/usr/share/axiom-20170501/src/algebra/DEGRED.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | )abbrev package DEGRED DegreeReductionPackage
++ Description:
++ This package has no description
DegreeReductionPackage(R1, R2) : SIG == CODE where
R1 : Ring
R2 : Join(IntegralDomain,OrderedSet)
I ==> Integer
PI ==> PositiveInteger
UP ==> SparseUnivariatePolynomial
RE ==> Expression R2
SIG ==> with
reduce : UP R1 -> Record(pol: UP R1, deg: PI)
++ reduce(p) \undocumented{}
expand : (RE, PI) -> List RE
++ expand(f,n) \undocumented{}
CODE ==> 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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