Non-exceptional rigged configuration bijections

[Travis Scrimshaw]

Implements the bijection between rigged configurations and tensor products of Kirillov-Reshetikhin tableaux for the non-exceptional types.

[Travis Scrimshaw]

New version over changes in #13871.

[Travis Scrimshaw]

Newer version over changes in #13871 and #13838.

[Anne Schilling]

Hi Travis,

Thanks for your changes we discussed via email. Next there are problems for D_4^{(2)}

sage: for t in KRT:
    rc = t.to_rigged_configuration()
    if not t==rc.to_tensor_product_of_Kirillov_Reshetikhin_tableaux():
        print t
....:
[[[1], [0], [0]], [[1, 2], [2, -2]], [[1, E]]]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-925815db1a74> in <module>()
      1 for t in KRT:
      2     rc = t.to_rigged_configuration()
----> 3     if not t==rc.to_tensor_product_of_Kirillov_Reshetikhin_tableaux():
      4         print t
      5

/Applications/sage-5.12.beta5/local/lib/python2.7/site-packages/sage/combinat/crystals/tensor_product.pyc in __eq__(self, other)
    146         return self.__class__ is other.__class__ and \
    147                self.parent() == other.parent() and \
--> 148                self._list == other._list
    149
    150     def __ne__(self, other):

/Applications/sage-5.12.beta5/local/lib/python2.7/site-packages/sage/combinat/crystals/tensor_product.pyc in __eq__(self, other)
    146         return self.__class__ is other.__class__ and \
    147                self.parent() == other.parent() and \
--> 148                self._list == other._list
    149
    150     def __ne__(self, other):

/Applications/sage-5.12.beta5/local/lib/python2.7/site-packages/sage/combinat/crystals/letters.so in sage.combinat.crystals.letters.Letter.__richcmp__ (sage/combinat/crystals/letters.c:6559)()

/Applications/sage-5.12.beta5/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.Element._richcmp (sage/structure/element.c:8765)()

/Applications/sage-5.12.beta5/local/lib/python2.7/site-packages/sage/combinat/crystals/letters.so in sage.combinat.crystals.letters.Letter._richcmp_c_impl (sage/combinat/crystals/letters.c:6617)()

TypeError: Cannot convert sage.combinat.crystals.letters.EmptyLetter to sage.combinat.crystals.letters.Letter

Best,

Anne

[Anne Schilling]

Hi Travis,

I am also confused since the cardinalities do not match up in your code:

sage: RC = RiggedConfigurations(['D',4,2], [[3,1],[2,2],[1,2]])
sage: RC.cardinality()
403025

sage: K1 = KirillovReshetikhinCrystal(['D',4,2],3,1)
sage: K2 = KirillovReshetikhinCrystal(['D',4,2],2,2)
sage: K3 = KirillovReshetikhinCrystal(['D',4,2],1,2)
sage: T = TensorProductOfCrystals(K1,K2,K3)
sage: T.cardinality()
92120

Best,

Anne

[Anne Schilling]

Hi Travis,

As we discussed, could you please add which bijections are conjectural and which ones are proven? Also, I currently get some doctest failures with the patch in sage-combinat queue:

rigged_configurations anne$ sage -t *.py
Running doctests with ID 2013-10-29-17-44-20-1f870a4b.
Doctesting 19 files.
sage -t __init__.py
    [0 tests, 0.00 s]
sage -t all.py
    [0 tests, 0.00 s]
sage -t bij_abstract_class.py
**********************************************************************
File "bij_abstract_class.py", line 358, in sage.combinat.rigged_configurations.bij_abstract_class.RCToKRTBijectionAbstract.run
Failed example:
    RCToKRTBijectionTypeA(RC(partition_list=[[1],[1],[1],[1]])).run()
Expected:
    [[5, 2]]
Got:
    [[2], [5]]
**********************************************************************
1 item had failures:
   1 of   4 in sage.combinat.rigged_configurations.bij_abstract_class.RCToKRTBijectionAbstract.run
    [54 tests, 1 failure, 0.77 s]
sage -t bij_type_A.py
    [19 tests, 0.17 s]
sage -t bij_type_A2_dual.py
    [19 tests, 0.27 s]
sage -t bij_type_A2_even.py
    [19 tests, 0.20 s]
sage -t bij_type_A2_odd.py
    [19 tests, 0.25 s]
sage -t bij_type_B.py
**********************************************************************
File "bij_type_B.py", line 532, in sage.combinat.rigged_configurations.bij_type_B.RCToKRTBijectionTypeB.run
Failed example:
    RCToKRTBijectionTypeB(RC(partition_list=[[1],[1,1],[1]])).run()
Expected:
    [[0, 3]]
Got:
    [[3], [0]]
**********************************************************************
File "bij_type_B.py", line 536, in sage.combinat.rigged_configurations.bij_type_B.RCToKRTBijectionTypeB.run
Failed example:
    RCToKRTBijectionTypeB(RC(partition_list=[[],[1],[1]])).run()
Expected:
    [[-2, 3, 1]]
Got:
    [[1], [3], [-2]]
**********************************************************************
1 item had failures:
   2 of   7 in sage.combinat.rigged_configurations.bij_type_B.RCToKRTBijectionTypeB.run
    [34 tests, 2 failures, 0.27 s]
sage -t bij_type_C.py
    [28 tests, 0.24 s]
sage -t bij_type_D.py
**********************************************************************
File "bij_type_D.py", line 428, in sage.combinat.rigged_configurations.bij_type_D.RCToKRTBijectionTypeD.run
Failed example:
    RCToKRTBijectionTypeD(RC(partition_list=[[1],[1],[1],[1]])).run()
Expected:
    [[-3, 2]]
Got:
    [[2], [-3]]
**********************************************************************
1 item had failures:
   1 of   4 in sage.combinat.rigged_configurations.bij_type_D.RCToKRTBijectionTypeD.run
    [75 tests, 1 failure, 0.21 s]
sage -t bij_type_D_twisted.py
**********************************************************************
File "bij_type_D_twisted.py", line 327, in sage.combinat.rigged_configurations.bij_type_D_twisted.RCToKRTBijectionTypeDTwisted.run
Failed example:
    RCToKRTBijectionTypeDTwisted(RC(partition_list=[[],[1],[1]])).run()
Expected:
    [[-2, 3, 1]]
Got:
    [[1], [3], [-2]]
**********************************************************************
1 item had failures:
   1 of   4 in sage.combinat.rigged_configurations.bij_type_D_twisted.RCToKRTBijectionTypeDTwisted.run
    [25 tests, 1 failure, 0.21 s]
sage -t bijection.py
    [6 tests, 0.16 s]
sage -t kleber_tree.py
    [201 tests, 4.01 s]
sage -t kr_tableaux.py
**********************************************************************
File "kr_tableaux.py", line 1363, in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper._build_module_generators
Failed example:
    KRT._build_module_generators()
Expected:
    ([(-1, 3)],)
Got:
    ([(1,)],)
**********************************************************************
File "kr_tableaux.py", line 1398, in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element._repr_diagram
Failed example:
    elt._repr_diagram()
Exception raised:
    Traceback (most recent call last):
      File "/Applications/sage-5.12/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 479, in _run
        self.execute(example, compiled, test.globs)
      File "/Applications/sage-5.12/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 838, in execute
        exec compiled in globs
      File "<doctest sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element._repr_diagram[2]>", line 1, in <module>
        elt._repr_diagram()
      File "/Applications/sage-5.12/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/kr_tableaux.py", line 1402, in _repr_diagram
        return self.to_tableau()._repr_diagram()
      File "cachefunc.pyx", line 1774, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__ (sage/misc/cachefunc.c:9546)
      File "/Applications/sage-5.12/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/kr_tableaux.py", line 1439, in to_tableau
        raise ValueError("cannot convert {} to a tableau".format(self))
    ValueError: cannot convert [(-1, 3)] to a tableau
**********************************************************************
File "kr_tableaux.py", line 1480, in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.weight
Failed example:
    KR.module_generators[0].weight()
Exception raised:
    Traceback (most recent call last):
      File "/Applications/sage-5.12/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 479, in _run
        self.execute(example, compiled, test.globs)
      File "/Applications/sage-5.12/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 838, in execute
        exec compiled in globs
      File "<doctest sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.weight[1]>", line 1, in <module>
        KR.module_generators[Integer(0)].weight()
    NameError: name 'KR' is not defined
**********************************************************************
File "kr_tableaux.py", line 1492, in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.e
Failed example:
    KRT.module_generators[0].e(0)
Expected:
    [[-2, 1], [-1, -1]]
Got:
    [(-2, 1)]
**********************************************************************
File "kr_tableaux.py", line 1507, in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.f
Failed example:
    KRT.module_generators[0].f(0)
Expected:
    [[1, 1], [2, -1]]
Got:
    <BLANKLINE>
**********************************************************************
5 items had failures:
   1 of   4 in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element._repr_diagram
   1 of   3 in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.e
   1 of   3 in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.f
   1 of   3 in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper.Element.weight
   1 of   3 in sage.combinat.rigged_configurations.kr_tableaux.KRTableauxWrapper._build_module_generators
    [217 tests, 5 failures, 37.97 s]
sage -t rigged_configuration_element.py
    [92 tests, 1.31 s]
sage -t rigged_configurations.py
    [180 tests, 5.29 s]
sage -t rigged_partition.py
    [54 tests, 0.22 s]
sage -t tensor_product_kr_tableaux.py
    [78 tests, 2.19 s]
sage -t tensor_product_kr_tableaux_element.py
    [61 tests, 0.86 s]
----------------------------------------------------------------------
sage -t bij_abstract_class.py  # 1 doctest failed
sage -t bij_type_B.py  # 2 doctests failed
sage -t bij_type_D.py  # 1 doctest failed
sage -t bij_type_D_twisted.py  # 1 doctest failed
sage -t kr_tableaux.py  # 5 doctests failed
----------------------------------------------------------------------
Total time for all tests: 56.2 seconds
    cpu time: 51.8 seconds
    cumulative wall time: 54.6 seconds

Best,

Anne

[Travis Scrimshaw]

New version with all of the fixes.

[git]

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

​307fef1

Removed some whitespaces, beautified code

[git]

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

​01891ba	Merge branch 'public/combinat/rigged_configurations/13872-bijections' of ​ssh://trac.sagemath.org:2222/sage into public/combinat/rigged_configurations/13872-bijections
​884e7cd	Fixed note in KR tableaux.

[git]

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

​d4cc8e0	Merge branch 'public/combinat/rigged_configurations/13872-bijections' of trac.sagemath.org:sage into public/combinat/rigged_configurations/13872-bijections
​3813946	removed some whitespace in kr_tableaux.py

[git]

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

​5c7e56d

fixed some documentation in kr_tableaux.py

[git]

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

​bced2b5

Changed method names and added more documentation.

[Anne Schilling]

Your current code does not give a bijection

sage: T = TensorProductOfKirillovReshetikhinTableaux(['D',4,1],[[2,1],[3,1],[2,2]])
sage: for t in T:
...:    if t.to_rigged_configuration().to_tensor_product_of_kirillov_reshetikhin_tableaux() != t:
....:       print t
....:         
[[[-4], [4]], [[1], [2], [3], [-4]], [[-2, 1], [-1, 2]]]
[[[-4], [4]], [[1], [2], [3], [-4]], [[1, 1], [2, -1]]]
...

[git]

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

​c5d2ec5

Fix to type D bijection. Some fixes to type B.

[git]

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

​71a886e

Fixed type B bijection.

[git]

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

​53f3324

Another fix for type B.

[git]

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

​c9a2521

Fixes for type A2 dual bijection.

[git]

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

​240e0b2

Fixed bijection for special case of A(2)_2.

[git]

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

​4a2dd71

Expanded on doctests for corner cases for rigged configurations.

[git]

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

​126e49b	went through RC code together with Travis
​8b9c022	Merge branch 'public/combinat/rigged_configurations/bijections-13872' of trac.sagemath.org:sage into public/combinat/rigged_configurations/bijections-13872
​01f4748	Merge branch 'public/combinat/rigged_configurations/bijections-13872' of trac.sagemath.org:sage into public/combinat/rigged_configurations/bijections-13872
​aaeb84d	Merge branch 'public/combinat/rigged_configurations/bijections-13872' of trac.sagemath.org:sage into public/combinat/rigged_configurations/bijections-13872

[git]

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

​18eb5ee	Changes that Anne and I discussed plus some printing improvements.
​ff969dc	Fixing docstrings and other misc things.
​c5f9eb3	Merge branch 'master' into public/combinat/rigged_configurations/bijections-13872

[git]

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

​9ce80e5

fixed some issues with the documentation

[Anne Schilling]

Hi Travis,

I just pushed some small changes to the documentation. Everything else looks good now. If you agree with the changes, please set a positive review on my behalf!

Anne

[Travis Scrimshaw]

Thank you Anne for your work in reviewing this.

[Anne Schilling]

Hi Travis,

The implementation of the fermionic sum does not seem correct. As is stated in the documentation, it depends on a weight \lambda whereas the implementation does not take a weight as an input! You can compare against the highest weight terms in

sage: K = KirillovReshetikhinCrystal(['A',2,1],1,1)
sage: T = TensorProductOfCrystals(K,K)
sage: T.one_dimensional_configuration_sum()
B[-2*Lambda[1] + 2*Lambda[2]] + (q+1)*B[-Lambda[1]] + (q+1)*B[Lambda[1] - Lambda[2]] + B[2*Lambda[1]] + B[-2*Lambda[2]] + (q+1)*B[Lambda[2]]

to check that your result is correct.

Anne

[git]

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

​a0160c8

Corrected and expanded fermoinic_formula() method, for RC's.

[Travis Scrimshaw]

Fixed. Now it can take a few arguments to change the output behavior as well.

[git]

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

​b9f49b8

Allow one_dimensional_configuration_sum() to work for TP of KR tableaux.

[Anne Schilling]

I looked at your latest changes. Why are the changes in crystals/tensor_product.py necessary? Also, the equality between the one-dimensional configuration sums and fermionic formula has been proven in many cases. So the statement that it is conjectural is not quite right. Please add references!

Also, with the new code I get doc test failures

sage -t tensor_product.py
**********************************************************************
File "tensor_product.py", line 278, in sage.combinat.crystals.tensor_product.CrystalOfWords.one_dimensional_configuration_sum
Failed example:
    LS.one_dimensional_configuration_sum() == T.one_dimensional_configuration_sum()
Expected:
    True
Got:
    False
**********************************************************************
1 item had failures:
   1 of  14 in sage.combinat.crystals.tensor_product.CrystalOfWords.one_dimensional_configuration_sum
    [361 tests, 1 failure, 48.77 s]
sage -t alcove_path.py
    [220 tests, 41.31 s]
sage -t littelmann_path.py
**********************************************************************
    True
Got:
    False
**********************************************************************
File "littelmann_path.py", line 693, in sage.combinat.crystals.littelmann_path.CrystalOfProjectedLevelZeroLSPaths.one_dimensional_configuration_sum
Failed example:
    T.one_dimensional_configuration_sum() == LS.one_dimensional_configuration_sum()
Expected:
    True
Got:
    False
**********************************************************************
File "littelmann_path.py", line 701, in sage.combinat.crystals.littelmann_path.CrystalOfProjectedLevelZeroLSPaths.one_dimensional_configuration_sum
Failed example:
    T.one_dimensional_configuration_sum() == LS.one_dimensional_configuration_sum()
Expected:
    True
Got:
    False
**********************************************************************

It would be good not to change the existing functionality in tensor_products.py!

Anne

[git]

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

​c9b3e43

Made all 1-dim config sum/fermionic formulas use QQt?. Added references to fermionic_formula().

[Travis Scrimshaw]

So the above errors came from the fact that I changed the 1-dim config sum to use ZZ['t'] instead of QQ['t'] since this made more sense to me as we are q-counting things. I reverted this back, although I do want to leave in the expanded type checking so 1-dim config sum works for tensors products of KR tableaux. I also added references to fermionic_formula() for when this is known to be equal to the 1-dim config sum.

[git]

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

​2c2ef93

some edits to docs

[Travis Scrimshaw]

Thank you Anne.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. Last 10 new commits:

​2e3e96d	Merge branch 'master' into public/combinat/rigged_configurations/bijections-13872
​0bc2bf7	Merge branch 'public/combinat/rigged_configurations/bijections-13872' of trac.sagemath.org:sage into public/combinat/rigged_configurations/bijections-13872
​0391615	Merge branch 'public/homology/chain_complex_parents-15161' of trac.sagemath.org:sage into public/combinat/rigged_configurations/bijections-13872
​dd02b22	Fixed minor bug introduced in chain_complex_morphism.py.
​7c51909	Some review changes -- code tweaks and doc formatting.
​84e22b5	Merge branch 'ticket/15161' into public/homology/chain_complex_parents-15161
​b2710cd	Merge branch 'master' into chain_complex_parents
​8ec7ded	fixed bug in is_boundary()
​7e075ed	Fixed super categories and all doctests
​7543b85	finished refactoring the homology() method

[Travis Scrimshaw]

Hmm...somehow I've (erroneously) merged the branch from #15161 into this one. I'll separate shortly.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Recent commits:

​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

[git]

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

​85b6446	Reorded all.py to match original (so fewer changes).
​a51b39f	Fixed minor typo in cobminat/crystals/letters.pyx.

[Travis Scrimshaw]

Okay, everything should be fixed now.

[Anne Schilling]

Replying to tscrim:

Okay, everything should be fixed now.

I am not sure. When I did git pull I got

d144:rigged_configurations anne$ git pull
Auto-merging src/sage/combinat/rigged_configurations/tensor_product_kr_tableaux.py
CONFLICT (content): Merge conflict in src/sage/combinat/rigged_configurations/tensor_product_kr_tableaux.py
Auto-merging src/sage/combinat/rigged_configurations/rigged_configurations.py
CONFLICT (content): Merge conflict in src/sage/combinat/rigged_configurations/rigged_configurations.py
Auto-merging src/sage/combinat/crystals/letters.pyx
CONFLICT (content): Merge conflict in src/sage/combinat/crystals/letters.pyx
Removing build/pkgs/r/patches/cygwin-logl.patch
Automatic merge failed; fix conflicts and then commit the result.

I did not have any local changes, so I am not sure why there is a conflict.

[Travis Scrimshaw]

(Unfortunately) I had to do some history rewriting, but I thought it would have been fine since it was about the merging of the master branch. I had too many issues trying to run git revert. I might have been better off using a git reset and then merge in via cherry-picking, but that probably would still result in merge conflicts since the histories wouldn't match. I'd recommend forcing a fetch from the trac branch into your local copy. (Another possible hindsight is we probably could've left this alone since #15161 is positively reviewed...I still have no idea how that got merged into here...)

[Anne Schilling]

Ok, looks good to me.

Anne