On Sat, May 15, 2010 at 08:58:35AM -0700, Brant Jones wrote:
> There is already a method CartanType.symmetrizer() which returns the
> entries of the D matrix, and there is also a test in
> AmbientSpace._test_norm_of_simple_roots() that ensures the root norms
> in AmbientSpace are scalar multiples of the D entries.
Oops, I actually probably implemented that one :-)
> Since D is defined only up to scalar.
The one returned by symmetrizer is guaranteed to be unique (see the
doc).
> It seems somewhat clearer to me to use the AmbientSpace to compute
> the root norm.
This assumes that you have an ambient space available. Which is not
the case currently for affine types. Whereas symmetrizer will work for
any symmetrizable Kac-Moody.
> I'm not sure how to create a "diagonal module morphism," but I'd be
> willing to try. Which class contains the documentation you suggested,
> and are there any existing examples I could look at?
sage: F = CombinatorialFreeModule(QQ, ZZ)
sage: F.module_morphism?
> Otherwise, I'd like to add the root_norm and associated_coroot methods
> to RootLatticeRealization.
Ok.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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