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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | )abbrev package GENMFACT GeneralizedMultivariateFactorize
++ Author: P. Gianni
++ Date Created: 1983
++ Date Last Updated: Sept. 1990
++ Description:
++ This is the top level package for doing multivariate factorization
++ over basic domains like \spadtype{Integer} or \spadtype{Fraction Integer}.
GeneralizedMultivariateFactorize(OV,E,S,R,P) : SIG == CODE where
R : IntegralDomain -- with factor on R[x]
S : IntegralDomain
OV : OrderedSet with
convert : % -> Symbol
++ convert(x) converts x to a symbol
variable : Symbol -> Union(%, "failed")
++ variable(s) makes an element from symbol s or fails.
E : OrderedAbelianMonoidSup
P : PolynomialCategory(R,E,OV)
SIG ==> with
factor : P -> Factored P
++ factor(p) factors the multivariate polynomial p over its coefficient
++ domain
CODE ==> add
factor(p:P) : Factored P ==
R has FiniteFieldCategory => factor(p)$MultFiniteFactorize(OV,E,R,P)
R is Polynomial(S) and S has EuclideanDomain =>
factor(p)$MPolyCatPolyFactorizer(E,OV,S,P)
R is Fraction(S) and S has CharacteristicZero and
S has EuclideanDomain =>
factor(p)$MRationalFactorize(E,OV,S,P)
R is Fraction Polynomial S =>
factor(p)$MPolyCatRationalFunctionFactorizer(E,OV,S,P)
R has CharacteristicZero and R has EuclideanDomain =>
factor(p)$MultivariateFactorize(OV,E,R,P)
squareFree p
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