How to compute the sums of squares of elements of a quotient ring?
Hi,
I'm new to Sage, and I would like to be able to test, given some q, whether \sum_{p(t) \in \mathbb{F}_{q}[t]/(f)}^{}{p^2(t)}=k \bmod (f) for some fixed f \in \mathbb{F}_q [t] and k \in \mathbb{F}_q.
I can get as far as (for q=3 and f=x^2+1):
sage: R = PolynomialRing(GF(3),'x'); x = R.gen()
sage: S = R.quotient(x^2 + 1)
But I'm not sure how to sum over all the elements of the quotient ring, let alone their squares.
Any hints?