I have some polynomial P with coefficients in a finite field
(represented in Sage by a NTL object) and I want to write it
as follows:
P(X) = P_0(X^r) + X*P_1(X^r) + ... + X^(r-1)*P_(r-1)(X^r)
where r is a fixed small integer (say r=3 for instance).
Of course, I can build the list of coefficients of P, split
it into r sublists (consisting of all entries whose index is
congruent to some fixed i modulo r) and then reconstruct the
P_i's from these sublists... but it's very very slow (almost
2 seconds for a polynomial P of degree 1000 over F_{2^50} on
my computer).
Hence, I'm wondering if someone knows some trick to compute
quickly this decomposition.
Thanks,
--Xavier
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