My suggestion for such a project is: compute all the S-integral points on an elliptic curve (which is a finite set, for any given finie set of primes S). First, over Q (assume that you are given a Mordell-Weil basis), which is also implemented in Magma. Then, over number fields -- not implemented anywhere which is available.
Sources: a psper of Stephens and Smart, and the Saarbruecken thesisof E Herrmann (in German). He is the one responsible for the Magma implementation over Q, and he also has his own implementation over number fields written in Simath. John On 19/11/2007, David Joyner <[EMAIL PROTECTED]> wrote: > > On Nov 19, 2007 12:21 PM, Martin Albrecht <[EMAIL PROTECTED]> wrote: > > > > Hi there, > > > > at Sage Days 6 Stefan Müller-Stach > > > > http://hodge.mathematik.uni-mainz.de/~stefan/index.html > > > > babelfish translation: > > > > http://babelfish.altavista.com/babelfish/tr?lp=de_en&url=http%3A//hodge.mathematik.uni-mainz.de/%7Estefan/index.html > > > > asked me whether the Sage project would like to name some projects suitable > > for a Diplomarbeit for some of his students. > > > > If you don't know the German system: it is safe to assume a "Diplomarbeit" > > is > > like a Master's thesis (except that you usually do a Diplom before pursuing > > a > > PhD). The idea is that we/you/the Sage developers name a project (in number > > theory) which is suitable for a Diplomarbeit (i.e. challenging enough but > > not > > overwhelming, timeframe: roughly a year) and Stefan tries to pass this > > project on to one of his students. > > > > To me this seems like a nice way to get stuff implemented that one hardly > > gets > > around to implement. > > > > Also, he is thinking about setting up a Sage seminar which could provide a > > similar 'service' for Sage: i.e. Students get credits for working on Sage. > > This would be suitable for more short term projects. > > > > Thoughts? > > > Just to narrow things down a bit, is it fair to say that the topics > his students > will probably focus on would be algebraic geometry and/or algebraic number > theory (not calculus or differential equations or something like that)? > > I think we are still lacking a good implementation of an algorithm computing > Riemann-Roch spaces. I'm not sure if that is too far afield or not though... > > > > > > Martin > > > > PS: Stefan, I hope I represented your idea correctly. > > -- > > name: Martin Albrecht > > _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 > > _www: http://www.informatik.uni-bremen.de/~malb > > _jab: [EMAIL PROTECTED] > > > > > > > > > > > > > -- John Cremona --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
