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 ∑p(t)∈Fq[t]/(f)p2(t)=kmod(f) for some fixed f∈Fq[t] and k∈Fq.
I can get as far as (for q=3 and f=x2+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?