A "sparse" GCM (generalized Cartan matrix)
can be implemented as list of items of the form
(i,j,a_{ij},a_{ji})
where i < j are elements in an index set.
I guess this is a skew symmetric matrix with
entries given by pairs (a_{ij},a_{ji}).
--Mark
> The generalized Cartan matrix (a_{ij}) is exactly what one needs to
> define a Kac-Moody ("simply-connected") root system.
> To define a Coxeter group or the Weyl group of a Kac-Moody algebra
> then one only needs a "Cartan datum", that is, the numbers a_{ij} a_{ji}
> for i not equal to j.
>
> Of course we use shortcut names like
> ['A',3] to refer to a root datum.
>
> --Mark
>
>>> What about allowing a skew-symmetric matrix (and an optional indexing
>>> list) as input for DynkinDiagram?
>>
>> Sure, this sounds good!
>>
>> Cheers,
>> Nicolas
>> --
>> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
>> http://Nicolas.Thiery.name/
>>
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