# Symbolic arithmetic in finite fields

I want to know whether and how we can perform symbolic arithmetic for finite fields in SAGEmath. Let me explain the problem. Let GF(2^n) be a finite field extension of GF(2) with a polynomial basis with respect to a root 'a' of an irreducible polynomial. My questions are:

- How to declare an indeterminate element x in this field with symbolic co-ordinates xi, i=1..n in GF(2).
- If x,y are indeterminates how to compute x^2, xy, xy^2 etc as functions symbolically. In other words, how to extract symbolic co-ordinates of these functions.