Hi Travis,
Thanks for the ultra quick reply. I'm impressed that so much work being
done on this as I assumed that it was all in the too hard basket. I'll have
a quick look at calls and see how hard it is to wrap something around
chevie's implementation.
Andrew
On Monday, 10 November 2014 15:43:30 UTC+11, Travis Scrimshaw wrote:
>
> Hey Andrew,
>
> 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.
>>
>
> AFAIK, there's no code in Sage or ticket about cells. +1 to adding them.
>
>>
>> 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:
>>
>
> I implemented the current CoxeterGroup and it uses Sage's (hence gap's)
> matrix group code. However the WeylGroup does have more information
> (features) since it is considered acting on the root/weight lattice, such
> as reflection_to_root on elements. Combining these classes might be taken
> care of by http://trac.sagemath.org/ticket/15703.
>
>>
>> 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
>>
>> There's currently http://trac.sagemath.org/ticket/16630 which should fix
> some (all?) of these issues (and I will get to that after next week).
>
> Best,
> Travis
>
>
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