Hey Joseph, There is currently a fair amount implemented with root systems:
sage: Phi = RootSystem(['A',2]) sage: P = Phi.root_lattice() sage: Q = Phi.root_lattice() sage: P = Phi.weight_lattice() sage: al = Q.simple_roots() sage: al[1] alpha[1] sage: al[1].weyl_action([1,2,1]) -alpha[2] sage: al[1] + 4*al[2] alpha[1] + 4*alpha[2] sage: (al[1] + 4*al[2]).weyl_action([2,1]) 3*alpha[1] - alpha[2] sage: La = P.fundamental_weights() sage: La[1].weyl_action([1,2,1]) -Lambda[2] Will this work for your purposes? Let me know if you have any specific questions too. I'm happy to contribute how and when I can. Best, Travis On Tuesday, December 13, 2016 at 10:31:27 AM UTC-6, David Roe wrote: > > I'm interested in helping out with this project. Julian Rüth, Xavier > Caruso and I are working on p-adics on the Sage IRC channel ( > http://www.sagemath.org/help-irc.html) at 4pm EST (10pm CET) today. If > you want to log in and chat about character lattices for a bit I'd be happy > to share ideas. > > I'll try to respond to this e-mail with more specific suggestions about > existing structures in the next week or so, but before then I have to write > and grade finals.... > David > > On Tue, Dec 13, 2016 at 11:12 AM, Joseph Hundley <joseph....@gmail.com > <javascript:>> wrote: > >> I'm playing around with implementing Based Root Data, with an eye towards >> eventually implementing groups attached to them. >> So, I need to instantiate the character and cocharacter lattices; they >> need to be free Z-modules with an action of the relevant Weyl group. In >> other words they are Z[W]-modules. Any suggestions on relevant existing >> structures would be welcome. >> >> -- >> 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 sage-devel+...@googlegroups.com <javascript:>. >> To post to this group, send email to sage-...@googlegroups.com >> <javascript:>. >> Visit this group at https://groups.google.com/group/sage-devel. >> For more options, visit https://groups.google.com/d/optout. >> > > -- 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 sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
