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Iterables
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cartes
------
Returns the cartesian product of sequences as a generator.
Examples::
>>> from sympy.utilities.iterables import cartes
>>> list(cartes([1,2,3], 'ab'))
[(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b'), (3, 'a'), (3, 'b')]
variations
----------
variations(seq, n) Returns all the variations of the list of size n.
Has an optional third argument. Must be a boolean value and makes the method
return the variations with repetition if set to True, or the variations
without repetition if set to False.
Examples::
>>> from sympy.utilities.iterables import variations
>>> list(variations([1,2,3], 2))
[(1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)]
>>> list(variations([1,2,3], 2, True))
[(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)]
partitions
----------
Although the combinatorics module contains Partition and IntegerPartition
classes for investigation and manipulation of partitions, there are a few
functions to generate partitions that can be used as low-level tools for
routines: ``partitions`` and ``multiset_partitions``. The former gives
integer partitions, and the latter gives enumerated partitions of elements.
There is also a routine ``kbins`` that will give a variety of permutations
of partions.
partitions::
>>> from sympy.utilities.iterables import partitions
>>> [p.copy() for s, p in partitions(7, m=2, size=True) if s == 2]
[{1: 1, 6: 1}, {2: 1, 5: 1}, {3: 1, 4: 1}]
multiset_partitions::
>>> from sympy.utilities.iterables import multiset_partitions
>>> [p for p in multiset_partitions(3, 2)]
[[[0, 1], [2]], [[0, 2], [1]], [[0], [1, 2]]]
>>> [p for p in multiset_partitions([1, 1, 1, 2], 2)]
[[[1, 1, 1], [2]], [[1, 1, 2], [1]], [[1, 1], [1, 2]]]
kbins::
>>> from sympy.utilities.iterables import kbins
>>> def show(k):
... rv = []
... for p in k:
... rv.append(','.join([''.join(j) for j in p]))
... return sorted(rv)
...
>>> show(kbins("ABCD", 2))
['A,BCD', 'AB,CD', 'ABC,D']
>>> show(kbins("ABC", 2))
['A,BC', 'AB,C']
>>> show(kbins("ABC", 2, ordered=0)) # same as multiset_partitions
['A,BC', 'AB,C', 'AC,B']
>>> show(kbins("ABC", 2, ordered=1))
['A,BC', 'A,CB',
'B,AC', 'B,CA',
'C,AB', 'C,BA']
>>> show(kbins("ABC", 2, ordered=10))
['A,BC', 'AB,C', 'AC,B',
'B,AC', 'BC,A',
'C,AB']
>>> show(kbins("ABC", 2, ordered=11))
['A,BC', 'A,CB', 'AB,C', 'AC,B',
'B,AC', 'B,CA', 'BA,C', 'BC,A',
'C,AB', 'C,BA', 'CA,B', 'CB,A']
Docstring
=========
.. automodule:: sympy.utilities.iterables
:members: