#9972: Add fan morphisms
------------------------------------------------+---------------------------
   Reporter:  novoselt                          |       Owner:  mhampton  
       Type:  enhancement                       |      Status:  needs_work
   Priority:  major                             |   Milestone:  sage-4.6.1
  Component:  geometry                          |    Keywords:            
     Author:  Andrey Novoseltsev, Volker Braun  |    Upstream:  N/A       
   Reviewer:  Volker Braun, Andrey Novoseltsev  |      Merged:            
Work_issues:                                    |  
------------------------------------------------+---------------------------
Changes (by vbraun):

  * status:  needs_review => needs_work


Comment:

 Ok now `image_cone` works but I can't compute the preimage:
 {{{
 sage: c = f.image_cone( Cone([(1,0),(0,1)]) )
 sage: c
 1-d cone of Rational polyhedral fan in 1-d lattice N
 sage: f.preimage_cones(c)
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)

 /home/vbraun/opt/sage-4.6/devel/sage-main/<ipython console> in <module>()

 /home/vbraun/Sage/sage/local/lib/python2.6/site-
 packages/sage/geometry/fan_morphism.pyc in preimage_cones(self, cone)
     858                 for dcone in dcones:
     859                     if
 (possible_rays.issuperset(dcone.ambient_ray_indices())
 --> 860                         and
 self.image_cone(dcone).is_face_of(cone)):
     861                         preimage_cones.append(dcone)
     862             self._preimage_cones[cone] = preimage_cones

 /home/vbraun/Sage/sage/local/lib/python2.6/site-
 packages/sage/geometry/fan_morphism.pyc in image_cone(self, cone)
     809                 RISGIS = self._RISGIS()
     810                 CSGIS = set(reduce(operator.and_,
 --> 811                             (RISGIS[i] for i in
 cone.ambient_ray_indices())))
     812                 image_cone =
 codomain_fan.generating_cone(CSGIS.pop())
     813                 for i in CSGIS:

 TypeError: reduce() of empty sequence with no initial value
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:51>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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