I must say I'm very excited about the new PARI/GP point counting code. As a side note I had a quick look at Bills new code and it seems some stuff we discussed at the last PARI workshop aren't implemented yet. So you might expect even better stugg if the next six months (another PARI workshop is planned next January). I did not look deeply enough to see if Bill uses Mike Harrison tricks to only deal with integral elements in Kedlaya's algorithm.
What's sure is that we should also wrap what's already in Sage for Kedlaya algorithm to be actually used for point counting (the Monsky Washnitzer stuff has been there for years...) though it should be less efficient than a C implementation. And yes the j invariant stuff already present in Sage is crucial as well. So we should definitely not just call PARI for cardinality of elliptic curves, but keep some Sage magic around it. As far as what to do with the a/b/c options I don't have a clear idea, I'm always happy to struggle with bleeding edge code, but don't really know how PARI's API evolves in devel versions and how much of a pain it would be to ship such a version with Sage. -- 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 post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
