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

[jdemeyer]

Changed author from tom denton to Tom Denton

[nthiery]

comment:6

Note: I had to (trivially) rebase #10998 on top of this patch. Please check that the queue apply next time :-)

[nthiery]

comment:7

Replying to @nthiery:

Note: I had to (trivially) rebase #10998 on top of this patch. Please check that the queue apply next time :-)

Oops, #9280 in fact.

[jdemeyer]

comment:8

The first line of the patch file is

exporting patch:

This should not be there. Probably you made some script which writes such a line, I think it is best to undo that.

[jdemeyer]

comment:9

Also, there are some problems building the documentation:

dochtml.log:/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.2.alpha1/devel/sage/doc/en/reference/sage/categories/examples/crystals.rst:69: WARNING: more than one target found for cross-reference u'cartan_type': sage.combinat.crystals.tensor_product.CrystalOfTableaux.cartan_type, sage.combinat.root_system.dynkin_diagram.DynkinDiagram_class.cartan_type, sage.combinat.root_system.weyl_characters.WeightRing.cartan_type, sage.combinat.root_system.weyl_characters.WeylCharacterRing.cartan_type, sage.combinat.root_system.weyl_group.WeylGroup_gens.cartan_type, sage.combinat.root_system.root_system.RootSystem.cartan_type, sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebraT.cartan_type, sage.categories.crystals.Crystals.ParentMethods.cartan_type, sage.combinat.root_system.weyl_group.ClassicalWeylSubgroup.cartan_type, sage.combinat.root_system.weyl_characters.WeylCharacterRing.Element.cartan_type, sage.combinat.root_system.weyl_characters.WeightRing.Element.cartan_type, sage.categories.crystals.Crystals.ElementMethods.cartan_type
dochtml.log:/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.2.alpha1/devel/sage/doc/en/reference/sage/categories/examples/crystals.rst:73: WARNING: more than one target found for cross-reference u'Element.weight': sage.combinat.crystals.direct_sum.DirectSumOfCrystals.Element.weight, sage.combinat.crystals.fast_crystals.FastCrystal.Element.weight

[anneschilling]

comment:10

Replying to @jdemeyer:

The first line of the patch file is

exporting patch:

This should not be there. Probably you made some script which writes such a line, I think it is best to undo that.

This spurious line was removed in the revised patch.

Best wishes,

Anne

[anneschilling]

Attachment: trac_11183-crystals_local_characterization-final.patch.gz

[anneschilling]

comment:11

Replying to @jdemeyer:

Also, there are some problems building the documentation:

dochtml.log:/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.2.alpha1/devel/sage/doc/en/reference/sage/categories/examples/crystals.rst:69: WARNING: more than one target found for cross-reference u'cartan_type': sage.combinat.crystals.tensor_product.CrystalOfTableaux.cartan_type, sage.combinat.root_system.dynkin_diagram.DynkinDiagram_class.cartan_type, sage.combinat.root_system.weyl_characters.WeightRing.cartan_type, sage.combinat.root_system.weyl_characters.WeylCharacterRing.cartan_type, sage.combinat.root_system.weyl_group.WeylGroup_gens.cartan_type, sage.combinat.root_system.root_system.RootSystem.cartan_type, sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebraT.cartan_type, sage.categories.crystals.Crystals.ParentMethods.cartan_type, sage.combinat.root_system.weyl_group.ClassicalWeylSubgroup.cartan_type, sage.combinat.root_system.weyl_characters.WeylCharacterRing.Element.cartan_type, sage.combinat.root_system.weyl_characters.WeightRing.Element.cartan_type, sage.categories.crystals.Crystals.ElementMethods.cartan_type
dochtml.log:/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.2.alpha1/devel/sage/doc/en/reference/sage/categories/examples/crystals.rst:73: WARNING: more than one target found for cross-reference u'Element.weight': sage.combinat.crystals.direct_sum.DirectSumOfCrystals.Element.weight, sage.combinat.crystals.fast_crystals.FastCrystal.Element.weight

The two warnings should be fixed in the revised patch.

Best wishes,

Anne

[jdemeyer]

Merged: sage-4.7.2.alpha1