#14610: Energy function for level zero LS paths for all types
-------------------------------------+-------------------------------------
       Reporter:  mshimo             |        Owner:  mshimo
           Type:  enhancement        |       Status:  positive_review
       Priority:  major              |    Milestone:  sage-5.12
      Component:  combinatorics      |   Resolution:
       Keywords:  crystal graph,     |    Merged in:
  days49                             |    Reviewers:  Anne Schilling, Mark
        Authors:  Mark Shimozono,    |  Shimozono, Ben Salisbury
  Anne Schilling                     |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------
Changes (by bsalisbury1):

 * status:  needs_review => positive_review


Comment:

 Here is the new output for the above situation:
 {{{
 sage: RootSystem(['D',2]).root_lattice().simple_root(1).is_short_root()
 ---------------------------------------------------------------------------
 ValueError                                Traceback (most recent call
 last)
 <ipython-input-1-31128c2ac44d> in <module>()
 ----> 1
 
RootSystem(['D',Integer(2)]).root_lattice().simple_root(Integer(1)).is_short_root()

 /Users/salis1bt/sage-5.12.beta0/local/lib/python2.7/site-
 packages/sage/combinat/root_system/root_lattice_realizations.pyc in
 is_short_root(self)
    3291             ct = self.parent().cartan_type()
    3292             if not ct.is_irreducible():
 -> 3293                 raise ValueError, "Cartan type needs to be
 irreducible!"
    3294             if not ct.is_finite():
    3295                 raise NotImplementedError, "Implemented only for
 irreducible finite root systems"

 ValueError: Cartan type needs to be irreducible!
 }}}
 All looks good to me.
 {{{
 ----------------------------------------------------------------------
 All tests passed!
 ----------------------------------------------------------------------
 Total time for all tests: 1835.0 seconds
     cpu time: 5844.4 seconds
     cumulative wall time: 7022.8 seconds
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/14610#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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