add .torsion_basis() method to EllipticCurve_finite_field

[yyyyx4]

Computing a basis of a particular m-torsion subgroup is an important subroutine in several algorithms for isogenies and endomorphism rings of elliptic curves over finite fields.

This patch adds a .torsion_basis() method to EllipticCurve_finite_field. Its current implementation is merely a thin wrapper around .abelian_group() and .torsion_subgroup() — the point of this patch is to introduce the interface first so that more optimizations can be incorporated later.

CC: @defeo

Component: elliptic curves

Author: Lorenz Panny

Issue created by migration from https://trac.sagemath.org/ticket/34718

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

f882209

add .torsion_basis() method to EllipticCurve_finite_field

[sagetrac-git]

Changed commit from e7e40f0 to f882209

[mkoeppe]

Removed branch from the issue description because it has been replaced by PR #34982