On Dec 20, 2007, at 3:21 AM, John Cremona wrote: > Topic 1: isomorphisms between Weierstrass models > > For Robert B as author of weierstrass_morphism.py: It's not a bug but > I would recommend that you test for equality of j-invariants before > doing the harder work (which you do by extracting 12th roots of the > ratio of the discriminants). Similarly in > > elliptic_curves/ell_generic.py > > in the function is_isomorphic().
Good point. > Also, I am yet to be convinced that > the code in weierstrass_morphism.py is correct, but I will reserve > judgement until I have a counterexample. > It certainly is *not* correct in char. 2 & 3 since you divide by 2 > and 3! I think I put a note in there about characteristic 2 and 3, but if not there should be one. Other than that, if I've made a mistake I'll be happy to be proven wrong, but I'm pretty confident. > I have always done this using the ratio of c4 and/or c6 invariants, > which is fine except in characteristics 2 and 3 anyway, and also > simpler (since unless j=0 or j=1728 you only need to test for > something being a square, not need for 12'th roots). That code can > already be found in simon's ellQ.gp (the new version incorporating > some improvements I suggested to him). But it does not deal with char > 2 & 3, which I'll sit down and work through one day, and then submit > an improved version of weierstrass_morphism.py. OK, I'll take a look at that. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
