The patch applies without any problems to Sage 4.4.
I have one concern which is that the relevant lattice
is the coroot lattice and (for the extended affine Weyl
group) the coweight lattice.
In the example, we have this:
We start by translations by elements of the coroot lattice::
sage:
R.reduced_word_of_alcove_morphism(alpha[0].translation)
[1, 2, 1, 0]
sage:
R.reduced_word_of_alcove_morphism(alpha[1].translation)
[0, 2, 0, 1]
sage:
R.reduced_word_of_alcove_morphism(alpha[2].translation)
[0, 1, 0, 2]
We continue with translations by elements of the classical
weight lattice, embedded at level 0:
sage: omega1 = Lambda[1] - Lambda[0]
sage: omega2 = Lambda[2] - Lambda[0]
Shouldn't we be working with the fundamental coweights, not the
fundamental weights?
In this example it makes no difference since the root system is
simply-laced.
Dan
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