.. _perm:

**perm.h** -- permutations
===============================================================================


Memory management
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.. function:: slong * _perm_init(slong n)

    Initialises the permutation for use.

.. function:: void _perm_clear(slong * vec)

    Clears the permutation.


Assignment
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.. function:: void _perm_set(slong * res, const slong * vec, slong n)

    Sets the permutation ``res`` to the same as the permutation ``vec``.

.. function:: void _perm_one(slong * vec, slong n)

    Sets the permutation to the identity permutation.

.. function:: void _perm_inv(slong * res, const slong * vec, slong n)

    Sets ``res`` to the inverse permutation of ``vec``.
    Allows aliasing of ``res`` and ``vec``.


Composition
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.. function:: void _perm_compose(slong * res, const slong * vec1, const slong * vec2, slong n)

    Forms the composition `\pi_1 \circ \pi_2` of two permutations 
    `\pi_1` and `\pi_2`.  Here, `\pi_2` is applied first, that is, 
    `(\pi_1 \circ \pi_2)(i) = \pi_1(\pi_2(i))`.

    Allows aliasing of ``res``, ``vec1`` and ``vec2``.


Parity
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.. function:: int _perm_parity(const slong * vec, slong n)

    Returns the parity of ``vec``, 0 if the permutation is even and 1 if
    the permutation is odd.


Randomisation
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.. function:: int _perm_randtest(slong * vec, slong n, flint_rand_t state)

    Generates a random permutation vector of length `n` and returns
    its parity, 0 or 1.

    This function uses the Knuth shuffle algorithm to generate a uniformly 
    random permutation without retries.