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solving for a normalized ℓ‑isogeny when ℓ is large compared to p #38481

Open yyyyx4 opened 3 months ago

yyyyx4 commented 3 months ago

Sage has long been able to compute a normalized isogeny of known degree ℓ from its domain and codomain (using Stark’s algorithm originally and BMSS as of recently, see #36285). However, both of these options require that p=0 or ℓ < p/4+O(1) where p is the characteristic, and there is currently no alternative for small p>0 and large ℓ. The literature does contain algorithms for this case (see e.g. the top of page 2 here for a few references), so it would be good to implement one of them.

Note that this functionality is used as a subroutine in various other functions, such as computing duals.

defeo commented 2 months ago

Have you started something or is this just a wish for the moment? I was thinking of proposing it as a MSc topic.

yyyyx4 commented 2 months ago

For me this is just a wishlist item. I've recently suggested it to Péter as a potential student project, though, so you may want to check if he's got any plans for it.