/usr/share/axiom-20170501/src/algebra/RATFACT.spad is in axiom-source 20170501-3.
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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 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | )abbrev package RATFACT RationalFactorize
++ Author: P. Gianni
++ Date last updated: December 1993
++ Description:
++ Factorization of extended polynomials with rational coefficients.
++ This package implements factorization of extended polynomials
++ whose coefficients are rational numbers. It does this by taking the
++ lcm of the coefficients of the polynomial and creating a polynomial
++ with integer coefficients. The algorithm in
++ \spadtype{GaloisGroupFactorizer} is then
++ used to factor the integer polynomial. The result is normalized
++ with respect to the original lcm of the denominators.
RationalFactorize(RP) : SIG == CODE where
RN ==> Fraction Integer
RP : UnivariatePolynomialCategory RN
I ==> Integer
BP ==> SparseUnivariatePolynomial(I)
SIG ==> with
factor : RP -> Factored RP
++ factor(p) factors an extended polynomial p over the rational numbers.
factorSquareFree : RP -> Factored RP
++ factorSquareFree(p) factors an extended squareFree
++ polynomial p over the rational numbers.
CODE ==> add
import GaloisGroupFactorizer (BP)
ParFact ==> Record(irr:BP,pow:I)
FinalFact ==> Record(contp:I,factors:List(ParFact))
URNI ==> UnivariatePolynomialCategoryFunctions2(RN,RP,I,BP)
UIRN ==> UnivariatePolynomialCategoryFunctions2(I,BP,RN,RP)
fUnion ==> Union("nil", "sqfr", "irred", "prime")
FFE ==> Record(flg:fUnion, fctr:RP, xpnt:I)
factor(p:RP) : Factored(RP) ==
p = 0 => 0
pden: I := lcm([denom c for c in coefficients p])
pol : RP := pden*p
ipol: BP := map(numer,pol)$URNI
ffact: FinalFact := henselFact(ipol,false)
makeFR(((ffact.contp)/pden)::RP,
[["prime",map(coerce,u.irr)$UIRN,u.pow]$FFE
for u in ffact.factors])
factorSquareFree(p:RP) : Factored(RP) ==
p = 0 => 0
pden: I := lcm([denom c for c in coefficients p])
pol : RP := pden*p
ipol: BP := map(numer,pol)$URNI
ffact: FinalFact := henselFact(ipol,true)
makeFR(((ffact.contp)/pden)::RP,
[["prime",map(coerce,u.irr)$UIRN,u.pow]$FFE
for u in ffact.factors])
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