Hi all,

Nicolas sez:

>>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.

Anne sez:

> To me it feels more natural to have the output on the basis of simple
> roots, rather than the ambient space.

I'm with Anne here. Consider what happens if you consistently ask
for roots and coroots through the domain of the Weyl group.
The most dramatic case is when you use the Weyl group acting on the
coweight lattice.

sage: W = RootSystem(['A',3]).coweight_lattice().weyl_group()
sage: w =W.from_reduced_word([2,1,3])
sage: w.inversions(inversion_type = 'roots')
[2*Lambdacheck[1] - Lambdacheck[2], -Lambdacheck[2] + 2*Lambdacheck[3],
Lambdacheck[1] + Lambdacheck[3]]
sage: w.inversions(inversion_type = 'coroots')
[alpha[1], alpha[3], alpha[1] + alpha[2] + alpha[3]]

This seems far more confusing than just always returning things labeled
with alphas for roots and alphachecks for coroots.

--Mark


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