By "algebraic groups" I mean "split connected reductive algebraic groups equipped with a choice of maximal torus, Borel subgroup, and realization/pinning/epinglage." (Though I am interested in principle in removing unnecessary hypotheses.)
By "Chevalley generators" I mean * elements of root subgroups (say, elements of the form x_a( expression ) where a is a root and x_a is the fixed isomorphism from the additive group scheme to the root subgroup) * elements of the fixed maximal torus * representatives for the simple reflections in the Weyl group which have been fixed in some natural way. (The choice of x_a's gives a couple obvious options.) Unless I've oversimplified here such elements generate and all the relations among them are determined by the Cartan matrix and the matrix of structure constants of the realization, but there is a fair amount of book-keeping to be done. I'm fairly regularly interested in forming two products of elements of root subgroups and conjugating one by the other (in exceptional groups where this generators and relations approach is perhaps easier than a matrix realization). Does Sage have some functionality for doing this sort of thing that I'm unaware of? Is there more that should be added? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
