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compute minimal polynomial of an isogeny & push such polynomials through other isogenies #40467

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@yyyyx4 yyyyx4 commented Jul 23, 2025

Back in #37125 we implemented Algorithms 3 and 4 from Deuring for the People. In this patch we add Algorithm 5, as well as a simple convenience method to compute the minimal polynomial of an isogeny.

This functionality is very convenient for computing chains of isogenies whose kernel points may live in extension fields — without explicitly constructing and working in those extension fields.

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yyyyx4 commented Jul 23, 2025

I suppose this should have a specialized implementation in EllipticCurveHom_composite, so that we do the pushing step by step rather than constructing the rational map for the entire chain. Is it worth doing this now?Edit: Done.

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LGTM, there's a FIXME, but I can't think of something obvious to replace this.

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