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

 Wonderful speed gain! However, when do you expect PPL to become a standard
 library? It is my impression that currently it is difficult to add new
 standard packages and it is more likely to become an optional one for a
 while. In which case there should be an option to use PPL, but its
 presence should not affect work of toric geometry.

 Little picks at the patch:
  1. I don't see why it is necessary to remove the possibility of `Cone`
 construction from a `Polyhedron`.
  1. I think that new possible input `C_Polyhedron` should be documented in
 the INPUT section rather than a note in the end.
  1. Is it possible to make `C_Polyhedrons` immutable (on demand)?
  1. I prefer all line generators to be put in the end of ray list for non-
 strictly convex cones, if they were determined automatically. Because if
 one works with faces of such a cone, then all these generators are the
 same and, therefore, others are more "important". That's very minor, of
 course.
  1. I am trying to follow PEP8 style guide
 http://www.python.org/dev/peps/pep-0008/ which says: When raising an
 exception, use "raise `ValueError`('message')" instead of the older form
 "raise `ValueError`, 'message'". New line 1167 tries to change this
 recommended form to an old one ;-)
  1. Looking at what you have done in facet normals, maybe we should change
 `cone.dual_lattice()` method to always return ZZ^n^ if there is no dual
 method for the lattice? Thinking of the class group situation, it seems
 like a more sensible default.
  1. I think cones should not be printed explicitly (i.e. using "print")
 when `ValueError` is raised due to attempt to intersect cones in lattices
 of different dimension. The reason is that maybe some users want to
 intercept this exception and deal with it in their own way without showing
 any output. Also, I think that the check should be done not for equality
 of lattice dimensions, but for equality of lattices themselves, because
 cones of different lattices should not be intersected.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10140#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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