On 2014-09-15 17:33, William A Stein wrote:
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.
(3) clearly seems the safest assuming it is obvious what the cutoff is.
If you say that (3) is the safest, you assume that Sage code is more
reliable than PARI code. I wouldn't want to bet on that :-)
The cutoff is not obvious but a try/except would easily work.
(1) is very hard to evaluate -- will it cause all kinds of extra
headaches or be easy? This depends immensely on the state of pari
development.
At least there is a precedent: in Sage we have used an unstable branch
of PARI for a long time before PARI-2.5.x came out and all went fine.
Upgrading PARI always gives "extra headaches", even from one stable to
another stable version (look at the patch for #15767). One could argue
that by tracking PARI master more closely, we spread out the one big
headache into smaller, more gradual headaches...
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