def __iter__(self):
"""
TESTS::
sage: [ p for p in OrderedSetPartitions([1,2,3,4], [2,1,1]) ]
[[{1, 2}, {3}, {4}],
[{1, 2}, {4}, {3}],
[{1, 3}, {2}, {4}],
[{1, 4}, {2}, {3}],
[{1, 3}, {4}, {2}],
[{1, 4}, {3}, {2}],
[{2, 3}, {1}, {4}],
[{2, 4}, {1}, {3}],
[{3, 4}, {1}, {2}],
[{2, 3}, {4}, {1}],
[{2, 4}, {3}, {1}],
[{3, 4}, {2}, {1}]]
"""
comp = self.c
lset = [x for x in self._set]
l = len(self.c)
dcomp = [-1] + comp.descents(final_descent=True)
p = []
for j in range(l):
p += [j + 1] * comp[j]
for x in permutation.Permutations(p):
res = permutation.Permutation(range(
1, len(lset))) * Word(x).standard_permutation().inverse()
res = [lset[x - 1] for x in res]
yield self.element_class(
self,
[Set(res[dcomp[i] + 1:dcomp[i + 1] + 1]) for i in range(l)])
def __iter__(self):
"""
TESTS::
sage: [ p for p in OrderedSetPartitions([1,2,3,4], [2,1,1]) ]
[[{1, 2}, {3}, {4}],
[{1, 2}, {4}, {3}],
[{1, 3}, {2}, {4}],
[{1, 4}, {2}, {3}],
[{1, 3}, {4}, {2}],
[{1, 4}, {3}, {2}],
[{2, 3}, {1}, {4}],
[{2, 4}, {1}, {3}],
[{3, 4}, {1}, {2}],
[{2, 3}, {4}, {1}],
[{2, 4}, {3}, {1}],
[{3, 4}, {2}, {1}]]
sage: len(OrderedSetPartitions([1,2,3,4], [1,1,1,1]))
24
sage: [ x for x in OrderedSetPartitions([1,4,7], [3]) ]
[[{1, 4, 7}]]
sage: [ x for x in OrderedSetPartitions([1,4,7], [1,2]) ]
[[{1}, {4, 7}], [{4}, {1, 7}], [{7}, {1, 4}]]
sage: [ p for p in OrderedSetPartitions([], []) ]
[[]]
sage: [ p for p in OrderedSetPartitions([1], [1]) ]
[[{1}]]
Let us check that it works for large size (:trac:`16646`)::
sage: OrderedSetPartitions(42).first()
[{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {12},
{13}, {14}, {15}, {16}, {17}, {18}, {19}, {20}, {21}, {22}, {23},
{24}, {25}, {26}, {27}, {28}, {29}, {30}, {31}, {32}, {33}, {34},
{35}, {36}, {37}, {38}, {39}, {40}, {41}, {42}]
"""
comp = self.c
lset = [x for x in self._set]
l = len(self.c)
dcomp = [-1] + comp.descents(final_descent=True)
p = []
for j in range(l):
p += [j + 1] * comp[j]
for x in permutation.Permutations(p):
res = permutation.to_standard(x).inverse()
res = [lset[x - 1] for x in res]
yield self.element_class(
self,
[Set(res[dcomp[i] + 1:dcomp[i + 1] + 1]) for i in range(l)])
