There is also this old trac ticket <https://github.com/sagemath/sage/issues/23154> about implementing fast arithmetic in genus 2 Jacobians, which never made it into Sage. I've CCed Mike Jabobson, who worked on it. David
On Tue, Mar 12, 2024 at 12:10 PM Giacomo Pope <giacomop...@gmail.com> wrote: > Thank you for linking this and I agree this is a great way to > cross-compare the work we have been doing. I am not an expert in this area > so I am not sure I should do a full review but I'm happy to look over it if > this helps. > > As a small update on this work, I now have > > class HyperellipticCurveSmoothModel(AlgebraicScheme_subscheme_toric) > > So this new class builds on top of AlgebraicScheme_subscheme_toric and the > smooth projective model is built using a toric variety. The points on the > curve are currently SchemeMorphism_point_toric_field, potentially I will > need to make a child class of these if methods on the points themselves are > required. > > With the working arithmetic and this new inheritance my work is now going > to be the rather slow and painful rewrite of all hyperelliptic methods from > the current implementation to ensure everything works on the smooth degree > model. > > On Monday, March 11, 2024 at 6:23:38 AM UTC Kwankyu Lee wrote: > >> On Friday, March 8, 2024 at 7:37:04 PM UTC+9 Giacomo Pope wrote: >> >> As a small update, the repository now contains code to >> >> - perform arithmetic for >> - the imaginary model (ramified, one point at infinity) for all cases >> - the real model (split, two points at infinity) for all cases >> - the real model (inert, zero points at infinity) for even genus >> Which allows us to do "as much" as Magma does for Jacobians of >> hyperellipticc curves from the perspective of arithmetic. >> >> My current "test" for the arithmetic is that D - D = 0 for all cases, >> that jacobian_order * D = zero and that order_from_multiple(D) works. If >> people have other ideas for tests, please let me know. Of course at the >> moment these tests are over finite fields but you can reasonable use other >> fields (as Sabrina's message shows) but I am less sure about how to do >> randomised testing here. >> >> >> I just set https://github.com/sagemath/sage/pull/35467 to "needs review" >> status. The PR implements Jacobian arithmetic for general projective curves. >> >> It is slow compared with Jacobian arithmetic using Mumford >> representation, but could be used to crosscheck the computations. >> > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/7f646c6d-bd0b-452d-a730-30144415f590n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/7f646c6d-bd0b-452d-a730-30144415f590n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAChs6_njyXKS4797cJxVpFsBdVdGt%2B7XFPNXyDEEfK%3DAPks%2BFA%40mail.gmail.com.
