Evaluate polynomial with imaginary number as input?
I am trying to evaluate the polynomial (19v^2 + 49v + 8
) raised to the 67th power where v^3 + 2 = 0
.
All computations are done mod 67.
Here's my first attempt:
R.<v> = PolynomialRing(GF(67))
poly = (19 * (v^2) + 49*v + 8)
after_frobenius = poly^67
after_frobenius(sqrt(-2))
But this gives the error: "positive characteristic not allowed in symbolic computation".
I suspect, I need to define the PolynomialRing
over an extension field where v^3 + 2 = 0
. But, I'm not sure how to do that.
Any ideas?