# perm.h – permutations

## Memory management

slong *_perm_init(slong n)

  Initialises the permutation for use.

void _perm_clear(slong *vec)

  Clears the permutation.

## Assignment

void _perm_set(slong *res, const slong *vec, slong n)

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

void _perm_one(slong *vec, slong n)

  Sets the permutation to the identity permutation.

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

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

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

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.