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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra cyclotom.spad}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package CYCLOTOM CyclotomicPolynomialPackage}
<<package CYCLOTOM CyclotomicPolynomialPackage>>=
)abbrev package CYCLOTOM CyclotomicPolynomialPackage
++ This package \undocumented{}
CyclotomicPolynomialPackage: public == private where
SUP ==> SparseUnivariatePolynomial(Integer)
LSUP ==> List(SUP)
NNI ==> NonNegativeInteger
FR ==> Factored SUP
IFP ==> IntegerFactorizationPackage Integer
public == with
cyclotomicDecomposition: Integer -> LSUP
++ cyclotomicDecomposition(n) \undocumented{}
cyclotomic: Integer -> SUP
++ cyclotomic(n) \undocumented{}
cyclotomicFactorization: Integer -> FR
++ cyclotomicFactorization(n) \undocumented{}
private == add
cyclotomic(n:Integer): SUP ==
x,y,z,l: SUP
g := factors factor(n)$IFP
--Now, for each prime in the factorization apply recursion
l := monomial(1,1) - monomial(1,0)
for u in g repeat
l := (monicDivide(multiplyExponents(l,u.factor::NNI),l)).quotient
if u.exponent>1 then
l := multiplyExponents(l,((u.factor)**((u.exponent-1)::NNI))::NNI)
l
cyclotomicDecomposition(n:Integer):LSUP ==
x,y,z: SUP
l,ll,m: LSUP
g := factors factor(n)$IFP
l := [monomial(1,1) - monomial(1,0)]
--Now, for each prime in the factorization apply recursion
for u in g repeat
m := [(monicDivide(
multiplyExponents(z,u.factor::NNI),z)).quotient for z in l]
for rr in 1..(u.exponent-1) repeat
l := append(l,m)
m := [multiplyExponents(z,u.factor::NNI) for z in m]
l := append(l,m)
l
cyclotomicFactorization(n:Integer):FR ==
fr : FR := 1$FR
for f in cyclotomicDecomposition(n) repeat
fr := fr * primeFactor(f,1$Integer)
fr
@
\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 CYCLOTOM CyclotomicPolynomialPackage>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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