Class CombinatorialClass

Returns the number of elements in the combinatorial class.

EXAMPLES:
    sage: len(Partitions(5))
    7

Returns the combinatorial object of rank i.

EXAMPLES:
    sage: p5 = Partitions(5)
    sage: p5[0]
    [5]
    sage: p5[6]
    [1, 1, 1, 1, 1]
    sage: p5[7]
    Traceback (most recent call last):
    ...
    ValueError: the value must be between 0 and 6 inclusive

Returns a string representation of self.

EXAMPLES:
    sage: str(Partitions(5))
    'Partitions of the integer 5'

Overrides: object.__str__

EXAMPLES:
    sage: repr(Partitions(5))
    'Partitions of the integer 5'

Overrides: structure.sage_object.SageObject.__repr__

Tests whether or not the combinatorial class contains the
object x.  This raises a NotImplementedError as a default
since _all_ subclasses of CombinatorialClass should
override this.

Note that we could replace this with a default implementation
that just iterates through the elements of the combinatorial
class and checks for equality.  However, since we use __contains__
for type checking, this operation should be cheap and should be
implemented manually for each combinatorial class.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: x in C
    Traceback (most recent call last):
    ...
    NotImplementedError

Allows the combinatorial class to be treated as an iterator.

EXAMPLES:
    sage: p5 = Partitions(5)
    sage: [i for i in p5]
    [[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]]

Compares two different combinatorial classes.  For now, the comparison
is done just on their repr's.

EXAMPLES:
    sage: p5 = Partitions(5)
    sage: p6 = Partitions(6)
    sage: repr(p5) == repr(p6)
    False
    sage: p5 == p6
    False

Default implmentation of count which just goes through the iterator
of the combinatorial class to count the number of objects.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: it = lambda: iter([1,2,3])
    sage: C.iterator = it
    sage: C.count() #indirect doctest
    3

Returns x as an element of the combinatorial class's object class.

EXAMPLES:
    sage: p5 = Partitions(5)
    sage: a = [2,2,1]
    sage: type(a)
    <type 'list'>
    sage: a = p5(a)
    sage: type(a)
    <class 'sage.combinat.partition.Partition_class'>
    sage: p5([2,1])
    Traceback (most recent call last):
    ...
    ValueError: [2, 1] not in Partitions of the integer 5

The default implementation of list which builds the list from
the iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: it = lambda: iter([1,2,3])
    sage: C.iterator = it
    sage: C.list() #indirect doctest
    [1, 2, 3]

Default implementation of iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.iterator()
    Traceback (most recent call last):
    ...
    NotImplementedError: iterator called but not implemented

Default implementation of unrank which goes through the iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.unrank(1) # indirect doctest
    2

Default implementation of random which uses unrank.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.random_element()
    1

Deprecated.  Use self.random_element() instead.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.random()
    Traceback (most recent call last):
    ...
    NotImplementedError: Deprecated: use random_element() instead

Default implementation of rank which uses iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.rank(3) # indirect doctest
    2

Default implementation for first which uses iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.first() # indirect doctest
    1

Default implementation for first which uses iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.last() # indirect doctest
    3

Default implementation for next which uses iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.next(2) # indirect doctest
    3

Default implementation for next which uses iterator.

EXAMPLES:
    sage: C = CombinatorialClass()
    sage: C.list = lambda: [1,2,3]
    sage: C.previous(2) # indirect doctest
    1

Returns the combinatorial subclass of f which consists of
the elements x of self such that f(x) is True.

EXAMPLES:
    sage: P = Permutations(3).filter(lambda x: x.avoids([1,2]))
    sage: P.list()
    [[3, 2, 1]]

Returns the combinatorial class representing the union
of self and right_cc.

EXAMPLES:
    sage: P = Permutations(2).union(Permutations(1))
    sage: P.list()
    [[1, 2], [2, 1], [1]]