class AbstractTensorProductOfKRTableaux(FullTensorProductOfCrystals):
r"""
Abstract class for all of tensor product of KR tableaux of a given Cartan type.
See :class:`TensorProductOfKirillovReshetikhinTableaux`. This class should
never be created directly.
"""
def __init__(self, cartan_type, B, biject_class):
r"""
Construct a tensor product of KR tableaux.
INPUT:
- ``cartan_type`` -- The crystal type and n value
- ``B`` -- An (ordered) list of dimensions
- ``biject_class`` -- The class the bijection creates
The dimensions (i.e. `B`) is a list whose entries are lists of the
form `[r, s]` which correspond to a tableau with `r` rows and `s`
columns (or of shape `[r]*s`) and corresponds to a
Kirillov-Reshetikhin crystal `B^{r,s}`.
TESTS::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,2]]); HW # indirect doctest
Highest weight tensor product of Kirillov-Reshetikhin tableaux of type ['A', 3, 1] and tableau shape(s) [[1, 1, 1], [2, 2]]
"""
assert cartan_type.is_affine()
self.affine_ct = cartan_type
self.dims = B
self.letters = CrystalOfLetters(cartan_type)
self._bijection_class = biject_class
tensorProd = []
for rectDims in B:
tensorProd.append(KirillovReshetikhinTableaux(
self.letters.cartan_type(),
rectDims[0], rectDims[1]))
FullTensorProductOfCrystals.__init__(self, tuple(tensorProd))
def _highest_weight_iter(self):
r"""
Iterate through all of the highest weight tensor product of Kirillov-Reshetikhin tableaux.
EXAMPLES::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,1]])
sage: list(HW) # indirect doctest
[[[1], [2], [3]] (X) [[1], [2]], [[1], [3], [4]] (X) [[1], [2]]]
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
sage: for x in HW: x # indirect doctest
...
[[1], [2]]
[[1], [-1]]
"""
# This is a hack solution since during construction, the bijection will
# (attempt to) create a new KRT object which hasn't been fully created
# and stored in the UniqueRepresentation's cache. So this will be
# called again, causing the cycle to repeat. This hack just passes
# our self as an optional argument to hide it from the end-user and
# so we don't try to create a new KRT object.
from sage.combinat.rigged_configurations.rigged_configurations import HighestWeightRiggedConfigurations
for x in HighestWeightRiggedConfigurations(self.affine_ct, self.dims):
yield x.to_tensor_product_of_Kirillov_Reshetikhin_tableaux(KRT_init_hack=self)
def _element_constructor_(self, *path, **options):
r"""
Construct a TensorProductOfKRTableauxElement.
Typically the user will call this with the option **pathlist** which
will receive a list and coerce it into a path.
EXAMPLES::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,1]])
sage: KRT(pathlist=[[4, 2, 1], [2, 1]]) # indirect doctest
[[1], [2], [4]] (X) [[1], [2]]
"""
from sage.combinat.crystals.kirillov_reshetikhin import KirillovReshetikhinGenericCrystalElement
if isinstance(path[0], KirillovReshetikhinGenericCrystalElement):
return self.element_class(self, *[x.to_Kirillov_Reshetikhin_tableau() for x in path])
from sage.combinat.crystals.tensor_product import TensorProductOfCrystalsElement
if isinstance(path[0], TensorProductOfCrystalsElement) and \
isinstance(path[0][0], KirillovReshetikhinGenericCrystalElement):
return self.element_class(self, *[x.to_Kirillov_Reshetikhin_tableau() for x in path[0]])
from sage.combinat.rigged_configurations.rigged_configuration_element import RiggedConfigurationElement
if isinstance(path[0], RiggedConfigurationElement):
if self.rigged_configurations() != path[0].parent():
raise ValueError("Incorrect bijection image.")
return path[0].to_tensor_product_of_Kirillov_Reshetikhin_tableaux()
return self.element_class(self, *path, **options)
def _convert_to_letters(self, index, tableauList):
"""
Convert the entries of the list to a list of letters.
This is a helper function to convert the list of ints to letters since
we do not convert an int to an Integer at compile time.
TESTS::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[1,3]])
sage: L = KRT._convert_to_letters(0, [3, 2, 2]); L
[3, 2, 2]
sage: type(L[0])
<class 'sage.combinat.crystals.letters.ClassicalCrystalOfLetters_with_category.element_class'>
sage: L[0].value
3
"""
return([self.letters(x) for x in tableauList])
def rigged_configurations(self):
"""
Return the corresponding set of rigged configurations.
EXAMPLES::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[1,3], [2,1]])
sage: KRT.rigged_configurations()
Rigged configurations of type ['A', 3, 1] and factors ((1, 3), (2, 1))
"""
return self._bijection_class(self.affine_ct, self.dims)
def list(self):
r"""
Create a list of the elements by using the iterator.
TESTS::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,1]])
sage: HW.list()
[[[1], [2], [3]] (X) [[1], [2]], [[1], [3], [4]] (X) [[1], [2]]]
"""
# This is needed to overwrite the list method from the FiniteCrystals
# category which generates the list via f_a applications.
return [x for x in self]
class AbstractTensorProductOfKRTableaux(FullTensorProductOfCrystals):
r"""
Abstract class for all of tensor product of KR tableaux of a given Cartan type.
See :class:`TensorProductOfKirillovReshetikhinTableaux`. This class should
never be created directly.
"""
def __init__(self, cartan_type, B, biject_class):
r"""
Construct a tensor product of KR tableaux.
INPUT:
- ``cartan_type`` -- The crystal type and n value
- ``B`` -- An (ordered) list of dimensions
- ``biject_class`` -- The class the bijection creates
The dimensions (i.e. `B`) is a list whose entries are lists of the
form `[r, s]` which correspond to a tableau with `r` rows and `s`
columns (or of shape `[r]*s`) and corresponds to a
Kirillov-Reshetikhin crystal `B^{r,s}`.
TESTS::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,2]]); HW # indirect doctest
Highest weight tensor product of Kirillov-Reshetikhin tableaux of type ['A', 3, 1] and tableau shape(s) [[1, 1, 1], [2, 2]]
"""
assert cartan_type.is_affine()
self.affine_ct = cartan_type
self.dims = B
self.letters = CrystalOfLetters(cartan_type)
self._bijection_class = biject_class
tensorProd = []
for rectDims in B:
tensorProd.append(
KirillovReshetikhinTableaux(self.letters.cartan_type(),
rectDims[0], rectDims[1]))
FullTensorProductOfCrystals.__init__(self, tuple(tensorProd))
def _highest_weight_iter(self):
r"""
Iterate through all of the highest weight tensor product of Kirillov-Reshetikhin tableaux.
EXAMPLES::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,1]])
sage: list(HW) # indirect doctest
[[[1], [2], [3]] (X) [[1], [2]], [[1], [3], [4]] (X) [[1], [2]]]
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
sage: for x in HW: x # indirect doctest
...
[[1], [2]]
[[1], [-1]]
"""
# This is a hack solution since during construction, the bijection will
# (attempt to) create a new KRT object which hasn't been fully created
# and stored in the UniqueRepresentation's cache. So this will be
# called again, causing the cycle to repeat. This hack just passes
# our self as an optional argument to hide it from the end-user and
# so we don't try to create a new KRT object.
from sage.combinat.rigged_configurations.rigged_configurations import HighestWeightRiggedConfigurations
for x in HighestWeightRiggedConfigurations(self.affine_ct, self.dims):
yield x.to_tensor_product_of_Kirillov_Reshetikhin_tableaux(
KRT_init_hack=self)
def _element_constructor_(self, *path, **options):
r"""
Construct a TensorProductOfKRTableauxElement.
Typically the user will call this with the option **pathlist** which
will receive a list and coerce it into a path.
EXAMPLES::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,1]])
sage: KRT(pathlist=[[4, 2, 1], [2, 1]]) # indirect doctest
[[1], [2], [4]] (X) [[1], [2]]
"""
from sage.combinat.crystals.kirillov_reshetikhin import KirillovReshetikhinGenericCrystalElement
if isinstance(path[0], KirillovReshetikhinGenericCrystalElement):
return self.element_class(
self, *[x.to_Kirillov_Reshetikhin_tableau() for x in path])
from sage.combinat.crystals.tensor_product import TensorProductOfCrystalsElement
if isinstance(path[0], TensorProductOfCrystalsElement) and \
isinstance(path[0][0], KirillovReshetikhinGenericCrystalElement):
return self.element_class(
self, *[x.to_Kirillov_Reshetikhin_tableau() for x in path[0]])
from sage.combinat.rigged_configurations.rigged_configuration_element import RiggedConfigurationElement
if isinstance(path[0], RiggedConfigurationElement):
if self.rigged_configurations() != path[0].parent():
raise ValueError("Incorrect bijection image.")
return path[0].to_tensor_product_of_Kirillov_Reshetikhin_tableaux()
return self.element_class(self, *path, **options)
def _convert_to_letters(self, index, tableauList):
"""
Convert the entries of the list to a list of letters.
This is a helper function to convert the list of ints to letters since
we do not convert an int to an Integer at compile time.
TESTS::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[1,3]])
sage: L = KRT._convert_to_letters(0, [3, 2, 2]); L
[3, 2, 2]
sage: type(L[0])
<class 'sage.combinat.crystals.letters.ClassicalCrystalOfLetters_with_category.element_class'>
sage: L[0].value
3
"""
return ([self.letters(x) for x in tableauList])
def rigged_configurations(self):
"""
Return the corresponding set of rigged configurations.
EXAMPLES::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[1,3], [2,1]])
sage: KRT.rigged_configurations()
Rigged configurations of type ['A', 3, 1] and factors ((1, 3), (2, 1))
"""
return self._bijection_class(self.affine_ct, self.dims)
def list(self):
r"""
Create a list of the elements by using the iterator.
TESTS::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,1]])
sage: HW.list()
[[[1], [2], [3]] (X) [[1], [2]], [[1], [3], [4]] (X) [[1], [2]]]
"""
# This is needed to overwrite the list method from the FiniteCrystals
# category which generates the list via f_a applications.
return [x for x in self]
