It turns out that for my problem it suffices to compute the
polynomials

1, f, f^2, ..., f^K

modulo N for some large but known number N, so I suspect that it may
be faster to work modulo p for various primes p and then use the
Chinese Remainder Theorem.

How large, roughly speaking, can I take my prime p to be without
slowing down the multiplication in (ZZ/pZZ)[x,y,z]  ?

Best,

Tom


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