Dear Nicolas and Dan,
Daniel Bump wrote:
I see Anne created a ticket #8811 which I think is supposed to be
for this patch.
Yes!
I have played with the patch some and it works well for type A2.
Good.
Nicolas Thiery wrote:
> Can you have a look at the patch, and point me to whatever might need some
work?
I wrote a reviewer patch following
trac_8811_reduced_word_of_translations-nt.patch
trac_8811_reduced_word_of_translations-review-as.patch
in the sage-combinat queue which addresses some small issues in the docs I
spotted
and which also adds extensive tests for type A_4^{(1)}, C_3^{(1)}, D_4^{(1)},
and D_5^{(1)}
comparing with Kashiwara's private notes. Feel free to fold it. All tests pass!
Here are a few more questions/comments:
* The translation_factor in line 1244 of combinat/root_system/cartan_type.py is
not
yet implemented for type A_{2n}^{(2)}.
* In line 1035 of combinat/root_system/root_lattice_realization.py do you
really want
def translation(t, x)
or rather
def translation(self, x) ? The doc would need to change as well.
* In line 194 of weight_lattice_realization.py it is suggested to test that the
element is indeed a translation.
* I agree with Dan that the role of the weight/coweight lattice is currently a
little
unclear in the patch. Proposition 6.5 of Kac which is cited states that the
extended
affine Weyl group is the semidirect product of the finite Weyl group and
translations
in the coweight lattice. The code itself always seems to use the weight
lattice.
This should be clarified.
Cheers,
Anne
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