#19481: No cardinality for virtual crystals
-----------------------------+-----------------------------
   Reporter:  aschilling     |            Owner:
       Type:  defect         |           Status:  new
   Priority:  major          |        Milestone:  sage-6.10
  Component:  combinatorics  |         Keywords:  crystals
  Merged in:                 |          Authors:
  Reviewers:                 |  Report Upstream:  N/A
Work issues:                 |           Branch:
     Commit:                 |     Dependencies:
   Stopgaps:                 |
-----------------------------+-----------------------------
 When one slightly changes the following example in the documentation:
 {{{
         sage: from sage.combinat.crystals.virtual_crystal import
 VirtualCrystal
         sage: A = crystals.Tableaux(['A',3], shape=[2,1,1])
         sage: V = VirtualCrystal(A, {1:(1,3), 2:(2,)}, {1:1, 2:2},
 cartan_type=['C',2])
         sage: G = crystals.Tableaux(['C',2], shape=[1]).digraph()
         sage: V.digraph().is_isomorphic(G, edge_labels=True)
         True
 }}}
 to
 {{{
         sage: from sage.combinat.crystals.virtual_crystal import
 VirtualCrystal
         sage: A = crystals.Tableaux(['A',3], shape=[2,1,1])
         sage: V = VirtualCrystal(A, {1:(1,3), 2:(2,)}, {1:1, 2:2},
 cartan_type=['C',2])
         sage: R = RootSystem(['C',2])
         sage: Lambda = R.weight_space()
         sage: La=Lambda.fundamental_weights()
         sage: G = crystals.LSPaths(La[1])
         sage: V.digraph().is_isomorphic(G, edge_labels=True)
 ---------------------------------------------------------------------------
 AttributeError                            Traceback (most recent call
 last)
 <ipython-input-8-d91276b648e9> in <module>()
 ----> 1 V.digraph().is_isomorphic(G, edge_labels=True)

 /Applications/sage/local/lib/python2.7/site-
 packages/sage/graphs/generic_graph.pyc in is_isomorphic(self, other,
 certify, verbosity, edge_labels)
   20442         """
   20443
 > 20444         if self.order() == other.order() == 0:
   20445             return (True, None) if certify else True
   20446

 /Applications/sage/src/sage/structure/parent.pyx in
 sage.structure.parent.Parent.__getattr__
 (/Applications/sage/src/build/cythonized/sage/structure/parent.c:8095)()
     840             return self.__cached_methods[name]
     841         except KeyError:
 --> 842             attr = getattr_from_other_class(self,
 self._category.parent_class, name)
     843             self.__cached_methods[name] = attr
     844             return attr

 /Applications/sage/src/sage/structure/misc.pyx in
 sage.structure.misc.getattr_from_other_class
 (/Applications/sage/src/build/cythonized/sage/structure/misc.c:1667)()
     251         dummy_error_message.cls = type(self)
     252         dummy_error_message.name = name
 --> 253         raise dummy_attribute_error
     254     try:
     255         attribute = getattr(cls, name)

 AttributeError: 'CrystalOfLSPaths_with_category' object has no attribute
 'order'
 }}}
 Also cardinality is not defined for virtual crystals:
 {{{
 sage: V.cardinality()
 ---------------------------------------------------------------------------
 AttributeError                            Traceback (most recent call
 last)
 <ipython-input-9-36235162fdc4> in <module>()
 ----> 1 V.cardinality()

 /Applications/sage/local/lib/python2.7/site-
 packages/sage/combinat/crystals/subcrystal.pyc in cardinality(self)
     262             if self in FiniteCrystals():
     263                 return Integer(len(self.list()))
 --> 264             card = super(Subcrystal, self).cardinality()
     265             if card == infinity:
     266                 self._cardinality = card

 AttributeError: 'super' object has no attribute 'cardinality'
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/19481>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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