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.. _perm:
**perm.h** -- permutations
===============================================================================
Memory management
--------------------------------------------------------------------------------
.. function:: slong * _perm_init(slong n)
Initialises the permutation for use.
.. function:: void _perm_clear(slong * vec)
Clears the permutation.
Assignment
--------------------------------------------------------------------------------
.. 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
--------------------------------------------------------------------------------
.. 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
--------------------------------------------------------------------------------
.. 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
--------------------------------------------------------------------------------
.. 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.
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