Finding roots of a polynomial over an extension field
Apologies if I am not articulating this very well. I am still in an early learning phase.
I am trying to find the roots of a polynomial s^37 + 7 over a finite field of size 241 and modulus x^32 + 44.
My code is as follows:
K.<x> = GF(241)
T.<a> = K.quotient(x^32 + 44)
J.<s> = T
G = s^32 + 7
and here I get : 'root finding with multiplicities for this polynomial not implemented (try the multiplicities=False option)'
I think I expressed this correctly as some sanity-checking with known roots is correctly evaluated as follows:
rootList = [20a^29, 51a^13, 221*a^13]
for r in rootList: assert(G(r) == 0)
It does not appear root finding is implemented for G.
Is there some alternative way to find the roots of G?