On 8/30/07, BarryS <[EMAIL PROTECTED]> wrote: > I am considering switching from doing computations directly in PARI/GP > to using the interface through SAGE.
Are you the Barry Smith I know from UCSD? > I have a few questions. > > 1. Can every function in PARI/GP be accessed somehow through SAGE? > For instance, I want to be able to use rnfkummer. PARI is included in SAGE, and every PARI function can be used somehow through SAGE. There are some examples here: http://sagemath.org/doc/html/ref/module-sage.interfaces.gp.html Basically, doing gp.eval('...') is identical to typing a command directly into the GP command line: sage: gp.eval('a = 5;') '' sage: gp.eval('sin(a)') '-0.9589242746631384688931544062' There is also an interface directly to the PARI C library, which is in some ways better / faster, but is sometimes less complete than the above gp interface (the implementation is completely different): sage: a = pari(5) sage: a.sin() -0.9589242746631384688931544062 Anything can be added to the pari C libary interface, but this requires knowing a fair amount about how SAGE works. > 2. I hate the PARI documentation, and am befuddled about what types > of computations involving L-functions are implemented. Understood. > I noticed in > the SAGE documentation that there seem to be 3 sets of functions > related to L-functions for elliptic curves. SAGE has by far more elliptic curve L-functions code than any other program out there. > What about Hecke and > Artin-L functions for number fields? > Or at least, since dirichlet > characters are implemented, are L-functions for absolutely Abelian > extensions implemented? SAGE includes Tim Dokchitser's PARI program for very general L-functions, which should be able to do such things. It also include Mike Rubinstein's lcalc program which can do a lot with computing zeros of such L-functions in some cases. That said, I don't think there is a simple straightforward way to work with such L-functions in SAGE right now. I hope somebody (a student, probably) will take this up as a project soon. The really hard underlying code is already there, but making it all work together nicely isn't. > 3. Is it possible to compute one bernoulli number mod p directly, > rather than computing a whole list of them with bernoulli_mod_p and > then picking a specific one out of the list? The algorithm of Buhler et al for computing bernoulli_mod_p involves series arithmetic and does not compute just one. There is no algorithm that I'm aware of that computes just one bernoulli number mod p without computing a lot more, and which doesn't just compute the Bernoulli number over QQ and reduce it mod p: sage: bernoulli(1000) % 389 251 Of course, if you're the Barry Smith I think you are, maybe you have a new algorithm for this problem :-). > Thanks for any information, > > Barry By the way, if you're still around UCSD, talk to Neal Harris and Kevin McGown. -- William Stein Associate Professor of Mathematics University of Washington http://www.williamstein.org --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
