On Jan 14, 2008 9:31 AM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > Does SAGE currently include any functionality for manipulating Lie > algebras? (I only need reductive Lie algebras, because I'm using them > to study compact Lie groups.) For instance, I'd like to be able to > manipulate irreducibles (encoded by their highest weights), so that I > can form a tensor product and decompose it into irreducibles.
GAP has this: http://www.gap-system.org/Manuals/doc/htm/ref/CHAP061.htm AFAIK, nothing is wrapped. On Jan 14, 2008 1:09 PM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > I just looked at the GAP docs, and I don't quite see how to do what I > want (decomposing some random thing into irreducibles, or at least > getting the multiplicity of the trivial representation), but I'm sure > it's possible. I don't know how you want to specify "some random thing". As a tensor product of a list of irreducibles determined by their highest weight? > > What I do know is that Magma has some of this functionality, > implemented in a fashion that I can understand. So that could be one > possible interface model if we decide to wrap this functionality from > GAP, LiE, or elsewhere. I vaguely remember that Willem de Graaf wrote that too. Could easily be wrong though... I'm ccing him, so he can chime in and correct me if he wants. > > Kiran > > On Jan 14, 9:41 am, "David Joyner" <[EMAIL PROTECTED]> wrote: > > > On Jan 14, 2008 9:31 AM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > > > > > > > > Does SAGE currently include any functionality for manipulating Lie > > > algebras? (I only need reductive Lie algebras, because I'm using them > > > to study compact Lie groups.) For instance, I'd like to be able to > > > manipulate irreducibles (encoded by their highest weights), so that I > > > can form a tensor product and decompose it into irreducibles. > > > > GAP has this:http://www.gap-system.org/Manuals/doc/htm/ref/CHAP061.htm > > AFAIK, nothing is wrapped. > > > > > > > > > In specific instances (like GL_n) I know in principle to translate > > > such questions into terms compatible with the combinatorics > > > functionality we have from Symmetrica. But I want to experiment with > > > other cases (like Sp_n) and I'd rather simply work at the Lie algebra > > > level, without having to keep track of the combinatorics myself. > > > > > In any case, I'm likely to be bugging people about this at SAGE Days > > > 7... > > > > It might be worth emailing Willem de Graaf about it > > too:http://www.science.unitn.it/~degraaf/ > > > > > > > > > Kiran > > > --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
