Energy function for level zero LS paths for all types

[sagetrac-mshimo]

Extend the energy function for level zero LS paths to work for dual untwisted affine root systems. Currently it only works for untwisted affine root systems.
This patch also implements is_short_root for finite irreducible types.

CC: @sagetrac-sage-combinat @bsalisbury1

Component: combinatorics

Keywords: crystal graph, days49

Author: Mark Shimozono, Anne Schilling

Reviewer: Anne Schilling, Mark Shimozono, Ben Salisbury

Merged: sage-5.12.beta1

Issue created by migration from https://trac.sagemath.org/ticket/14610

[anneschilling]

Reviewer: Anne Schilling, Mark Shimozono

[anneschilling]

Author: Mark Shimozono, Anne Schilling

[anneschilling]

Changed keywords from crystal graph to crystal graph, days49

[anneschilling]

Changed author from Mark Shimozono, Anne Schilling to Mark Shimozono, Anne Schilling, Ben Salisbury

[anneschilling]

comment:8

Hi Ben,

The patch is now ready for the final review.

Thanks,

Anne

[bsalisbury1]

comment:9

Hi Anne and Mark,

Thank you for your work on this! Everything looks good!

----------------------------------------------------------------------
All tests passed!
----------------------------------------------------------------------
Total time for all tests: 1692.1 seconds
    cpu time: 5689.0 seconds
    cumulative wall time: 9948.0 seconds

~Ben

[bsalisbury1]

Changed author from Mark Shimozono, Anne Schilling, Ben Salisbury to Mark Shimozono, Anne Schilling

[bsalisbury1]

Changed reviewer from Anne Schilling, Mark Shimozono to Anne Schilling, Mark Shimozono, Ben Salisbury

[anneschilling]

comment:10

Ben, thank you for the review!

[jdemeyer]

comment:12

This AssertionError should be changed into a ValueError or TypeError:

sage: RootSystem(['D',2]).root_lattice().simple_root(1).is_short_root() 
---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-25-e961de76571c> in <module>()
----> 1 RootSystem(['D',Integer(2)]).root_lattice().simple_root(Integer(1)).is_short_root()

/mazur/release/merger/sage-5.12.beta1/local/lib/python2.7/site-packages/sage/combinat/root_system/root_lattice_realizations.pyc in is_short_root(self)
   3290             """
   3291             ct = self.parent().cartan_type()
-> 3292             assert ct.is_irreducible()
   3293             if not ct.is_finite():
   3294                 raise NotImplementedError, "Implemented only for irreducible finite root systems"

AssertionError: 

[anneschilling]

Attachment: trac_14610-LSenergy-ms.patch.gz

[anneschilling]

comment:13

Fixed!

[bsalisbury1]

comment:15

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

[anneschilling]

comment:16

Thank you!

Anne

[jdemeyer]

Merged: sage-5.12.beta1