Ask Your Question

jimbo's profile - activity

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.<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?

Thank you.