ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 09 Feb 2022 00:46:33 +0100Evaluate polynomial with imaginary number as input?https://ask.sagemath.org/question/61023/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?vroomerifyWed, 09 Feb 2022 00:46:33 +0100https://ask.sagemath.org/question/61023/