division of elliptic-curve morphisms #38902
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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
EllipticCurveHominterface, 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.