def __init__(self, parent, vecpar):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = VectorPartition([[3, 2, 1], [2, 2, 1]])
sage: TestSuite(elt).run()
"""
CombinatorialElement.__init__(self, parent, sorted(vecpar))
def __init__(self, parent, t):
r"""
Initialize a composition tableau.
TESTS::
sage: t = CompositionTableaux()([[1],[2,2]])
sage: s = CompositionTableaux(3)([[1],[2,2]])
sage: s==t
True
sage: t.parent()
Composition Tableaux
sage: s.parent()
Composition Tableaux of size 3 and maximum entry 3
sage: r = CompositionTableaux()(s)
sage: r.parent()
Composition Tableaux
"""
if isinstance(t, CompositionTableau):
CombinatorialElement.__init__(self, parent, t._list)
return
# CombinatorialObject verifies that t is a list
# We must verify t is a list of lists
if not all(isinstance(row, list) for row in t):
raise ValueError("A composition tableau must be a list of lists.")
if not [len(_) for _ in t] in Compositions():
raise ValueError(
"A composition tableau must be a list of non-empty lists.")
# Verify rows weakly decrease from left to right
for row in t:
if any(row[i] < row[i + 1] for i in range(len(row) - 1)):
raise ValueError(
"Rows must weakly decrease from left to right.")
# Verify leftmost column strictly increases from top to bottom
first_col = [row[0] for row in t if t != [[]]]
if any(first_col[i] >= first_col[i + 1] for i in range(len(t) - 1)):
raise ValueError(
"Leftmost column must strictly increase from top to bottom.")
# Verify triple condition
l = len(t)
m = max([len(_) for _ in t] + [0])
TT = [row + [0] * (m - len(row)) for row in t]
for i in range(l):
for j in range(i + 1, l):
for k in range(1, m):
if TT[j][k] != 0 and TT[j][k] >= TT[i][k] and TT[j][
k] <= TT[i][k - 1]:
raise ValueError("Triple condition must be satisfied.")
CombinatorialElement.__init__(self, parent, t)
def __init__(self, parent, t):
r"""
Initialize a composition tableau.
TESTS::
sage: t = CompositionTableaux()([[1],[2,2]])
sage: s = CompositionTableaux(3)([[1],[2,2]])
sage: s==t
True
sage: t.parent()
Composition Tableaux
sage: s.parent()
Composition Tableaux of size 3 and maximum entry 3
sage: r = CompositionTableaux()(s)
sage: r.parent()
Composition Tableaux
"""
if isinstance(t, CompositionTableau):
CombinatorialElement.__init__(self, parent, t._list)
return
# CombinatorialObject verifies that t is a list
# We must verify t is a list of lists
if not all(isinstance(row, list) for row in t):
raise ValueError("A composition tableau must be a list of lists.")
if not [len(_) for _ in t] in Compositions():
raise ValueError("A composition tableau must be a list of non-empty lists.")
# Verify rows weakly decrease from left to right
for row in t:
if any(row[i] < row[i+1] for i in range(len(row)-1)):
raise ValueError("Rows must weakly decrease from left to right.")
# Verify leftmost column strictly increases from top to bottom
first_col = [row[0] for row in t if t!=[[]]]
if any(first_col[i] >= first_col[i+1] for i in range(len(t)-1)):
raise ValueError("Leftmost column must strictly increase from top to bottom.")
# Verify triple condition
l = len(t)
m = max([len(_) for _ in t]+[0])
TT = [row+[0]*(m-len(row)) for row in t]
for i in range(l):
for j in range(i+1,l):
for k in range(1,m):
if TT[j][k] != 0 and TT[j][k] >= TT[i][k] and TT[j][k] <= TT[i][k-1]:
raise ValueError("Triple condition must be satisfied.")
CombinatorialElement.__init__(self, parent, t)
def __init__(self,parent,data):
r"""
EXAMPLES::
sage: Y = crystals.infinity.GeneralizedYoungWalls(2)
sage: mg = Y.module_generators[0]
sage: TestSuite(mg).run()
"""
i = len(data)-1
while i >= 0 and len(data[i]) == 0:
data.pop()
i -= 1
self.rows = len(data)
if data == []:
self.cols = 0
else:
self.cols = max([len(r) for r in data])
self.data = data
CombinatorialElement.__init__(self, parent, data)
def __init__(self, parent, data):
r"""
EXAMPLES::
sage: Y = crystals.infinity.GeneralizedYoungWalls(2)
sage: mg = Y.module_generators[0]
sage: TestSuite(mg).run()
"""
i = len(data) - 1
while i >= 0 and len(data[i]) == 0:
data.pop()
i -= 1
self.rows = len(data)
if data == []:
self.cols = 0
else:
self.cols = max([len(r) for r in data])
self.data = data
CombinatorialElement.__init__(self, parent, data)
def __init__(self, parent, core):
"""
TESTS::
sage: C = Cores(4,3)
sage: c = C([2,1]); c
[2, 1]
sage: type(c)
<class 'sage.combinat.core.Cores_length_with_category.element_class'>
sage: c.parent()
4-Cores of length 3
sage: TestSuite(c).run()
sage: C = Cores(3,3)
sage: C([2,1])
Traceback (most recent call last):
...
ValueError: [2, 1] is not a 3-core
"""
k = parent.k
part = Partition(core)
if not part.is_core(k):
raise ValueError("%s is not a %s-core" % (part, k))
CombinatorialElement.__init__(self, parent, core)
def __init__(self, parent, core):
"""
TESTS::
sage: C = Cores(4,3)
sage: c = C([2,1]); c
[2, 1]
sage: type(c)
<class 'sage.combinat.core.Cores_length_with_category.element_class'>
sage: c.parent()
4-Cores of length 3
sage: TestSuite(c).run()
sage: C = Cores(3,3)
sage: C([2,1])
Traceback (most recent call last):
...
ValueError: [2, 1] is not a 3-core
"""
k = parent.k
part = Partition(core)
if not part.is_core(k):
raise ValueError("%s is not a %s-core"%(part, k))
CombinatorialElement.__init__(self, parent, core)
