\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra updivp.spad}
\author{Frederic Lehobey}
\maketitle
\begin{abstract}
\end{abstract}
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\tableofcontents
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\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)
      ((lc := leadingCoefficient p2) = 1) => 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(x +-> x + 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>>
@
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