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.