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Computes the parity of a permutation in array form.

The parity of a permutation reflects the parity of the
number of inversions in the permutation, i.e., the
number of pairs of x and y such that x > y but p[x] < p[y].

Examples
========

>>> from sympy.combinatorics.permutations import _af_parity(more...)

        def _af_parity(pi):
    """
    Computes the parity of a permutation in array form.

    The parity of a permutation reflects the parity of the
    number of inversions in the permutation, i.e., the
    number of pairs of x and y such that x > y but p[x] < p[y].

    Examples
    ========

    >>> from sympy.combinatorics.permutations import _af_parity
    >>> _af_parity([0,1,2,3])
    0
    >>> _af_parity([3,2,0,1])
    1

    See Also
    ========

    Permutation
    """
    n = len(pi)
    a = [0] * n
    c = 0
    for j in range(n):
        if a[j] == 0:
            c += 1
            a[j] = 1
            i = j
            while pi[i] != j:
                i = pi[i]
                a[i] = 1
    return (n - c) % 2
        


src/s/y/sympy-0.7.5/sympy/combinatorics/tests/test_permutations.py   sympy(Download)
from itertools import permutations
 
from sympy.combinatorics.permutations import (Permutation, _af_parity,
    _af_rmul, _af_rmuln, Cycle)
from sympy.utilities.pytest import raises
    assert s.is_even
    assert Permutation([0, 1, 4, 3, 2]).parity() == 1
    assert _af_parity([0, 4, 1, 3, 2]) == 0
    assert _af_parity([0, 1, 4, 3, 2]) == 1
 

src/s/y/sympy-HEAD/sympy/combinatorics/tests/test_permutations.py   sympy(Download)
from itertools import permutations
 
from sympy.combinatorics.permutations import (Permutation, _af_parity,
    _af_rmul, _af_rmuln, Cycle)
from sympy.utilities.pytest import raises
    assert s.is_even
    assert Permutation([0, 1, 4, 3, 2]).parity() == 1
    assert _af_parity([0, 4, 1, 3, 2]) == 0
    assert _af_parity([0, 1, 4, 3, 2]) == 1