I should point out that we have some point-counting available already for hyperelliptic curves courtesy from PARI, but of the p-adic sort (small characteristic) rather than the Schoof-Pila sort (larger characteristic).
What I think is needed to go further is to implement the group law in the Jacobian. This has been long overdue and would be a great topic for a GSoC project! Kiran On Wednesday, April 7, 2021 at 11:42:10 PM UTC-7 vdelecroix wrote: > Dear Simon, dear all, > > @all: forwarding from sage-gsoc > > @Simon: your project seems great for a GSoc project. I am > unsure about SageMath capabilities to deal with hyperellitpic > curves but it has some features > > > https://doc.sagemath.org/html/en/reference/arithmetic_curves/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.html > > Since your project not listed on the wiki > https://wiki.sagemath.org/GSoC/2021 the possible candidates > for mentors might not be around. I forward your message to the > sage-nt group. > > Best > Vincent > > -------- Message transféré -------- > Sujet : [sage-gsoc] Wanted: Mentor for Project with Hyperelliptic Curves > Date : Wed, 7 Apr 2021 05:46:11 -0700 (PDT) > De : Simon Schwarz <[email protected]> > Répondre à : [email protected] > Pour : sage-gsoc <[email protected]> > > Hello all, > > my name is Simon and I am currently a postgraduate student in Computer > Science at the University of Cambridge. > > As a GSoC 2021 project, I would be interested in extending SageMath's > implementation of Jacobians of hyperelliptic curves. In particular, I'd > like to add point counting methods over finite fields (relevant paper > <https://hal.inria.fr/inria-00512403/document>) and implement the Weil > pairing (and possibly additional pairings) on hyperelliptic curves > (relevant paper > <http://cacr.uwaterloo.ca/techreports/2009/cacr2009-30.pdf>). > Note that SageMath already supports those over elliptic curves, but > currently lacks support for hyperelliptic curves. In contrast, Magma > already includes those methods (see Magma documentation here > <https://magma.maths.usyd.edu.au/magma/handbook/text/1557>), so I think > it would be a great addition if this functionality is also supported by > SageMath. > > If anybody can imagine being a mentor for this project please get in > touch with me so we can discuss this project a bit further. Likewise, if > you have any other questions do not hesitate to contact me. > > Best regards, > Simon > > -- > You received this message because you are subscribed to the Google > Groups "sage-gsoc" group. > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > To view this discussion on the web visit > > https://groups.google.com/d/msgid/sage-gsoc/046c240b-2800-4f1e-baa2-5f8d40d62426n%40googlegroups.com > . > > -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/dcb05ef8-fd33-4cd9-bf03-23a7cfa6be6fn%40googlegroups.com.
