 1586080 1586253 1586475 "MAPPKG2" 1586923 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-698 1584579 1584863 1585190 "MAPPKG1" 1585786 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-697 1583658 1583985 1584162 "MAPPAST" 1584422 T MAPPAST (NIL) -8 NIL NIL NIL) (-696 1583269 1583327 1583450 "MAPHACK3" 1583594 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-695 1582861 1582922 1583036 "MAPHACK2" 1583201 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-694 1582299 1582402 1582544 "MAPHACK1" 1582752 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-693 1580378 1580999 1581303 "MAGMA" 1582027 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-692 1579857 1580102 1580193 "MACROAST" 1580307 T MACROAST (NIL) -8 NIL NIL NIL) (-691 1576278 1578096 1578557 "M3D" 1579429 NIL M3D (NIL T) -8 NIL NIL NIL) (-690 1570328 1574589 1574630 "LZSTAGG" 1575412 NIL LZSTAGG (NIL T) -9 NIL 1575707 NIL) (-689 1566286 1567459 1568916 "LZSTAGG-" 1568921 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-688 1563373 1564177 1564664 "LWORD" 1565831 NIL LWORD (NIL T) -8 NIL NIL NIL) (-687 1562949 1563177 1563252 "LSTAST" 1563318 T LSTAST (NIL) -8 NIL NIL NIL) (-686 1555839 1562720 1562854 "LSQM" 1562859 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-685 1555063 1555202 1555430 "LSPP" 1555694 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-684 1552875 1553176 1553632 "LSMP" 1554752 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-683 1549654 1550328 1551058 "LSMP1" 1552177 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-682 1543456 1548744 1548785 "LSAGG" 1548847 NIL LSAGG (NIL T) -9 NIL 1548925 NIL) (-681 1540151 1541075 1542288 "LSAGG-" 1542293 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-680 1537750 1539295 1539544 "LPOLY" 1539946 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-679 1537332 1537417 1537540 "LPEFRAC" 1537659 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-678 1535653 1536426 1536679 "LO" 1537164 NIL LO (NIL T T T) -8 NIL NIL NIL) (-677 1535265 1535403 1535431 "LOGIC" 1535542 T LOGIC (NIL) -9 NIL 1535623 NIL) (-676 1535127 1535150 1535221 "LOGIC-" 1535226 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-675 1534320 1534460 1534653 "LODOOPS" 1534983 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-674 1531743 1534236 1534302 "LODO" 1534307 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1530281 1530516 1530869 "LODOF" 1531490 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-672 1526485 1528916 1528957 "LODOCAT" 1529395 NIL LODOCAT (NIL T) -9 NIL 1529606 NIL) (-671 1526218 1526276 1526403 "LODOCAT-" 1526408 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-670 1523538 1526059 1526177 "LODO2" 1526182 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-669 1520973 1523475 1523520 "LODO1" 1523525 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-668 1519854 1520019 1520324 "LODEEF" 1520796 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-667 1515132 1518020 1518061 "LNAGG" 1518923 NIL LNAGG (NIL T) -9 NIL 1519358 NIL) (-666 1514279 1514493 1514835 "LNAGG-" 1514840 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-665 1510415 1511204 1511843 "LMOPS" 1513694 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-664 1509804 1510192 1510233 "LMODULE" 1510238 NIL LMODULE (NIL T) -9 NIL 1510264 NIL) (-663 1507005 1509449 1509572 "LMDICT" 1509714 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-662 1506623 1506795 1506836 "LLINSET" 1506897 NIL LLINSET (NIL T) -9 NIL 1506941 NIL) (-661 1506322 1506531 1506591 "LITERAL" 1506596 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-660 1499488 1505256 1505560 "LIST" 1506051 NIL LIST (NIL T) -8 NIL NIL NIL) (-659 1499013 1499087 1499226 "LIST3" 1499408 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-658 1498020 1498198 1498426 "LIST2" 1498831 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-657 1496154 1496466 1496865 "LIST2MAP" 1497667 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-656 1495785 1495973 1496014 "LINSET" 1496019 NIL LINSET (NIL T) -9 NIL 1496053 NIL) (-655 1494725 1495293 1495460 "LINFORM" 1495670 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-654 1493138 1493752 1493793 "LINEXP" 1494283 NIL LINEXP (NIL T) -9 NIL 1494556 NIL) (-653 1491876 1492618 1492799 "LINELT" 1493009 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-652 1490453 1490713 1491024 "LINDEP" 1491628 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-651 1489697 1490185 1490295 "LINBASIS" 1490383 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-650 1486464 1487183 1487960 "LIMITRF" 1488952 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-649 1484767 1485063 1485472 "LIMITPS" 1486159 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-648 1479195 1484278 1484506 "LIE" 1484588 NIL LIE (NIL T T) -8 NIL NIL NIL) (-647 1478129 1478598 1478638 "LIECAT" 1478778 NIL LIECAT (NIL T) -9 NIL 1478929 NIL) (-646 1477970 1477997 1478085 "LIECAT-" 1478090 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-645 1470563 1477510 1477666 "LIB" 1477834 T LIB (NIL) -8 NIL NIL NIL) (-644 1466198 1467081 1468016 "LGROBP" 1469680 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-643 1464196 1464470 1464820 "LF" 1465919 NIL LF (NIL T T) -7 NIL NIL NIL) (-642 1463036 1463728 1463756 "LFCAT" 1463963 T LFCAT (NIL) -9 NIL 1464102 NIL) (-641 1459938 1460568 1461256 "LEXTRIPK" 1462400 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-640 1456682 1457508 1458011 "LEXP" 1459518 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-639 1456158 1456403 1456495 "LETAST" 1456610 T LETAST (NIL) -8 NIL NIL NIL) (-638 1454556 1454869 1455270 "LEADCDET" 1455840 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-637 1453746 1453820 1454049 "LAZM3PK" 1454477 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-636 1448663 1451823 1452361 "LAUPOL" 1453258 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-635 1448242 1448286 1448447 "LAPLACE" 1448613 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-634 1446181 1447343 1447594 "LA" 1448075 NIL LA (NIL T T T) -8 NIL NIL NIL) (-633 1445161 1445745 1445786 "LALG" 1445848 NIL LALG (NIL T) -9 NIL 1445907 NIL) (-632 1444875 1444934 1445070 "LALG-" 1445075 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-631 1444710 1444734 1444775 "KVTFROM" 1444837 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-630 1443633 1444077 1444262 "KTVLOGIC" 1444545 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-629 1443468 1443492 1443533 "KRCFROM" 1443595 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-628 1442372 1442559 1442858 "KOVACIC" 1443268 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-627 1442207 1442231 1442272 "KONVERT" 1442334 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-626 1442042 1442066 1442107 "KOERCE" 1442169 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-625 1439873 1440635 1441012 "KERNEL" 1441698 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-624 1439369 1439450 1439582 "KERNEL2" 1439787 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-623 1433080 1437846 1437900 "KDAGG" 1438277 NIL KDAGG (NIL T T) -9 NIL 1438483 NIL) (-622 1432609 1432733 1432938 "KDAGG-" 1432943 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-621 1425757 1432270 1432425 "KAFILE" 1432487 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-620 1420185 1425268 1425496 "JORDAN" 1425578 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1419564 1419834 1419955 "JOINAST" 1420084 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1419410 1419469 1419524 "JAVACODE" 1419529 T JAVACODE (NIL) -8 NIL NIL NIL) (-617 1415637 1417587 1417641 "IXAGG" 1418570 NIL IXAGG (NIL T T) -9 NIL 1419029 NIL) (-616 1414556 1414862 1415281 "IXAGG-" 1415286 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-615 1410089 1414478 1414537 "IVECTOR" 1414542 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-614 1408855 1409092 1409358 "ITUPLE" 1409856 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-613 1407357 1407534 1407829 "ITRIGMNP" 1408677 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-612 1406102 1406306 1406589 "ITFUN3" 1407133 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-611 1405734 1405791 1405900 "ITFUN2" 1406039 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-610 1404893 1405214 1405388 "ITFORM" 1405580 T ITFORM (NIL) -8 NIL NIL NIL) (-609 1402854 1403913 1404191 "ITAYLOR" 1404648 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-608 1391799 1396991 1398154 "ISUPS" 1401724 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-607 1390903 1391043 1391279 "ISUMP" 1391646 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-606 1386281 1390848 1390889 "ISTRING" 1390894 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-605 1385757 1386002 1386094 "ISAST" 1386209 T ISAST (NIL) -8 NIL NIL NIL) (-604 1384966 1385048 1385264 "IRURPK" 1385671 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-603 1383902 1384103 1384343 "IRSN" 1384746 T IRSN (NIL) -7 NIL NIL NIL) (-602 1381973 1382328 1382757 "IRRF2F" 1383540 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-601 1381720 1381758 1381834 "IRREDFFX" 1381929 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-600 1380335 1380594 1380893 "IROOT" 1381453 NIL IROOT (NIL T) -7 NIL NIL NIL) (-599 1376939 1378019 1378711 "IR" 1379675 NIL IR (NIL T) -8 NIL NIL NIL) (-598 1376144 1376432 1376583 "IRFORM" 1376808 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1373757 1374252 1374818 "IR2" 1375622 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-596 1372857 1372970 1373184 "IR2F" 1373640 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-595 1372648 1372682 1372742 "IPRNTPK" 1372817 T IPRNTPK (NIL) -7 NIL NIL NIL) (-594 1369229 1372537 1372606 "IPF" 1372611 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-593 1367556 1369154 1369211 "IPADIC" 1369216 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-592 1366868 1367116 1367246 "IP4ADDR" 1367446 T IP4ADDR (NIL) -8 NIL NIL NIL) (-591 1366242 1366497 1366629 "IOMODE" 1366756 T IOMODE (NIL) -8 NIL NIL NIL) (-590 1365315 1365839 1365966 "IOBFILE" 1366135 T IOBFILE (NIL) -8 NIL NIL NIL) (-589 1364803 1365219 1365247 "IOBCON" 1365252 T IOBCON (NIL) -9 NIL 1365273 NIL) (-588 1364314 1364372 1364555 "INVLAPLA" 1364739 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-587 1353962 1356316 1358702 "INTTR" 1361978 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-586 1350297 1351039 1351904 "INTTOOLS" 1353147 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-585 1349883 1349974 1350091 "INTSLPE" 1350200 T INTSLPE (NIL) -7 NIL NIL NIL) (-584 1347836 1349806 1349865 "INTRVL" 1349870 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-583 1345438 1345950 1346525 "INTRF" 1347321 NIL INTRF (NIL T) -7 NIL NIL NIL) (-582 1344849 1344946 1345088 "INTRET" 1345336 NIL INTRET (NIL T) -7 NIL NIL NIL) (-581 1342846 1343235 1343705 "INTRAT" 1344457 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-580 1340109 1340692 1341311 "INTPM" 1342331 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-579 1336854 1337453 1338191 "INTPAF" 1339495 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-578 1332033 1332995 1334046 "INTPACK" 1335823 T INTPACK (NIL) -7 NIL NIL NIL) (-577 1328845 1331830 1331939 "INT" 1331944 T INT (NIL) -8 NIL NIL NIL) (-576 1328097 1328249 1328457 "INTHERTR" 1328687 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1327536 1327616 1327804 "INTHERAL" 1328011 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1325382 1325825 1326282 "INTHEORY" 1327099 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1316788 1318409 1320181 "INTG0" 1323734 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1297361 1302151 1306961 "INTFTBL" 1311998 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1296610 1296748 1296921 "INTFACT" 1297220 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1294037 1294483 1295040 "INTEF" 1296164 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1292390 1293129 1293157 "INTDOM" 1293458 T INTDOM (NIL) -9 NIL 1293665 NIL) (-568 1291759 1291933 1292175 "INTDOM-" 1292180 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1288119 1290048 1290102 "INTCAT" 1290901 NIL INTCAT (NIL T) -9 NIL 1291222 NIL) (-566 1287591 1287694 1287822 "INTBIT" 1288011 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1286290 1286444 1286751 "INTALG" 1287436 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1285773 1285863 1286020 "INTAF" 1286194 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1279122 1285583 1285723 "INTABL" 1285728 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1278455 1278921 1278986 "INT8" 1279020 T INT8 (NIL) -8 NIL NIL 1279065) (-561 1277787 1278253 1278318 "INT64" 1278352 T INT64 (NIL) -8 NIL NIL 1278397) (-560 1277119 1277585 1277650 "INT32" 1277684 T INT32 (NIL) -8 NIL NIL 1277729) (-559 1276451 1276917 1276982 "INT16" 1277016 T INT16 (NIL) -8 NIL NIL 1277061) (-558 1271146 1273999 1274027 "INS" 1274961 T INS (NIL) -9 NIL 1275626 NIL) (-557 1268386 1269157 1270131 "INS-" 1270204 NIL INS- (NIL T) -8 NIL NIL NIL) (-556 1267161 1267388 1267686 "INPSIGN" 1268139 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-555 1266279 1266396 1266593 "INPRODPF" 1267041 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-554 1265173 1265290 1265527 "INPRODFF" 1266159 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-553 1264173 1264325 1264585 "INNMFACT" 1265009 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-552 1263370 1263467 1263655 "INMODGCD" 1264072 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-551 1261878 1262123 1262447 "INFSP" 1263115 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-550 1261062 1261179 1261362 "INFPROD0" 1261758 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-549 1257917 1259127 1259642 "INFORM" 1260555 T INFORM (NIL) -8 NIL NIL NIL) (-548 1257527 1257587 1257685 "INFORM1" 1257852 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1257050 1257139 1257253 "INFINITY" 1257433 T INFINITY (NIL) -7 NIL NIL NIL) (-546 1256226 1256770 1256871 "INETCLTS" 1256969 T INETCLTS (NIL) -8 NIL NIL NIL) (-545 1254842 1255092 1255413 "INEP" 1255974 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-544 1254047 1254739 1254804 "INDE" 1254809 NIL INDE (NIL T) -8 NIL NIL NIL) (-543 1253611 1253679 1253796 "INCRMAPS" 1253974 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-542 1252429 1252880 1253086 "INBFILE" 1253425 T INBFILE (NIL) -8 NIL NIL NIL) (-541 1247728 1248665 1249609 "INBFF" 1251517 NIL INBFF (NIL T) -7 NIL NIL NIL) (-540 1246636 1246905 1246933 "INBCON" 1247446 T INBCON (NIL) -9 NIL 1247712 NIL) (-539 1245888 1246111 1246387 "INBCON-" 1246392 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-538 1245367 1245612 1245703 "INAST" 1245817 T INAST (NIL) -8 NIL NIL NIL) (-537 1244794 1245046 1245152 "IMPTAST" 1245281 T IMPTAST (NIL) -8 NIL NIL NIL) (-536 1241195 1244638 1244742 "IMATRIX" 1244747 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-535 1239903 1240026 1240342 "IMATQF" 1241051 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-534 1238123 1238350 1238687 "IMATLIN" 1239659 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-533 1232704 1238047 1238105 "ILIST" 1238110 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-532 1230612 1232564 1232677 "IIARRAY2" 1232682 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-531 1226010 1230523 1230587 "IFF" 1230592 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-530 1225357 1225627 1225743 "IFAST" 1225914 T IFAST (NIL) -8 NIL NIL NIL) (-529 1220355 1224649 1224837 "IFARRAY" 1225214 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-528 1219535 1220259 1220332 "IFAMON" 1220337 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-527 1219119 1219184 1219238 "IEVALAB" 1219445 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-526 1218794 1218862 1219022 "IEVALAB-" 1219027 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-525 1218241 1218709 1218771 "IDPO" 1218776 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-524 1217449 1218130 1218205 "IDPOAMS" 1218210 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1216714 1217338 1217413 "IDPOAM" 1217418 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1215260 1215721 1215773 "IDPC" 1216285 NIL IDPC (NIL T T) -9 NIL 1216566 NIL) (-521 1214688 1215152 1215225 "IDPAM" 1215230 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-520 1214023 1214580 1214653 "IDPAG" 1214658 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-519 1213668 1213859 1213934 "IDENT" 1213968 T IDENT (NIL) -8 NIL NIL NIL) (-518 1209923 1210771 1211666 "IDECOMP" 1212825 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-517 1202760 1203846 1204893 "IDEAL" 1208959 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-516 1201920 1202032 1202232 "ICDEN" 1202644 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-515 1200991 1201400 1201547 "ICARD" 1201793 T ICARD (NIL) -8 NIL NIL NIL) (-514 1199051 1199364 1199769 "IBPTOOLS" 1200668 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-513 1194658 1198671 1198784 "IBITS" 1198970 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-512 1191381 1191957 1192652 "IBATOOL" 1194075 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-511 1189160 1189622 1190155 "IBACHIN" 1190916 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-510 1186992 1189006 1189109 "IARRAY2" 1189114 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-509 1183101 1186918 1186975 "IARRAY1" 1186980 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-508 1176961 1181513 1181994 "IAN" 1182640 T IAN (NIL) -8 NIL NIL NIL) (-507 1176472 1176529 1176702 "IALGFACT" 1176898 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-506 1176000 1176113 1176141 "HYPCAT" 1176348 T HYPCAT (NIL) -9 NIL NIL NIL) (-505 1175538 1175655 1175841 "HYPCAT-" 1175846 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-504 1175133 1175333 1175416 "HOSTNAME" 1175475 T HOSTNAME (NIL) -8 NIL NIL NIL) (-503 1174978 1175015 1175056 "HOMOTOP" 1175061 NIL HOMOTOP (NIL T) -9 NIL 1175094 NIL) (-502 1171535 1172910 1172951 "HOAGG" 1173932 NIL HOAGG (NIL T) -9 NIL 1174661 NIL) (-501 1170129 1170528 1171054 "HOAGG-" 1171059 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-500 1163845 1169722 1169872 "HEXADEC" 1169999 T HEXADEC (NIL) -8 NIL NIL NIL) (-499 1162593 1162815 1163078 "HEUGCD" 1163622 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-498 1161669 1162430 1162560 "HELLFDIV" 1162565 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-497 1159851 1161446 1161534 "HEAP" 1161613 NIL HEAP (NIL T) -8 NIL NIL NIL) (-496 1159114 1159403 1159537 "HEADAST" 1159737 T HEADAST (NIL) -8 NIL NIL NIL) (-495 1152957 1159029 1159091 "HDP" 1159096 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-494 1146669 1152592 1152744 "HDMP" 1152858 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-493 1145993 1146133 1146297 "HB" 1146525 T HB (NIL) -7 NIL NIL NIL) (-492 1139385 1145839 1145943 "HASHTBL" 1145948 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-491 1138861 1139106 1139198 "HASAST" 1139313 T HASAST (NIL) -8 NIL NIL NIL) (-490 1136639 1138483 1138665 "HACKPI" 1138699 T HACKPI (NIL) -8 NIL NIL NIL) (-489 1132307 1136492 1136605 "GTSET" 1136610 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-488 1125728 1132185 1132283 "GSTBL" 1132288 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-487 1118115 1124893 1125149 "GSERIES" 1125528 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-486 1117242 1117659 1117687 "GROUP" 1117890 T GROUP (NIL) -9 NIL 1118024 NIL) (-485 1116608 1116767 1117018 "GROUP-" 1117023 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-484 1114975 1115296 1115683 "GROEBSOL" 1116285 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-483 1113875 1114163 1114214 "GRMOD" 1114743 NIL GRMOD (NIL T T) -9 NIL 1114911 NIL) (-482 1113643 1113679 1113807 "GRMOD-" 1113812 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-481 1108933 1109997 1110997 "GRIMAGE" 1112663 T GRIMAGE (NIL) -8 NIL NIL NIL) (-480 1107399 1107660 1107984 "GRDEF" 1108629 T GRDEF (NIL) -7 NIL NIL NIL) (-479 1106843 1106959 1107100 "GRAY" 1107278 T GRAY (NIL) -7 NIL NIL NIL) (-478 1106016 1106422 1106473 "GRALG" 1106626 NIL GRALG (NIL T T) -9 NIL 1106719 NIL) (-477 1105677 1105750 1105913 "GRALG-" 1105918 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-476 1102452 1105260 1105439 "GPOLSET" 1105583 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-475 1101806 1101863 1102121 "GOSPER" 1102389 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-474 1097538 1098244 1098770 "GMODPOL" 1101505 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-473 1096543 1096727 1096965 "GHENSEL" 1097350 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-472 1090699 1091542 1092562 "GENUPS" 1095627 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-471 1090396 1090447 1090536 "GENUFACT" 1090642 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-470 1089808 1089885 1090050 "GENPGCD" 1090314 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-469 1089282 1089317 1089530 "GENMFACT" 1089767 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-468 1087848 1088105 1088412 "GENEEZ" 1089025 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-467 1081720 1087459 1087621 "GDMP" 1087771 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-466 1071063 1075491 1076597 "GCNAALG" 1080703 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-465 1069376 1070238 1070266 "GCDDOM" 1070521 T GCDDOM (NIL) -9 NIL 1070678 NIL) (-464 1068846 1068973 1069188 "GCDDOM-" 1069193 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-463 1067518 1067703 1068007 "GB" 1068625 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-462 1056134 1058464 1060856 "GBINTERN" 1065209 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1053971 1054263 1054684 "GBF" 1055809 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1052752 1052917 1053184 "GBEUCLID" 1053787 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1052101 1052226 1052375 "GAUSSFAC" 1052623 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-458 1050468 1050770 1051084 "GALUTIL" 1051820 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-457 1048776 1049050 1049374 "GALPOLYU" 1050195 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-456 1046141 1046431 1046838 "GALFACTU" 1048473 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-455 1037947 1039446 1041054 "GALFACT" 1044573 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-454 1035335 1035993 1036021 "FVFUN" 1037177 T FVFUN (NIL) -9 NIL 1037897 NIL) (-453 1034601 1034783 1034811 "FVC" 1035102 T FVC (NIL) -9 NIL 1035285 NIL) (-452 1034244 1034426 1034494 "FUNDESC" 1034553 T FUNDESC (NIL) -8 NIL NIL NIL) (-451 1033859 1034041 1034122 "FUNCTION" 1034196 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-450 1031603 1032181 1032647 "FT" 1033413 T FT (NIL) -8 NIL NIL NIL) (-449 1030394 1030904 1031107 "FTEM" 1031420 T FTEM (NIL) -8 NIL NIL NIL) (-448 1028685 1028974 1029371 "FSUPFACT" 1030085 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-447 1027082 1027371 1027703 "FST" 1028373 T FST (NIL) -8 NIL NIL NIL) (-446 1026281 1026387 1026575 "FSRED" 1026964 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-445 1024980 1025236 1025583 "FSPRMELT" 1025996 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-444 1022286 1022724 1023210 "FSPECF" 1024543 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-443 1003351 1012060 1012101 "FS" 1015985 NIL FS (NIL T) -9 NIL 1018274 NIL) (-442 991994 994987 999044 "FS-" 999344 NIL FS- (NIL T T) -8 NIL NIL NIL) (-441 991522 991576 991746 "FSINT" 991935 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-440 989814 990515 990818 "FSERIES" 991301 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-439 988856 988972 989196 "FSCINT" 989694 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-438 985064 987800 987841 "FSAGG" 988211 NIL FSAGG (NIL T) -9 NIL 988470 NIL) (-437 982826 983427 984223 "FSAGG-" 984318 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 981868 982011 982238 "FSAGG2" 982679 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-435 979546 979826 980374 "FS2UPS" 981586 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-434 979180 979223 979352 "FS2" 979497 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 978058 978229 978531 "FS2EXPXP" 979005 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-432 977484 977599 977751 "FRUTIL" 977938 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-431 968897 972979 974337 "FR" 976158 NIL FR (NIL T) -8 NIL NIL NIL) (-430 963911 966586 966626 "FRNAALG" 967946 NIL FRNAALG (NIL T) -9 NIL 968544 NIL) (-429 959584 960660 961935 "FRNAALG-" 962685 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 959222 959265 959392 "FRNAAF2" 959535 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 957597 958071 958367 "FRMOD" 959034 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 955340 955972 956290 "FRIDEAL" 957388 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-425 954531 954618 954909 "FRIDEAL2" 955247 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-424 953664 954078 954119 "FRETRCT" 954124 NIL FRETRCT (NIL T) -9 NIL 954300 NIL) (-423 952776 953007 953358 "FRETRCT-" 953363 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 949850 951060 951119 "FRAMALG" 952001 NIL FRAMALG (NIL T T) -9 NIL 952293 NIL) (-421 947984 948439 949069 "FRAMALG-" 949292 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 941627 947457 947734 "FRAC" 947739 NIL FRAC (NIL T) -8 NIL NIL NIL) (-419 941263 941320 941427 "FRAC2" 941564 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-418 940899 940956 941063 "FR2" 941200 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 935384 938278 938306 "FPS" 939425 T FPS (NIL) -9 NIL 939982 NIL) (-416 934833 934942 935106 "FPS-" 935252 NIL FPS- (NIL T) -8 NIL NIL NIL) (-415 932121 933790 933818 "FPC" 934043 T FPC (NIL) -9 NIL 934185 NIL) (-414 931914 931954 932051 "FPC-" 932056 NIL FPC- (NIL T) -8 NIL NIL NIL) (-413 930704 931402 931443 "FPATMAB" 931448 NIL FPATMAB (NIL T) -9 NIL 931600 NIL) (-412 928943 929446 929793 "FPARFRAC" 930420 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-411 924337 924835 925517 "FORTRAN" 928375 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-410 922053 922553 923092 "FORT" 923818 T FORT (NIL) -7 NIL NIL NIL) (-409 919729 920291 920319 "FORTFN" 921379 T FORTFN (NIL) -9 NIL 922003 NIL) (-408 919493 919543 919571 "FORTCAT" 919630 T FORTCAT (NIL) -9 NIL 919692 NIL) (-407 917599 918109 918499 "FORMULA" 919123 T FORMULA (NIL) -8 NIL NIL NIL) (-406 917387 917417 917486 "FORMULA1" 917563 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-405 916910 916962 917135 "FORDER" 917329 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-404 916006 916170 916363 "FOP" 916737 T FOP (NIL) -7 NIL NIL NIL) (-403 914587 915286 915460 "FNLA" 915888 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-402 913302 913717 913745 "FNCAT" 914205 T FNCAT (NIL) -9 NIL 914465 NIL) (-401 912841 913261 913289 "FNAME" 913294 T FNAME (NIL) -8 NIL NIL NIL) (-400 911377 912340 912368 "FMTC" 912373 T FMTC (NIL) -9 NIL 912409 NIL) (-399 910123 911313 911359 "FMONOID" 911364 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-398 906910 908078 908119 "FMONCAT" 909336 NIL FMONCAT (NIL T) -9 NIL 909941 NIL) (-397 906060 906652 906801 "FM" 906806 NIL FM (NIL T T) -8 NIL NIL NIL) (-396 903484 904130 904158 "FMFUN" 905302 T FMFUN (NIL) -9 NIL 906010 NIL) (-395 902753 902934 902962 "FMC" 903252 T FMC (NIL) -9 NIL 903434 NIL) (-394 899818 900678 900732 "FMCAT" 901927 NIL FMCAT (NIL T T) -9 NIL 902422 NIL) (-393 898684 899584 899684 "FM1" 899763 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-392 896458 896874 897368 "FLOATRP" 898235 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-391 890036 894187 894808 "FLOAT" 895857 T FLOAT (NIL) -8 NIL NIL NIL) (-390 887474 887974 888552 "FLOATCP" 889503 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-389 886122 887066 887107 "FLINEXP" 887112 NIL FLINEXP (NIL T) -9 NIL 887205 NIL) (-388 885276 885511 885839 "FLINEXP-" 885844 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-387 884352 884496 884720 "FLASORT" 885128 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-386 881454 882322 882374 "FLALG" 883601 NIL FLALG (NIL T T) -9 NIL 884068 NIL) (-385 875114 878863 878904 "FLAGG" 880166 NIL FLAGG (NIL T) -9 NIL 880818 NIL) (-384 873840 874179 874669 "FLAGG-" 874674 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 872882 873025 873252 "FLAGG2" 873693 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-382 869719 870727 870786 "FINRALG" 871914 NIL FINRALG (NIL T T) -9 NIL 872422 NIL) (-381 868879 869108 869447 "FINRALG-" 869452 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-380 868245 868484 868512 "FINITE" 868708 T FINITE (NIL) -9 NIL 868815 NIL) (-379 860588 862775 862815 "FINAALG" 866482 NIL FINAALG (NIL T) -9 NIL 867935 NIL) (-378 855920 856970 858114 "FINAALG-" 859493 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-377 855288 855675 855778 "FILE" 855850 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 853932 854270 854324 "FILECAT" 855008 NIL FILECAT (NIL T T) -9 NIL 855224 NIL) (-375 851634 853162 853190 "FIELD" 853230 T FIELD (NIL) -9 NIL 853310 NIL) (-374 850254 850639 851150 "FIELD-" 851155 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-373 848104 848889 849236 "FGROUP" 849940 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-372 847194 847358 847578 "FGLMICPK" 847936 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-371 843026 847119 847176 "FFX" 847181 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-370 842627 842688 842823 "FFSLPE" 842959 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-369 838617 839399 840195 "FFPOLY" 841863 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 838121 838157 838366 "FFPOLY2" 838575 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-367 833967 838040 838103 "FFP" 838108 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-366 829365 833878 833942 "FF" 833947 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-365 824491 828708 828898 "FFNBX" 829219 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-364 819419 823626 823884 "FFNBP" 824345 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-363 814052 818703 818914 "FFNB" 819252 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-362 812884 813082 813397 "FFINTBAS" 813849 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-361 808910 811131 811159 "FFIELDC" 811779 T FFIELDC (NIL) -9 NIL 812155 NIL) (-360 807572 807943 808440 "FFIELDC-" 808445 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-359 807141 807187 807311 "FFHOM" 807514 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-358 804836 805323 805840 "FFF" 806656 NIL FFF (NIL T) -7 NIL NIL NIL) (-357 800454 804578 804679 "FFCGX" 804779 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-356 796076 800186 800293 "FFCGP" 800397 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-355 791259 795803 795911 "FFCG" 796012 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-354 770788 780991 781077 "FFCAT" 786242 NIL FFCAT (NIL T T T) -9 NIL 787693 NIL) (-353 765985 767033 768347 "FFCAT-" 769577 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-352 765396 765439 765674 "FFCAT2" 765936 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-351 754719 758368 759588 "FEXPR" 764248 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-350 753681 754116 754157 "FEVALAB" 754241 NIL FEVALAB (NIL T) -9 NIL 754502 NIL) (-349 752840 753050 753388 "FEVALAB-" 753393 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-348 751406 752223 752426 "FDIV" 752739 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-347 748412 749153 749268 "FDIVCAT" 750836 NIL FDIVCAT (NIL T T T T) -9 NIL 751273 NIL) (-346 748174 748201 748371 "FDIVCAT-" 748376 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-345 747394 747481 747758 "FDIV2" 748081 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 746368 746689 746891 "FCTRDATA" 747212 T FCTRDATA (NIL) -8 NIL NIL NIL) (-343 745054 745313 745602 "FCPAK1" 746099 T FCPAK1 (NIL) -7 NIL NIL NIL) (-342 744153 744554 744695 "FCOMP" 744945 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-341 727858 731303 734841 "FC" 740635 T FC (NIL) -8 NIL NIL NIL) (-340 720151 724179 724219 "FAXF" 726021 NIL FAXF (NIL T) -9 NIL 726713 NIL) (-339 717428 718085 718910 "FAXF-" 719375 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-338 712483 716804 716980 "FARRAY" 717285 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-337 707363 709430 709483 "FAMR" 710506 NIL FAMR (NIL T T) -9 NIL 710966 NIL) (-336 706253 706555 706990 "FAMR-" 706995 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-335 705422 706175 706228 "FAMONOID" 706233 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-334 703194 703904 703957 "FAMONC" 704898 NIL FAMONC (NIL T T) -9 NIL 705284 NIL) (-333 701858 702948 703085 "FAGROUP" 703090 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-332 699653 699972 700375 "FACUTIL" 701539 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-331 698752 698937 699159 "FACTFUNC" 699463 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-330 691174 698055 698254 "EXPUPXS" 698608 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-329 688657 689197 689783 "EXPRTUBE" 690608 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-328 684928 685520 686250 "EXPRODE" 687996 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-327 670412 683577 684006 "EXPR" 684532 NIL EXPR (NIL T) -8 NIL NIL NIL) (-326 664966 665553 666359 "EXPR2UPS" 669710 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-325 664598 664655 664764 "EXPR2" 664903 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-324 655595 663749 664040 "EXPEXPAN" 664434 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-323 655395 655552 655581 "EXIT" 655586 T EXIT (NIL) -8 NIL NIL NIL) (-322 654875 655119 655210 "EXITAST" 655324 T EXITAST (NIL) -8 NIL NIL NIL) (-321 654502 654564 654677 "EVALCYC" 654807 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-320 654043 654161 654202 "EVALAB" 654372 NIL EVALAB (NIL T) -9 NIL 654476 NIL) (-319 653524 653646 653867 "EVALAB-" 653872 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-318 650878 652180 652208 "EUCDOM" 652763 T EUCDOM (NIL) -9 NIL 653113 NIL) (-317 649283 649725 650315 "EUCDOM-" 650320 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-316 636822 639581 642331 "ESTOOLS" 646553 T ESTOOLS (NIL) -7 NIL NIL NIL) (-315 636454 636511 636620 "ESTOOLS2" 636759 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-314 636205 636247 636327 "ESTOOLS1" 636406 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-313 630228 631836 631864 "ES" 634632 T ES (NIL) -9 NIL 636042 NIL) (-312 625175 626462 628279 "ES-" 628443 NIL ES- (NIL T) -8 NIL NIL NIL) (-311 621549 622310 623090 "ESCONT" 624415 T ESCONT (NIL) -7 NIL NIL NIL) (-310 621294 621326 621408 "ESCONT1" 621511 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-309 620969 621019 621119 "ES2" 621238 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-308 620599 620657 620766 "ES1" 620905 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-307 619815 619944 620120 "ERROR" 620443 T ERROR (NIL) -7 NIL NIL NIL) (-306 613213 619674 619765 "EQTBL" 619770 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-305 605716 608527 609976 "EQ" 611797 NIL -3037 (NIL T) -8 NIL NIL NIL) (-304 605348 605405 605514 "EQ2" 605653 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-303 600639 601686 602779 "EP" 604287 NIL EP (NIL T) -7 NIL NIL NIL) (-302 599239 599530 599836 "ENV" 600353 T ENV (NIL) -8 NIL NIL NIL) (-301 598319 598873 598901 "ENTIRER" 598906 T ENTIRER (NIL) -9 NIL 598952 NIL) (-300 595013 596501 596862 "EMR" 598127 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-299 594143 594328 594382 "ELTAGG" 594762 NIL ELTAGG (NIL T T) -9 NIL 594973 NIL) (-298 593862 593924 594065 "ELTAGG-" 594070 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-297 593626 593655 593709 "ELTAB" 593793 NIL ELTAB (NIL T T) -9 NIL 593845 NIL) (-296 592752 592898 593097 "ELFUTS" 593477 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-295 592494 592550 592578 "ELEMFUN" 592683 T ELEMFUN (NIL) -9 NIL NIL NIL) (-294 592364 592385 592453 "ELEMFUN-" 592458 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-293 587153 590406 590447 "ELAGG" 591387 NIL ELAGG (NIL T) -9 NIL 591850 NIL) (-292 585438 585872 586535 "ELAGG-" 586540 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-291 584750 584887 585043 "ELABOR" 585302 T ELABOR (NIL) -8 NIL NIL NIL) (-290 583411 583690 583984 "ELABEXPR" 584476 T ELABEXPR (NIL) -8 NIL NIL NIL) (-289 576245 578048 578877 "EFUPXS" 582686 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-288 569693 571494 572305 "EFULS" 575520 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-287 567178 567536 568008 "EFSTRUC" 569325 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-286 556969 558535 560083 "EF" 565693 NIL EF (NIL T T) -7 NIL NIL NIL) (-285 556043 556454 556603 "EAB" 556840 T EAB (NIL) -8 NIL NIL NIL) (-284 555225 556002 556030 "E04UCFA" 556035 T E04UCFA (NIL) -8 NIL NIL NIL) (-283 554407 555184 555212 "E04NAFA" 555217 T E04NAFA (NIL) -8 NIL NIL NIL) (-282 553589 554366 554394 "E04MBFA" 554399 T E04MBFA (NIL) -8 NIL NIL NIL) (-281 552771 553548 553576 "E04JAFA" 553581 T E04JAFA (NIL) -8 NIL NIL NIL) (-280 551955 552730 552758 "E04GCFA" 552763 T E04GCFA (NIL) -8 NIL NIL NIL) (-279 551139 551914 551942 "E04FDFA" 551947 T E04FDFA (NIL) -8 NIL NIL NIL) (-278 550321 551098 551126 "E04DGFA" 551131 T E04DGFA (NIL) -8 NIL NIL NIL) (-277 544494 545846 547210 "E04AGNT" 548977 T E04AGNT (NIL) -7 NIL NIL NIL) (-276 543252 543795 543835 "DVARCAT" 544176 NIL DVARCAT (NIL T) -9 NIL 544339 NIL) (-275 542456 542668 542982 "DVARCAT-" 542987 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-274 535317 542255 542384 "DSMP" 542389 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-273 533740 534459 534500 "DSEXT" 534863 NIL DSEXT (NIL T) -9 NIL 535157 NIL) (-272 532025 532453 533119 "DSEXT-" 533124 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-271 526806 527970 529038 "DROPT" 530977 T DROPT (NIL) -8 NIL NIL NIL) (-270 526471 526530 526628 "DROPT1" 526741 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-269 521586 522712 523849 "DROPT0" 525354 T DROPT0 (NIL) -7 NIL NIL NIL) (-268 519931 520256 520642 "DRAWPT" 521220 T DRAWPT (NIL) -7 NIL NIL NIL) (-267 514518 515441 516520 "DRAW" 518905 NIL DRAW (NIL T) -7 NIL NIL NIL) (-266 514151 514204 514322 "DRAWHACK" 514459 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-265 512882 513151 513442 "DRAWCX" 513880 T DRAWCX (NIL) -7 NIL NIL NIL) (-264 512397 512466 512617 "DRAWCURV" 512808 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-263 502865 504827 506942 "DRAWCFUN" 510302 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-262 499604 501530 501571 "DQAGG" 502200 NIL DQAGG (NIL T) -9 NIL 502474 NIL) (-261 487069 493815 493898 "DPOLCAT" 495750 NIL DPOLCAT (NIL T T T T) -9 NIL 496295 NIL) (-260 481906 483254 485212 "DPOLCAT-" 485217 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-259 475253 481767 481865 "DPMO" 481870 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-258 468503 475033 475200 "DPMM" 475205 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-257 468073 468287 468376 "DOMTMPLT" 468434 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-256 467506 467875 467955 "DOMCTOR" 468013 T DOMCTOR (NIL) -8 NIL NIL NIL) (-255 466718 466986 467137 "DOMAIN" 467375 T DOMAIN (NIL) -8 NIL NIL NIL) (-254 460430 466353 466505 "DMP" 466619 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-253 458375 459497 459538 "DMEXT" 459543 NIL DMEXT (NIL T) -9 NIL 459719 NIL) (-252 457975 458031 458175 "DLP" 458313 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 451800 457302 457492 "DLIST" 457817 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 448572 450625 450666 "DLAGG" 451216 NIL DLAGG (NIL T) -9 NIL 451446 NIL) (-249 447234 447898 447926 "DIVRING" 448018 T DIVRING (NIL) -9 NIL 448101 NIL) (-248 446471 446661 446961 "DIVRING-" 446966 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 444573 444930 445336 "DISPLAY" 446085 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 438436 444487 444550 "DIRPROD" 444555 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 437284 437487 437752 "DIRPROD2" 438229 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 425959 431995 432048 "DIRPCAT" 432306 NIL DIRPCAT (NIL NIL T) -9 NIL 433181 NIL) (-243 423285 423927 424808 "DIRPCAT-" 425145 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 422572 422732 422918 "DIOSP" 423119 T DIOSP (NIL) -7 NIL NIL NIL) (-241 419202 421456 421497 "DIOPS" 421931 NIL DIOPS (NIL T) -9 NIL 422160 NIL) (-240 418751 418865 419056 "DIOPS-" 419061 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 417802 418430 418458 "DIFRING" 418463 T DIFRING (NIL) -9 NIL 418485 NIL) (-238 417474 417548 417576 "DIFFSPC" 417695 T DIFFSPC (NIL) -9 NIL 417770 NIL) (-237 417119 417197 417349 "DIFFSPC-" 417354 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 416175 416653 416694 "DIFFMOD" 416699 NIL DIFFMOD (NIL T) -9 NIL 416797 NIL) (-235 415883 415928 415969 "DIFFDOM" 416090 NIL DIFFDOM (NIL T) -9 NIL 416158 NIL) (-234 415736 415760 415844 "DIFFDOM-" 415849 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 413668 414940 414981 "DIFEXT" 414986 NIL DIFEXT (NIL T) -9 NIL 415139 NIL) (-232 410918 413172 413213 "DIAGG" 413218 NIL DIAGG (NIL T) -9 NIL 413238 NIL) (-231 410302 410459 410711 "DIAGG-" 410716 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-230 405674 409261 409538 "DHMATRIX" 410071 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-229 401286 402195 403205 "DFSFUN" 404684 T DFSFUN (NIL) -7 NIL NIL NIL) (-228 396364 400217 400529 "DFLOAT" 400994 T DFLOAT (NIL) -8 NIL NIL NIL) (-227 394627 394908 395297 "DFINTTLS" 396072 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-226 391656 392648 393048 "DERHAM" 394293 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-225 389460 391431 391520 "DEQUEUE" 391600 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-224 388714 388847 389030 "DEGRED" 389322 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-223 385144 385889 386735 "DEFINTRF" 387942 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-222 382699 383168 383760 "DEFINTEF" 384663 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-221 382049 382319 382434 "DEFAST" 382604 T DEFAST (NIL) -8 NIL NIL NIL) (-220 375765 381642 381792 "DECIMAL" 381919 T DECIMAL (NIL) -8 NIL NIL NIL) (-219 373277 373735 374241 "DDFACT" 375309 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-218 372873 372916 373067 "DBLRESP" 373228 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-217 372176 372643 372734 "DBASIS" 372822 NIL DBASIS (NIL NIL) -8 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 3266845 3266850 3266855 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3266830 3266835 3266840 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3266815 3266820 3266825 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3266800 3266805 3266810 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1321 3265943 3266675 3266752 "ZMOD" 3266757 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1320 3264997 3265161 3265384 "ZLINDEP" 3265775 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1319 3254297 3256065 3258037 "ZDSOLVE" 3263127 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1318 3253543 3253684 3253873 "YSTREAM" 3254143 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1317 3252971 3253217 3253330 "YDIAGRAM" 3253452 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1316 3250745 3252272 3252476 "XRPOLY" 3252814 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1315 3247298 3248616 3249191 "XPR" 3250217 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1314 3245019 3246629 3246833 "XPOLY" 3247129 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1313 3242658 3244026 3244081 "XPOLYC" 3244369 NIL XPOLYC (NIL T T) -9 NIL 3244482 NIL) (-1312 3239034 3241175 3241563 "XPBWPOLY" 3242316 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1311 3234715 3237010 3237052 "XF" 3237673 NIL XF (NIL T) -9 NIL 3238073 NIL) (-1310 3234336 3234424 3234593 "XF-" 3234598 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1309 3229518 3230807 3230862 "XFALG" 3233034 NIL XFALG (NIL T T) -9 NIL 3233823 NIL) (-1308 3228651 3228755 3228960 "XEXPPKG" 3229410 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1307 3226760 3228501 3228597 "XDPOLY" 3228602 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1306 3225553 3226153 3226196 "XALG" 3226201 NIL XALG (NIL T) -9 NIL 3226312 NIL) (-1305 3218995 3223530 3224024 "WUTSET" 3225145 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1304 3217251 3218047 3218370 "WP" 3218806 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1303 3216853 3217073 3217143 "WHILEAST" 3217203 T WHILEAST (NIL) -8 NIL NIL NIL) (-1302 3216325 3216570 3216664 "WHEREAST" 3216781 T WHEREAST (NIL) -8 NIL NIL NIL) (-1301 3215211 3215409 3215704 "WFFINTBS" 3216122 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1300 3213115 3213542 3214004 "WEIER" 3214783 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1299 3212147 3212597 3212639 "VSPACE" 3212775 NIL VSPACE (NIL T) -9 NIL 3212849 NIL) (-1298 3211985 3212012 3212103 "VSPACE-" 3212108 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1297 3211794 3211836 3211904 "VOID" 3211939 T VOID (NIL) -8 NIL NIL NIL) (-1296 3209930 3210289 3210695 "VIEW" 3211410 T VIEW (NIL) -7 NIL NIL NIL) (-1295 3206354 3206993 3207730 "VIEWDEF" 3209215 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1294 3195658 3197902 3200075 "VIEW3D" 3204203 T VIEW3D (NIL) -8 NIL NIL NIL) (-1293 3187909 3189569 3191148 "VIEW2D" 3194101 T VIEW2D (NIL) -8 NIL NIL NIL) (-1292 3183265 3187679 3187771 "VECTOR" 3187852 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1291 3181842 3182101 3182419 "VECTOR2" 3182995 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1290 3175240 3179546 3179589 "VECTCAT" 3180584 NIL VECTCAT (NIL T) -9 NIL 3181171 NIL) (-1289 3174254 3174508 3174898 "VECTCAT-" 3174903 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3173708 3173905 3174025 "VARIABLE" 3174169 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1287 3173641 3173646 3173676 "UTYPE" 3173681 T UTYPE (NIL) -9 NIL NIL NIL) (-1286 3172471 3172625 3172887 "UTSODETL" 3173467 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1285 3169911 3170371 3170895 "UTSODE" 3172012 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1284 3161859 3167672 3168152 "UTS" 3169489 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1283 3152423 3157793 3157836 "UTSCAT" 3158948 NIL UTSCAT (NIL T) -9 NIL 3159706 NIL) (-1282 3149771 3150493 3151482 "UTSCAT-" 3151487 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1281 3149398 3149441 3149574 "UTS2" 3149722 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1280 3143599 3146208 3146251 "URAGG" 3148321 NIL URAGG (NIL T) -9 NIL 3149044 NIL) (-1279 3140538 3141401 3142524 "URAGG-" 3142529 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1278 3136247 3139173 3139638 "UPXSSING" 3140202 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1277 3128423 3135629 3135893 "UPXS" 3136041 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1276 3121496 3128327 3128399 "UPXSCONS" 3128404 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1275 3110903 3117699 3117761 "UPXSCCA" 3118335 NIL UPXSCCA (NIL T T) -9 NIL 3118568 NIL) (-1274 3110541 3110626 3110800 "UPXSCCA-" 3110805 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1273 3099800 3106369 3106412 "UPXSCAT" 3107060 NIL UPXSCAT (NIL T) -9 NIL 3107669 NIL) (-1272 3099230 3099309 3099488 "UPXS2" 3099715 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1271 3097884 3098137 3098488 "UPSQFREE" 3098973 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1270 3091092 3094152 3094207 "UPSCAT" 3095287 NIL UPSCAT (NIL T T) -9 NIL 3096052 NIL) (-1269 3090296 3090503 3090830 "UPSCAT-" 3090835 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1268 3075378 3083423 3083466 "UPOLYC" 3085567 NIL UPOLYC (NIL T) -9 NIL 3086788 NIL) (-1267 3066706 3069132 3072279 "UPOLYC-" 3072284 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1266 3066333 3066376 3066509 "UPOLYC2" 3066657 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3057868 3066016 3066145 "UP" 3066252 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1264 3057207 3057314 3057478 "UPMP" 3057757 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1263 3056760 3056841 3056980 "UPDIVP" 3057120 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1262 3055328 3055577 3055893 "UPDECOMP" 3056509 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1261 3054559 3054671 3054857 "UPCDEN" 3055212 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1260 3054078 3054147 3054296 "UP2" 3054484 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1259 3052545 3053282 3053559 "UNISEG" 3053836 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1258 3051760 3051887 3052092 "UNISEG2" 3052388 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1257 3050820 3051000 3051226 "UNIFACT" 3051576 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1256 3033572 3050132 3050374 "ULS" 3050636 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3021202 3033476 3033548 "ULSCONS" 3033553 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1254 3001923 3014283 3014345 "ULSCCAT" 3014983 NIL ULSCCAT (NIL T T) -9 NIL 3015272 NIL) (-1253 3000973 3001218 3001606 "ULSCCAT-" 3001611 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1252 2990037 2996520 2996563 "ULSCAT" 2997426 NIL ULSCAT (NIL T) -9 NIL 2998157 NIL) (-1251 2989467 2989546 2989725 "ULS2" 2989952 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1250 2988586 2989096 2989203 "UINT8" 2989314 T UINT8 (NIL) -8 NIL NIL 2989399) (-1249 2987704 2988214 2988321 "UINT64" 2988432 T UINT64 (NIL) -8 NIL NIL 2988517) (-1248 2986822 2987332 2987439 "UINT32" 2987550 T UINT32 (NIL) -8 NIL NIL 2987635) (-1247 2985940 2986450 2986557 "UINT16" 2986668 T UINT16 (NIL) -8 NIL NIL 2986753) (-1246 2984229 2985186 2985216 "UFD" 2985428 T UFD (NIL) -9 NIL 2985542 NIL) (-1245 2984023 2984069 2984164 "UFD-" 2984169 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1244 2983105 2983288 2983504 "UDVO" 2983829 T UDVO (NIL) -7 NIL NIL NIL) (-1243 2980921 2981330 2981801 "UDPO" 2982669 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1242 2980854 2980859 2980889 "TYPE" 2980894 T TYPE (NIL) -9 NIL NIL NIL) (-1241 2980614 2980809 2980840 "TYPEAST" 2980845 T TYPEAST (NIL) -8 NIL NIL NIL) (-1240 2979585 2979787 2980027 "TWOFACT" 2980408 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1239 2978608 2978994 2979229 "TUPLE" 2979385 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1238 2976299 2976818 2977357 "TUBETOOL" 2978091 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1237 2975148 2975353 2975594 "TUBE" 2976092 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1236 2969877 2974120 2974403 "TS" 2974900 NIL TS (NIL T) -8 NIL NIL NIL) (-1235 2958515 2962634 2962731 "TSETCAT" 2968000 NIL TSETCAT (NIL T T T T) -9 NIL 2969532 NIL) (-1234 2953247 2954847 2956738 "TSETCAT-" 2956743 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1233 2947886 2948733 2949662 "TRMANIP" 2952383 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1232 2947327 2947390 2947553 "TRIMAT" 2947818 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1231 2945193 2945430 2945787 "TRIGMNIP" 2947076 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1230 2944713 2944826 2944856 "TRIGCAT" 2945069 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1229 2944382 2944461 2944602 "TRIGCAT-" 2944607 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1228 2941230 2943240 2943521 "TREE" 2944136 NIL TREE (NIL T) -8 NIL NIL NIL) (-1227 2940504 2941032 2941062 "TRANFUN" 2941097 T TRANFUN (NIL) -9 NIL 2941163 NIL) (-1226 2939783 2939974 2940254 "TRANFUN-" 2940259 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1225 2939587 2939619 2939680 "TOPSP" 2939744 T TOPSP (NIL) -7 NIL NIL NIL) (-1224 2938935 2939050 2939204 "TOOLSIGN" 2939468 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1223 2937569 2938112 2938351 "TEXTFILE" 2938718 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1222 2935481 2936022 2936451 "TEX" 2937162 T TEX (NIL) -8 NIL NIL NIL) (-1221 2935262 2935293 2935365 "TEX1" 2935444 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1220 2934910 2934973 2935063 "TEMUTL" 2935194 T TEMUTL (NIL) -7 NIL NIL NIL) (-1219 2933064 2933344 2933669 "TBCMPPK" 2934633 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1218 2924773 2931150 2931206 "TBAGG" 2931606 NIL TBAGG (NIL T T) -9 NIL 2931817 NIL) (-1217 2919843 2921331 2923085 "TBAGG-" 2923090 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1216 2919227 2919334 2919479 "TANEXP" 2919732 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1215 2918738 2919002 2919092 "TALGOP" 2919172 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1214 2912134 2918595 2918688 "TABLE" 2918693 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1213 2911546 2911645 2911783 "TABLEAU" 2912031 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1212 2906154 2907374 2908622 "TABLBUMP" 2910332 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1211 2905376 2905523 2905704 "SYSTEM" 2905995 T SYSTEM (NIL) -8 NIL NIL NIL) (-1210 2901835 2902534 2903317 "SYSSOLP" 2904627 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1209 2901633 2901790 2901821 "SYSPTR" 2901826 T SYSPTR (NIL) -8 NIL NIL NIL) (-1208 2900669 2901174 2901293 "SYSNNI" 2901479 NIL SYSNNI (NIL NIL) -8 NIL NIL 2901564) (-1207 2899968 2900427 2900506 "SYSINT" 2900566 NIL SYSINT (NIL NIL) -8 NIL NIL 2900611) (-1206 2896300 2897246 2897956 "SYNTAX" 2899280 T SYNTAX (NIL) -8 NIL NIL NIL) (-1205 2893458 2894060 2894692 "SYMTAB" 2895690 T SYMTAB (NIL) -8 NIL NIL NIL) (-1204 2888707 2889609 2890592 "SYMS" 2892497 T SYMS (NIL) -8 NIL NIL NIL) (-1203 2885942 2888165 2888395 "SYMPOLY" 2888512 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1202 2885459 2885534 2885657 "SYMFUNC" 2885854 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1201 2881479 2882771 2883584 "SYMBOL" 2884668 T SYMBOL (NIL) -8 NIL NIL NIL) (-1200 2875018 2876707 2878427 "SWITCH" 2879781 T SWITCH (NIL) -8 NIL NIL NIL) (-1199 2868362 2873974 2874268 "SUTS" 2874782 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1198 2860538 2867744 2868008 "SUPXS" 2868156 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 2852021 2860156 2860282 "SUP" 2860447 NIL SUP (NIL T) -8 NIL NIL NIL) (-1196 2851180 2851307 2851524 "SUPFRACF" 2851889 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1195 2850801 2850860 2850973 "SUP2" 2851115 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1194 2849249 2849523 2849879 "SUMRF" 2850500 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1193 2848584 2848650 2848842 "SUMFS" 2849170 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1192 2831371 2847896 2848138 "SULS" 2848400 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2830973 2831193 2831263 "SUCHTAST" 2831323 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1190 2830268 2830498 2830638 "SUCH" 2830881 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1189 2824135 2825174 2826133 "SUBSPACE" 2829356 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1188 2823565 2823655 2823819 "SUBRESP" 2824023 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1187 2816933 2818230 2819541 "STTF" 2822301 NIL STTF (NIL T) -7 NIL NIL NIL) (-1186 2811106 2812226 2813373 "STTFNC" 2815833 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1185 2802419 2804288 2806082 "STTAYLOR" 2809347 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1184 2795555 2802283 2802366 "STRTBL" 2802371 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1183 2790516 2795264 2795363 "STRING" 2795478 T STRING (NIL) -8 NIL NIL NIL) (-1182 2783272 2788135 2788746 "STREAM" 2789940 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1181 2782782 2782859 2783003 "STREAM3" 2783189 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1180 2781764 2781947 2782182 "STREAM2" 2782595 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1179 2781452 2781504 2781597 "STREAM1" 2781706 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1178 2780468 2780649 2780880 "STINPROD" 2781268 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1177 2780006 2780216 2780246 "STEP" 2780326 T STEP (NIL) -9 NIL 2780404 NIL) (-1176 2779193 2779495 2779643 "STEPAST" 2779880 T STEPAST (NIL) -8 NIL NIL NIL) (-1175 2772631 2779092 2779169 "STBL" 2779174 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1174 2767701 2771794 2771837 "STAGG" 2771990 NIL STAGG (NIL T) -9 NIL 2772079 NIL) (-1173 2765403 2766005 2766877 "STAGG-" 2766882 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1172 2763553 2765173 2765265 "STACK" 2765346 NIL STACK (NIL T) -8 NIL NIL NIL) (-1171 2756248 2761694 2762150 "SREGSET" 2763183 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1170 2748673 2750042 2751555 "SRDCMPK" 2754854 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1169 2741510 2746032 2746062 "SRAGG" 2747365 T SRAGG (NIL) -9 NIL 2747973 NIL) (-1168 2740527 2740782 2741161 "SRAGG-" 2741166 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1167 2734711 2739474 2739895 "SQMATRIX" 2740153 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1166 2728399 2731429 2732156 "SPLTREE" 2734056 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1165 2724362 2725055 2725701 "SPLNODE" 2727825 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1164 2723409 2723642 2723672 "SPFCAT" 2724116 T SPFCAT (NIL) -9 NIL NIL NIL) (-1163 2722146 2722356 2722620 "SPECOUT" 2723167 T SPECOUT (NIL) -7 NIL NIL NIL) (-1162 2713242 2715114 2715144 "SPADXPT" 2719820 T SPADXPT (NIL) -9 NIL 2721984 NIL) (-1161 2713003 2713043 2713112 "SPADPRSR" 2713195 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1160 2711052 2712958 2712989 "SPADAST" 2712994 T SPADAST (NIL) -8 NIL NIL NIL) (-1159 2702983 2704756 2704799 "SPACEC" 2709172 NIL SPACEC (NIL T) -9 NIL 2710988 NIL) (-1158 2701113 2702915 2702964 "SPACE3" 2702969 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1157 2699865 2700036 2700327 "SORTPAK" 2700918 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1156 2697957 2698260 2698672 "SOLVETRA" 2699529 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1155 2697007 2697229 2697490 "SOLVESER" 2697730 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1154 2692311 2693199 2694194 "SOLVERAD" 2696059 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1153 2688126 2688735 2689464 "SOLVEFOR" 2691678 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1152 2682395 2687474 2687571 "SNTSCAT" 2687576 NIL SNTSCAT (NIL T T T T) -9 NIL 2687646 NIL) (-1151 2676501 2680718 2681109 "SMTS" 2682085 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1150 2670910 2676389 2676466 "SMP" 2676471 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1149 2669069 2669370 2669768 "SMITH" 2670607 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1148 2661173 2665648 2665751 "SMATCAT" 2667102 NIL SMATCAT (NIL NIL T T T) -9 NIL 2667652 NIL) (-1147 2658113 2658936 2660114 "SMATCAT-" 2660119 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1146 2655754 2657321 2657364 "SKAGG" 2657625 NIL SKAGG (NIL T) -9 NIL 2657760 NIL) (-1145 2651944 2655227 2655411 "SINT" 2655563 T SINT (NIL) -8 NIL NIL 2655725) (-1144 2651716 2651754 2651820 "SIMPAN" 2651900 T SIMPAN (NIL) -7 NIL NIL NIL) (-1143 2650995 2651251 2651391 "SIG" 2651598 T SIG (NIL) -8 NIL NIL NIL) (-1142 2649833 2650054 2650329 "SIGNRF" 2650754 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1141 2648666 2648817 2649101 "SIGNEF" 2649662 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1140 2647972 2648249 2648373 "SIGAST" 2648564 T SIGAST (NIL) -8 NIL NIL NIL) (-1139 2645662 2646116 2646622 "SHP" 2647513 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1138 2639491 2645563 2645639 "SHDP" 2645644 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1137 2639050 2639242 2639272 "SGROUP" 2639365 T SGROUP (NIL) -9 NIL 2639427 NIL) (-1136 2638908 2638934 2639007 "SGROUP-" 2639012 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1135 2635699 2636397 2637120 "SGCF" 2638207 T SGCF (NIL) -7 NIL NIL NIL) (-1134 2630066 2635145 2635242 "SFRTCAT" 2635247 NIL SFRTCAT (NIL T T T T) -9 NIL 2635286 NIL) (-1133 2623487 2624505 2625641 "SFRGCD" 2629049 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1132 2616613 2617686 2618872 "SFQCMPK" 2622420 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2616233 2616322 2616433 "SFORT" 2616554 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1130 2615351 2616073 2616194 "SEXOF" 2616199 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1129 2614458 2615232 2615300 "SEX" 2615305 T SEX (NIL) -8 NIL NIL NIL) (-1128 2610239 2610954 2611049 "SEXCAT" 2613671 NIL SEXCAT (NIL T T T T T) -9 NIL 2614231 NIL) (-1127 2607392 2610173 2610221 "SET" 2610226 NIL SET (NIL T) -8 NIL NIL NIL) (-1126 2605616 2606105 2606410 "SETMN" 2607133 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1125 2605182 2605334 2605364 "SETCAT" 2605481 T SETCAT (NIL) -9 NIL 2605566 NIL) (-1124 2604962 2605014 2605113 "SETCAT-" 2605118 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1123 2601323 2603423 2603466 "SETAGG" 2604336 NIL SETAGG (NIL T) -9 NIL 2604676 NIL) (-1122 2600781 2600897 2601134 "SETAGG-" 2601139 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1121 2600224 2600477 2600578 "SEQAST" 2600702 T SEQAST (NIL) -8 NIL NIL NIL) (-1120 2599423 2599717 2599778 "SEGXCAT" 2600064 NIL SEGXCAT (NIL T T) -9 NIL 2600184 NIL) (-1119 2598429 2599089 2599271 "SEG" 2599276 NIL SEG (NIL T) -8 NIL NIL NIL) (-1118 2597408 2597622 2597665 "SEGCAT" 2598187 NIL SEGCAT (NIL T) -9 NIL 2598408 NIL) (-1117 2596340 2596771 2596979 "SEGBIND" 2597235 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1116 2595961 2596020 2596133 "SEGBIND2" 2596275 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1115 2595534 2595762 2595839 "SEGAST" 2595906 T SEGAST (NIL) -8 NIL NIL NIL) (-1114 2594753 2594879 2595083 "SEG2" 2595378 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1113 2594124 2594688 2594735 "SDVAR" 2594740 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1112 2586375 2593894 2594024 "SDPOL" 2594029 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1111 2584968 2585234 2585553 "SCPKG" 2586090 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1110 2584132 2584304 2584496 "SCOPE" 2584798 T SCOPE (NIL) -8 NIL NIL NIL) (-1109 2583352 2583486 2583665 "SCACHE" 2583987 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1108 2582984 2583170 2583200 "SASTCAT" 2583205 T SASTCAT (NIL) -9 NIL 2583218 NIL) (-1107 2582471 2582819 2582895 "SAOS" 2582930 T SAOS (NIL) -8 NIL NIL NIL) (-1106 2582036 2582071 2582244 "SAERFFC" 2582430 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1105 2575699 2581933 2582013 "SAE" 2582018 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1104 2575292 2575327 2575486 "SAEFACT" 2575658 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1103 2573613 2573927 2574328 "RURPK" 2574958 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1102 2572250 2572556 2572861 "RULESET" 2573447 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1101 2569473 2570003 2570461 "RULE" 2571931 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1100 2569085 2569267 2569350 "RULECOLD" 2569425 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1099 2568875 2568903 2568974 "RTVALUE" 2569036 T RTVALUE (NIL) -8 NIL NIL NIL) (-1098 2568346 2568592 2568686 "RSTRCAST" 2568803 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1097 2563194 2563989 2564909 "RSETGCD" 2567545 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1096 2552423 2557502 2557599 "RSETCAT" 2561718 NIL RSETCAT (NIL T T T T) -9 NIL 2562815 NIL) (-1095 2550350 2550889 2551713 "RSETCAT-" 2551718 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1094 2542736 2544112 2545632 "RSDCMPK" 2548949 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2540701 2541168 2541242 "RRCC" 2542328 NIL RRCC (NIL T T) -9 NIL 2542672 NIL) (-1092 2540052 2540226 2540505 "RRCC-" 2540510 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1091 2539495 2539748 2539849 "RPTAST" 2539973 T RPTAST (NIL) -8 NIL NIL NIL) (-1090 2512971 2522607 2522674 "RPOLCAT" 2533340 NIL RPOLCAT (NIL T T T) -9 NIL 2536500 NIL) (-1089 2504469 2506809 2509931 "RPOLCAT-" 2509936 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1088 2495406 2502680 2503162 "ROUTINE" 2504009 T ROUTINE (NIL) -8 NIL NIL NIL) (-1087 2492067 2495032 2495172 "ROMAN" 2495288 T ROMAN (NIL) -8 NIL NIL NIL) (-1086 2490311 2490927 2491187 "ROIRC" 2491872 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1085 2486515 2488800 2488830 "RNS" 2489134 T RNS (NIL) -9 NIL 2489408 NIL) (-1084 2485024 2485407 2485941 "RNS-" 2486016 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1083 2484413 2484821 2484851 "RNG" 2484856 T RNG (NIL) -9 NIL 2484877 NIL) (-1082 2483416 2483778 2483980 "RNGBIND" 2484264 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1081 2482801 2483189 2483232 "RMODULE" 2483237 NIL RMODULE (NIL T) -9 NIL 2483264 NIL) (-1080 2481637 2481731 2482067 "RMCAT2" 2482702 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1079 2478487 2480983 2481280 "RMATRIX" 2481399 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1078 2471314 2473574 2473689 "RMATCAT" 2477048 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2478030 NIL) (-1077 2470689 2470836 2471143 "RMATCAT-" 2471148 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1076 2470304 2470476 2470519 "RLINSET" 2470581 NIL RLINSET (NIL T) -9 NIL 2470625 NIL) (-1075 2469871 2469946 2470074 "RINTERP" 2470223 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1074 2468915 2469469 2469499 "RING" 2469555 T RING (NIL) -9 NIL 2469647 NIL) (-1073 2468707 2468751 2468848 "RING-" 2468853 NIL RING- (NIL T) -8 NIL NIL NIL) (-1072 2467548 2467785 2468043 "RIDIST" 2468471 T RIDIST (NIL) -7 NIL NIL NIL) (-1071 2458837 2467016 2467222 "RGCHAIN" 2467396 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1070 2458173 2458579 2458620 "RGBCSPC" 2458678 NIL RGBCSPC (NIL T) -9 NIL 2458730 NIL) (-1069 2457317 2457698 2457739 "RGBCMDL" 2457971 NIL RGBCMDL (NIL T) -9 NIL 2458085 NIL) (-1068 2454311 2454925 2455595 "RF" 2456681 NIL RF (NIL T) -7 NIL NIL NIL) (-1067 2453957 2454020 2454123 "RFFACTOR" 2454242 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1066 2453682 2453717 2453814 "RFFACT" 2453916 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1065 2451799 2452163 2452545 "RFDIST" 2453322 T RFDIST (NIL) -7 NIL NIL NIL) (-1064 2451252 2451344 2451507 "RETSOL" 2451701 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1063 2450888 2450968 2451011 "RETRACT" 2451144 NIL RETRACT (NIL T) -9 NIL 2451231 NIL) (-1062 2450737 2450762 2450849 "RETRACT-" 2450854 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1061 2450339 2450559 2450629 "RETAST" 2450689 T RETAST (NIL) -8 NIL NIL NIL) (-1060 2443083 2449992 2450119 "RESULT" 2450234 T RESULT (NIL) -8 NIL NIL NIL) (-1059 2441674 2442352 2442551 "RESRING" 2442986 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1058 2441310 2441359 2441457 "RESLATC" 2441611 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1057 2441015 2441050 2441157 "REPSQ" 2441269 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1056 2438437 2439017 2439619 "REP" 2440435 T REP (NIL) -7 NIL NIL NIL) (-1055 2438134 2438169 2438280 "REPDB" 2438396 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1054 2432034 2433423 2434646 "REP2" 2436946 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1053 2428411 2429092 2429900 "REP1" 2431261 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1052 2421107 2426552 2427008 "REGSET" 2428041 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1051 2419872 2420255 2420505 "REF" 2420892 NIL REF (NIL T) -8 NIL NIL NIL) (-1050 2419249 2419352 2419519 "REDORDER" 2419756 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1049 2415217 2418462 2418689 "RECLOS" 2419077 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1048 2414269 2414450 2414665 "REALSOLV" 2415024 T REALSOLV (NIL) -7 NIL NIL NIL) (-1047 2414115 2414156 2414186 "REAL" 2414191 T REAL (NIL) -9 NIL 2414226 NIL) (-1046 2410598 2411400 2412284 "REAL0Q" 2413280 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1045 2406199 2407187 2408248 "REAL0" 2409579 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1044 2405670 2405916 2406010 "RDUCEAST" 2406127 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1043 2405075 2405147 2405354 "RDIV" 2405592 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1042 2404143 2404317 2404530 "RDIST" 2404897 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1041 2402740 2403027 2403399 "RDETRS" 2403851 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1040 2400552 2401006 2401544 "RDETR" 2402282 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1039 2399177 2399455 2399852 "RDEEFS" 2400268 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1038 2397686 2397992 2398417 "RDEEF" 2398865 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1037 2391719 2394640 2394670 "RCFIELD" 2395965 T RCFIELD (NIL) -9 NIL 2396696 NIL) (-1036 2389783 2390287 2390983 "RCFIELD-" 2391058 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1035 2386027 2387856 2387899 "RCAGG" 2388983 NIL RCAGG (NIL T) -9 NIL 2389448 NIL) (-1034 2385655 2385749 2385912 "RCAGG-" 2385917 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1033 2384990 2385102 2385267 "RATRET" 2385539 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1032 2384543 2384610 2384731 "RATFACT" 2384918 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1031 2383851 2383971 2384123 "RANDSRC" 2384413 T RANDSRC (NIL) -7 NIL NIL NIL) (-1030 2383585 2383629 2383702 "RADUTIL" 2383800 T RADUTIL (NIL) -7 NIL NIL NIL) (-1029 2376413 2382416 2382727 "RADIX" 2383308 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1028 2366873 2376255 2376385 "RADFF" 2376390 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1027 2366520 2366595 2366625 "RADCAT" 2366785 T RADCAT (NIL) -9 NIL NIL NIL) (-1026 2366302 2366350 2366450 "RADCAT-" 2366455 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1025 2364403 2366072 2366164 "QUEUE" 2366245 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1024 2360664 2364336 2364384 "QUAT" 2364389 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1023 2360295 2360338 2360469 "QUATCT2" 2360615 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2353093 2356718 2356760 "QUATCAT" 2357551 NIL QUATCAT (NIL T) -9 NIL 2358317 NIL) (-1021 2349232 2350269 2351659 "QUATCAT-" 2351755 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2346672 2348280 2348323 "QUAGG" 2348704 NIL QUAGG (NIL T) -9 NIL 2348879 NIL) (-1019 2346274 2346494 2346564 "QQUTAST" 2346624 T QQUTAST (NIL) -8 NIL NIL NIL) (-1018 2345287 2345787 2345952 "QFORM" 2346155 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1017 2335619 2341134 2341176 "QFCAT" 2341844 NIL QFCAT (NIL T) -9 NIL 2342845 NIL) (-1016 2331186 2332387 2333981 "QFCAT-" 2334077 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1015 2330817 2330860 2330991 "QFCAT2" 2331137 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2330272 2330382 2330514 "QEQUAT" 2330707 T QEQUAT (NIL) -8 NIL NIL NIL) (-1013 2323398 2324471 2325657 "QCMPACK" 2329205 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1012 2320936 2321384 2321814 "QALGSET" 2323053 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1011 2320171 2320347 2320583 "QALGSET2" 2320754 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1010 2318856 2319080 2319399 "PWFFINTB" 2319944 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1009 2317031 2317199 2317555 "PUSHVAR" 2318670 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1008 2312920 2313974 2314017 "PTRANFN" 2315928 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1007 2311311 2311602 2311926 "PTPACK" 2312631 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1006 2310940 2310997 2311108 "PTFUNC2" 2311248 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1005 2305335 2309729 2309772 "PTCAT" 2310072 NIL PTCAT (NIL T) -9 NIL 2310225 NIL) (-1004 2304990 2305025 2305151 "PSQFR" 2305294 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1003 2303580 2303878 2304214 "PSEUDLIN" 2304688 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1002 2290304 2292675 2295001 "PSETPK" 2301340 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1001 2283300 2286040 2286138 "PSETCAT" 2289179 NIL PSETCAT (NIL T T T T) -9 NIL 2289993 NIL) (-1000 2281133 2281767 2282591 "PSETCAT-" 2282596 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-999 2280482 2280647 2280675 "PSCURVE" 2280943 T PSCURVE (NIL) -9 NIL 2281110 NIL) (-998 2276466 2277982 2278047 "PSCAT" 2278891 NIL PSCAT (NIL T T T) -9 NIL 2279131 NIL) (-997 2275529 2275745 2276145 "PSCAT-" 2276150 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-996 2273888 2274598 2274861 "PRTITION" 2275286 T PRTITION (NIL) -8 NIL NIL NIL) (-995 2273363 2273609 2273701 "PRTDAST" 2273816 T PRTDAST (NIL) -8 NIL NIL NIL) (-994 2262453 2264667 2266855 "PRS" 2271225 NIL PRS (NIL T T) -7 NIL NIL NIL) (-993 2260239 2261775 2261815 "PRQAGG" 2261998 NIL PRQAGG (NIL T) -9 NIL 2262100 NIL) (-992 2259575 2259880 2259908 "PROPLOG" 2260047 T PROPLOG (NIL) -9 NIL 2260162 NIL) (-991 2259179 2259236 2259359 "PROPFUN2" 2259498 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-990 2258494 2258615 2258787 "PROPFUN1" 2259040 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-989 2256675 2257241 2257538 "PROPFRML" 2258230 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-988 2256144 2256251 2256379 "PROPERTY" 2256567 T PROPERTY (NIL) -8 NIL NIL NIL) (-987 2250202 2254310 2255130 "PRODUCT" 2255370 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-986 2247480 2249660 2249894 "PR" 2250013 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2247276 2247308 2247367 "PRINT" 2247441 T PRINT (NIL) -7 NIL NIL NIL) (-984 2246616 2246733 2246885 "PRIMES" 2247156 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-983 2244681 2245082 2245548 "PRIMELT" 2246195 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-982 2244410 2244459 2244487 "PRIMCAT" 2244611 T PRIMCAT (NIL) -9 NIL NIL NIL) (-981 2240528 2244348 2244393 "PRIMARR" 2244398 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-980 2239535 2239713 2239941 "PRIMARR2" 2240346 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-979 2239178 2239234 2239345 "PREASSOC" 2239473 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-978 2238653 2238786 2238814 "PPCURVE" 2239019 T PPCURVE (NIL) -9 NIL 2239155 NIL) (-977 2238248 2238448 2238531 "PORTNUM" 2238590 T PORTNUM (NIL) -8 NIL NIL NIL) (-976 2235607 2236006 2236598 "POLYROOT" 2237829 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-975 2229513 2235211 2235371 "POLY" 2235480 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2228896 2228954 2229188 "POLYLIFT" 2229449 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-973 2225171 2225620 2226249 "POLYCATQ" 2228441 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-972 2211513 2216918 2216983 "POLYCAT" 2220497 NIL POLYCAT (NIL T T T) -9 NIL 2222375 NIL) (-971 2204962 2206824 2209208 "POLYCAT-" 2209213 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-970 2204549 2204617 2204737 "POLY2UP" 2204888 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-969 2204181 2204238 2204347 "POLY2" 2204486 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-968 2202866 2203105 2203381 "POLUTIL" 2203955 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-967 2201221 2201498 2201829 "POLTOPOL" 2202588 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-966 2196687 2201155 2201202 "POINT" 2201207 NIL POINT (NIL T) -8 NIL NIL NIL) (-965 2194874 2195231 2195606 "PNTHEORY" 2196332 T PNTHEORY (NIL) -7 NIL NIL NIL) (-964 2193332 2193629 2194028 "PMTOOLS" 2194572 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-963 2192925 2193003 2193120 "PMSYM" 2193248 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-962 2192433 2192502 2192677 "PMQFCAT" 2192850 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-961 2191788 2191898 2192054 "PMPRED" 2192310 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-960 2191181 2191267 2191429 "PMPREDFS" 2191689 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-959 2189845 2190053 2190431 "PMPLCAT" 2190943 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-958 2189377 2189456 2189608 "PMLSAGG" 2189760 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-957 2188850 2188926 2189108 "PMKERNEL" 2189295 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-956 2188467 2188542 2188655 "PMINS" 2188769 NIL PMINS (NIL T) -7 NIL NIL NIL) (-955 2187909 2187978 2188187 "PMFS" 2188392 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-954 2187137 2187255 2187460 "PMDOWN" 2187786 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-953 2186304 2186462 2186643 "PMASS" 2186976 T PMASS (NIL) -7 NIL NIL NIL) (-952 2185577 2185687 2185850 "PMASSFS" 2186191 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-951 2185232 2185300 2185394 "PLOTTOOL" 2185503 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-950 2179839 2181043 2182191 "PLOT" 2184104 T PLOT (NIL) -8 NIL NIL NIL) (-949 2175643 2176687 2177608 "PLOT3D" 2178938 T PLOT3D (NIL) -8 NIL NIL NIL) (-948 2174555 2174732 2174967 "PLOT1" 2175447 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-947 2149946 2154621 2159472 "PLEQN" 2169821 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-946 2149264 2149386 2149566 "PINTERP" 2149811 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-945 2148957 2149004 2149107 "PINTERPA" 2149211 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-944 2148173 2148721 2148808 "PI" 2148848 T PI (NIL) -8 NIL NIL 2148915) (-943 2146456 2147431 2147459 "PID" 2147641 T PID (NIL) -9 NIL 2147775 NIL) (-942 2146207 2146244 2146319 "PICOERCE" 2146413 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-941 2145527 2145666 2145842 "PGROEB" 2146063 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-940 2141114 2141928 2142833 "PGE" 2144642 T PGE (NIL) -7 NIL NIL NIL) (-939 2139237 2139484 2139850 "PGCD" 2140831 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-938 2138575 2138678 2138839 "PFRPAC" 2139121 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-937 2135215 2137123 2137476 "PFR" 2138254 NIL PFR (NIL T) -8 NIL NIL NIL) (-936 2133604 2133848 2134173 "PFOTOOLS" 2134962 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-935 2132137 2132376 2132727 "PFOQ" 2133361 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-934 2130638 2130850 2131206 "PFO" 2131921 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-933 2127191 2130527 2130596 "PF" 2130601 NIL PF (NIL NIL) -8 NIL NIL NIL) (-932 2124511 2125782 2125810 "PFECAT" 2126395 T PFECAT (NIL) -9 NIL 2126779 NIL) (-931 2123956 2124110 2124324 "PFECAT-" 2124329 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-930 2122559 2122811 2123112 "PFBRU" 2123705 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-929 2120425 2120777 2121209 "PFBR" 2122210 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-928 2116471 2117937 2118584 "PERM" 2119811 NIL PERM (NIL T) -8 NIL NIL NIL) (-927 2111705 2112678 2113548 "PERMGRP" 2115634 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-926 2109769 2110729 2110770 "PERMCAT" 2111170 NIL PERMCAT (NIL T) -9 NIL 2111468 NIL) (-925 2109422 2109463 2109587 "PERMAN" 2109722 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-924 2106913 2109087 2109209 "PENDTREE" 2109333 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-923 2105842 2106057 2106098 "PDSPC" 2106631 NIL PDSPC (NIL T) -9 NIL 2106876 NIL) (-922 2104945 2105163 2105525 "PDSPC-" 2105530 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-921 2103827 2104595 2104636 "PDRING" 2104641 NIL PDRING (NIL T) -9 NIL 2104669 NIL) (-920 2102714 2103332 2103386 "PDMOD" 2103391 NIL PDMOD (NIL T T) -9 NIL 2103495 NIL) (-919 2099929 2100707 2101375 "PDEPROB" 2102066 T PDEPROB (NIL) -8 NIL NIL NIL) (-918 2097474 2097978 2098533 "PDEPACK" 2099394 T PDEPACK (NIL) -7 NIL NIL NIL) (-917 2096386 2096576 2096827 "PDECOMP" 2097273 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-916 2093951 2094794 2094822 "PDECAT" 2095609 T PDECAT (NIL) -9 NIL 2096322 NIL) (-915 2093580 2093635 2093689 "PDDOM" 2093854 NIL PDDOM (NIL T T) -9 NIL 2093934 NIL) (-914 2093399 2093429 2093536 "PDDOM-" 2093541 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-913 2093150 2093183 2093273 "PCOMP" 2093360 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-912 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T) -8 NIL NIL NIL) (-876 2027813 2028162 2028251 "OSI" 2028364 T OSI (NIL) -8 NIL NIL NIL) (-875 2027316 2027654 2027682 "OSGROUP" 2027687 T OSGROUP (NIL) -9 NIL 2027709 NIL) (-874 2026061 2026288 2026573 "ORTHPOL" 2027063 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-873 2023612 2025896 2026017 "OREUP" 2026022 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-872 2021015 2023303 2023430 "ORESUP" 2023554 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-871 2018543 2019043 2019604 "OREPCTO" 2020504 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-870 2012215 2014416 2014457 "OREPCAT" 2016805 NIL OREPCAT (NIL T) -9 NIL 2017909 NIL) (-869 2009362 2010144 2011202 "OREPCAT-" 2011207 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-868 2008609 2008832 2008860 "ORDTYPE" 2009169 T ORDTYPE (NIL) -9 NIL 2009332 NIL) (-867 2007952 2008126 2008381 "ORDTYPE-" 2008386 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-866 2007378 2007691 2007849 "ORDSTRCT" 2007854 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-865 2006948 2007246 2007274 "ORDSET" 2007279 T ORDSET (NIL) -9 NIL 2007301 NIL) (-864 2005486 2006277 2006305 "ORDRING" 2006507 T ORDRING (NIL) -9 NIL 2006632 NIL) (-863 2005131 2005225 2005369 "ORDRING-" 2005374 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-862 2004484 2004947 2004975 "ORDMON" 2004980 T ORDMON (NIL) -9 NIL 2005001 NIL) (-861 2003646 2003793 2003988 "ORDFUNS" 2004333 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-860 2002957 2003376 2003404 "ORDFIN" 2003469 T ORDFIN (NIL) -9 NIL 2003543 NIL) (-859 1999516 2001543 2001952 "ORDCOMP" 2002581 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-858 1998782 1998909 1999095 "ORDCOMP2" 1999376 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-857 1995363 1996273 1997087 "OPTPROB" 1997988 T OPTPROB (NIL) -8 NIL NIL NIL) (-856 1992165 1992804 1993508 "OPTPACK" 1994679 T OPTPACK (NIL) -7 NIL NIL NIL) (-855 1989838 1990604 1990632 "OPTCAT" 1991451 T OPTCAT (NIL) -9 NIL 1992101 NIL) (-854 1989222 1989515 1989620 "OPSIG" 1989753 T OPSIG (NIL) -8 NIL NIL NIL) (-853 1988990 1989029 1989095 "OPQUERY" 1989176 T OPQUERY (NIL) -7 NIL NIL NIL) (-852 1986121 1987301 1987805 "OP" 1988519 NIL OP (NIL T) -8 NIL NIL NIL) (-851 1985481 1985707 1985748 "OPERCAT" 1985960 NIL OPERCAT (NIL T) -9 NIL 1986057 NIL) (-850 1985236 1985292 1985409 "OPERCAT-" 1985414 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-849 1982049 1984033 1984402 "ONECOMP" 1984900 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-848 1981354 1981469 1981643 "ONECOMP2" 1981921 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1980773 1980879 1981009 "OMSERVER" 1981244 T OMSERVER (NIL) -7 NIL NIL NIL) (-846 1977635 1980213 1980253 "OMSAGG" 1980314 NIL OMSAGG (NIL T) -9 NIL 1980378 NIL) (-845 1976258 1976521 1976803 "OMPKG" 1977373 T OMPKG (NIL) -7 NIL NIL NIL) (-844 1975688 1975791 1975819 "OM" 1976118 T OM (NIL) -9 NIL NIL NIL) (-843 1974235 1975237 1975406 "OMLO" 1975569 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-842 1973195 1973342 1973562 "OMEXPR" 1974061 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-841 1972486 1972741 1972877 "OMERR" 1973079 T OMERR (NIL) -8 NIL NIL NIL) (-840 1971637 1971907 1972067 "OMERRK" 1972346 T OMERRK (NIL) -8 NIL NIL NIL) (-839 1971088 1971314 1971422 "OMENC" 1971549 T OMENC (NIL) -8 NIL NIL NIL) (-838 1964983 1966168 1967339 "OMDEV" 1969937 T OMDEV (NIL) -8 NIL NIL NIL) (-837 1964052 1964223 1964417 "OMCONN" 1964809 T OMCONN (NIL) -8 NIL NIL NIL) (-836 1962546 1963522 1963550 "OINTDOM" 1963555 T OINTDOM (NIL) -9 NIL 1963576 NIL) (-835 1959884 1961234 1961571 "OFMONOID" 1962241 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-834 1959256 1959821 1959866 "ODVAR" 1959871 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-833 1956679 1959001 1959156 "ODR" 1959161 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-832 1948984 1956455 1956581 "ODPOL" 1956586 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-831 1942783 1948856 1948961 "ODP" 1948966 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-830 1941549 1941764 1942039 "ODETOOLS" 1942557 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-829 1938516 1939174 1939890 "ODESYS" 1940882 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-828 1933398 1934306 1935331 "ODERTRIC" 1937591 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-827 1932824 1932906 1933100 "ODERED" 1933310 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-826 1929712 1930260 1930937 "ODERAT" 1932247 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-825 1926671 1927136 1927733 "ODEPRRIC" 1929241 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-824 1924614 1925210 1925696 "ODEPROB" 1926205 T ODEPROB (NIL) -8 NIL NIL NIL) (-823 1921134 1921619 1922266 "ODEPRIM" 1924093 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-822 1920383 1920485 1920745 "ODEPAL" 1921026 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-821 1916545 1917336 1918200 "ODEPACK" 1919539 T ODEPACK (NIL) -7 NIL NIL NIL) (-820 1915606 1915713 1915935 "ODEINT" 1916434 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-819 1909707 1911132 1912579 "ODEIFTBL" 1914179 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-818 1905105 1905891 1906843 "ODEEF" 1908866 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-817 1904454 1904543 1904766 "ODECONST" 1905010 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-816 1902565 1903226 1903254 "ODECAT" 1903859 T ODECAT (NIL) -9 NIL 1904390 NIL) (-815 1899420 1902270 1902392 "OCT" 1902475 NIL OCT (NIL T) -8 NIL NIL NIL) (-814 1899058 1899101 1899228 "OCTCT2" 1899371 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-813 1893665 1896101 1896141 "OC" 1897238 NIL OC (NIL T) -9 NIL 1898096 NIL) (-812 1890892 1891640 1892630 "OC-" 1892724 NIL OC- (NIL T T) -8 NIL NIL NIL) (-811 1890217 1890685 1890713 "OCAMON" 1890718 T OCAMON (NIL) -9 NIL 1890739 NIL) (-810 1889721 1890062 1890090 "OASGP" 1890095 T OASGP (NIL) -9 NIL 1890115 NIL) (-809 1888955 1889444 1889472 "OAMONS" 1889512 T OAMONS (NIL) -9 NIL 1889555 NIL) (-808 1888342 1888775 1888803 "OAMON" 1888808 T OAMON (NIL) -9 NIL 1888828 NIL) (-807 1887573 1888091 1888119 "OAGROUP" 1888124 T OAGROUP (NIL) -9 NIL 1888144 NIL) (-806 1887263 1887313 1887401 "NUMTUBE" 1887517 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-805 1880836 1882354 1883890 "NUMQUAD" 1885747 T NUMQUAD (NIL) -7 NIL NIL NIL) (-804 1876592 1877580 1878605 "NUMODE" 1879831 T NUMODE (NIL) -7 NIL NIL NIL) (-803 1873933 1874813 1874841 "NUMINT" 1875764 T NUMINT (NIL) -9 NIL 1876528 NIL) (-802 1872881 1873078 1873296 "NUMFMT" 1873735 T NUMFMT (NIL) -7 NIL NIL NIL) (-801 1859240 1862185 1864717 "NUMERIC" 1870388 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-800 1853609 1858688 1858783 "NTSCAT" 1858788 NIL NTSCAT (NIL T T T T) -9 NIL 1858827 NIL) (-799 1852803 1852968 1853161 "NTPOLFN" 1853448 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-798 1840604 1849628 1850440 "NSUP" 1852024 NIL NSUP (NIL T) -8 NIL NIL NIL) (-797 1840236 1840293 1840402 "NSUP2" 1840541 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-796 1830186 1840010 1840143 "NSMP" 1840148 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-795 1828618 1828919 1829276 "NREP" 1829874 NIL NREP (NIL T) -7 NIL NIL NIL) (-794 1827209 1827461 1827819 "NPCOEF" 1828361 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-793 1826275 1826390 1826606 "NORMRETR" 1827090 NIL NORMRETR (NIL T T T T NIL) 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"NAGE02" 1770974 T NAGE02 (NIL) -7 NIL NIL NIL) (-767 1760206 1761153 1762117 "NAGE01" 1763309 T NAGE01 (NIL) -7 NIL NIL NIL) (-766 1758001 1758535 1759093 "NAGD03" 1759668 T NAGD03 (NIL) -7 NIL NIL NIL) (-765 1749751 1751679 1753633 "NAGD02" 1756067 T NAGD02 (NIL) -7 NIL NIL NIL) (-764 1743562 1744987 1746427 "NAGD01" 1748331 T NAGD01 (NIL) -7 NIL NIL NIL) (-763 1739771 1740593 1741430 "NAGC06" 1742745 T NAGC06 (NIL) -7 NIL NIL NIL) (-762 1738236 1738568 1738924 "NAGC05" 1739435 T NAGC05 (NIL) -7 NIL NIL NIL) (-761 1737612 1737731 1737875 "NAGC02" 1738112 T NAGC02 (NIL) -7 NIL NIL NIL) (-760 1736557 1737140 1737180 "NAALG" 1737259 NIL NAALG (NIL T) -9 NIL 1737320 NIL) (-759 1736392 1736421 1736511 "NAALG-" 1736516 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-758 1730342 1731450 1732637 "MULTSQFR" 1735288 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-757 1729661 1729736 1729920 "MULTFACT" 1730254 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-756 1722332 1726246 1726299 "MTSCAT" 1727369 NIL MTSCAT (NIL T T) -9 NIL 1727884 NIL) (-755 1722044 1722098 1722190 "MTHING" 1722272 NIL MTHING (NIL T) -7 NIL NIL NIL) (-754 1721836 1721869 1721929 "MSYSCMD" 1722004 T MSYSCMD (NIL) -7 NIL NIL NIL) (-753 1717918 1720591 1720911 "MSET" 1721549 NIL MSET (NIL T) -8 NIL NIL NIL) (-752 1714987 1717479 1717520 "MSETAGG" 1717525 NIL MSETAGG (NIL T) -9 NIL 1717559 NIL) (-751 1710829 1712366 1713111 "MRING" 1714287 NIL MRING (NIL T T) -8 NIL NIL NIL) (-750 1710395 1710462 1710593 "MRF2" 1710756 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-749 1710013 1710048 1710192 "MRATFAC" 1710354 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-748 1707625 1707920 1708351 "MPRFF" 1709718 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-747 1701646 1707479 1707576 "MPOLY" 1707581 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-746 1701136 1701171 1701379 "MPCPF" 1701605 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-745 1700650 1700693 1700877 "MPC3" 1701087 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-744 1699845 1699926 1700147 "MPC2" 1700565 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-743 1698146 1698483 1698873 "MONOTOOL" 1699505 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-742 1697357 1697674 1697702 "MONOID" 1697921 T MONOID (NIL) -9 NIL 1698068 NIL) (-741 1696903 1697022 1697203 "MONOID-" 1697208 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-740 1686493 1692723 1692782 "MONOGEN" 1693456 NIL MONOGEN (NIL T T) -9 NIL 1693912 NIL) (-739 1683711 1684446 1685446 "MONOGEN-" 1685565 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-738 1682530 1682976 1683004 "MONADWU" 1683396 T MONADWU (NIL) -9 NIL 1683634 NIL) (-737 1681902 1682061 1682309 "MONADWU-" 1682314 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-736 1681247 1681491 1681519 "MONAD" 1681726 T MONAD (NIL) -9 NIL 1681838 NIL) (-735 1680932 1681010 1681142 "MONAD-" 1681147 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-734 1679221 1679845 1680124 "MOEBIUS" 1680685 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-733 1678485 1678889 1678929 "MODULE" 1678934 NIL MODULE (NIL T) -9 NIL 1678973 NIL) (-732 1678053 1678149 1678339 "MODULE-" 1678344 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-731 1675733 1676417 1676744 "MODRING" 1677877 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1672677 1673838 1674359 "MODOP" 1675262 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-729 1671265 1671744 1672021 "MODMONOM" 1672540 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-728 1661033 1669556 1669970 "MODMON" 1670902 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-727 1658189 1659877 1660153 "MODFIELD" 1660908 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1657166 1657470 1657660 "MMLFORM" 1658019 T MMLFORM (NIL) -8 NIL NIL NIL) (-725 1656692 1656735 1656914 "MMAP" 1657117 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-724 1654757 1655524 1655565 "MLO" 1655988 NIL MLO (NIL T) -9 NIL 1656230 NIL) (-723 1652123 1652639 1653241 "MLIFT" 1654238 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-722 1651514 1651598 1651752 "MKUCFUNC" 1652034 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-721 1651113 1651183 1651306 "MKRECORD" 1651437 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-720 1650160 1650322 1650550 "MKFUNC" 1650924 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-719 1649548 1649652 1649808 "MKFLCFN" 1650043 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-718 1648825 1648927 1649112 "MKBCFUNC" 1649441 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-717 1645414 1648379 1648515 "MINT" 1648709 T MINT (NIL) -8 NIL NIL NIL) (-716 1644226 1644469 1644746 "MHROWRED" 1645169 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-715 1639606 1642761 1643166 "MFLOAT" 1643841 T MFLOAT (NIL) -8 NIL NIL NIL) (-714 1638963 1639039 1639210 "MFINFACT" 1639518 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-713 1635278 1636126 1637010 "MESH" 1638099 T MESH (NIL) -7 NIL NIL NIL) (-712 1633668 1633980 1634333 "MDDFACT" 1634965 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-711 1630438 1632799 1632840 "MDAGG" 1633095 NIL MDAGG (NIL T) -9 NIL 1633238 NIL) (-710 1619132 1629731 1629938 "MCMPLX" 1630251 T MCMPLX (NIL) -8 NIL NIL NIL) (-709 1618269 1618415 1618616 "MCDEN" 1618981 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-708 1616159 1616429 1616809 "MCALCFN" 1617999 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-707 1615084 1615324 1615557 "MAYBE" 1615965 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-706 1612696 1613219 1613781 "MATSTOR" 1614555 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-705 1608608 1612068 1612316 "MATRIX" 1612481 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-704 1604374 1605081 1605817 "MATLIN" 1607965 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-703 1594200 1597431 1597508 "MATCAT" 1602540 NIL MATCAT (NIL T T T) -9 NIL 1604012 NIL) (-702 1590393 1591463 1592876 "MATCAT-" 1592881 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-701 1588987 1589140 1589473 "MATCAT2" 1590228 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-700 1587099 1587423 1587807 "MAPPKG3" 1588662 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-699 1586080 1586253 1586475 "MAPPKG2" 1586923 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-698 1584579 1584863 1585190 "MAPPKG1" 1585786 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-697 1583658 1583985 1584162 "MAPPAST" 1584422 T MAPPAST (NIL) -8 NIL NIL NIL) (-696 1583269 1583327 1583450 "MAPHACK3" 1583594 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-695 1582861 1582922 1583036 "MAPHACK2" 1583201 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-694 1582299 1582402 1582544 "MAPHACK1" 1582752 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-693 1580378 1580999 1581303 "MAGMA" 1582027 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-692 1579857 1580102 1580193 "MACROAST" 1580307 T MACROAST (NIL) -8 NIL NIL NIL) (-691 1576278 1578096 1578557 "M3D" 1579429 NIL M3D (NIL T) -8 NIL NIL NIL) (-690 1570328 1574589 1574630 "LZSTAGG" 1575412 NIL LZSTAGG (NIL T) -9 NIL 1575707 NIL) (-689 1566286 1567459 1568916 "LZSTAGG-" 1568921 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-688 1563373 1564177 1564664 "LWORD" 1565831 NIL LWORD (NIL T) -8 NIL NIL NIL) (-687 1562949 1563177 1563252 "LSTAST" 1563318 T LSTAST (NIL) -8 NIL NIL NIL) (-686 1555839 1562720 1562854 "LSQM" 1562859 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-685 1555063 1555202 1555430 "LSPP" 1555694 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-684 1552875 1553176 1553632 "LSMP" 1554752 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-683 1549654 1550328 1551058 "LSMP1" 1552177 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-682 1543456 1548744 1548785 "LSAGG" 1548847 NIL LSAGG (NIL T) -9 NIL 1548925 NIL) (-681 1540151 1541075 1542288 "LSAGG-" 1542293 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-680 1537750 1539295 1539544 "LPOLY" 1539946 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-679 1537332 1537417 1537540 "LPEFRAC" 1537659 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-678 1535653 1536426 1536679 "LO" 1537164 NIL LO (NIL T T T) -8 NIL NIL NIL) (-677 1535265 1535403 1535431 "LOGIC" 1535542 T LOGIC (NIL) -9 NIL 1535623 NIL) (-676 1535127 1535150 1535221 "LOGIC-" 1535226 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-675 1534320 1534460 1534653 "LODOOPS" 1534983 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-674 1531743 1534236 1534302 "LODO" 1534307 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1530281 1530516 1530869 "LODOF" 1531490 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-672 1526485 1528916 1528957 "LODOCAT" 1529395 NIL LODOCAT (NIL T) -9 NIL 1529606 NIL) (-671 1526218 1526276 1526403 "LODOCAT-" 1526408 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-670 1523538 1526059 1526177 "LODO2" 1526182 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-669 1520973 1523475 1523520 "LODO1" 1523525 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-668 1519854 1520019 1520324 "LODEEF" 1520796 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-667 1515132 1518020 1518061 "LNAGG" 1518923 NIL LNAGG (NIL T) -9 NIL 1519358 NIL) (-666 1514279 1514493 1514835 "LNAGG-" 1514840 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-665 1510415 1511204 1511843 "LMOPS" 1513694 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-664 1509804 1510192 1510233 "LMODULE" 1510238 NIL LMODULE (NIL T) -9 NIL 1510264 NIL) (-663 1507005 1509449 1509572 "LMDICT" 1509714 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-662 1506623 1506795 1506836 "LLINSET" 1506897 NIL LLINSET (NIL T) -9 NIL 1506941 NIL) (-661 1506322 1506531 1506591 "LITERAL" 1506596 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-660 1499488 1505256 1505560 "LIST" 1506051 NIL LIST (NIL T) -8 NIL NIL NIL) (-659 1499013 1499087 1499226 "LIST3" 1499408 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-658 1498020 1498198 1498426 "LIST2" 1498831 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-657 1496154 1496466 1496865 "LIST2MAP" 1497667 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-656 1495785 1495973 1496014 "LINSET" 1496019 NIL LINSET (NIL T) -9 NIL 1496053 NIL) (-655 1494725 1495293 1495460 "LINFORM" 1495670 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-654 1493138 1493752 1493793 "LINEXP" 1494283 NIL LINEXP (NIL T) -9 NIL 1494556 NIL) (-653 1491876 1492618 1492799 "LINELT" 1493009 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-652 1490453 1490713 1491024 "LINDEP" 1491628 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-651 1489697 1490185 1490295 "LINBASIS" 1490383 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-650 1486464 1487183 1487960 "LIMITRF" 1488952 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-649 1484767 1485063 1485472 "LIMITPS" 1486159 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-648 1479195 1484278 1484506 "LIE" 1484588 NIL LIE (NIL T T) -8 NIL NIL NIL) (-647 1478129 1478598 1478638 "LIECAT" 1478778 NIL LIECAT (NIL T) -9 NIL 1478929 NIL) (-646 1477970 1477997 1478085 "LIECAT-" 1478090 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-645 1470563 1477510 1477666 "LIB" 1477834 T LIB (NIL) -8 NIL NIL NIL) (-644 1466198 1467081 1468016 "LGROBP" 1469680 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-643 1464196 1464470 1464820 "LF" 1465919 NIL LF (NIL T T) -7 NIL NIL NIL) (-642 1463036 1463728 1463756 "LFCAT" 1463963 T LFCAT (NIL) -9 NIL 1464102 NIL) (-641 1459938 1460568 1461256 "LEXTRIPK" 1462400 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-640 1456682 1457508 1458011 "LEXP" 1459518 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-639 1456158 1456403 1456495 "LETAST" 1456610 T LETAST (NIL) -8 NIL NIL NIL) (-638 1454556 1454869 1455270 "LEADCDET" 1455840 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-637 1453746 1453820 1454049 "LAZM3PK" 1454477 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-636 1448663 1451823 1452361 "LAUPOL" 1453258 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-635 1448242 1448286 1448447 "LAPLACE" 1448613 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-634 1446181 1447343 1447594 "LA" 1448075 NIL LA (NIL T T T) -8 NIL NIL NIL) (-633 1445161 1445745 1445786 "LALG" 1445848 NIL LALG (NIL T) -9 NIL 1445907 NIL) (-632 1444875 1444934 1445070 "LALG-" 1445075 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-631 1444710 1444734 1444775 "KVTFROM" 1444837 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-630 1443633 1444077 1444262 "KTVLOGIC" 1444545 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-629 1443468 1443492 1443533 "KRCFROM" 1443595 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-628 1442372 1442559 1442858 "KOVACIC" 1443268 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-627 1442207 1442231 1442272 "KONVERT" 1442334 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-626 1442042 1442066 1442107 "KOERCE" 1442169 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-625 1439873 1440635 1441012 "KERNEL" 1441698 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-624 1439369 1439450 1439582 "KERNEL2" 1439787 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-623 1433080 1437846 1437900 "KDAGG" 1438277 NIL KDAGG (NIL T T) -9 NIL 1438483 NIL) (-622 1432609 1432733 1432938 "KDAGG-" 1432943 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-621 1425757 1432270 1432425 "KAFILE" 1432487 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-620 1420185 1425268 1425496 "JORDAN" 1425578 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1419564 1419834 1419955 "JOINAST" 1420084 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1419410 1419469 1419524 "JAVACODE" 1419529 T JAVACODE (NIL) -8 NIL NIL NIL) (-617 1415637 1417587 1417641 "IXAGG" 1418570 NIL IXAGG (NIL T T) -9 NIL 1419029 NIL) (-616 1414556 1414862 1415281 "IXAGG-" 1415286 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-615 1410089 1414478 1414537 "IVECTOR" 1414542 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-614 1408855 1409092 1409358 "ITUPLE" 1409856 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-613 1407357 1407534 1407829 "ITRIGMNP" 1408677 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-612 1406102 1406306 1406589 "ITFUN3" 1407133 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-611 1405734 1405791 1405900 "ITFUN2" 1406039 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-610 1404893 1405214 1405388 "ITFORM" 1405580 T ITFORM (NIL) -8 NIL NIL NIL) (-609 1402854 1403913 1404191 "ITAYLOR" 1404648 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-608 1391799 1396991 1398154 "ISUPS" 1401724 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-607 1390903 1391043 1391279 "ISUMP" 1391646 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-606 1386281 1390848 1390889 "ISTRING" 1390894 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-605 1385757 1386002 1386094 "ISAST" 1386209 T ISAST (NIL) -8 NIL NIL NIL) (-604 1384966 1385048 1385264 "IRURPK" 1385671 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-603 1383902 1384103 1384343 "IRSN" 1384746 T IRSN (NIL) -7 NIL NIL NIL) (-602 1381973 1382328 1382757 "IRRF2F" 1383540 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-601 1381720 1381758 1381834 "IRREDFFX" 1381929 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-600 1380335 1380594 1380893 "IROOT" 1381453 NIL IROOT (NIL T) -7 NIL NIL NIL) (-599 1376939 1378019 1378711 "IR" 1379675 NIL IR (NIL T) -8 NIL NIL NIL) (-598 1376144 1376432 1376583 "IRFORM" 1376808 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1373757 1374252 1374818 "IR2" 1375622 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-596 1372857 1372970 1373184 "IR2F" 1373640 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-595 1372648 1372682 1372742 "IPRNTPK" 1372817 T IPRNTPK (NIL) -7 NIL NIL NIL) (-594 1369229 1372537 1372606 "IPF" 1372611 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-593 1367556 1369154 1369211 "IPADIC" 1369216 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-592 1366868 1367116 1367246 "IP4ADDR" 1367446 T IP4ADDR (NIL) -8 NIL NIL NIL) (-591 1366242 1366497 1366629 "IOMODE" 1366756 T IOMODE (NIL) -8 NIL NIL NIL) (-590 1365315 1365839 1365966 "IOBFILE" 1366135 T IOBFILE (NIL) -8 NIL NIL NIL) (-589 1364803 1365219 1365247 "IOBCON" 1365252 T IOBCON (NIL) -9 NIL 1365273 NIL) (-588 1364314 1364372 1364555 "INVLAPLA" 1364739 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-587 1353962 1356316 1358702 "INTTR" 1361978 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-586 1350297 1351039 1351904 "INTTOOLS" 1353147 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-585 1349883 1349974 1350091 "INTSLPE" 1350200 T INTSLPE (NIL) -7 NIL NIL NIL) (-584 1347836 1349806 1349865 "INTRVL" 1349870 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-583 1345438 1345950 1346525 "INTRF" 1347321 NIL INTRF (NIL T) -7 NIL NIL NIL) (-582 1344849 1344946 1345088 "INTRET" 1345336 NIL INTRET (NIL T) -7 NIL NIL NIL) (-581 1342846 1343235 1343705 "INTRAT" 1344457 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-580 1340109 1340692 1341311 "INTPM" 1342331 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-579 1336854 1337453 1338191 "INTPAF" 1339495 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-578 1332033 1332995 1334046 "INTPACK" 1335823 T INTPACK (NIL) -7 NIL NIL NIL) (-577 1328845 1331830 1331939 "INT" 1331944 T INT (NIL) -8 NIL NIL NIL) (-576 1328097 1328249 1328457 "INTHERTR" 1328687 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1327536 1327616 1327804 "INTHERAL" 1328011 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1325382 1325825 1326282 "INTHEORY" 1327099 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1316788 1318409 1320181 "INTG0" 1323734 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1297361 1302151 1306961 "INTFTBL" 1311998 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1296610 1296748 1296921 "INTFACT" 1297220 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1294037 1294483 1295040 "INTEF" 1296164 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1292390 1293129 1293157 "INTDOM" 1293458 T INTDOM (NIL) -9 NIL 1293665 NIL) (-568 1291759 1291933 1292175 "INTDOM-" 1292180 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1288119 1290048 1290102 "INTCAT" 1290901 NIL INTCAT (NIL T) -9 NIL 1291222 NIL) (-566 1287591 1287694 1287822 "INTBIT" 1288011 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1286290 1286444 1286751 "INTALG" 1287436 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1285773 1285863 1286020 "INTAF" 1286194 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1279122 1285583 1285723 "INTABL" 1285728 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1278455 1278921 1278986 "INT8" 1279020 T INT8 (NIL) -8 NIL NIL 1279065) (-561 1277787 1278253 1278318 "INT64" 1278352 T INT64 (NIL) -8 NIL NIL 1278397) (-560 1277119 1277585 1277650 "INT32" 1277684 T INT32 (NIL) -8 NIL NIL 1277729) (-559 1276451 1276917 1276982 "INT16" 1277016 T INT16 (NIL) -8 NIL NIL 1277061) (-558 1271146 1273999 1274027 "INS" 1274961 T INS (NIL) -9 NIL 1275626 NIL) (-557 1268386 1269157 1270131 "INS-" 1270204 NIL INS- (NIL T) -8 NIL NIL NIL) (-556 1267161 1267388 1267686 "INPSIGN" 1268139 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-555 1266279 1266396 1266593 "INPRODPF" 1267041 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-554 1265173 1265290 1265527 "INPRODFF" 1266159 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-553 1264173 1264325 1264585 "INNMFACT" 1265009 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-552 1263370 1263467 1263655 "INMODGCD" 1264072 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-551 1261878 1262123 1262447 "INFSP" 1263115 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-550 1261062 1261179 1261362 "INFPROD0" 1261758 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-549 1257917 1259127 1259642 "INFORM" 1260555 T INFORM (NIL) -8 NIL NIL NIL) (-548 1257527 1257587 1257685 "INFORM1" 1257852 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1257050 1257139 1257253 "INFINITY" 1257433 T INFINITY (NIL) -7 NIL NIL NIL) (-546 1256226 1256770 1256871 "INETCLTS" 1256969 T INETCLTS (NIL) -8 NIL NIL NIL) (-545 1254842 1255092 1255413 "INEP" 1255974 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-544 1254047 1254739 1254804 "INDE" 1254809 NIL INDE (NIL T) -8 NIL NIL NIL) (-543 1253611 1253679 1253796 "INCRMAPS" 1253974 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-542 1252429 1252880 1253086 "INBFILE" 1253425 T INBFILE (NIL) -8 NIL NIL NIL) (-541 1247728 1248665 1249609 "INBFF" 1251517 NIL INBFF (NIL T) -7 NIL NIL NIL) (-540 1246636 1246905 1246933 "INBCON" 1247446 T INBCON (NIL) -9 NIL 1247712 NIL) (-539 1245888 1246111 1246387 "INBCON-" 1246392 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-538 1245367 1245612 1245703 "INAST" 1245817 T INAST (NIL) -8 NIL NIL NIL) (-537 1244794 1245046 1245152 "IMPTAST" 1245281 T IMPTAST (NIL) -8 NIL NIL NIL) (-536 1241195 1244638 1244742 "IMATRIX" 1244747 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-535 1239903 1240026 1240342 "IMATQF" 1241051 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-534 1238123 1238350 1238687 "IMATLIN" 1239659 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-533 1232704 1238047 1238105 "ILIST" 1238110 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-532 1230612 1232564 1232677 "IIARRAY2" 1232682 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-531 1226010 1230523 1230587 "IFF" 1230592 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-530 1225357 1225627 1225743 "IFAST" 1225914 T IFAST (NIL) -8 NIL NIL NIL) (-529 1220355 1224649 1224837 "IFARRAY" 1225214 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-528 1219535 1220259 1220332 "IFAMON" 1220337 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-527 1219119 1219184 1219238 "IEVALAB" 1219445 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-526 1218794 1218862 1219022 "IEVALAB-" 1219027 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-525 1218241 1218709 1218771 "IDPO" 1218776 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-524 1217449 1218130 1218205 "IDPOAMS" 1218210 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1216714 1217338 1217413 "IDPOAM" 1217418 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1215260 1215721 1215773 "IDPC" 1216285 NIL IDPC (NIL T T) -9 NIL 1216566 NIL) (-521 1214688 1215152 1215225 "IDPAM" 1215230 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-520 1214023 1214580 1214653 "IDPAG" 1214658 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-519 1213668 1213859 1213934 "IDENT" 1213968 T IDENT (NIL) -8 NIL NIL NIL) (-518 1209923 1210771 1211666 "IDECOMP" 1212825 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-517 1202760 1203846 1204893 "IDEAL" 1208959 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-516 1201920 1202032 1202232 "ICDEN" 1202644 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-515 1200991 1201400 1201547 "ICARD" 1201793 T ICARD (NIL) -8 NIL NIL NIL) (-514 1199051 1199364 1199769 "IBPTOOLS" 1200668 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-513 1194658 1198671 1198784 "IBITS" 1198970 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-512 1191381 1191957 1192652 "IBATOOL" 1194075 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-511 1189160 1189622 1190155 "IBACHIN" 1190916 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-510 1186992 1189006 1189109 "IARRAY2" 1189114 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-509 1183101 1186918 1186975 "IARRAY1" 1186980 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-508 1176961 1181513 1181994 "IAN" 1182640 T IAN (NIL) -8 NIL NIL NIL) (-507 1176472 1176529 1176702 "IALGFACT" 1176898 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-506 1176000 1176113 1176141 "HYPCAT" 1176348 T HYPCAT (NIL) -9 NIL NIL NIL) (-505 1175538 1175655 1175841 "HYPCAT-" 1175846 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-504 1175133 1175333 1175416 "HOSTNAME" 1175475 T HOSTNAME (NIL) -8 NIL NIL NIL) (-503 1174978 1175015 1175056 "HOMOTOP" 1175061 NIL HOMOTOP (NIL T) -9 NIL 1175094 NIL) (-502 1171535 1172910 1172951 "HOAGG" 1173932 NIL HOAGG (NIL T) -9 NIL 1174661 NIL) (-501 1170129 1170528 1171054 "HOAGG-" 1171059 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-500 1163845 1169722 1169872 "HEXADEC" 1169999 T HEXADEC (NIL) -8 NIL NIL NIL) (-499 1162593 1162815 1163078 "HEUGCD" 1163622 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-498 1161669 1162430 1162560 "HELLFDIV" 1162565 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-497 1159851 1161446 1161534 "HEAP" 1161613 NIL HEAP (NIL T) -8 NIL NIL NIL) (-496 1159114 1159403 1159537 "HEADAST" 1159737 T HEADAST (NIL) -8 NIL NIL NIL) (-495 1152957 1159029 1159091 "HDP" 1159096 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-494 1146669 1152592 1152744 "HDMP" 1152858 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-493 1145993 1146133 1146297 "HB" 1146525 T HB (NIL) -7 NIL NIL NIL) (-492 1139385 1145839 1145943 "HASHTBL" 1145948 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-491 1138861 1139106 1139198 "HASAST" 1139313 T HASAST (NIL) -8 NIL NIL NIL) (-490 1136639 1138483 1138665 "HACKPI" 1138699 T HACKPI (NIL) -8 NIL NIL NIL) (-489 1132307 1136492 1136605 "GTSET" 1136610 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-488 1125728 1132185 1132283 "GSTBL" 1132288 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-487 1118115 1124893 1125149 "GSERIES" 1125528 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-486 1117242 1117659 1117687 "GROUP" 1117890 T GROUP (NIL) -9 NIL 1118024 NIL) (-485 1116608 1116767 1117018 "GROUP-" 1117023 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-484 1114975 1115296 1115683 "GROEBSOL" 1116285 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-483 1113875 1114163 1114214 "GRMOD" 1114743 NIL GRMOD (NIL T T) -9 NIL 1114911 NIL) (-482 1113643 1113679 1113807 "GRMOD-" 1113812 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-481 1108933 1109997 1110997 "GRIMAGE" 1112663 T GRIMAGE (NIL) -8 NIL NIL NIL) (-480 1107399 1107660 1107984 "GRDEF" 1108629 T GRDEF (NIL) -7 NIL NIL NIL) (-479 1106843 1106959 1107100 "GRAY" 1107278 T GRAY (NIL) -7 NIL NIL NIL) (-478 1106016 1106422 1106473 "GRALG" 1106626 NIL GRALG (NIL T T) -9 NIL 1106719 NIL) (-477 1105677 1105750 1105913 "GRALG-" 1105918 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-476 1102452 1105260 1105439 "GPOLSET" 1105583 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-475 1101806 1101863 1102121 "GOSPER" 1102389 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-474 1097538 1098244 1098770 "GMODPOL" 1101505 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-473 1096543 1096727 1096965 "GHENSEL" 1097350 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-472 1090699 1091542 1092562 "GENUPS" 1095627 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-471 1090396 1090447 1090536 "GENUFACT" 1090642 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-470 1089808 1089885 1090050 "GENPGCD" 1090314 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-469 1089282 1089317 1089530 "GENMFACT" 1089767 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-468 1087848 1088105 1088412 "GENEEZ" 1089025 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-467 1081720 1087459 1087621 "GDMP" 1087771 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-466 1071063 1075491 1076597 "GCNAALG" 1080703 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-465 1069376 1070238 1070266 "GCDDOM" 1070521 T GCDDOM (NIL) -9 NIL 1070678 NIL) (-464 1068846 1068973 1069188 "GCDDOM-" 1069193 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-463 1067518 1067703 1068007 "GB" 1068625 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-462 1056134 1058464 1060856 "GBINTERN" 1065209 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1053971 1054263 1054684 "GBF" 1055809 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1052752 1052917 1053184 "GBEUCLID" 1053787 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1052101 1052226 1052375 "GAUSSFAC" 1052623 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-458 1050468 1050770 1051084 "GALUTIL" 1051820 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-457 1048776 1049050 1049374 "GALPOLYU" 1050195 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-456 1046141 1046431 1046838 "GALFACTU" 1048473 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-455 1037947 1039446 1041054 "GALFACT" 1044573 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-454 1035335 1035993 1036021 "FVFUN" 1037177 T FVFUN (NIL) -9 NIL 1037897 NIL) (-453 1034601 1034783 1034811 "FVC" 1035102 T FVC (NIL) -9 NIL 1035285 NIL) (-452 1034244 1034426 1034494 "FUNDESC" 1034553 T FUNDESC (NIL) -8 NIL NIL NIL) (-451 1033859 1034041 1034122 "FUNCTION" 1034196 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-450 1031603 1032181 1032647 "FT" 1033413 T FT (NIL) -8 NIL NIL NIL) (-449 1030394 1030904 1031107 "FTEM" 1031420 T FTEM (NIL) -8 NIL NIL NIL) (-448 1028685 1028974 1029371 "FSUPFACT" 1030085 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-447 1027082 1027371 1027703 "FST" 1028373 T FST (NIL) -8 NIL NIL NIL) (-446 1026281 1026387 1026575 "FSRED" 1026964 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-445 1024980 1025236 1025583 "FSPRMELT" 1025996 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-444 1022286 1022724 1023210 "FSPECF" 1024543 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-443 1003351 1012060 1012101 "FS" 1015985 NIL FS (NIL T) -9 NIL 1018274 NIL) (-442 991994 994987 999044 "FS-" 999344 NIL FS- (NIL T T) -8 NIL NIL NIL) (-441 991522 991576 991746 "FSINT" 991935 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-440 989814 990515 990818 "FSERIES" 991301 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-439 988856 988972 989196 "FSCINT" 989694 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-438 985064 987800 987841 "FSAGG" 988211 NIL FSAGG (NIL T) -9 NIL 988470 NIL) (-437 982826 983427 984223 "FSAGG-" 984318 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 981868 982011 982238 "FSAGG2" 982679 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-435 979546 979826 980374 "FS2UPS" 981586 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-434 979180 979223 979352 "FS2" 979497 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 978058 978229 978531 "FS2EXPXP" 979005 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-432 977484 977599 977751 "FRUTIL" 977938 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-431 968897 972979 974337 "FR" 976158 NIL FR (NIL T) -8 NIL NIL NIL) (-430 963911 966586 966626 "FRNAALG" 967946 NIL FRNAALG (NIL T) -9 NIL 968544 NIL) (-429 959584 960660 961935 "FRNAALG-" 962685 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 959222 959265 959392 "FRNAAF2" 959535 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 957597 958071 958367 "FRMOD" 959034 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 955340 955972 956290 "FRIDEAL" 957388 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-425 954531 954618 954909 "FRIDEAL2" 955247 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-424 953664 954078 954119 "FRETRCT" 954124 NIL FRETRCT (NIL T) -9 NIL 954300 NIL) (-423 952776 953007 953358 "FRETRCT-" 953363 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 949850 951060 951119 "FRAMALG" 952001 NIL FRAMALG (NIL T T) -9 NIL 952293 NIL) (-421 947984 948439 949069 "FRAMALG-" 949292 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 941627 947457 947734 "FRAC" 947739 NIL FRAC (NIL T) -8 NIL NIL NIL) (-419 941263 941320 941427 "FRAC2" 941564 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-418 940899 940956 941063 "FR2" 941200 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 935384 938278 938306 "FPS" 939425 T FPS (NIL) -9 NIL 939982 NIL) (-416 934833 934942 935106 "FPS-" 935252 NIL FPS- (NIL T) -8 NIL NIL NIL) (-415 932121 933790 933818 "FPC" 934043 T FPC (NIL) -9 NIL 934185 NIL) (-414 931914 931954 932051 "FPC-" 932056 NIL FPC- (NIL T) -8 NIL NIL NIL) (-413 930704 931402 931443 "FPATMAB" 931448 NIL FPATMAB (NIL T) -9 NIL 931600 NIL) (-412 928943 929446 929793 "FPARFRAC" 930420 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-411 924337 924835 925517 "FORTRAN" 928375 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-410 922053 922553 923092 "FORT" 923818 T FORT (NIL) -7 NIL NIL NIL) (-409 919729 920291 920319 "FORTFN" 921379 T FORTFN (NIL) -9 NIL 922003 NIL) (-408 919493 919543 919571 "FORTCAT" 919630 T FORTCAT (NIL) -9 NIL 919692 NIL) (-407 917599 918109 918499 "FORMULA" 919123 T FORMULA (NIL) -8 NIL NIL NIL) (-406 917387 917417 917486 "FORMULA1" 917563 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-405 916910 916962 917135 "FORDER" 917329 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-404 916006 916170 916363 "FOP" 916737 T FOP (NIL) -7 NIL NIL NIL) (-403 914587 915286 915460 "FNLA" 915888 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-402 913302 913717 913745 "FNCAT" 914205 T FNCAT (NIL) -9 NIL 914465 NIL) (-401 912841 913261 913289 "FNAME" 913294 T FNAME (NIL) -8 NIL NIL NIL) (-400 911377 912340 912368 "FMTC" 912373 T FMTC (NIL) -9 NIL 912409 NIL) (-399 910123 911313 911359 "FMONOID" 911364 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-398 906910 908078 908119 "FMONCAT" 909336 NIL FMONCAT (NIL T) -9 NIL 909941 NIL) (-397 906060 906652 906801 "FM" 906806 NIL FM (NIL T T) -8 NIL NIL NIL) (-396 903484 904130 904158 "FMFUN" 905302 T FMFUN (NIL) -9 NIL 906010 NIL) (-395 902753 902934 902962 "FMC" 903252 T FMC (NIL) -9 NIL 903434 NIL) (-394 899818 900678 900732 "FMCAT" 901927 NIL FMCAT (NIL T T) -9 NIL 902422 NIL) (-393 898684 899584 899684 "FM1" 899763 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-392 896458 896874 897368 "FLOATRP" 898235 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-391 890036 894187 894808 "FLOAT" 895857 T FLOAT (NIL) -8 NIL NIL NIL) (-390 887474 887974 888552 "FLOATCP" 889503 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-389 886122 887066 887107 "FLINEXP" 887112 NIL FLINEXP (NIL T) -9 NIL 887205 NIL) (-388 885276 885511 885839 "FLINEXP-" 885844 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-387 884352 884496 884720 "FLASORT" 885128 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-386 881454 882322 882374 "FLALG" 883601 NIL FLALG (NIL T T) -9 NIL 884068 NIL) (-385 875114 878863 878904 "FLAGG" 880166 NIL FLAGG (NIL T) -9 NIL 880818 NIL) (-384 873840 874179 874669 "FLAGG-" 874674 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 872882 873025 873252 "FLAGG2" 873693 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-382 869719 870727 870786 "FINRALG" 871914 NIL FINRALG (NIL T T) -9 NIL 872422 NIL) (-381 868879 869108 869447 "FINRALG-" 869452 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-380 868245 868484 868512 "FINITE" 868708 T FINITE (NIL) -9 NIL 868815 NIL) (-379 860588 862775 862815 "FINAALG" 866482 NIL FINAALG (NIL T) -9 NIL 867935 NIL) (-378 855920 856970 858114 "FINAALG-" 859493 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-377 855288 855675 855778 "FILE" 855850 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 853932 854270 854324 "FILECAT" 855008 NIL FILECAT (NIL T T) -9 NIL 855224 NIL) (-375 851634 853162 853190 "FIELD" 853230 T FIELD (NIL) -9 NIL 853310 NIL) (-374 850254 850639 851150 "FIELD-" 851155 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-373 848104 848889 849236 "FGROUP" 849940 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-372 847194 847358 847578 "FGLMICPK" 847936 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-371 843026 847119 847176 "FFX" 847181 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-370 842627 842688 842823 "FFSLPE" 842959 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-369 838617 839399 840195 "FFPOLY" 841863 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 838121 838157 838366 "FFPOLY2" 838575 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-367 833967 838040 838103 "FFP" 838108 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-366 829365 833878 833942 "FF" 833947 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-365 824491 828708 828898 "FFNBX" 829219 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-364 819419 823626 823884 "FFNBP" 824345 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-363 814052 818703 818914 "FFNB" 819252 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-362 812884 813082 813397 "FFINTBAS" 813849 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-361 808910 811131 811159 "FFIELDC" 811779 T FFIELDC (NIL) -9 NIL 812155 NIL) (-360 807572 807943 808440 "FFIELDC-" 808445 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-359 807141 807187 807311 "FFHOM" 807514 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-358 804836 805323 805840 "FFF" 806656 NIL FFF (NIL T) -7 NIL NIL NIL) (-357 800454 804578 804679 "FFCGX" 804779 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-356 796076 800186 800293 "FFCGP" 800397 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-355 791259 795803 795911 "FFCG" 796012 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-354 770788 780991 781077 "FFCAT" 786242 NIL FFCAT (NIL T T T) -9 NIL 787693 NIL) (-353 765985 767033 768347 "FFCAT-" 769577 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-352 765396 765439 765674 "FFCAT2" 765936 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-351 754719 758368 759588 "FEXPR" 764248 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-350 753681 754116 754157 "FEVALAB" 754241 NIL FEVALAB (NIL T) -9 NIL 754502 NIL) (-349 752840 753050 753388 "FEVALAB-" 753393 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-348 751406 752223 752426 "FDIV" 752739 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-347 748412 749153 749268 "FDIVCAT" 750836 NIL FDIVCAT (NIL T T T T) -9 NIL 751273 NIL) (-346 748174 748201 748371 "FDIVCAT-" 748376 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-345 747394 747481 747758 "FDIV2" 748081 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 746368 746689 746891 "FCTRDATA" 747212 T FCTRDATA (NIL) -8 NIL NIL NIL) (-343 745054 745313 745602 "FCPAK1" 746099 T FCPAK1 (NIL) -7 NIL NIL NIL) (-342 744153 744554 744695 "FCOMP" 744945 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-341 727858 731303 734841 "FC" 740635 T FC (NIL) -8 NIL NIL NIL) (-340 720151 724179 724219 "FAXF" 726021 NIL FAXF (NIL T) -9 NIL 726713 NIL) (-339 717428 718085 718910 "FAXF-" 719375 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-338 712483 716804 716980 "FARRAY" 717285 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-337 707363 709430 709483 "FAMR" 710506 NIL FAMR (NIL T T) -9 NIL 710966 NIL) (-336 706253 706555 706990 "FAMR-" 706995 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-335 705422 706175 706228 "FAMONOID" 706233 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-334 703194 703904 703957 "FAMONC" 704898 NIL FAMONC (NIL T T) -9 NIL 705284 NIL) (-333 701858 702948 703085 "FAGROUP" 703090 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-332 699653 699972 700375 "FACUTIL" 701539 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-331 698752 698937 699159 "FACTFUNC" 699463 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-330 691174 698055 698254 "EXPUPXS" 698608 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-329 688657 689197 689783 "EXPRTUBE" 690608 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-328 684928 685520 686250 "EXPRODE" 687996 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-327 670412 683577 684006 "EXPR" 684532 NIL EXPR (NIL T) -8 NIL NIL NIL) (-326 664966 665553 666359 "EXPR2UPS" 669710 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-325 664598 664655 664764 "EXPR2" 664903 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-324 655595 663749 664040 "EXPEXPAN" 664434 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-323 655395 655552 655581 "EXIT" 655586 T EXIT (NIL) -8 NIL NIL NIL) (-322 654875 655119 655210 "EXITAST" 655324 T EXITAST (NIL) -8 NIL NIL NIL) (-321 654502 654564 654677 "EVALCYC" 654807 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-320 654043 654161 654202 "EVALAB" 654372 NIL EVALAB (NIL T) -9 NIL 654476 NIL) (-319 653524 653646 653867 "EVALAB-" 653872 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-318 650878 652180 652208 "EUCDOM" 652763 T EUCDOM (NIL) -9 NIL 653113 NIL) (-317 649283 649725 650315 "EUCDOM-" 650320 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-316 636822 639581 642331 "ESTOOLS" 646553 T ESTOOLS (NIL) -7 NIL NIL NIL) (-315 636454 636511 636620 "ESTOOLS2" 636759 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-314 636205 636247 636327 "ESTOOLS1" 636406 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-313 630228 631836 631864 "ES" 634632 T ES (NIL) -9 NIL 636042 NIL) (-312 625175 626462 628279 "ES-" 628443 NIL ES- (NIL T) -8 NIL NIL NIL) (-311 621549 622310 623090 "ESCONT" 624415 T ESCONT (NIL) -7 NIL NIL NIL) (-310 621294 621326 621408 "ESCONT1" 621511 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-309 620969 621019 621119 "ES2" 621238 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-308 620599 620657 620766 "ES1" 620905 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-307 619815 619944 620120 "ERROR" 620443 T ERROR (NIL) -7 NIL NIL NIL) (-306 613213 619674 619765 "EQTBL" 619770 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-305 605716 608527 609976 "EQ" 611797 NIL -3023 (NIL T) -8 NIL NIL NIL) (-304 605348 605405 605514 "EQ2" 605653 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-303 600639 601686 602779 "EP" 604287 NIL EP (NIL T) -7 NIL NIL NIL) (-302 599239 599530 599836 "ENV" 600353 T ENV (NIL) -8 NIL NIL NIL) (-301 598319 598873 598901 "ENTIRER" 598906 T ENTIRER (NIL) -9 NIL 598952 NIL) (-300 595013 596501 596862 "EMR" 598127 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-299 594143 594328 594382 "ELTAGG" 594762 NIL ELTAGG (NIL T T) -9 NIL 594973 NIL) (-298 593862 593924 594065 "ELTAGG-" 594070 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-297 593626 593655 593709 "ELTAB" 593793 NIL ELTAB (NIL T T) -9 NIL 593845 NIL) (-296 592752 592898 593097 "ELFUTS" 593477 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-295 592494 592550 592578 "ELEMFUN" 592683 T ELEMFUN (NIL) -9 NIL NIL NIL) (-294 592364 592385 592453 "ELEMFUN-" 592458 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-293 587153 590406 590447 "ELAGG" 591387 NIL ELAGG (NIL T) -9 NIL 591850 NIL) (-292 585438 585872 586535 "ELAGG-" 586540 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-291 584750 584887 585043 "ELABOR" 585302 T ELABOR (NIL) -8 NIL NIL NIL) (-290 583411 583690 583984 "ELABEXPR" 584476 T ELABEXPR (NIL) -8 NIL NIL NIL) (-289 576245 578048 578877 "EFUPXS" 582686 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-288 569693 571494 572305 "EFULS" 575520 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-287 567178 567536 568008 "EFSTRUC" 569325 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-286 556969 558535 560083 "EF" 565693 NIL EF (NIL T T) -7 NIL NIL NIL) (-285 556043 556454 556603 "EAB" 556840 T EAB (NIL) -8 NIL NIL NIL) (-284 555225 556002 556030 "E04UCFA" 556035 T E04UCFA (NIL) -8 NIL NIL NIL) (-283 554407 555184 555212 "E04NAFA" 555217 T E04NAFA (NIL) -8 NIL NIL NIL) (-282 553589 554366 554394 "E04MBFA" 554399 T E04MBFA (NIL) -8 NIL NIL NIL) (-281 552771 553548 553576 "E04JAFA" 553581 T E04JAFA (NIL) -8 NIL NIL NIL) (-280 551955 552730 552758 "E04GCFA" 552763 T E04GCFA (NIL) -8 NIL NIL NIL) (-279 551139 551914 551942 "E04FDFA" 551947 T E04FDFA (NIL) -8 NIL NIL NIL) (-278 550321 551098 551126 "E04DGFA" 551131 T E04DGFA (NIL) -8 NIL NIL NIL) (-277 544494 545846 547210 "E04AGNT" 548977 T E04AGNT (NIL) -7 NIL NIL NIL) (-276 543252 543795 543835 "DVARCAT" 544176 NIL DVARCAT (NIL T) -9 NIL 544339 NIL) (-275 542456 542668 542982 "DVARCAT-" 542987 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-274 535317 542255 542384 "DSMP" 542389 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-273 533740 534459 534500 "DSEXT" 534863 NIL DSEXT (NIL T) -9 NIL 535157 NIL) (-272 532025 532453 533119 "DSEXT-" 533124 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-271 526806 527970 529038 "DROPT" 530977 T DROPT (NIL) -8 NIL NIL NIL) (-270 526471 526530 526628 "DROPT1" 526741 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-269 521586 522712 523849 "DROPT0" 525354 T DROPT0 (NIL) -7 NIL NIL NIL) (-268 519931 520256 520642 "DRAWPT" 521220 T DRAWPT (NIL) -7 NIL NIL NIL) (-267 514518 515441 516520 "DRAW" 518905 NIL DRAW (NIL T) -7 NIL NIL NIL) (-266 514151 514204 514322 "DRAWHACK" 514459 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-265 512882 513151 513442 "DRAWCX" 513880 T DRAWCX (NIL) -7 NIL NIL NIL) (-264 512397 512466 512617 "DRAWCURV" 512808 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-263 502865 504827 506942 "DRAWCFUN" 510302 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-262 499604 501530 501571 "DQAGG" 502200 NIL DQAGG (NIL T) -9 NIL 502474 NIL) (-261 487069 493815 493898 "DPOLCAT" 495750 NIL DPOLCAT (NIL T T T T) -9 NIL 496295 NIL) (-260 481906 483254 485212 "DPOLCAT-" 485217 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-259 475253 481767 481865 "DPMO" 481870 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-258 468503 475033 475200 "DPMM" 475205 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-257 468073 468287 468376 "DOMTMPLT" 468434 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-256 467506 467875 467955 "DOMCTOR" 468013 T DOMCTOR (NIL) -8 NIL NIL NIL) (-255 466718 466986 467137 "DOMAIN" 467375 T DOMAIN (NIL) -8 NIL NIL NIL) (-254 460430 466353 466505 "DMP" 466619 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-253 458375 459497 459538 "DMEXT" 459543 NIL DMEXT (NIL T) -9 NIL 459719 NIL) (-252 457975 458031 458175 "DLP" 458313 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 451800 457302 457492 "DLIST" 457817 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 448572 450625 450666 "DLAGG" 451216 NIL DLAGG (NIL T) -9 NIL 451446 NIL) (-249 447234 447898 447926 "DIVRING" 448018 T DIVRING (NIL) -9 NIL 448101 NIL) (-248 446471 446661 446961 "DIVRING-" 446966 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 444573 444930 445336 "DISPLAY" 446085 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 438436 444487 444550 "DIRPROD" 444555 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 437284 437487 437752 "DIRPROD2" 438229 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 425959 431995 432048 "DIRPCAT" 432306 NIL DIRPCAT (NIL NIL T) -9 NIL 433181 NIL) (-243 423285 423927 424808 "DIRPCAT-" 425145 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 422572 422732 422918 "DIOSP" 423119 T DIOSP (NIL) -7 NIL NIL NIL) (-241 419202 421456 421497 "DIOPS" 421931 NIL DIOPS (NIL T) -9 NIL 422160 NIL) (-240 418751 418865 419056 "DIOPS-" 419061 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 417802 418430 418458 "DIFRING" 418463 T DIFRING (NIL) -9 NIL 418485 NIL) (-238 417474 417548 417576 "DIFFSPC" 417695 T DIFFSPC (NIL) -9 NIL 417770 NIL) (-237 417119 417197 417349 "DIFFSPC-" 417354 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 416175 416653 416694 "DIFFMOD" 416699 NIL DIFFMOD (NIL T) -9 NIL 416797 NIL) (-235 415883 415928 415969 "DIFFDOM" 416090 NIL DIFFDOM (NIL T) -9 NIL 416158 NIL) (-234 415736 415760 415844 "DIFFDOM-" 415849 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 413668 414940 414981 "DIFEXT" 414986 NIL DIFEXT (NIL T) -9 NIL 415139 NIL) (-232 410918 413172 413213 "DIAGG" 413218 NIL DIAGG (NIL T) -9 NIL 413238 NIL) (-231 410302 410459 410711 "DIAGG-" 410716 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-230 405674 409261 409538 "DHMATRIX" 410071 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-229 401286 402195 403205 "DFSFUN" 404684 T DFSFUN (NIL) -7 NIL NIL NIL) (-228 396364 400217 400529 "DFLOAT" 400994 T DFLOAT (NIL) -8 NIL NIL NIL) (-227 394627 394908 395297 "DFINTTLS" 396072 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-226 391656 392648 393048 "DERHAM" 394293 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-225 389460 391431 391520 "DEQUEUE" 391600 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-224 388714 388847 389030 "DEGRED" 389322 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-223 385144 385889 386735 "DEFINTRF" 387942 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-222 382699 383168 383760 "DEFINTEF" 384663 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-221 382049 382319 382434 "DEFAST" 382604 T DEFAST (NIL) -8 NIL NIL NIL) (-220 375765 381642 381792 "DECIMAL" 381919 T DECIMAL (NIL) -8 NIL NIL NIL) (-219 373277 373735 374241 "DDFACT" 375309 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-218 372873 372916 373067 "DBLRESP" 373228 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-217 372176 372643 372734 "DBASIS" 372822 NIL DBASIS (NIL NIL) -8 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 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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 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"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))
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(-660 (-341))))) + (-5 *2 (-2 (|:| |localSymbols| (-1205)) (|:| -2957 (-660 (-341))))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-341)) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-660 (-341))) (-4 *1 (-454)))) @@ -2643,7 +2428,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-660 (-2 (|:| -2270 *3) (|:| -4212 *4)))) + (-12 (-5 *2 (-660 (-2 (|:| -2519 *3) (|:| -2276 *4)))) (-4 *3 (-1074)) (-4 *4 (-742)) (-5 *1 (-751 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-577)) (-4 *1 (-779)))) ((*1 *1 *2) @@ -2652,25 +2437,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228))) - (|:| -1628 (-1119 (-859 (-228)))) (|:| |abserr| (-228)) + (|:| -3656 (-1119 (-859 (-228)))) (|:| |abserr| (-228)) (|:| |relerr| (-228)))) (|:| |mdnia| (-2 (|:| |fn| (-327 (-228))) - (|:| -1628 (-660 (-1119 (-859 (-228))))) + (|:| -3656 (-660 (-1119 (-859 (-228))))) (|:| |abserr| (-228)) (|:| |relerr| (-228)))))) (-5 *1 (-785)))) ((*1 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(-12 (-5 *2 (-577)) (-5 *1 (-574))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1201)) (-5 *5 (-660 *3)) + (-4 *3 (-13 (-27) (-1227) (-443 *6))) + (-4 *6 (-13 (-465) (-148) (-1063 (-577)) (-654 (-577)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-660 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-570 *6 *3))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-660 (-1183))) (-5 *1 (-1222))))) +(((*1 *2 *1) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1242)) (-4 *4 (-385 *3)) + (-4 *5 (-385 *3)) (-5 *2 (-577)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1078 *3 *4 *5 *6 *7)) (-4 *5 (-1074)) + (-4 *6 (-244 *4 *5)) (-4 *7 (-244 *3 *5)) (-5 *2 (-577))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1242)) (-5 *1 (-387 *4 *2)) + (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4471))))))) +(((*1 *2 *3 *4 *4 *3 *5 *3 *3 *4 *3 *6) + (-12 (-5 *3 (-577)) (-5 *4 (-705 (-228))) (-5 *5 (-228)) + (-5 *6 (-3 (|:| |fn| (-401)) (|:| |fp| (-78 FUNCTN)))) + (-5 *2 (-1060)) (-5 *1 (-764))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -1632 *6) (|:| |sol?| (-112))) (-577) + *6)) + (-4 *6 (-375)) (-4 *7 (-1268 *6)) + (-5 *2 (-2 (|:| |answer| (-599 (-420 *7))) (|:| |a0| *6))) + (-5 *1 (-587 *6 *7)) (-5 *3 (-420 *7))))) +(((*1 *2 *3 *1) + (|partial| -12 (-5 *3 (-1 (-112) *2)) (-4 *1 (-152 *2)) + (-4 *2 (-1242))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -5214,50 +5223,50 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-660 (-577))) (-5 *1 (-285))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1182 *4)) (-5 *3 (-577)) (-4 *4 (-1074)) + (-5 *1 (-1185 *4)))) + ((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-577)) (-5 *1 (-1284 *3 *4 *5)) (-4 *3 (-1074)) + (-14 *4 (-1201)) (-14 *5 *3)))) (((*1 *2 *3) - (-12 (-5 *3 (-660 *2)) (-5 *1 (-499 *2)) (-4 *2 (-1268 (-577)))))) -(((*1 *1) - (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-577)) (-14 *3 (-787)) - (-4 *4 (-174))))) -(((*1 *2 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*4)))) - ((*1 *2) (-12 (-4 *1 (-379 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -5274,50 +5283,66 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-944)) (-5 *4 (-1183)) (-5 *2 (-1297)) (-5 *1 (-1293))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-465)) (-4 *6 (-809)) (-4 *7 (-865)) - (-4 *3 (-1090 *5 *6 *7)) - (-5 *2 (-660 (-2 (|:| |val| (-112)) (|:| -3889 *4)))) - (-5 *1 (-1133 *5 *6 *7 *3 *4)) (-4 *4 (-1096 *5 *6 *7 *3))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228))) - (|:| -1628 (-1119 (-859 (-228)))) (|:| |abserr| (-228)) - (|:| |relerr| (-228)))) + (-12 (-5 *3 (-431 *5)) (-4 *5 (-569)) (-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 *2 *2) (-12 (-5 *1 (-984 *2)) (-4 *2 (-558))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1235 *2 *3 *4 *5)) (-4 *2 (-569)) (-4 *3 (-809)) - (-4 *4 (-865)) (-4 *5 (-1090 *2 *3 *4))))) -(((*1 *2 *3) (-12 (-5 *2 (-660 (-577))) (-5 *1 (-574)) (-5 *3 (-577))))) + (-2 (|:| -2844 (-787)) (|:| -2519 *5) (|:| |radicand| (-660 *5)))) + (-5 *1 (-331 *5)) (-5 *4 (-787)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1027)) (-5 *2 (-577))))) (((*1 *2 *1) - (-12 (-4 *3 (-375)) (-4 *4 (-809)) (-4 *5 (-865)) (-5 *2 (-112)) - (-5 *1 (-517 *3 *4 *5 *6)) (-4 *6 (-972 *3 *4 *5))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-465)) (-4 *7 (-809)) (-4 *8 (-865)) - (-4 *3 (-1090 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-660 *4)) - (|:| |todo| (-660 (-2 (|:| |val| (-660 *3)) (|:| -3889 *4)))))) - (-5 *1 (-1094 *6 *7 *8 *3 *4)) (-4 *4 (-1096 *6 *7 *8 *3)))) + (-12 (-5 *2 (-880)) (-5 *1 (-403 *3 *4 *5)) (-14 *3 (-787)) + (-14 *4 (-787)) (-4 *5 (-174))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-577)) (-5 *1 (-176 *3)) (-4 *3 (-318)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-577)) (-4 *1 (-690 *3)) (-4 *3 (-1242)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-787)) (-4 *1 (-756 *3 *4)) (-4 *3 (-1074)) + (-4 *4 (-865)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-887 *3)) (-5 *2 (-577)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-660 *3)) (-4 *1 (-1005 *3)) (-4 *3 (-1074)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-660 *1)) (-5 *3 (-660 *7)) (-4 *1 (-1096 *4 *5 *6 *7)) + (-4 *4 (-465)) (-4 *5 (-809)) (-4 *6 (-865)) + (-4 *7 (-1090 *4 *5 *6)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-660 *7)) (-4 *7 (-1090 *4 *5 *6)) (-4 *4 (-465)) + (-4 *5 (-809)) (-4 *6 (-865)) (-5 *2 (-660 *1)) + (-4 *1 (-1096 *4 *5 *6 *7)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-660 *1)) (-4 *1 (-1096 *4 *5 *6 *3)) (-4 *4 (-465)) + (-4 *5 (-809)) (-4 *6 (-865)) (-4 *3 (-1090 *4 *5 *6)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-465)) (-4 *5 (-809)) (-4 *6 (-865)) + (-4 *3 (-1090 *4 *5 *6)) (-5 *2 (-660 *1)) + (-4 *1 (-1096 *4 *5 *6 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*4)) - (|:| |todo| (-660 (-2 (|:| |val| (-660 *3)) (|:| -3889 *4)))))) - (-5 *1 (-1170 *5 *6 *7 *3 *4)) (-4 *4 (-1134 *5 *6 *7 *3))))) + (-12 (-5 *3 (-660 *8)) (-5 *4 (-660 *9)) (-4 *8 (-1090 *5 *6 *7)) + (-4 *9 (-1134 *5 *6 *7 *8)) (-4 *5 (-465)) (-4 *6 (-809)) + (-4 *7 (-865)) (-5 *2 (-787)) (-5 *1 (-1170 *5 *6 *7 *8 *9))))) (((*1 *2 *3) - (-12 (-5 *3 (-327 (-228))) (-5 *2 (-420 (-577))) (-5 *1 (-316))))) + (-12 (-5 *3 (-1 *2 *2)) (-5 *1 (-698 *2)) (-4 *2 (-1125)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1 (-660 *5) (-660 *5))) (-5 *4 (-577)) + (-5 *2 (-660 *5)) (-5 *1 (-698 *5)) (-4 *5 (-1125))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -5334,50 +5359,40 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) - (-4 *4 (-865)) (-4 *2 (-465))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1182 *4)) (-5 *3 (-577)) (-4 *4 (-1074)) + (-5 *1 (-1185 *4)))) + ((*1 *1 *2 *2 *1) + (-12 (-5 *2 (-577)) (-5 *1 (-1284 *3 *4 *5)) (-4 *3 (-1074)) + (-14 *4 (-1201)) (-14 *5 *3)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1201)) (-5 *2 (-391)) (-5 *1 (-1088))))) +(((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1297)) (-5 *1 (-449))))) +(((*1 *2 *1) (-12 (-5 *2 (-1297)) (-5 *1 (-838))))) +(((*1 *2 *1) (-12 (-5 *2 (-344)) (-5 *1 (-256))))) +(((*1 *2 *3 *3 *4 *5 *5) + (-12 (-5 *5 (-112)) (-4 *6 (-465)) (-4 *7 (-809)) (-4 *8 (-865)) + (-4 *3 (-1090 *6 *7 *8)) + (-5 *2 (-660 (-2 (|:| |val| *3) (|:| -1943 *4)))) + (-5 *1 (-1133 *6 *7 *8 *3 *4)) (-4 *4 (-1096 *6 *7 *8 *3)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-660 (-2 (|:| |val| (-660 *8)) (|:| -1943 *9)))) + (-5 *5 (-112)) (-4 *8 (-1090 *6 *7 *4)) (-4 *9 (-1096 *6 *7 *4 *8)) + (-4 *6 (-465)) (-4 *7 (-809)) (-4 *4 (-865)) + (-5 *2 (-660 (-2 (|:| |val| *8) (|:| -1943 *9)))) + (-5 *1 (-1133 *6 *7 *4 *8 *9))))) +(((*1 *2 *1) (-12 (-5 *2 (-302)) (-5 *1 (-291))))) (((*1 *2 *1) - (-12 (-4 *1 (-926 *3)) (-4 *3 (-1125)) (-5 *2 (-1127 *3)))) + (-12 (-4 *4 (-1125)) (-5 *2 (-112)) (-5 *1 (-904 *3 *4 *5)) + (-4 *3 (-1125)) (-4 *5 (-682 *4)))) ((*1 *2 *1) - (-12 (-5 *2 (-1127 *3)) (-5 *1 (-927 *3)) (-4 *3 (-1125))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1201)) (-5 *2 (-549)) (-5 *1 (-548 *4)) - (-4 *4 (-1242))))) -(((*1 *2) - (-12 (-4 *1 (-354 *3 *4 *5)) (-4 *3 (-1246)) (-4 *4 (-1268 *3)) - (-4 *5 (-1268 (-420 *4))) (-5 *2 (-112))))) -(((*1 *1 *2 *2) - (-12 (-5 *2 (-660 (-577))) (-5 *1 (-1029 *3)) (-14 *3 (-577))))) -(((*1 *2 *3) - (-12 (-4 *4 (-569)) (-5 *2 (-112)) (-5 *1 (-286 *4 *3)) - (-4 *3 (-13 (-443 *4) (-1027)))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-1316 *3 *4)) (-4 *1 (-386 *3 *4)) (-4 *3 (-865)) - (-4 *4 (-174)))) - ((*1 *1 *1 *1) (|partial| -12 (-4 *1 (-398 *2)) (-4 *2 (-1125)))) - ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-835 *2)) (-4 *2 (-865)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1309 *2 *3)) (-4 *2 (-865)) (-4 *3 (-1074)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-835 *3)) (-4 *1 (-1309 *3 *4)) (-4 *3 (-865)) - (-4 *4 (-1074)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1309 *2 *3)) (-4 *2 (-865)) (-4 *3 (-1074))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-569) (-1063 (-577)) (-654 (-577)))) - (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-27) (-1227) (-443 *3))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1201)) - (-4 *4 (-13 (-569) (-1063 (-577)) (-654 (-577)))) - (-5 *1 (-287 *4 *2)) (-4 *2 (-13 (-27) (-1227) (-443 *4))))) - ((*1 *1 *1) (-5 *1 (-391))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-465)) (-4 *6 (-809)) (-4 *7 (-865)) - (-4 *3 (-1090 *5 *6 *7)) - (-5 *2 (-660 (-2 (|:| |val| *3) (|:| -3889 *4)))) - (-5 *1 (-792 *5 *6 *7 *3 *4)) (-4 *4 (-1096 *5 *6 *7 *3))))) + (-12 (-5 *2 (-112)) (-5 *1 (-908 *3 *4)) (-4 *3 (-1125)) + (-4 *4 (-1125))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-608 *2)) (-4 *2 (-38 (-420 (-577)))) (-4 *2 (-1074))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1 (-228) (-228) (-228) (-228))) (-5 *1 (-271)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-228) (-228) (-228))) (-5 *1 (-271)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-228) (-228))) (-5 *1 (-271))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -5394,33 +5409,27 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) - (-12 (-5 *3 (-577)) (-5 *5 (-705 (-228))) (-5 *4 (-228)) - (-5 *2 (-1060)) (-5 *1 (-768))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1125)) (-4 *3 (-921 *5)) (-5 *2 (-705 *3)) - (-5 *1 (-708 *5 *3 *6 *4)) (-4 *6 (-385 *3)) - (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4470))))))) -(((*1 *2 *1) (-12 (-4 *1 (-402)) (-5 *2 (-1183))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1159 *3)) (-4 *3 (-1074)) - (-5 *2 (-660 (-660 (-660 (-966 *3)))))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 (-966 *3) (-966 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-375) (-1227) (-1027)))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-569)) - (-5 *2 (-2 (|:| -2742 *3) (|:| -3041 *3))) (-5 *1 (-1263 *4 *3)) - (-4 *3 (-1268 *4))))) -(((*1 *2) - (-12 (-5 *2 (-1292 (-1126 *3 *4))) (-5 *1 (-1126 *3 *4)) - (-14 *3 (-944)) (-14 *4 (-944))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-577)) (-5 *1 (-574)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1197 (-420 (-577)))) (-5 *1 (-965)) (-5 *3 (-577))))) +(((*1 *1 *1 *1 *1) (-5 *1 (-880))) ((*1 *1 *1 *1) (-5 *1 (-880))) + ((*1 *1 *1) (-5 *1 (-880)))) +(((*1 *1 *1) + (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) + (-4 *4 (-865)) (-4 *2 (-465))))) +(((*1 *2 *3 *3 *1) + (-12 (-5 *3 (-519)) (-5 *2 (-707 (-1129))) (-5 *1 (-302))))) +(((*1 *2) (-12 (-5 *2 (-577)) (-5 *1 (-1031)))) + ((*1 *2 *2) (-12 (-5 *2 (-577)) (-5 *1 (-1031))))) +(((*1 *2 *2) + (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) + (-4 *2 (-13 (-443 *3) (-1027)))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1037)) (-5 *2 (-880))))) +(((*1 *2 *1) (-12 (-5 *2 (-660 (-966 (-228)))) (-5 *1 (-1293))))) +(((*1 *2 *2) + (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) + (-4 *2 (-13 (-443 *3) (-1027)))))) (((*1 *2 *3) - (-12 (-5 *3 (-660 (-2 (|:| -4280 *4) (|:| -2894 (-577))))) - (-4 *4 (-1125)) (-5 *2 (-1 *4)) (-5 *1 (-1042 *4))))) + (-12 (-4 *4 (-569)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3449 *4))) + (-5 *1 (-994 *4 *3)) (-4 *3 (-1268 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) (-4 *2 (-13 (-443 *3) (-1027))))) @@ -5437,35 +5446,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1 (-391))) (-5 *1 (-1065)) (-5 *3 (-391))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-870 *2)) (-4 *2 (-1074)) (-4 *2 (-375))))) -(((*1 *1 *1) (-12 (-4 *1 (-385 *2)) (-4 *2 (-1242)))) - ((*1 *2 *2) - (-12 (-4 *3 (-1074)) (-5 *1 (-457 *3 *2)) (-4 *2 (-1268 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-665 *2 *3 *4)) (-4 *2 (-1125)) (-4 *3 (-23)) - (-14 *4 *3)))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 (-660 *5))) (-4 *5 (-1283 *4)) - (-4 *4 (-38 (-420 (-577)))) - (-5 *2 (-1 (-1182 *4) (-660 (-1182 *4)))) (-5 *1 (-1285 *4 *5))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-1169)) (-5 *2 (-112))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1096 *4 *5 *6 *3)) (-4 *4 (-465)) (-4 *5 (-809)) - (-4 *6 (-865)) (-4 *3 (-1090 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-660 (-2 (|:| |totdeg| (-787)) (|:| -1850 *3)))) - (-5 *4 (-787)) (-4 *3 (-972 *5 *6 *7)) (-4 *5 (-465)) (-4 *6 (-809)) - (-4 *7 (-865)) (-5 *1 (-462 *5 *6 *7 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1297)) (-5 *1 (-838))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3 *3 *3) + (-12 (-5 *3 (-577)) (-5 *5 (-705 (-228))) (-5 *4 (-228)) + (-5 *2 (-1060)) (-5 *1 (-768))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-115))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-228)) (-5 *4 (-577)) (-5 *2 (-1060)) (-5 *1 (-774))))) (((*1 *2 *2) - (|partial| -12 (-5 *2 (-1197 *3)) (-4 *3 (-361)) (-5 *1 (-369 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-660 (-705 *4))) (-5 *2 (-705 *4)) (-4 *4 (-1074)) - (-5 *1 (-1054 *4))))) + (|partial| -12 (-5 *2 (-660 (-975 *3))) (-4 *3 (-465)) + (-5 *1 (-372 *3 *4)) (-14 *4 (-660 (-1201))))) + ((*1 *2 *2) + (|partial| -12 (-5 *2 (-660 (-796 *3 (-882 *4)))) (-4 *3 (-465)) + (-14 *4 (-660 (-1201))) (-5 *1 (-641 *3 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-228)) (-5 *1 (-838))))) +(((*1 *2 *1 *2) (-12 (-5 *1 (-1051 *2)) (-4 *2 (-1242))))) +(((*1 *2 *1 *1) + (|partial| -12 (-4 *1 (-340 *3)) (-4 *3 (-375)) (-4 *3 (-380)) + (-5 *2 (-1197 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-340 *3)) (-4 *3 (-375)) (-4 *3 (-380)) + (-5 *2 (-1197 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-660 (-52))) (-5 *1 (-911 *3)) (-4 *3 (-1125))))) -(((*1 *2 *1) (-12 (-4 *1 (-540)) (-5 *2 (-707 (-1247)))))) + (-12 (-5 *2 (-1051 (-859 (-577)))) (-5 *1 (-608 *3)) (-4 *3 (-1074))))) (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) (-4 *2 (-13 (-443 *3) (-1027))))) @@ -5482,28 +5485,73 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2) (-12 (-5 *2 (-1183)) (-5 *1 (-404))))) -(((*1 *2 *2) - (-12 (-4 *3 (-569)) (-5 *1 (-159 *3 *2)) (-4 *2 (-443 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1201)) (-4 *4 (-569)) (-5 *1 (-159 *4 *2)) - (-4 *2 (-443 *4)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-161)) (-5 *2 (-1201)))) - ((*1 *1 *1) (-4 *1 (-161)))) -(((*1 *1) (-5 *1 (-1088)))) -(((*1 *2 *1) (-12 (-5 *2 (-660 (-1201))) (-5 *1 (-1205))))) -(((*1 *2 *3) - (-12 (-4 *4 (-809)) - (-4 *5 (-13 (-865) (-10 -8 (-15 -4150 ((-1201) $))))) (-4 *6 (-569)) - (-5 *2 (-2 (|:| -2639 (-975 *6)) (|:| -3125 (-975 *6)))) - (-5 *1 (-748 *4 *5 *6 *3)) (-4 *3 (-972 (-420 (-975 *6)) *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-663 *3)) (-4 *3 (-1125))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-1197 (-975 *4))) (-5 *1 (-429 *3 *4)) + (-4 *3 (-430 *4)))) + ((*1 *2) + (-12 (-4 *1 (-430 *3)) (-4 *3 (-174)) (-4 *3 (-375)) + (-5 *2 (-1197 (-975 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1197 (-420 (-975 *3)))) (-5 *1 (-466 *3 *4 *5 *6)) + (-4 *3 (-569)) (-4 *3 (-174)) (-14 *4 (-944)) + (-14 *5 (-660 (-1201))) (-14 *6 (-1292 (-705 *3)))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-660 (-975 (-577)))) (-5 *4 (-660 (-1201))) + (-5 *2 (-660 (-660 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((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -5935,52 +6034,67 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *1) - (-12 (-4 *1 (-417)) (-2332 (|has| *1 (-6 -4461))) - (-2332 (|has| *1 (-6 -4453))))) - ((*1 *2 *1) (-12 (-4 *1 (-438 *2)) (-4 *2 (-1125)) (-4 *2 (-865)))) - ((*1 *2 *1) (-12 (-4 *1 (-846 *2)) (-4 *2 (-865)))) - ((*1 *1) (-4 *1 (-860))) ((*1 *1 *1 *1) (-4 *1 (-868)))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-569)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 (-966 *3) (-966 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-375) (-1227) (-1027)))))) +(((*1 *2) + (-12 (-4 *3 (-569)) (-5 *2 (-660 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-430 *3))))) +(((*1 *2 *2 *3 *4 *4) + (-12 (-5 *4 (-577)) (-4 *3 (-174)) (-4 *5 (-385 *3)) + (-4 *6 (-385 *3)) (-5 *1 (-704 *3 *5 *6 *2)) + (-4 *2 (-703 *3 *5 *6))))) (((*1 *1 *2) - (-12 (-5 *2 (-660 *3)) (-4 *3 (-1242)) (-5 *1 (-1172 *3))))) + (-12 (-5 *2 (-688 *3)) (-4 *3 (-865)) (-4 *1 (-386 *3 *4)) + (-4 *4 (-174))))) +(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) + (-12 (-5 *3 (-944)) (-5 *4 (-228)) (-5 *5 (-577)) (-5 *6 (-892)) + (-5 *2 (-1297)) (-5 *1 (-1293))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-420 *2)) (-5 *4 (-1 *2 *2)) (-4 *2 (-1268 *5)) - (-5 *1 (-743 *5 *2)) (-4 *5 (-375))))) -(((*1 *2 *3 *3 *4 *4) - (-12 (-5 *3 (-705 (-228))) (-5 *4 (-577)) (-5 *2 (-1060)) - (-5 *1 (-764))))) -(((*1 *2 *3) - (-12 (-5 *3 (-944)) (-5 *2 (-1197 *4)) (-5 *1 (-369 *4)) - (-4 *4 (-361))))) -(((*1 *2 *3) - (-12 (-5 *3 (-950)) + (-12 (-5 *3 (-669 (-420 *6))) (-5 *4 (-420 *6)) (-4 *6 (-1268 *5)) + (-4 *5 (-13 (-375) (-148) (-1063 (-577)) (-1063 (-420 (-577))))) (-5 *2 - (-2 (|:| |brans| (-660 (-660 (-966 (-228))))) - (|:| |xValues| (-1119 (-228))) (|:| |yValues| (-1119 (-228))))) - (-5 *1 (-154)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-950)) (-5 *4 (-420 (-577))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2006 (-660 *4)))) + (-5 *1 (-826 *5 *6)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-669 (-420 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*6 *2))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-420 (-577))) (-5 *1 (-608 *3)) (-4 *3 (-38 *2)) - (-4 *3 (-1074))))) + (-12 (-5 *3 (-660 (-254 *4 *5))) (-5 *2 (-254 *4 *5)) + (-14 *4 (-660 (-1201))) (-4 *5 (-465)) (-5 *1 (-644 *4 *5))))) +(((*1 *2 *3 *4 *5 *6) + (|partial| -12 (-5 *4 (-1201)) (-5 *6 (-660 (-625 *3))) + (-5 *5 (-625 *3)) (-4 *3 (-13 (-27) (-1227) (-443 *7))) + (-4 *7 (-13 (-465) (-148) (-1063 (-577)) (-654 (-577)))) + (-5 *2 (-2 (|:| -3691 *3) (|:| |coeff| *3))) + (-5 *1 (-570 *7 *3))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -6000,39 +6114,84 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) - (-4 *2 (-13 (-443 *3) (-1027)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5 *5)) (-4 *5 (-1283 *4)) - (-4 *4 (-38 (-420 (-577)))) - (-5 *2 (-1 (-1182 *4) (-1182 *4) (-1182 *4))) (-5 *1 (-1285 *4 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-944)) (-5 *1 (-369 *3)) (-4 *3 (-361))))) +(((*1 *2 *2) (-12 (-5 *2 (-944)) (-5 *1 (-1295)))) + ((*1 *2) (-12 (-5 *2 (-944)) (-5 *1 (-1295))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-787)) (-5 *3 (-966 *4)) (-4 *1 (-1159 *4)) + (-4 *4 (-1074)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-787)) (-5 *4 (-966 (-228))) (-5 *2 (-1297)) + (-5 *1 (-1294))))) +(((*1 *2 *2 *3) + (-12 (-4 *4 (-809)) + (-4 *3 (-13 (-865) (-10 -8 (-15 -2210 ((-1201) $))))) (-4 *5 (-569)) + (-5 *1 (-748 *4 *3 *5 *2)) (-4 *2 (-972 (-420 (-975 *5)) *4 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *4 (-1074)) (-4 *5 (-809)) + (-4 *3 + (-13 (-865) + (-10 -8 (-15 -2210 ((-1201) $)) + (-15 -4183 ((-3 $ "failed") (-1201)))))) + (-5 *1 (-1009 *4 *5 *3 *2)) (-4 *2 (-972 (-975 *4) *5 *3)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-660 *6)) + (-4 *6 + (-13 (-865) + (-10 -8 (-15 -2210 ((-1201) $)) + (-15 -4183 ((-3 $ "failed") (-1201)))))) + (-4 *4 (-1074)) (-4 *5 (-809)) (-5 *1 (-1009 *4 *5 *6 *2)) + (-4 *2 (-972 (-975 *4) *5 *6))))) (((*1 *2 *1) (-12 (-5 *2 (-660 - (-660 - (-3 (|:| -4138 (-1201)) - (|:| -3881 (-660 (-3 (|:| S (-1201)) (|:| P (-975 (-577)))))))))) - (-5 *1 (-1205))))) -(((*1 *2 *1) (-12 (-5 *2 (-577)) (-5 *1 (-880))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1268 *2)) (-4 *2 (-1074))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1223))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1197 (-577))) (-5 *1 (-965)) (-5 *3 (-577))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-660 (-911 *3))) (-5 *1 (-911 *3)) - (-4 *3 (-1125))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-158)) (-5 *2 (-1297)) (-5 *1 (-1294))))) -(((*1 *2 *1) - (-12 (-4 *1 (-340 *3)) (-4 *3 (-375)) (-4 *3 (-380)) - (-5 *2 (-1197 *3))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-375)) (-5 *1 (-1050 *3 *2)) (-4 *2 (-672 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-375)) (-5 *2 (-2 (|:| -2733 *3) (|:| -3935 (-660 *5)))) - (-5 *1 (-1050 *5 *3)) (-5 *4 (-660 *5)) (-4 *3 (-672 *5))))) + (-2 + (|:| -2327 + (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228))) + (|:| -3656 (-1119 (-859 (-228)))) (|:| |abserr| (-228)) + (|:| |relerr| (-228)))) + (|:| -2909 + (-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| (-1182 (-228))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3656 + (-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 (-572)))) + ((*1 *2 *1) + (-12 (-4 *1 (-617 *3 *4)) (-4 *3 (-1125)) (-4 *4 (-1242)) + (-5 *2 (-660 *4))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-481)) (-5 *4 (-944)) (-5 *2 (-1297)) (-5 *1 (-1293))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-660 *6)) (-5 *4 (-660 (-1182 *7))) (-4 *6 (-865)) + (-4 *7 (-972 *5 (-544 *6) *6)) (-4 *5 (-1074)) + (-5 *2 (-1 (-1182 *7) *7)) (-5 *1 (-1151 *5 *6 *7))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) + (-4 *4 (-865)) (-4 *2 (-569)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) + (-4 *4 (-865)) (-4 *2 (-569))))) +(((*1 *1 *2) (-12 (-5 *2 (-660 (-341))) (-5 *1 (-341))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) @@ -6052,30 +6211,47 @@ ((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3))))) -(((*1 *2 *1 *2 *3) - (|partial| -12 (-5 *2 (-1183)) (-5 *3 (-577)) (-5 *1 (-1088))))) -(((*1 *2) (-12 (-5 *2 (-577)) (-5 *1 (-480)))) - ((*1 *2 *2) (-12 (-5 *2 (-577)) (-5 *1 (-480)))) - ((*1 *2) (-12 (-5 *2 (-577)) (-5 *1 (-950))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-569) (-1063 (-577)))) (-5 *2 (-420 (-577))) - (-5 *1 (-446 *4 *3)) (-4 *3 (-443 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-625 *3)) (-4 *3 (-443 *5)) - (-4 *5 (-13 (-569) (-1063 (-577)))) (-5 *2 (-1197 (-420 (-577)))) - (-5 *1 (-446 *5 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-966 *2)) (-5 *1 (-1007 *2)) (-4 *2 (-1074))))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-124)))) -(((*1 *2 *1) (-12 (-4 *1 (-540)) (-5 *2 (-707 (-560)))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-455 *3)) (-4 *3 (-1268 (-577)))))) + (-12 (-5 *2 (-625 *4)) (-5 *1 (-624 *3 *4)) (-4 *3 (-1125)) + (-4 *4 (-1125))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1235 *3 *4 *5 *2)) (-4 *3 (-569)) (-4 *4 (-809)) + (-4 *5 (-865)) (-4 *2 (-1090 *3 *4 *5))))) +(((*1 *2 *3 *1) (-12 (-5 *3 (-1201)) (-5 *2 (-450)) (-5 *1 (-1205))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-660 (-944))) (-5 *4 (-660 (-577))) - (-5 *2 (-705 (-577))) (-5 *1 (-1135))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) - (-4 *4 (-865)) (-4 *2 (-569))))) + (-12 (-5 *3 (-705 *8)) (-4 *8 (-972 *5 *7 *6)) + (-4 *5 (-13 (-318) (-148))) (-4 *6 (-13 (-865) (-627 (-1201)))) + (-4 *7 (-809)) + (-5 *2 + (-660 + (-2 (|:| -3829 (-787)) + (|:| |eqns| + (-660 + (-2 (|:| |det| *8) (|:| |rows| (-660 (-577))) + (|:| |cols| (-660 (-577)))))) + (|:| |fgb| (-660 *8))))) + (-5 *1 (-947 *5 *6 *7 *8)) (-5 *4 (-787))))) +(((*1 *2 *2 *3 *4) + (-12 (-5 *3 (-660 (-625 *6))) (-5 *4 (-1201)) (-5 *2 (-625 *6)) + (-4 *6 (-443 *5)) (-4 *5 (-1125)) (-5 *1 (-586 *5 *6))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-378 *3 *4)) + (-4 *3 (-379 *4)))) + ((*1 *2) (-12 (-4 *1 (-379 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-787)) (-4 *4 (-1074)) + (-5 *2 (-2 (|:| -1880 *1) (|:| -4079 *1))) (-4 *1 (-1268 *4))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1086 (-1049 *4) (-1197 (-1049 *4)))) (-5 *3 (-880)) + (-5 *1 (-1049 *4)) (-4 *4 (-13 (-864) (-375) (-1047)))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-228)) (|:| |xend| (-228)) + (|:| |fn| (-1292 (-327 (-228)))) (|:| |yinit| (-660 (-228))) + (|:| |intvals| (-660 (-228))) (|:| |g| (-327 (-228))) + (|:| |abserr| (-228)) (|:| |relerr| (-228)))) + (-5 *2 (-391)) (-5 *1 (-207))))) (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) (-4 *2 (-13 (-443 *3) (-1027))))) @@ -6092,131 +6268,40 @@ (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3)))) ((*1 *1 *1) (-4 *1 (-1230)))) -(((*1 *2 *3 *2 *2) - (-12 (-5 *2 (-660 (-494 *4 *5))) (-5 *3 (-882 *4)) - (-14 *4 (-660 (-1201))) (-4 *5 (-465)) (-5 *1 (-644 *4 *5))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-660 (-796 *5 (-882 *6)))) (-5 *4 (-112)) (-4 *5 (-465)) - (-14 *6 (-660 (-1201))) +(((*1 *2 *3) + (-12 (-4 *4 (-865)) (-5 *2 - (-660 (-1171 *5 (-544 (-882 *6)) (-882 *6) (-796 *5 (-882 *6))))) - (-5 *1 (-641 *5 *6))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-703 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-385 *2)) - (-4 *4 (-385 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1206))))) -(((*1 *1 *2) - (-12 (-5 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- (-12 (-5 *2 (-966 *3)) (-4 *3 (-1074)) (-4 *1 (-1159 *3)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-787)) (-4 *1 (-1159 *3)) (-4 *3 (-1074)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-660 *3)) (-4 *1 (-1159 *3)) (-4 *3 (-1074)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-966 *3)) (-4 *1 (-1159 *3)) (-4 *3 (-1074)))) - ((*1 *2 *3 *3 *3 *3) - (-12 (-5 *2 (-966 (-228))) (-5 *1 (-1238)) (-5 *3 (-228))))) +(((*1 *1 *1 *1) (-4 *1 (-144))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-569)) (-5 *1 (-159 *3 *2)) (-4 *2 (-443 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-558))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-870 *2)) (-4 *2 (-1074)) (-4 *2 (-375))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-378 *3 *4)) + (-4 *3 (-379 *4)))) + ((*1 *2) (-12 (-4 *1 (-379 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-840))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-787)) (-4 *4 (-361)) (-5 *1 (-219 *4 *2)) + (-4 *2 (-1268 *4))))) +(((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-577)) (-4 *1 (-667 *3)) (-4 *3 (-1242)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-577)) (-4 *1 (-667 *2)) (-4 *2 (-1242))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-944)) (-5 *4 (-431 *6)) (-4 *6 (-1268 *5)) + (-4 *5 (-1074)) (-5 *2 (-660 *6)) (-5 *1 (-457 *5 *6))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-787)) (-5 *2 (-112)) (-5 *1 (-600 *3)) (-4 *3 (-558))))) +(((*1 *2 *1) (-12 (-4 *1 (-379 *2)) (-4 *2 (-174))))) +(((*1 *2 *1) (-12 (-5 *2 (-660 (-975 (-577)))) (-5 *1 (-450)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1201)) (-5 *4 (-705 (-228))) (-5 *2 (-1129)) + (-5 *1 (-775)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1201)) (-5 *4 (-705 (-577))) (-5 *2 (-1129)) + (-5 *1 (-775))))) (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) (-4 *2 (-13 (-443 *3) (-1027))))) @@ -6488,70 +6466,38 @@ (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3)))) ((*1 *1 *1) (-4 *1 (-1230)))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *3 (-1 *2 (-787) *2)) (-5 *4 (-787)) (-4 *2 (-1125)) + (-5 *1 (-694 *2)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1 *3 (-787) *3)) (-4 *3 (-1125)) (-5 *1 (-698 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1297)) (-5 *1 (-1294))))) +(((*1 *1 *1 *1) (-5 *1 (-163))) + ((*1 *1 *2) (-12 (-5 *2 (-577)) (-5 *1 (-163))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1265 *5 *4)) (-4 *4 (-836)) (-14 *5 (-1201)) + (-5 *2 (-660 *4)) (-5 *1 (-1139 *4 *5))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-1268 *2)) (-4 *2 (-1246)) (-5 *1 (-149 *2 *4 *3)) + (-4 *3 (-1268 (-420 *4)))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-228)) (-5 *4 (-577)) (-5 *2 (-1060)) (-5 *1 (-774))))) -(((*1 *2 *3 *2) - (-12 (-4 *1 (-803)) (-5 *2 (-1060)) - (-5 *3 - (-2 (|:| |fn| (-327 (-228))) - (|:| -1628 (-660 (-1119 (-859 (-228))))) (|:| |abserr| (-228)) - (|:| |relerr| (-228)))))) - ((*1 *2 *3 *2) - (-12 (-4 *1 (-803)) (-5 *2 (-1060)) - (-5 *3 - (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228))) - (|:| -1628 (-1119 (-859 (-228)))) (|:| |abserr| (-228)) - (|:| |relerr| (-228))))))) -(((*1 *1 *1) - (|partial| -12 (-4 *1 (-379 *2)) (-4 *2 (-174)) (-4 *2 (-569)))) - 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(-228)) - (-5 *6 (-3 (|:| |fn| (-401)) (|:| |fp| (-61 COEFFN)))) - (-5 *7 (-3 (|:| |fn| (-401)) (|:| |fp| (-87 BDYVAL)))) - (-5 *8 (-401)) (-5 *2 (-1060)) (-5 *1 (-765))))) -(((*1 *2 *3 *4 *4 *3 *5 *3 *3 *3 *6) - (-12 (-5 *3 (-577)) (-5 *4 (-705 (-228))) (-5 *5 (-228)) - (-5 *6 (-3 (|:| |fn| (-401)) (|:| |fp| (-78 FUNCTN)))) - (-5 *2 (-1060)) (-5 *1 (-764))))) -(((*1 *2 *1) - (-12 (-4 *1 (-47 *3 *4)) (-4 *3 (-1074)) (-4 *4 (-808)) - (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-394 *3 *4)) (-4 *3 (-1074)) (-4 *4 (-1125)) - (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-608 *3)) (-4 *3 (-1074)))) - ((*1 *2 *1) - (-12 (-4 *3 (-569)) (-5 *2 (-112)) (-5 *1 (-636 *3 *4)) - (-4 *4 (-1268 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-751 *3 *4)) (-4 *3 (-1074)) - (-4 *4 (-742)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1309 *3 *4)) (-4 *3 (-865)) (-4 *4 (-1074)) - (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-4 *1 (-690 *2)) (-4 *2 (-1242))))) -(((*1 *2 *2) - (-12 (-4 *3 (-465)) (-5 *1 (-1233 *3 *2)) - (-4 *2 (-13 (-443 *3) (-1227)))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-787)) (-4 *4 (-569)) (-5 *1 (-994 *4 *2)) - (-4 *2 (-1268 *4))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-318) (-148))) (-4 *5 (-13 (-865) (-627 (-1201)))) - (-4 *6 (-809)) (-5 *2 (-660 *3)) (-5 *1 (-947 *4 *5 *6 *3)) - (-4 *3 (-972 *4 *6 *5))))) + (-4 *4 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) + (-5 *1 (-820 *4 *2)) (-4 *2 (-13 (-29 *4) (-1227) (-982))))) + ((*1 *1 *1 *1 *1) (-5 *1 (-880))) ((*1 *1 *1 *1) (-5 *1 (-880))) + ((*1 *1 *1) (-5 *1 (-880))) + ((*1 *2 *3) + (-12 (-5 *2 (-1182 *3)) (-5 *1 (-1185 *3)) (-4 *3 (-1074))))) (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-286 *3 *2)) (-4 *2 (-13 (-443 *3) (-1027))))) @@ -6572,218 +6518,134 @@ (-12 (-5 *2 (-1182 *3)) (-4 *3 (-38 (-420 (-577)))) (-5 *1 (-1187 *3)))) ((*1 *1 *1) (-4 *1 (-1230)))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-1201)) (-5 *1 (-599 *2)) (-4 *2 (-1063 *3)) - (-4 *2 (-375)))) - ((*1 *1 *2 *2) (-12 (-5 *1 (-599 *2)) (-4 *2 (-375)))) - 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*3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) + (-4 *4 (-865)) (-4 *2 (-569)))) + ((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-465)) (-4 *5 (-809)) (-4 *6 (-865)) + (-4 *3 (-1090 *4 *5 *6)) + (-5 *2 (-660 (-2 (|:| |val| *3) (|:| -1943 *1)))) + (-4 *1 (-1096 *4 *5 *6 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1297)) (-5 *1 (-838))))) +(((*1 *2 *1) (-12 (-5 *2 (-1297)) (-5 *1 (-838))))) +(((*1 *2 *3 *4) (-12 (-5 *3 (-660 (-420 (-975 (-577))))) (-5 *2 (-660 (-660 (-305 (-975 *4))))) (-5 *1 (-392 *4)) (-4 *4 (-13 (-864) (-375))))) @@ -10031,7 +9606,7 @@ (|partial| -12 (-5 *5 (-1201)) (-4 *6 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) (-4 *4 (-13 (-29 *6) (-1227) (-982))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -1521 (-660 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2006 (-660 *4)))) (-5 *1 (-668 *6 *4 *3)) (-4 *3 (-672 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1201)) (-5 *5 (-660 *2)) @@ -10042,40 +9617,40 @@ (-12 (-5 *3 (-705 *5)) (-4 *5 (-375)) (-5 *2 (-2 (|:| |particular| (-3 (-1292 *5) "failed")) - (|:| -1521 (-660 (-1292 *5))))) + (|:| -2006 (-660 (-1292 *5))))) (-5 *1 (-683 *5)) (-5 *4 (-1292 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-660 (-660 *5))) (-4 *5 (-375)) (-5 *2 (-2 (|:| |particular| (-3 (-1292 *5) "failed")) - (|:| -1521 (-660 (-1292 *5))))) + (|:| -2006 (-660 (-1292 *5))))) (-5 *1 (-683 *5)) (-5 *4 (-1292 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-705 *5)) (-4 *5 (-375)) (-5 *2 (-660 (-2 (|:| |particular| (-3 (-1292 *5) "failed")) - (|:| -1521 (-660 (-1292 *5)))))) + (|:| -2006 (-660 (-1292 *5)))))) (-5 *1 (-683 *5)) (-5 *4 (-660 (-1292 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-660 (-660 *5))) (-4 *5 (-375)) (-5 *2 (-660 (-2 (|:| |particular| (-3 (-1292 *5) "failed")) - (|:| -1521 (-660 (-1292 *5)))))) + (|:| -2006 (-660 (-1292 *5)))))) (-5 *1 (-683 *5)) (-5 *4 (-660 (-1292 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-375)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4471)))) (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4471)))) (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1521 (-660 *4)))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2006 (-660 *4)))) (-5 *1 (-684 *5 *6 *4 *3)) (-4 *3 (-703 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-375)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4471)))) (-4 *7 (-13 (-385 *5) (-10 -7 (-6 -4471)))) (-5 *2 (-660 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -1521 (-660 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -2006 (-660 *7))))) (-5 *1 (-684 *5 *6 *7 *3)) (-5 *4 (-660 *7)) (-4 *3 (-703 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -10093,7 +9668,7 @@ (-4 *7 (-13 (-29 *6) (-1227) (-982))) (-4 *6 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1292 *7)) (|:| -1521 (-660 (-1292 *7))))) + (-2 (|:| |particular| (-1292 *7)) (|:| -2006 (-660 (-1292 *7))))) (-5 *1 (-818 *6 *7)) (-5 *4 (-1292 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-705 *6)) (-5 *4 (-1201)) @@ -10105,27 +9680,27 @@ (-5 *5 (-1201)) (-4 *7 (-13 (-29 *6) (-1227) (-982))) (-4 *6 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1292 *7)) (|:| -1521 (-660 (-1292 *7))))) + (-2 (|:| |particular| (-1292 *7)) (|:| -2006 (-660 (-1292 *7))))) (-5 *1 (-818 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-660 *7)) (-5 *4 (-660 (-115))) (-5 *5 (-1201)) (-4 *7 (-13 (-29 *6) (-1227) (-982))) (-4 *6 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1292 *7)) (|:| -1521 (-660 (-1292 *7))))) + (-2 (|:| |particular| (-1292 *7)) (|:| -2006 (-660 (-1292 *7))))) (-5 *1 (-818 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-305 *7)) (-5 *4 (-115)) (-5 *5 (-1201)) (-4 *7 (-13 (-29 *6) (-1227) (-982))) (-4 *6 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -1521 (-660 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -2006 (-660 *7))) *7 "failed")) (-5 *1 (-818 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-115)) (-5 *5 (-1201)) (-4 *6 (-13 (-318) (-1063 (-577)) (-654 (-577)) (-148))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -1521 (-660 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -2006 (-660 *3))) *3 "failed")) (-5 *1 (-818 *6 *3)) (-4 *3 (-13 (-29 *6) (-1227) (-982))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-305 *2)) (-5 *4 (-115)) (-5 *5 (-660 *2)) @@ -10161,10 +9736,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -1521 (-660 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -2006 (-660 *6))) "failed") *7 *6)) (-4 *6 (-375)) (-4 *7 (-672 *6)) - (-5 *2 (-2 (|:| |particular| (-1292 *6)) (|:| -1521 (-705 *6)))) + (-5 *2 (-2 (|:| |particular| (-1292 *6)) (|:| -2006 (-705 *6)))) (-5 *1 (-829 *6 *7)) (-5 *3 (-705 *6)) (-5 *4 (-1292 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-919)) (-5 *2 (-1060)) (-5 *1 (-918)))) ((*1 *2 *3 *4) @@ -10237,251 +9812,166 @@ ((*1 *2 *3) (-12 (-4 *4 (-569)) (-5 *2 (-660 (-305 (-420 (-975 *4))))) (-5 *1 (-1210 *4)) (-5 *3 (-305 (-420 (-975 *4))))))) -(((*1 *1) - (-12 (-5 *1 (-665 *2 *3 *4)) (-4 *2 (-1125)) (-4 *3 (-23)) - (-14 *4 *3)))) -(((*1 *2 *2) 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