On Wednesday 6 March 2024 at 04:52:16 UTC-8 Giacomo Pope wrote:

I think aside from maybe needing additional methods on the hyperelliptic 
curve, once the projective model is right and points on the curve are well 
defined for all cases. I do not have any intuition on whether the balanced 
model will for example have issues with the p-Adic implementation as I have 
no experience in this area.

Tiny bit of feedback on the p-adic bit: as far as I know, things like 
Cantor's algorithm use euclidean division, wwhich is a big problem 
p-adically: coefficients may vanish unexpectedly and p-adically you cannot 
distinguish that from loss of precision. I think that's already a problem 
in the existing implementation and I think it will be in yours as well. So 
I think you can ignore p-adics to begin with. If you can get it working 
usefully and reliably for p-adic base fields as well then that's a real 
win! 

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