Hi Marc,
On Sat, Mar 24, 2012 at 08:52:04PM -0400, msh...@math.vt.edu wrote:
> Now you should get
>
> sage: W=WeylGroup(['A',2])
> sage: w=W.from_reduced_word([1,2,1])
> sage: w.inversions()
> [alpha[1], alpha[1] + alpha[2], alpha[2]]
Sorry for the slow answer. Here W is a Weyl group implemented as a
group of matrices acting on some root lattice realization L. In that
case, I have the feeling that it would be more natural if a method of
W (or of it's elements) returning some roots would return then as
elements of L.
Other feelings anyone?
If the user, e.g., doesn't like the "dense" notation for the elements
of the ambient lattice, then he can build the Weyl group acting on
that root lattice:
sage: L = RootSystem(["A",3]).root_lattice()
sage: L.weyl_group()
Weyl Group of type ['A', 3] (as a matrix group acting on the root lattice)
sage: W = L.weyl_group()
Alternatively, we could make the notation for the elements of the
ambient lattice configurable, so that we would have:
sage: L.simple_root(1)
e(0)-e(1)
instead of::
sage: L.simple_root(1)
(1, -1, 0, 0)
Btw: we should have a debate on the indexing set for the basis of the
ambient space; i.e. we might want to have:
sage: L.simple_root(1)
e(1)-e(2)
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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