Implement GF(p^n) as relative extension of GF(p^d)

Over at #2384 Robert wrote:

On another note, I think I remember hearing somewhere that magma uses zech logs as coefficients, e.g. GF(pⁿ) is implemented as a relative extension of GF(p^d) where p^d is small enough for the log representation. Would this be worth looking at?

and David replied:

This would only work when n is sufficiently composite, but in that case I think it's a great idea. Still, you need to have very good generic polynomial arithmetic to make this work. I think this is something to work on later.

CC: @robertwb @sagetrac-dmharvey @koffie

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/2750

sagemath / sage

Implement GF(p^n) as relative extension of GF(p^d) #2750