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Fast multiplication of polynomials mod p
I'm running a huge job on Mathematica, and the bulk of the running time is used on computing products of polynomials mod prime p (the program has to handle hundreds of polynomials of degrees up to hundreds, maybe even a 1000, mod p). The generic PolynomialMod function is slow (at O(d^2), d being the degree). Is there any add-on to speed up this process? I do know there's a 'FiniteFields' package, but any other recommendations? [ I just realized that I need to perform Gaussian elimination mod p as well. And the matrix is not sparse. Is there a good Mathematica library for that? ] Thanks in advance.