On 9/3/11 1:18 PM, Nicolas M. Thiery wrote:
On Fri, Sep 02, 2011 at 11:48:13PM -0700, Anne Schilling wrote:
I just noticed that we have
sage: W = WeylGroup(["A",3,1])
sage: w = W.an_element()
sage: w.bruhat_lower_covers
but not
sage: w.bruhat_upper_covers
Is there a reason for this? Both methods do exist for weak order.
Because the algorithm implemented in Sage for weak order is symmetric
w.r.t. going up and down, whereas the algorithm for Bruhat order is
not (in the finite case, we achieve that symmetry for Bruhat by
considering a reduced word to w_0 instead of to 1, but of course that
does not work in the infinite case).
I just added upper covers for Bruhat order to the patch
trac_11742-cores-add-as.patch.
If it looks ok, I will fold it into the cores patch.
Best,
Anne
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