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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra genufact.spad}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package GENUFACT GenUFactorize}
<<package GENUFACT GenUFactorize>>=
)abbrev package GENUFACT GenUFactorize
++ Description
++ This package provides operations for the factorization of univariate polynomials with integer
++ coefficients. The factorization is done by "lifting" the
++ finite "berlekamp's" factorization
GenUFactorize(R) : public == private where
R : EuclideanDomain
PR ==> SparseUnivariatePolynomial R -- with factor
-- should be UnivariatePolynomialCategory
NNI ==> NonNegativeInteger
SUP ==> SparseUnivariatePolynomial
public == with
factor : PR -> Factored PR
++ factor(p) returns the factorisation of p
private == add
-- Factorisation currently fails when algebraic extensions have multiple
-- generators.
factorWarning(f:OutputForm):Void ==
import AnyFunctions1(String)
import AnyFunctions1(OutputForm)
outputList(["WARNING (genufact): No known algorithm to factor "::Any, _
f::Any, _
", trying square-free."::Any])$OutputPackage
factor(f:PR) : Factored PR ==
R is Integer => (factor f)$GaloisGroupFactorizer(PR)
R is Fraction Integer =>
(factor f)$RationalFactorize(PR)
-- R has Field and R has Finite =>
R has FiniteFieldCategory =>
(factor f)$DistinctDegreeFactorize(R,PR)
R is (Complex Integer) => (factor f)$ComplexFactorization(Integer,PR)
R is (Complex Fraction Integer) =>
(factor f)$ComplexFactorization(Fraction Integer,PR)
R is AlgebraicNumber => (factor f)$AlgFactor(PR)
-- following is to handle SAE
R has generator : () -> R =>
var := symbol(convert(generator()::OutputForm)@InputForm)
up:=UnivariatePolynomial(var,Fraction Integer)
R has MonogenicAlgebra(Fraction Integer, up) =>
factor(f)$SimpleAlgebraicExtensionAlgFactor(up, R, PR)
upp:=UnivariatePolynomial(var,Fraction Polynomial Integer)
R has MonogenicAlgebra(Fraction Polynomial Integer, upp) =>
factor(f)$SAERationalFunctionAlgFactor(upp, R, PR)
factorWarning(f::OutputForm)
squareFree f
factorWarning(f::OutputForm)
squareFree f
@
\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 GENUFACT GenUFactorize>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
