Add methods to rigged configurations

[tscrim]

Adds some extra methods to rigged configurations: the action of the left column splitting and the basic operation in the bijection with tensor product of KR tableaux.

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​365b520	Added methods to RC's.
​c1cda2b	Merge branch 'public/combinat/rigged_configurations/bijections-13872' into public/combinat/rigged_configurations/improvements
​85b6446	Reorded all.py to match original (so fewer changes).
​a51b39f	Fixed minor typo in cobminat/crystals/letters.pyx.
​17a04d7	Added deprecatd classes back with warnings.
​538c594	Merge branch 'master' into public/combinat/rigged_configurations/bijections-13872
​29c9d34	[FIXUP] 5.13.beta5: update git specific files
​0aa3fed	5.13.beta5
​8f2b136	5.13.beta5
​42bc8b6	some edits to docs

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0050d2e	Forbade spinor cases.
​21bf27f	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​8bac0b2	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​e17c7c8	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​fd8b9c0	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​c7c399e	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​d9a96c2	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​3ccd75d	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​bf56c7f	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​bb910cc	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​4695e88

Implemented changes Anne and I discussed.

[tscrim]

Thanks in advance for doing the review.

[aschilling]

Hi Travis,

Here are further comments:

+ If we are construction a rigged configuration from a rigged configuration
+ (say of another type) and we don't want to recompute the vacancy numbers,
+ we can use the ``use_vacancy_numbers`` to avoid the recomputation.

This is not a sentence. Perhaps you want "If we are constructing"?

Also, it would be great to add left_split as a method to KirillovReshetikhinTableaux? and possibly also the right_split method! This can be just done by using the bijection to rigged configurations, but it would be very handy to have these methods directly on KirillovReshetikhinTableaux? as well.

Thanks,

Anne

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​78489a6	trac #15882: review (typos)
​968f9f6	Fixing broken links and other misc cleanup.
​faa5507	Fixed failing doctests.
​207f38e	Fixed last doc errors.
​007043b	Fixed failing doctests and some cleanup of classical_crystals.
​6314a36	Fixed doc of classical_crystals and added regular_crystals to doc.
​ac1dcd5	Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560
​2cc751e	Fixed doctest failures in rigged_configurations folder.
​3be2a08	Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560
​df3a9eb	Some doctest fixes.

[tscrim]

Here's the major changes:

• Based this off #15882.

• Added the Luzstig involution to (tensor products of) KR tableaux, KR crystals, and rigged configurations.

• Added left/right splitting maps to (tensor products of) KR tableaux and rigged configurations. (The right splitting map is non-trivial on KR tableaux; look in type D₄⁽¹⁾ at the B^2,2 module generators.)

• Moved opposition_automorphism() from the crystals category into Cartan types.

• Fixed the typo noted above.

Best,
Travis

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b2b3fa6	Merge branch 'develop' into public/combinat/crystals/catalog-15882
​e7e2ad5	Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​d262371	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​6729c22	Merge branch 'u/tscrim/q_dims' into public/combinat/crystals/catalog-15882
​e9dd3a2	Fixed doctests for q-dims.
​d9e9370	Merge branch 'develop' into public/combinat/crystals/catalog-15882
​24216f8	Merge branch 'develop' into public/combinat/crystals/catalog-15882
​6328bf0	Reworked the entry points to KR crystals.
​a7f2e1e	Moved the KR RiggedConfigurations to rigged_configurations.py.
​8120e16	Merge branch 'public/combinat/crystals/catalog' of trac.sagemath.org:sage into public/combinat/crystals/catalog-15882
​bc0a691	Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e67176e	More changes to the catalog.
​482ca9c	Fixed last bad link.
​6402c54	fixed some documentation issues
​a596cdd	Merge branch 'public/combinat/crystals/catalog' of trac.sagemath.org:sage into public/combinat/crystals/catalog-15882
​698ae7e	some small changes to the documentation
​eaf48a9	Merge branch 'public/combinat/crystals/catalog' of trac.sagemath.org:sage into public/combinat/rigged_configurations/methods-15560
​0942e81	Fixed failing doctests.
​3fe79c7	Merge branch 'public/combinat/crystals/catalog' into public/combinat/rigged_configurations/methods-15560

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​46a0d0a

Fixes for lusztig involution.

[rws]

Based on 6.2beta1 it fails:

sage -t --long src/sage/combinat/rigged_configurations/rigged_configurations.py  # 1 doctest failed

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​59260e8	Merge branch 'public/combinat/rigged_configurations/methods-15560' of trac.sagemath.org:sage into public/combinat/rigged_configurations/methods-15560
​695b0d9	Fixed issue with type B bijection.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b5b442f	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​43da3ef	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​c821bde	Initial graph viewing. Only for type D and types w/o special run() methods.
​8d173ee	Merge branch 'develop' into u/tscrim/rc_bij_pdf
​e8011bd	Changed input method and added constructions to other types.
​54f1a4a	Merge branch 'develop' into u/tscrim/rc_bij_pdf
​e103d1e	Merge branch 'u/tscrim/rc_bij_pdf' into public/combinat/rigged_configurations/methods-15560

[aschilling]

Hi Travis,

Here are some more comments:

• The documentation of right_split has a ` missing. Please run the documentation to see that it actually compiles!

• Please add the map \theta to rigged configuration and compare to lusztig_involution.

• Please add tests and more explanations what build_graph does. Explain which graph it is computing. Also the following fails:

sage: RC = RiggedConfigurations(['D', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: RCToKRTBijectionTypeD(RC(partition_list=[[1],[1],[1],[1]])).run()
[[2], [-3]]

sage: RCToKRTBijectionTypeD(RC(partition_list=[[1],[1],[1],[1]])).run(build_graph=True)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-10-1c82ae944c4d> in <module>()
----> 1 RCToKRTBijectionTypeD(RC(partition_list=[[Integer(1)],[Integer(1)],[Integer(1)],[Integer(1)]])).run(build_graph=True)

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/bij_type_D.pyc in run(self, verbose, build_graph)
    513 
    514                     if build_graph:
--> 515                         y = self.rigged_con.parent()(*[x._clone() for x in self.cur_partitions])
    516                         self._graph.append([self._graph[-1][1], (y, len(self._graph)), letters(b)])
    517 

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8924)()

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (sage/structure/coerce_maps.c:4637)()

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (sage/structure/coerce_maps.c:4501)()

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configurations.pyc in _element_constructor_(self, *lst, **options)
    717             lst = lst[0]
    718 
--> 719         return self.element_class(self, list(lst), **options)
    720 
    721     def _calc_vacancy_number(self, partitions, a, i, **options):

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configuration_element.pyc in __init__(self, parent, rigged_partitions, **options)
    289             nu[-1] = RiggedPartitionTypeB(nu[-1])
    290 
--> 291         ClonableArray.__init__(self, parent, nu)
    292 
    293     def _repr_(self):

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/list_clone.so in sage.structure.list_clone.ClonableArray.__init__ (sage/structure/list_clone.c:3758)()

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/list_clone.so in sage.structure.list_clone.ClonableArray.check (sage/structure/list_clone.c:5758)()

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configuration_element.pyc in check(self)
    492             for i, vac_num in enumerate(partition.vacancy_numbers):
    493                 if vac_num < partition.rigging[i]:
--> 494                     raise ValueError("rigging can be at most the vacancy number")
    495 
    496     def to_tensor_product_of_kirillov_reshetikhin_tableaux(self, display_steps=False, build_graph=False):

ValueError: rigging can be at most the vacancy number

Anne

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​c612e7f	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​40c98dc	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​56119bf	Added theta map, fixed bugs and expanded doc.
​2874083	Minor rewording of build_graph param in bijections.

[tscrim]

Replying to aschilling:

• The documentation of right_split has a ` missing. Please run the documentation to see that it actually compiles!

I couldn't find this and the documentation built without an issue and looks okay to me (although there was a missing 'u').

• Please add the map \theta to rigged configuration and compare to lusztig_involution.

Added under the name complement. In general, it will be different than lusztig_involution, which fixes each classical component, whereas \theta fixes the classical structure but permutes the classical components. Or did you mean you wanted me to add a doctest showing this?

• Please add tests and more explanations what build_graph does. Explain which graph it is computing. Also the following fails:

This was due to before, the element constructor always preserved the vacancy numbers and now it recomputes it unless explicitly stated. Fixed with added tests. I expanded the documentation in to_tensor_..._tableaux() as well.

[aschilling]

Replying to tscrim:

Replying to aschilling:

• The documentation of right_split has a ` missing. Please run the documentation to see that it actually compiles!

I couldn't find this and the documentation built without an issue and looks okay to me (although there was a missing 'u').

There is a ` missing in

+ Let `\ast` denote the :meth:`Lusztig involution<lusztig_involution>`,
+ and `\mathrm{ls}` as the :meth:`left splitting map<left_split>`.
+ The right splitting map is defined as
+ \mathrm{rs} := \ast \circ \mathrm{ls} \circ \ast`.

• Please add the map \theta to rigged configuration and compare to lusztig_involution.

Added under the name complement. In general, it will be different than lusztig_involution, which fixes each classical component, whereas \theta fixes the classical structure but permutes the classical components. Or did you mean you wanted me to add a doctest showing this?

Under \bar \Phi the map \star (which I guess is what you call lusztig_involution) intertwines with \theta. It would be good to add a check like that.

• Please add tests and more explanations what build_graph does. Explain which graph it is computing. Also the following fails:

This was due to before, the element constructor always preserved the vacancy numbers and now it recomputes it unless explicitly stated. Fixed with added tests. I expanded the documentation in to_tensor_..._tableaux() as well.

Even though it is stated in the documentation, that build_graph is an optional parameter, it does not seem to take this input:

sage: rc = RC(partition_list=[[1],[1],[1],[1]])
sage: rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-702cb808a701> in <module>()
----> 1 rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)

TypeError: to_tensor_product_of_kirillov_reshetikhin_crystals() got an unexpected keyword argument 'build_graph'

What is the difference between build_graph and display_steps?

Anne

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6552c61

Fixed doc, added intertwining doctest, and added build_graph to to_*_crystals.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a985081

Tweaked wording of param display_steps doc.

[tscrim]

Replying to aschilling:

There is a ` missing in ...

Ah, I forgot about the right split for KR tableaux. :P Fixed.

Under \bar \Phi the map \star (which I guess is what you call lusztig_involution) intertwines with \theta. It would be good to add a check like that.

I've added a doctest.

Even though it is stated in the documentation, that build_graph is an optional parameter, it does not seem to take this input:

sage: rc = RC(partition_list=[[1],[1],[1],[1]])
sage: rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-702cb808a701> in <module>()
----> 1 rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)

TypeError: to_tensor_product_of_kirillov_reshetikhin_crystals() got an unexpected keyword argument 'build_graph'

This is because this was not a parameter in to_tensor_product_of_kirillov_reshetikhin_crystals, but in *_tableaux. I've also added the parameter (and doc/test) to the 'to TP of KR crystals' methods.

What is the difference between build_graph and display_steps?

The first one constructs and returns the graph, the latter outputs each step to the terminal. I've changed output to print to avoid some ambiguity.

[aschilling]

Why is the right_split that you implemented the correct map? I thought that rs = * ls * using the * map.

[tscrim]

Replying to aschilling:

Why is the right_split that you implemented the correct map? I thought that rs = * ls * using the * map.

right_split is implemented as * ls * (where * is the Lusztig involution) for both rigged configurations and KR tableaux.

[aschilling]

With your current code

sage: RC = RiggedConfigurations(['D', 4, 1], [[2,2],[2, 2]])
sage: all((rc.right_split()).to_tensor_product_of_kirillov_reshetikhin_tableaux() == (rc.to_tensor_product_of_kirillov_reshetikhin_tableaux()).right_split() for rc in RC)
False

I think you need to use complement in the definition the RC side. Also, it might be better to rename complement to complement_rigging for a more descriptive name.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​dc3202e	Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560
​51c8ba2	Changed complement -> complement_rigging and fixed right_split on RC side.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​013737b

Added right_box method for symmetry.

[aschilling]

Hi Travis,

Thanks for the changes. I get the following failure when trying to play with the code

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[2,2], [1,2]])
sage: all(b.to_rigged_configuration().lusztig_involution() == b.lusztig_involution().to_rigged_configuration() for b in KRT)
False

Anne

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​1e15993

Removed lusztig_involution and right_box.

[tscrim]

Hey Anne,

I've removed the lusztig_involution() and right_box() methods for rigged configurations as per our discussion.

[aschilling]

Ok, looks good now!

Anne