#9839: Add dual cone computation
----------------------------------+-----------------------------------------
   Reporter:  novoselt            |       Owner:  mhampton    
       Type:  enhancement         |      Status:  needs_review
   Priority:  major               |   Milestone:  sage-4.5.3  
  Component:  geometry            |    Keywords:              
     Author:  Andrey Novoseltsev  |    Upstream:  N/A         
   Reviewer:                      |      Merged:              
Work_issues:                      |  
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Comment(by vbraun):

 I don't like that your lattice now needs to have `self.dual()`
 implemented:
 {{{
 sage: c = Cone([(1,0), [0,1]], lattice = ZZ^2)
 sage: c.facet_normals()
 ---------------------------------------------------------------------------
 AttributeError                            Traceback (most recent call
 last)

 /home/vbraun/opt/sage-4.5.2/devel/sage-main/<ipython console> in
 <module>()

 /home/vbraun/Sage/sage/local/lib/python2.6/site-
 packages/sage/geometry/cone.pyc in facet_normals(self)
    1808         """
    1809         if "_facet_normals" not in self.__dict__:
 -> 1810             M = self.lattice().dual()
    1811             P = self.lattice_polytope()
    1812             rotate_lifts = not self.is_strictly_convex()

 /home/vbraun/Sage/sage/local/lib/python2.6/site-
 packages/sage/structure/parent.so in
 sage.structure.parent.Parent.__getattr__ (sage/structure/parent.c:5311)()

 /home/vbraun/Sage/sage/local/lib/python2.6/site-
 packages/sage/structure/parent.so in
 sage.structure.parent.getattr_from_other_class
 (sage/structure/parent.c:2757)()

 /home/vbraun/Sage/sage/local/lib/python2.6/site-
 packages/sage/structure/parent.so in
 sage.structure.parent.raise_attribute_error
 (sage/structure/parent.c:2629)()

 AttributeError: 'FreeModule_ambient_pid_with_category' object has no
 attribute 'dual'
 }}}
 This essentially limits you to `ToricLattice`s now. I think it would be
 good for `factet_normals()` to use the same lattice otherwise, so `ZZ^n`
 works as well.

 The rest looks good!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9839#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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