Hi -- last week, Nicolas and I had a first look at how to get root systems for non-crystallographic and infinite Coxeter groups.
Here is a basic problem of which I have either not yet understood its reason in the implementation, or which might be done better: - all constructions depend on a Cartan matrix, but we do not have a class CartanMatrix - we do have a class DynkinDiagram that (seems to me to) serve(s) as the Cartan datum including the Cartan matrix. But Dynkin diagrams are hard to manipulate, can only be constructed from known types, and keep their string rep and pretty print after being manipulated. This makes it hard to construct the Dynkin diagram from a given Cartan matrix, while I might only want to use it to get its Cartan matrix in order to construct the root system. Why don't we implement a class CartanMatrix containing a symmetrizable matrix, and the indexing. If one constructs a Cartan matrix from a Cartan type, then we might also want to store this. From this, one can then get back everything including Dynkin diagrams and root systems. What do you think? After solving this, I would then go and start solving glitches when working with Cartan matrices over the universal cyclotomic field. Christian -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
