# How to do symbolic computation over a finite field [closed]

I want to carry out finite field arithmetic symbolically in SAGEmath. Need help. Let me explain the problem. Suppose I declare the finite field GF(2^n) with an irreducible polynomial specified with root a. I want to declare indeterminates x,y in this field with co-ordinates xi,yi i=1,...,n in the polynomial basis in a. Then extract symbolic co-ordinates of functions such as x^2,xy,x^3 in the same basis. How can this be done?