/usr/lib/open-axiom/src/algebra/degred.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
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)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]
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