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2016-07-07 09:06:35 -0500 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.

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2016-07-07 04:11:12 -0500 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.<x> = GF(241)[]

T.<a> = K.quotient(x^32 + 44)

J.<s> = 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.