does someone knows a simple library to do
calculations on Polynomial with modular coefficients?
I've seen numpy, but this one seems like it does not support modular coefficients...
Thanks, Shai.
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buc030
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What do you mean by modular coefficients? – Oliver Charlesworth Jan 05 '13 at 15:02
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I mean coefficients over Z_p for some prime p: for example 3 (mod 5) = 2 (mod 5) – buc030 Jan 05 '13 at 15:24
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What kind of operations do you intend to do? If it's just evaluation, then you don't need a special library. I guess if you're doing operations on the coeffs themselves, then you need some more sophistication! – Oliver Charlesworth Jan 05 '13 at 15:52
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Add, mult, fiv, mod, gcd, lcm, roots, stuff like this. – buc030 Jan 05 '13 at 18:29
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It suffices to lift coefficients to integers. For example if you want to compute
(1+2x+3x^2)(3+2x+x^2) in Z/5[x], simply you compute (1+2x+3x^2)(3+2x+x^2) in Z[x]
and reduce it to Z/5[x].
Thus
>>> import numpy.polynomial.polynomial
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> numpy.fmod(numpy.polynomial.polynomial.polymul(c1,c2),5)
>>> numpy.fmod(numpy.polynomial.polynomial.polymul(c1,c2),5)
gives
array([ 3., 3., 4., 3., 3.])
