Is there a way to generate the primitive elements in $GF(p^n)$, in say Sagemath, and perform operations with these elements?
For example, using the irreducible polynomial $p(x)=1+x+x^3$ in $GF(2^3)$, how can i generate these primitive elements and how would I go about adding/multiplying them?
I have looked at the online manual, but can't seem to find what I am looking for. Thank you.