*Goal*-- Create an option for Zq and Qq to generate their defining polynomial by lifting from GF(p)[x] to a factor of x^q-1 (as opposed to lifting naively)*Type*-- Convenience feature (computing Frobenius in such a representation is very fast)*Priority*-- Medium-Low*Difficulty*-- Medium*Prerequisites*-- might rely on some polynomial code from p-adic polynomial precision*Background*-- See this talk*Contributors*--*Progress*- not started*Related Tickets*--

## Discussion

## Tasks

Given an irreducible polynomial f of degree n over GF(p), compute a lift of f that divides

`x^(p^n)-1`. Plug this into Zq and Qq, and change the code for Frobenius to take advantage of this representation.