I am working on extending (non-affine) DynkinDiagrams so they allow arbitrary labels over the nodes as well as different type of nodes (i.e. crosses). The purpose is using sage for producing examples to be included in papers. See e.g. http://arxiv.org/abs/1303.1307 page 36. I haven't created a ticket yet, but I already have a patch with bugfix for these docstrings. This fits into #15272 which I am polishing right now.
I am not familiar with Kac and affine case so please let me know if there are some clashes. Dne středa, 19. února 2014 0:56:21 UTC+1 bump napsal(a): > > In the Cartan type documentation (cartan_type.py) we find the following > statement: > > The direction of the arrows is the **opposite** (i.e. the > transpose) > > > of Bourbaki's convention, but agrees with > Kac's. > > > > > > > > For example, in type `C_2`, we > have:: > > > > > > > > sage: C2 = DynkinDiagram(['C',2]); > C2 > > > > > O=<=O > > > > 1 > 2 > > > > > C2 > > > > sage: > C2.cartan_matrix() > > > > [ 2 > -2] > > > > [-1 > 2] > > > > > This appears in the reference manual on this page: > > > http://www.sagemath.org/doc/reference/combinat/sage/combinat/root_system/cartan_type.html > > It is correct that Bourbaki's Cartan matrix is the transpose of Kac. > However both have > the same convention regarding Dynkin diagrams: the arrow points from the > long root > to the short. > > I think we should correct this. > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
