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# Tuples

`sage.combinat.tuple.``Tuples`(S, k)

  Returns the combinatorial class of ordered tuples of S of length k.

  An ordered tuple of length k of set is an ordered selection with repetition and is represented by a list of length k containing elements of set.

  EXAMPLES:

      sage: S = [1,2]
      sage: Tuples(S,3).list()
      [[1, 1, 1], [2, 1, 1], [1, 2, 1], [2, 2, 1], [1, 1, 2], [2, 1, 2], [1, 2, 2], [2, 2, 2]]
      sage: mset = ["s","t","e","i","n"]
      sage: Tuples(mset,2).list()
      [['s', 's'], ['t', 's'], ['e', 's'], ['i', 's'], ['n', 's'], ['s', 't'], ['t', 't'],
       ['e', 't'], ['i', 't'], ['n', 't'], ['s', 'e'], ['t', 'e'], ['e', 'e'], ['i', 'e'],
       ['n', 'e'], ['s', 'i'], ['t', 'i'], ['e', 'i'], ['i', 'i'], ['n', 'i'], ['s', 'n'],
       ['t', 'n'], ['e', 'n'], ['i', 'n'], ['n', 'n']]

      sage: K.<a> = GF(4, 'a')
      sage: mset = [x for x in K if x!=0]
      sage: Tuples(mset,2).list()
      [[a, a], [a + 1, a], [1, a], [a, a + 1], [a + 1, a + 1], [1, a + 1], [a, 1], [a + 1, 1], [1, 1]]

class `sage.combinat.tuple.``Tuples_sk`(S, k)

  Bases: `sage.combinat.combinat.CombinatorialClass`

  TESTS:

      sage: T = Tuples([1,2,3],2)
      sage: T == loads(dumps(T))
      True

  `cardinality`()

    EXAMPLES:

        sage: S = [1,2,3,4,5]
        sage: Tuples(S,2).cardinality()
        25
        sage: S = [1,1,2,3,4,5]
        sage: Tuples(S,2).cardinality()
        25

`sage.combinat.tuple.``UnorderedTuples`(S, k)

  Returns the combinatorial class of unordered tuples of S of length k.

  An unordered tuple of length k of set is a unordered selection with repetitions of set and is represented by a sorted list of length k containing elements from set.

  EXAMPLES:

      sage: S = [1,2]
      sage: UnorderedTuples(S,3).list()
      [[1, 1, 1], [1, 1, 2], [1, 2, 2], [2, 2, 2]]
      sage: UnorderedTuples(["a","b","c"],2).list()
      [['a', 'a'], ['a', 'b'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['c', 'c']]

class `sage.combinat.tuple.``UnorderedTuples_sk`(S, k)

  Bases: `sage.combinat.combinat.CombinatorialClass`

  TESTS:

      sage: T = Tuples([1,2,3],2)
      sage: T == loads(dumps(T))
      True

  `cardinality`()

    EXAMPLES:

        sage: S = [1,2,3,4,5]
        sage: UnorderedTuples(S,2).cardinality()
        15

  `list`()

    EXAMPLES:

        sage: S = [1,2]
        sage: UnorderedTuples(S,3).list()
        [[1, 1, 1], [1, 1, 2], [1, 2, 2], [2, 2, 2]]
        sage: UnorderedTuples(["a","b","c"],2).list()
        [['a', 'a'], ['a', 'b'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['c', 'c']]

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