#6588: Categories for root systems and many misc improvements
--------------------------------------------------------+-------------------
   Reporter:  nthiery                                   |          Owner:  
mhansen                 
       Type:  enhancement                               |         Status:  
needs_review            
   Priority:  major                                     |      Milestone:  
sage-5.0                
  Component:  combinatorics                             |       Keywords:  root 
systems, categories
Work_issues:                                            |       Upstream:  N/A  
                   
   Reviewer:  Anne Schilling, Mark Shimozono, PatchBot  |         Author:  
Nicolas M. ThiƩry       
     Merged:                                            |   Dependencies:  
#10817                  
--------------------------------------------------------+-------------------

Comment(by nthiery):

 Replying to [comment:18 aschilling]:
 > But these are not categories, they are classes. In your case, a
 cateogory is in
 > /sage/combinat/root_systems/

 Yes: unlike for crystals, and like for symmetric functions (well for
 NCSF actually; the categorification of symmetric functions is yet to
 be done), I want to keep the categories close to the classes. As I
 said, it's borderline, but it feels better to me this way.

 > How about self.fundamental_weights(extended = True) with default
 extended = False?

 Well, since it's an abuse, and one that we might want to get rid of,
 I'd rather not abuse yet another function. Unless you have a natural
 use case for this notation? (for the extended weight lattice, that's
 just self.basis()).

 > Sorry, I forgot to push.

 Given how many times I played that gag to you, I am not going
 to throw the first rock :-)

 > It should be there now.

 Yes, thanks! I have folded together all patches and posted them
 here. I also did the reindentation and renaming *_lattice_realization
 -> *_lattice_realizations. On my side, the patch is good to go.

 Cheers,
                         Nicolas

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6588#comment:21>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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