Fwd: [sage-gsoc] Wanted: Mentor for Project with Hyperelliptic Curves

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Vincent Delecroix

Apr 8, 2021, 2:42:10 AM4/8/21
to sag...@googlegroups.com
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


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.


-------- 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 <simonsc...@gmail.com>
Répondre à : sage...@googlegroups.com
Pour : sage-gsoc <sage...@googlegroups.com>

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
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

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,

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Kiran Kedlaya

Apr 9, 2021, 1:19:24 PM4/9/21
to sage-nt
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!


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