2019-04-17 04:39:30 -0600 received badge ● Popular Question (source) 2016-07-07 09:06:35 -0600 commented answer Finding roots of a polynomial over an extension field Oh my goodness...thanks so much Bruno!! I racked my brain so much over this. 2016-07-07 09:06:24 -0600 received badge ● Scholar (source) 2016-07-07 09:03:01 -0600 received badge ● Student (source) 2016-07-07 04:11:12 -0600 asked a question 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. = GF(241)[] T. = K.quotient(x^32 + 44) J. = T[] G = s^32 + 7 G.roots() 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? Thank you.