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division of elliptic-curve morphisms #38902

Open yyyyx4 opened 3 weeks ago

yyyyx4 commented 3 weeks ago

This patch adds a class for representing symbolic fractions $\phi/d$ of elliptic-curve morphisms. As a corollary, we get left- and right-division of isogenies, which are emulated by composing with the dual and dividing out the degree. Fractional isogenies often appear in computations with endomorphism rings (e.g., $(1+\pi_q)/2$ is an endomorphism of any elliptic curve over $\mathbb F_q$ with rational $2$-torsion).

The new class is designed to fully support the EllipticCurveHom interface, albeit with extremely basic algorithms in some cases. Indeed, the goal of this patch is to establish the interface and basic functionality — any optimizations are left for future work.

github-actions[bot] commented 3 weeks ago

Documentation preview for this PR (built with commit 58c1817446ecbaf5662901606cd99d9283d7c8e9; changes) is ready! :tada: This preview will update shortly after each push to this PR.