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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/updivp.spad.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{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)
+ ((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(#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}