Folded and uploaded to trac.
Thank you. I set a positive review.
Yes! In this test, we want to check not only translations by roots
(preserving polygons) but also translations by weights (preserving
alcoves only); e.g. play with the extended Weyl group. And there is
the same question of appropriate "translation factors" for the
fundamental weights. It seems that using the `c_i` just does the
job. I remember having a rationale for this for untwisted/dual
thereof; for type BC, this seems to just work (whereas using the same
translation factors as for the roots breaks); but that might be plain
luck, and the current tests only ensure that the factors are not too
small; they might be too large.
Ok, then this is correct since the lattice of the extended Weyl group is
indeed
\oplus_{i \in I \setminus {0} } \ZZ c_i \omega_i
even for A_{2n}^{(2)}.
Cheers,
Anne
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