/usr/lib/open-axiom/src/algebra/updivp.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
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)abbrev package UPDIVP UnivariatePolynomialDivisionPackage
++ Author: Frederic Lehobey
++ Date Created: 3 June 1997
++ Date Last Updated: 3 June 1997
++ Basic Operations:
++ Related Domains:
++ Also See:
++ AMS Classifications:
++ Keyword:
++ Exemples:
++ References:
++ Description: UnivariatePolynomialDivisionPackage provides a
++ division for non monic univarite polynomials with coefficients in
++ an \spad{IntegralDomain}.
UnivariatePolynomialDivisionPackage(R,UP): Exports == Implementation where
R : IntegralDomain
UP : UnivariatePolynomialCategory(R)
N ==> NonNegativeInteger
QR ==> Record(quotient: UP, remainder: UP)
Exports ==> with
divideIfCan: (UP,UP) -> Union(QR,"failed")
++ divideIfCan(f,g) returns quotient and remainder of the
++ division of f by g or "failed" if it has not succeeded.
Implementation ==> add
divideIfCan(p1:UP,p2:UP):Union(QR,"failed") ==
zero? p2 => error "divideIfCan: division by zero"
one? (lc := leadingCoefficient p2) => monicDivide(p1,p2)
q: UP := 0
while not ((e := subtractIfCan(degree(p1),degree(p2))) case "failed")
repeat
c := leadingCoefficient(p1) exquo lc
c case "failed" => return "failed"
ee := e::N
q := q+monomial(c::R,ee)
p1 := p1-c*mapExponents(#1+ee,p2)
[q,p1]
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