We implement an EllipticCurveHom child class EllipticCurveHom_frobenius encapsulating purely inseparable Frobenius isogenies. As every isogeny decomposes into a separable and a purely inseparable part, we can (together with EllipticCurveHom_composite) now express any isogeny between two elliptic curves in Sage.

One immediate application (also implemented in the patch) is that separable isogenies of degree divisible by the characteristic now have a working .dual() method. Other than that, changes to the existing codebase are kept minimal.

This is one of the items on the "isogeny wish-list" #7368. It is also an important step towards implementing endomorphism rings later; cf. #32826 comment:3.

Diff without the dependency: sagemath/sagetrac-mirror@79ae468...e953939

Depends on #32826

CC: @defeo @JohnCremona @categorie @tscrim @videlec @fchapoton @kwankyu

Component: elliptic curves

Author: Lorenz Panny, Mickaël Montessinos

Branch/Commit: 2ebbfae

Reviewer: John Cremona

Issue created by migration from https://trac.sagemath.org/ticket/33915