On Thursday, January 30, 2014 2:44:10 PM UTC+1, John Cremona wrote: > > 1. We use pari's SEA for elliptic curves over prime fields. the next > version of pari, 2.7, is supposed to have point-counting over > non-prime fields. > Yes for elliptic curves PARI 2.7 will have SEA over non-prime field (I think there is some limitation which makes it unsuitable for small (but not so small) characteristic, don't really remember what), and fast canonical lift algorithms for small char (when X_0(N) has genus 0, and should have quite quickly the same when X_0(N)/W_N has genus 0 as well, maybe more later). PARI 2.6.2 which should be an RC for PARI 2.7 should be out real soon, at least that's what was announced at the latest PARI workshop a few weeks ago, so we could begin packaging it.
> 2. There is also very good code out there for hyperelliptics, I think > by Sutherland. > There is hypellfrob by David Harvey which is awfully fast, but does not work for midly small characteristic when the genus is high. It's available in Sage, by the way some tickets enhancing the interface or related functions need review: #15148 and #11980. To circumvent the liumiataion of Harvey's algorithm, we would need an implementation of the plain Kedlaya algorithm and the char 2 variation by Denef Vercauteren. For non-prime field with moderate characteristic, we would also need some method using deformation theory. There is C code on top of FLINT (2.3) by Pancratz but it targets higher dimensional hypersurfaces. > > Do you need more general curves than that? > Nope. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
