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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/updivp.spad.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/algebra/updivp.spad.pamphlet')
-rw-r--r-- | src/algebra/updivp.spad.pamphlet | 99 |
1 files changed, 99 insertions, 0 deletions
diff --git a/src/algebra/updivp.spad.pamphlet b/src/algebra/updivp.spad.pamphlet new file mode 100644 index 00000000..67934a57 --- /dev/null +++ b/src/algebra/updivp.spad.pamphlet @@ -0,0 +1,99 @@ +\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} |