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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra degred.spad}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package DEGRED DegreeReductionPackage}
<<package DEGRED DegreeReductionPackage>>=
)abbrev package DEGRED DegreeReductionPackage
++ This package \undocumented{}
DegreeReductionPackage(R1, R2): Cat == Capsule where
R1: Ring
R2: Join(IntegralDomain,OrderedSet)
I ==> Integer
PI ==> PositiveInteger
UP ==> SparseUnivariatePolynomial
RE ==> Expression R2
Cat == with
reduce: UP R1 -> Record(pol: UP R1, deg: PI)
++ reduce(p) \undocumented{}
expand: (RE, PI) -> List RE
++ expand(f,n) \undocumented{}
Capsule == add
degrees(u: UP R1): List Integer ==
l: List Integer := []
while u ~= 0 repeat
l := concat(degree u,l)
u := reductum u
l
reduce(u: UP R1) ==
g := "gcd"/[d for d in degrees u]
u := divideExponents(u, g:PI)::(UP R1)
[u, g:PI]
import Fraction Integer
rootOfUnity(j:I,n:I):RE ==
j = 0 => 1
arg:RE := 2*j*pi()/(n::RE)
cos arg + (-1)**(1/2) * sin arg
expand(s, g) ==
g = 1 => [s]
[rootOfUnity(i,g)*s**(1/g) for i in 0..g-1]
@
\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 DEGRED DegreeReductionPackage>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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