Stembridge local characterization for crystal bases

[sdenton4]

Implementation of the Stembridge local axioms for crystal bases. Some functions added for checking these axioms, and _test_stembridge_local_axioms() was added to the test suite for highest weight crystals.

CC: @sagetrac-sage-combinat @anneschilling

Component: combinatorics

Keywords: crystals

Author: Tom Denton

Reviewer: Anne Schilling

Merged: sage-4.7.2.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/11183

[sdenton4]

Attachment: trac_11183-crystals_local_characterization-td.patch.gz

exported patch file

[anneschilling]

Reviewer: Anne Schilling

[anneschilling]

comment:2

This patch implements the local axioms for highest weight crystals of simply-laced types. This is a very useful test to check that a given crystal is actually consistent (for simply-laced types these tests are necessary and sufficient, for nonsimply-laced types only necessary). I tested this patch mathematically on several crystals.

sage -t on all relevant crystal code passes. If the buildbot gives green light for all tests, this is a positive review!

[anneschilling]

comment:3

Currently, the tests in /sage/categories/examples/crystals.py do not pass and need to be updated. In addition, it would be good to provide an implementation of a simple "crystal" that does not pass the Stembridge tests in this file.

So I set this to "needs work".

Anne

[anneschilling]

comment:4

I reviewed the final version of the patch and it looks good now! The tests of all modified files pass. If the buildbot gives a green light, this has a positive review!

Anne

Apply: trac_11183-crystals_local_characterization-final.patch