Am I right in thinking that sage does not (yet) know about the left, right
and two-sided Kazhdan-Lusztig cells of Coxeter groups? As sage can compute
Kazhdan-Lusztig polynomials I assumed that it knew about cells as well, but
it doesn't seem to. Please tell me if I am missing something.
Incidentally, I also noticed that we have some identity issues -- that I am
sure are well known:
sage: WeylGroup("A5")
Weyl Group of type ['A', 5] (as a matrix group acting on the ambient space)
sage: CoxeterGroup("A5")
Coxeter group over Universal Cyclotomic Field with Coxeter matrix:
[1 3 2 2 2]
[3 1 3 2 2]
[2 3 1 3 2]
[2 2 3 1 3]
[2 2 2 3 1]
I am guessing that one of these is just wrapping code from chevie, but I
haven't checked. Is there any reason not to amalgamate these two classes?
Currently the CoxeterGroup code seems marginally faster but perhaps the
WeylGroup classes have more functionality:
sage: WeylGroup("A5").cardinality()
720
sage: CoxeterGroup("A5").cardinality()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
<ipython-input-6-42496321af01> in <module>()
----> 1 CoxeterGroup("A5").cardinality()
/usr/local/src/sage/local/lib/python2.7/site-packages/sage/categories/
sets_cat.pyc in cardinality(self)
1370 NotImplementedError: unknown cardinality
1371 """
-> 1372 raise NotImplementedError("unknown cardinality")
1373
1374 # Functorial constructions
NotImplementedError: unknown cardinality
Andrew
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