Michael Beeson <[email protected]> writes: > Dear John (please forgive my use of your first name, I should use your proper > title but I don't know it) > > Thank you very much for taking the time to write that letter. I certainly > did > not mean to complain! I am > very grateful to you for writing mwrank and making it available to us all! I > did not mean to imply that the > output was "cryptic". I am not an expert on elliptic curves nor am I an > expert on Sage. Thank you also > for showing me the proper way to interrogate Sage about an elliptic curve. > The > function E.rank() is indeed > mentioned in the Sage Tutorial, p. 30, but not E.torsion_subgroup(). > > That said, the output I receive from mwrank is not the output you quote in > your > email. There is probably some > mundane reason for that, but as the author, you might want to investigate why. > Below I've pasted in what I got one minute ago > (and also before of course) on Mac OSX with Sage version 4.8. You can see > it's not quite as nice as what you quoted.
Well, the function has returned a string, which is being displayed in standard literal form, rather than actually being printed (with unprintable characters being escaped rather than interpreted, i.e. with '\n' not actually turning into a line break). I think that if you instead do the following: sage: print E.mwrank() ... then you will get approximately the same thing that John posted (modulo spacing errors introduced by his mail client). > Again, I'm not complaining about the output. I'm just reporting that it's > not, on my machine, what it apparently is on your machine. > The words "found points of rank 0" were the ones I did not understand, and I > still don't understand, probably because I know only the > very basics about elliptic curves, but I only know what "rank" means when > applied to the MW group, not when applied to a point, so > that is what confused me. As John said, the message is not saying that the points themselves have rank 0 but that the subgroup generated by the points found was of rank 0 (matching with the rank computed earlier). I guess maybe the message could be changed to "found points generating rank 0", or "found enough points to give rank 0", or something? I know less about elliptic curves than you do, though, so don't listen to me... > I note that the output you quote doesn't contain > that phrase. It looks to me like it does... -Keshav ---- Join us in #sagemath on irc.freenode.net ! -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
