Hello,
I would like some opinions about ticket #16931. This ticket is about
using PARI for point counting on elliptic curves over F_q (it's only
recently that PARI supports this, earlier versions only did prime fields
F_p).
The main algorithm PARI uses is SEA, which breaks down if the
characteristic is too small compared to the size of the field. I posted
a bug report about this:
http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1606
This issue has been "fixed" upstream by implementing Kedlaya. However
upstream considers this a change which is "too complex" to go into a
PARI-2.7.x release. So it will be a while before this fix goes into a
stable release.
I see three possible options (in decreasing order of preference for me):
(1) Upgrade PARI to latest master instead of a stable version.
(2) Backport the Kedlaya implementation to PARI-2.7.x and put that in Sage.
(3) Keep the current slow Sage algorithm for point counting over F_q in
the cases where PARI SEA doesn't work.
Any opinions?
Jeroen.
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