# 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_set_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.

## Input and output¶

int _perm_print(const slong * vec, slong n)

Prints the permutation vector of length $$n$$ to stdout.