Hi, We can move this over the sage-nt, but let me reply here.
One improvement should be to, in fact, follow what John [Cremona)] did for elliptic curves -- replace points-as-morphisms with points as simple coordinates. In analogy with matrices and homomorphisms, for reasons of efficiency (and intended uses) the "correct" mathematical interprettation of a point on a scheme as a scheme morphism should require an explicit coercion to a Homset. William and I set this up in complete generality, without concern for efficiency. However, I hope that the framework (as set up in Sage and as I put in Magma previously) for working on the sets of rational points E(L) for L/K an extension field or a K-algebra will remain and be supported. I also noticed that John (or someone) put in some nice printing functions for elliptic curves and their points that could be move up to general curves/points. After e-mail exchange, I was also wrapping David Harvey's code just to see what was there. I'm happy that Nick is taking the on the full job of writing a frobenius_charpoly function. Note that naive point counting over the prime field F_p can be done in one line with a legendre symbol. I look forward to seeing the result. I suggest keeping us informed on sage-nt. Cheers, David --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
