Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Sorry. Bad question. I meant something more like "I always normalize the symmetric inner product so that the short roots have norm one. From what point of view is this different normalization natural?" I guess I can find the answer in Kac's book. Thanks for your answer. On Thursday, July 28, 2

Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

On Wednesday, July 27, 2016 at 2:39:48 PM UTC-5, Joseph Hundley wrote: > > Awesome. Thank you! > > Out of curiosity is there a reason .norm_squared() doesn't just divide by > 2 for us? > > Because it is just the (symmetric) inner product of the root with itself, and I was following Kac's book

Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Awesome. Thank you! Out of curiosity is there a reason .norm_squared() doesn't just divide by 2 for us? Joe On Tuesday, July 26, 2016 at 4:29:00 PM UTC-4, Travis Scrimshaw wrote: > > > > On Tuesday, July 26, 2016 at 3:07:04 PM UTC-5, Joseph Hundley wrote: >> >> I recently looked at Computing

Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

On Tuesday, July 26, 2016 at 3:07:04 PM UTC-5, Joseph Hundley wrote: > > I recently looked at Computing in Groups of Lie Type > by > > Cohen, Murray and

Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

I recently looked at Computing in Groups of Lie Type by Cohen, Murray and Taylor. The basic approach to representation and calculation which is taken there is essentially the one I had in mind. Plus they've worked a number of details I thought I w

Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Hey David, Thank you for the links. To add to all this: GAP has already implemented some related objects: > (1) Lie algebras > (http://www.gap-system.org/Manuals/doc/ref/chap64.html, > http://www.gap-system.org/Datalib/lie.html, > http://www.science.unitn.it/~degraaf/sla.html >

Re: [sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Joe and Travis: To add to all this: GAP has already implemented some related objects: (1) Lie algebras (http://www.gap-system.org/Manuals/doc/ref/chap64.html, http://www.gap-system.org/Datalib/lie.html, http://www.science.unitn.it/~degraaf/sla.html) (2) real Lie groups (http://users.monash.edu/~hei

[sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Hey Joe, > > I guess I am inclined to try to build this thing and see who is interested > in it. The ticket you linked is very helpful to me. > Let me know what you need from me wrt #14901 or any additional feature requests. > > I'm interested to know more about your plans for Lie groups and

[sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Thanks, Travis. I guess I am inclined to try to build this thing and see who is interested in it. The ticket you linked is very helpful to me. I'm interested to know more about your plans for Lie groups and Groups of Lie type. In some sense it seems to me that the objects I'm really working

[sage-devel] Re: symbolic computation with Chevalley generators for algebraic groups

Hey Joseph As far as I know, none of that functionality has been implemented in Sage. In a strongly related direction, at some point I hope to implement the classical Lie groups and what are known as geometric crystals (in the sense of Berenstein and Kazhdan). Groups of Lie type would also be