On Mon, Jan 10, 2011 at 06:24:18AM -0800, Anne Schilling wrote:
> I have a question about the Cartan type code:
>
> sage: C = CartanType(['A',4,2])
> sage: C.classical()
> ['C', 2]
> sage: C.dual().classical()
> ['C', 2] relabelled by {1: 1, 2: 0}
>
> Wouldn't it be better to output
> ['B', 2] in this case?
That could sound nicer indeed. It depends partly on what special node
we want by default for C.dual():
sage: C.dual().special_node()
2
sage: C.dual().classical().index_set()
[0, 1]
sage: CartanType(["B",2]).index_set()
[1, 2]
Changing C.dual to return a "dual cartan type", instead of a
"relabelled cartan type" should do the job. But then we somehow loose
the information that type BC dual is isomorphic to type BC. I don't
know if this is relevant.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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