Hi Christian,
On Sun, Feb 20, 2011 at 08:08:07AM -0800, Christian Stump wrote:
> I encountered a problem with roots and coroots for the root lattice:
>
> if I take the coroot_space of a root lattice (i.e., the root space
> over ZZ), I get the coroot space over QQ. Therefore,
> to_coroot_lattice_morphism and associated_coroot do not work. On the
> other hand, when I fix this problem, there is the next problem as in
> type B, the coroot lattice corresponding to the root lattice over ZZ
> is over 1/2 ZZ.
Just to make sure (and for future regression tests), could you send a
little session demonstrating this?
> Another simple question in this context is: is there an easy way to
> bet the coefficient of a simple root alpha of an element beta in the
> root space? To use coefficient, I need to get the index of alpha, and
> this doesn't seem to me like the right way to do it.
The conceptual way (and thus independent on the realization at hand)
is to take the scalar product of beta with the simple coweight
corresponding to alpha. This should (be made to) work; however there
are things to straighten out around scalar products and coweights ...
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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