\documentclass{article}
\usepackage{open-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: IntegralDomain
 
    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
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\bibitem{1} nothing
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\end{document}