def __contains__(self, s):
"""
TESTS::
sage: S = Subsets([1,2,2,3], submultiset=True)
sage: [] in S
True
sage: [1, 2, 2] in S
True
sage: all(i in S for i in S)
True
sage: [1, 2, 2, 2] in S
False
sage: [1, 3, 2, 2] in S
True
sage: [4] in S
False
"""
return sorted(s) in subword.Subwords(self._s)
def __iter__(self):
"""
Iterates through the subsets of s.
EXAMPLES::
sage: [sub for sub in Subsets(Set([1,2,3]))]
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
sage: [sub for sub in Subsets(3)]
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
sage: [sub for sub in Subsets([1,2,3,3])]
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
"""
lset = __builtin__.list(self.s)
#We use the iterator for the subwords of range(len(self.s))
ind_set = lambda index_list: Set([lset[i] for i in index_list])
it = itertools.imap(ind_set, subword.Subwords(range(len(lset))))
for sub in it:
yield sub
