" For consistency, what about adding a style 'coroots' for
" weight_multiplicities() too?
After the patch #13461 you can do the following:
sage: A2=WeylCharacterRing("A2",style="coroots")
sage: rep = A2(1,0)
sage: a2 = WeightRing(A2)
sage: a2(rep)
a2(0,-1) + a2(-1,1) + a2(1,0)
However the internal representation of the monomials is still
by weights:
sage: a2(rep).monomial_coefficients()
{(-1/3, -1/3, 2/3): 1, (2/3, -1/3, -1/3): 1, (-1/3, 2/3, -1/3): 1}
sage: rep.weight_multiplicities()
{(-1/3, -1/3, 2/3): 1, (2/3, -1/3, -1/3): 1, (-1/3, 2/3, -1/3): 1}
Since this patch won't be merged until sage-5.5 there may be time
to add the feature you are asking for.
Dan
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