#10140: Base sage.geometry.cone on the Parma Polyhedra Library (PPL)
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   Reporter:  vbraun              |       Owner:  mhampton  
       Type:  enhancement         |      Status:  needs_info
   Priority:  major               |   Milestone:  sage-4.7  
  Component:  geometry            |    Keywords:  ppl       
     Author:  Volker Braun        |    Upstream:  N/A       
   Reviewer:  Andrey Novoseltsev  |      Merged:            
Work_issues:                      |  
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Comment(by novoselt):

 Replying to [comment:25 vbraun]:
 > I think its easier to just go with PPL's ordering. It also matches the
 behaviour of the Polyhedron class which will reorder generators. We
 already have the `Cone_of_fan` to keep track of ray orderings with respect
 to some particular enumeration of rays.

 It is very annoying to deal with several objects that are "the same" but
 are slightly different, e.g. have different ordering of rays. Also, users
 may have some ideas about "convenient order" and provide rays in it: if I
 create the first quadrant as `Cone([(1,0), (0,1)])`, I expect that the
 first ray will be the first basis vector and the second - the second, as
 it was given. Remembering to add `check=False` is annoying. Making
 `check=False` default is very dangerous, as I have learned the hard way. I
 really really want to preserve the order whenever possible. I even plan to
 add the possibility to manually provide the order of facets and points for
 lattice polytopes, since it will allow convenient work with Cayley cones
 and polytopes of nef-partitions - they are easy to create with current
 code, but keeping track of face duality is very ugly.

 I will be very happy to add the sorting myself on top your patch, fixing
 all affected doctests, so pleeease let me do it ;-)

 > I can add back in a check that the polyhedron is really a cone, perhaps
 tomorrow. Generating a Cone from a Polyhedron is only for convenience, I
 don't see any need to make it fast. All actual computations are now done
 with PPL.

 I am more concerned about validity checks than performance here. And I am
 also happy to do the necessary copy-pasting here. So you don't really have
 to do anything, just say that you are OK with it!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10140#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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