On Mon, Feb 13, 2012 at 09:14:17AM +0100, Christian Stump wrote:
> for your attantion. http://arxiv.org/pdf/1201.5566v1.pdf
> 
> If someone has the time to look into it: please, please report!

I  did  not  know  Meinolf  was  doing  that.  I guess that he did it as an
exercise to learn Python. There are 2 aspects to it.

-A  new  algorithm  to  compute  Kazhdan-Luztig  cells  recursively,  using
parabolic  subgroups, which is apparently  several orders of magnitude more
efficient that previous algorithms: very interesting!

-A  naive (in the sense of straightforward)  port of the needed parts of (a
rather  old version of) Chevie to plain Python. I do not know if much of it
is easily usable for a Sage port.

By  the way, I have a question: what is  a Sage port? I ask this because it
is my plan to eventually work in Sage (when GAP3 becomes too obsolete). But
I  must confess that  I have not  yet started on  this plan since I want to
finish  some large projects on Chevie and I think it is not yet time for me
to discard GAP3. I  understand that  there are several levels of porting:

-  The first is that Chevie can be used in Sage through the interface
to  GAP3, thanks  to Saliola. 

-Next,  one could  map each  Chevie type  of object  to an appropriate Sage
class  or category; since the design in  Sage could be quite different this
could  be non trivial. Since  I have not yet  learned properly Sage this is
the hardest for me, and is where I am stuck.

-One could then write the high-level code of Chevie in Sage, calling GAP3 or
GAP4 for the low-level stuff.

-Or  one  could  port  all  the  code  of  Chevie in Sage. This requires in
particular  efficient cyclotomic numbers (mostly done, if I understand) and
efficient  permutations (anything  done there?).  This second question begs
the  question  wether  one  would  also  port much of the permutation group
library of GAP3/4 to Sage.

Even if I do not do it myself, I would be happy to help anyone trying to do
any of the above.

Best regards,
------------------------------------------------------------------------
Jean MICHEL, Equipe des groupes finis, Institut de Mathematiques UMR7586 
Bureau 9D17 tel.(33)157279144, 175, rue du Chevaleret 75013 Paris

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