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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra updivp.spad}
\author{Frederic Lehobey}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package UPDIVP UnivariatePolynomialDivisionPackage}
<<package UPDIVP UnivariatePolynomialDivisionPackage>>=
)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 nothing)
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]
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - Redistributions in binary form must reproduce the above copyright
-- notice, this list of conditions and the following disclaimer in
-- the documentation and/or other materials provided with the
-- distribution.
--
-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>
<<package UPDIVP UnivariatePolynomialDivisionPackage>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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