def __init__(self, crystals, facade, keepkey, category, **options):
"""
TESTS::
sage: C = crystals.Letters(['A',2])
sage: B = crystals.DirectSum([C,C], keepkey=True)
sage: B
Direct sum of the crystals Family (The crystal of letters for type ['A', 2], The crystal of letters for type ['A', 2])
sage: B.cartan_type()
['A', 2]
sage: from sage.combinat.crystals.direct_sum import DirectSumOfCrystals
sage: isinstance(B, DirectSumOfCrystals)
True
"""
if facade:
Parent.__init__(self, facade=tuple(crystals), category=category)
else:
Parent.__init__(self, category=category)
DisjointUnionEnumeratedSets.__init__(self, crystals, keepkey=keepkey, facade=facade)
self.rename("Direct sum of the crystals {}".format(crystals))
self._keepkey = keepkey
self.crystals = crystals
if len(crystals) == 0:
raise ValueError("The direct sum is empty")
else:
assert(crystal.cartan_type() == crystals[0].cartan_type() for crystal in crystals)
self._cartan_type = crystals[0].cartan_type()
if keepkey:
self.module_generators = [ self(tuple([i,b])) for i in range(len(crystals))
for b in crystals[i].module_generators ]
else:
self.module_generators = sum( (list(B.module_generators) for B in crystals), [])
def __init__(self):
"""
TESTS::
sage: from sage.combinat.ordered_tree import OrderedTrees_all
sage: B = OrderedTrees_all()
sage: B.cardinality()
+Infinity
sage: it = iter(B)
sage: (next(it), next(it), next(it), next(it), next(it))
([], [[]], [[], []], [[[]]], [[], [], []])
sage: next(it).parent()
Ordered trees
sage: B([])
[]
sage: B is OrderedTrees_all()
True
sage: TestSuite(B).run() # long time
"""
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(),
OrderedTrees_size),
facade=True,
keepkey=False)
def __init__(self, weights):
"""
TESTS::
sage: C = WeightedIntegerVectors([2,1,3])
sage: C.__class__
<class 'sage.combinat.integer_vector_weighted.WeightedIntegerVectors_all_with_category'>
sage: C.category()
Join of Category of sets with grading and Category of infinite enumerated sets
sage: TestSuite(C).run()
"""
self._weights = weights
from sage.sets.all import Family, NonNegativeIntegers
# Use "partial" to make the basis function (with the weights
# argument specified) pickleable. Otherwise, it seems to
# cause problems...
from functools import partial
F = Family(NonNegativeIntegers(),
partial(WeightedIntegerVectors, weight=weights))
DisjointUnionEnumeratedSets.__init__(
self,
F,
facade=True,
keepkey=False,
category=(SetsWithGrading(), InfiniteEnumeratedSets()))
def __init__(self, **keywords):
DisjointUnionEnumeratedSets.__init__(
self,
Family(NonNegativeIntegers(),
lambda i: Relations_size(i, **keywords)),
facade=True,
keepkey=False,
category=(Posets(), EnumeratedSets()))
self._sign = None
self._initialise_properties(keywords)
def __init__(self, max_entry=None):
r"""
Initialize ``self``.
TESTS::
sage: CT = CompositionTableaux()
sage: TestSuite(CT).run()
"""
self.max_entry = max_entry
CT_n = lambda n: CompositionTableaux_size(n, max_entry)
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(), CT_n),
facade=True, keepkey = False)
def __init__(self, max_entry=None):
r"""
Initialize ``self``.
TESTS::
sage: CT = CompositionTableaux()
sage: TestSuite(CT).run()
"""
self.max_entry = max_entry
CT_n = lambda n: CompositionTableaux_size(n, max_entry)
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(), CT_n),
facade=True, keepkey = False)
def __init__(self):
"""
TESTS::
sage: sum(x**len(t) for t in
....: set(RootedTree(t) for t in OrderedTrees(6)))
x^5 + x^4 + 3*x^3 + 6*x^2 + 9*x
sage: sum(x**len(t) for t in RootedTrees(6))
x^5 + x^4 + 3*x^3 + 6*x^2 + 9*x
sage: TestSuite(RootedTrees()).run() # long time
"""
DisjointUnionEnumeratedSets.__init__(
self, Family(NonNegativeIntegers(), RootedTrees_size),
facade=True, keepkey=False)
def __init__(self, n=None):
r"""
EXAMPLES::
sage: from sage.combinat.baxter_permutations import BaxterPermutations_all
sage: BaxterPermutations_all()
Baxter permutations
"""
self.element_class = Permutations().element_class
from sage.categories.examples.infinite_enumerated_sets import NonNegativeIntegers
from sage.sets.family import Family
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(),
BaxterPermutations_size),
facade=False, keepkey=False)
def __init__(self, n=None):
r"""
EXAMPLES::
sage: from sage.combinat.baxter_permutations import BaxterPermutations_all
sage: BaxterPermutations_all()
Baxter permutations
"""
self.element_class = Permutations().element_class
from sage.categories.examples.infinite_enumerated_sets import NonNegativeIntegers
from sage.sets.family import Family
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(),
BaxterPermutations_size),
facade=False, keepkey=False)
def __init__(self):
"""
TESTS::
sage: sum(x**len(t) for t in
....: set(RootedTree(t) for t in OrderedTrees(6)))
x^5 + x^4 + 3*x^3 + 6*x^2 + 9*x
sage: sum(x**len(t) for t in RootedTrees(6))
x^5 + x^4 + 3*x^3 + 6*x^2 + 9*x
sage: TestSuite(RootedTrees()).run() # long time
"""
DisjointUnionEnumeratedSets.__init__(
self, Family(NonNegativeIntegers(), RootedTrees_size),
facade=True, keepkey=False)
def __init__(self, crystals, **options):
"""
TESTS::
sage: C = crystals.Letters(['A',2])
sage: B = crystals.DirectSum([C,C], keepkey=True)
sage: B
Direct sum of the crystals Family (The crystal of letters for type ['A', 2], The crystal of letters for type ['A', 2])
sage: B.cartan_type()
['A', 2]
sage: from sage.combinat.crystals.direct_sum import DirectSumOfCrystals
sage: isinstance(B, DirectSumOfCrystals)
True
"""
if 'keepkey' in options:
keepkey = options['keepkey']
else:
keepkey = False
# facade = options['facade']
if keepkey:
facade = False
else:
facade = True
category = Category.meet(
[Category.join(crystal.categories()) for crystal in crystals])
Parent.__init__(self, category=category)
DisjointUnionEnumeratedSets.__init__(self,
crystals,
keepkey=keepkey,
facade=facade)
self.rename("Direct sum of the crystals %s" % (crystals, ))
self._keepkey = keepkey
self.crystals = crystals
if len(crystals) == 0:
raise ValueError("The direct sum is empty")
else:
assert (crystal.cartan_type() == crystals[0].cartan_type()
for crystal in crystals)
self._cartan_type = crystals[0].cartan_type()
if keepkey:
self.module_generators = [
self(tuple([i, b])) for i in range(len(crystals))
for b in crystals[i].module_generators
]
else:
self.module_generators = sum(
(list(B.module_generators) for B in crystals), [])
def __init__(self, n):
r"""
Initializes the class of all standard super tableaux of size ``n``.
TESTS::
sage: TestSuite( StandardSuperTableaux(4) ).run()
"""
StandardSuperTableaux.__init__(self)
from sage.combinat.partition import Partitions_n
DisjointUnionEnumeratedSets.__init__(self,
Family(Partitions_n(n),
StandardSuperTableaux_shape),
category=FiniteEnumeratedSets(),
facade=True, keepkey=False)
self.size = Integer(n)
def __init__(self):
r"""
Initializes the class of all standard super tableaux.
TESTS::
sage: from sage.combinat.super_tableau import StandardSuperTableaux_all
sage: SST = StandardSuperTableaux_all(); SST
Standard super tableaux
sage: TestSuite(SST).run()
"""
StandardSuperTableaux.__init__(self)
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(),
StandardSuperTableaux_size),
facade=True, keepkey=False)
def __init__(self, weight):
"""
TESTS::
sage: C = WeightedIntegerVectors([2,1,3])
sage: C.category()
Category of facade infinite enumerated sets with grading
sage: TestSuite(C).run()
"""
self._weights = weight
from sage.sets.all import Family, NonNegativeIntegers
# Use "partial" to make the basis function (with the weights
# argument specified) pickleable. Otherwise, it seems to
# cause problems...
from functools import partial
F = Family(NonNegativeIntegers(), partial(WeightedIntegerVectors, weight=weight))
cat = (SetsWithGrading(), InfiniteEnumeratedSets())
DisjointUnionEnumeratedSets.__init__(self, F, facade=True, keepkey=False,
category=cat)
def __init__(self, crystals, **options):
"""
TESTS::
sage: C = CrystalOfLetters(['A',2])
sage: B = DirectSumOfCrystals([C,C], keepkey=True)
sage: B
Direct sum of the crystals Family (The crystal of letters for type ['A', 2], The crystal of letters for type ['A', 2])
sage: B.cartan_type()
['A', 2]
sage: isinstance(B, DirectSumOfCrystals)
True
"""
if options.has_key('keepkey'):
keepkey = options['keepkey']
else:
keepkey = False
# facade = options['facade']
if keepkey:
facade = False
else:
facade = True
category = Category.meet([Category.join(crystal.categories()) for crystal in crystals])
Parent.__init__(self, category = category)
DisjointUnionEnumeratedSets.__init__(self, crystals, keepkey = keepkey, facade = facade)
self.rename("Direct sum of the crystals %s"%(crystals,))
self._keepkey = keepkey
self.crystals = crystals
if len(crystals) == 0:
raise ValueError, "The direct sum is empty"
else:
assert(crystal.cartan_type() == crystals[0].cartan_type() for crystal in crystals)
self._cartan_type = crystals[0].cartan_type()
if keepkey:
self.module_generators = [ self(tuple([i,b])) for i in range(len(crystals))
for b in crystals[i].module_generators ]
else:
self.module_generators = sum( (list(B.module_generators) for B in crystals), [])
def __init__(self, crystals, facade, keepkey, category, **options):
"""
TESTS::
sage: C = crystals.Letters(['A',2])
sage: B = crystals.DirectSum([C,C], keepkey=True)
sage: B
Direct sum of the crystals Family (The crystal of letters for type ['A', 2], The crystal of letters for type ['A', 2])
sage: B.cartan_type()
['A', 2]
sage: from sage.combinat.crystals.direct_sum import DirectSumOfCrystals
sage: isinstance(B, DirectSumOfCrystals)
True
"""
DisjointUnionEnumeratedSets.__init__(self,
crystals,
keepkey=keepkey,
facade=facade,
category=category)
self.rename("Direct sum of the crystals {}".format(crystals))
self._keepkey = keepkey
self.crystals = crystals
if len(crystals) == 0:
raise ValueError("the direct sum is empty")
else:
assert (crystal.cartan_type() == crystals[0].cartan_type()
for crystal in crystals)
self._cartan_type = crystals[0].cartan_type()
if keepkey:
self.module_generators = tuple([
self((i, b)) for i, B in enumerate(crystals)
for b in B.module_generators
])
else:
self.module_generators = sum(
(tuple(B.module_generators) for B in crystals), ())
def __init__(self):
"""
TESTS::
sage: from sage.combinat.ordered_tree import OrderedTrees_all
sage: B = OrderedTrees_all()
sage: B.cardinality()
+Infinity
sage: it = iter(B)
sage: (next(it), next(it), next(it), next(it), next(it))
([], [[]], [[], []], [[[]]], [[], [], []])
sage: next(it).parent()
Ordered trees
sage: B([])
[]
sage: B is OrderedTrees_all()
True
sage: TestSuite(B).run() # long time
"""
DisjointUnionEnumeratedSets.__init__(
self, Family(NonNegativeIntegers(), OrderedTrees_size),
facade=True, keepkey=False)
def __init__(self):
"""
TESTS::
sage: from sage.combinat.binary_tree import BinaryTrees_all
sage: B = BinaryTrees_all()
sage: B.cardinality()
+Infinity
sage: it = iter(B)
sage: (it.next(), it.next(), it.next(), it.next(), it.next())
(., [., .], [., [., .]], [[., .], .], [., [., [., .]]])
sage: it.next().parent()
Binary trees
sage: B([])
[., .]
sage: B is BinaryTrees_all()
True
sage: TestSuite(B).run()
"""
DisjointUnionEnumeratedSets.__init__(
self, Family(NonNegativeIntegers(), BinaryTrees_size),
facade=True, keepkey = False)
