# Question:How do I construct a polynomial over a finite field?

## Question:How do I construct a polynomial over a finite field?

Maple 13

Hi, I am new to Maple, and, though I have scoured the internet and Maple's help, I have been unable to find a way to construct an element of F[x], where F is a finite field. Just to clarify, I am looking to construct a polynomial with variable x (eventually it will be multivariate, but I think I can extend to that easily), with coefficients from some finite field of size p^k, p and k being given.

I have seen a few examples online of people converting polynomials to this form - however, once converted, the polynomial does not behave correctly. For instance, when multiplied by elements of the finite field or other polynomials of that form, the numerical parts of the coefficients resume acting like integers, while the root of your irreducible polynomial behaves as if it were simply another variable and, most importantly, does not reduce down when it achieves higher degrees.

I know that SAGE has a very simple implementation - for various reasons, I have to use Maple to implement this algorithm that I am working on, and this algorithm requires a construction of this sort.