This ticket mainly aims to separate the auxiliary F-algebra in another file.

This file implements a better custom-made F-algebra, with additional useful methods.

CC: @videlec @tscrim

Component: number theory

Author: Frédéric Chapoton

Branch/Commit: 8a8cdf3

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34562