Returns the combinatorial class of combinations of mset. If k is specified, then it returns the combinatorial class of combinations of mset of size k.
The combinatorial classes correctly handle the cases where mset has duplicate elements.
EXAMPLES:
sage: C = Combinations(range(4)); C
Combinations of [0, 1, 2, 3]
sage: C.list()
[[],
[0],
[1],
[2],
[3],
[0, 1],
[0, 2],
[0, 3],
[1, 2],
[1, 3],
[2, 3],
[0, 1, 2],
[0, 1, 3],
[0, 2, 3],
[1, 2, 3],
[0, 1, 2, 3]]
sage: C.cardinality()
16
sage: C2 = Combinations(range(4),2); C2
Combinations of [0, 1, 2, 3] of length 2
sage: C2.list()
[[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]]
sage: C2.cardinality()
6
sage: Combinations([1,2,2,3]).list()
[[],
[1],
[2],
[3],
[1, 2],
[1, 3],
[2, 2],
[2, 3],
[1, 2, 2],
[1, 2, 3],
[2, 2, 3],
[1, 2, 2, 3]]
EXAMPLES:
sage: c = Combinations(range(4))
sage: all( i in c for i in c )
True
sage: [3,4] in c
False
sage: [0,0] in c
False
TESTS:
sage: C = Combinations(range(4))
sage: C == loads(dumps(C))
True
TESTS:
sage: Combinations(['a','a','b']).list() #indirect doctest
[[], ['a'], ['b'], ['a', 'a'], ['a', 'b'], ['a', 'a', 'b']]
TESTS:
sage: repr(Combinations(range(4)))
'Combinations of [0, 1, 2, 3]'
TESTS:
sage: Combinations([1,2,3]).cardinality()
8
sage: Combinations(['a','a','b']).cardinality()
6
EXAMPLES:
sage: c = Combinations(range(4),2)
sage: all( i in c for i in c )
True
sage: [0,1] in c
True
sage: [0,1,2] in c
False
sage: [3,4] in c
False
sage: [0,0] in c
False
TESTS:
sage: C = Combinations([1,2,3],2)
sage: C == loads(dumps(C))
True
EXAMPLES:
sage: Combinations(['a','a','b'],2).list() # indirect doctest
[['a', 'a'], ['a', 'b']]
TESTS:
sage: repr(Combinations([1,2,2,3],2))
'Combinations of [1, 2, 2, 3] of length 2'
Returns the size of combinations(mset,k). IMPLEMENTATION: Wraps GAP’s NrCombinations.
EXAMPLES:
sage: mset = [1,1,2,3,4,4,5]
sage: Combinations(mset,2).cardinality()
12
EXAMPLES:
sage: Combinations([1,2,3]).list() #indirect doctest
[[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]
EXAMPLES:
sage: c = Combinations([1,2,3])
sage: range(c.cardinality()) == map(c.rank, c)
True
EXAMPLES:
sage: c = Combinations([1,2,3])
sage: c.list() == map(c.unrank, range(c.cardinality()))
True
Posted by Raymond Hettinger, 2006/03/23, to the Python Cookbook: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/474124
EXAMPLES:
sage: Combinations([1,2,3,4,5],3).list() # indirect doctest
[[1, 2, 3],
[1, 2, 4],
[1, 2, 5],
[1, 3, 4],
[1, 3, 5],
[1, 4, 5],
[2, 3, 4],
[2, 3, 5],
[2, 4, 5],
[3, 4, 5]]
An iterator for all the n-combinations of items.
EXAMPLES:
sage: it = Combinations([1,2,3,4],3)._iterator([1,2,3,4],4,3)
sage: list(it)
[[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]
An iterator which just returns the empty list.
EXAMPLES:
sage: it = Combinations([1,2,3,4,5],3)._iterator_zero()
sage: list(it)
[[]]
EXAMPLES:
sage: Combinations([1,2,3,4,5],3).list()
[[1, 2, 3],
[1, 2, 4],
[1, 2, 5],
[1, 3, 4],
[1, 3, 5],
[1, 4, 5],
[2, 3, 4],
[2, 3, 5],
[2, 4, 5],
[3, 4, 5]]
EXAMPLES:
sage: c = Combinations([1,2,3], 2)
sage: range(c.cardinality()) == map(c.rank, c.list())
True
EXAMPLES:
sage: c = Combinations([1,2,3], 2)
sage: c.list() == map(c.unrank, range(c.cardinality()))
True