# nmod_mpoly_factor.h – factorisation of multivariate polynomials over integers mod n (word-size n)

## Types, macros and constants

type nmod_mpoly_factor_struct

  A struct for holding a factored polynomial. There is a single constant and a product of bases to corresponding exponents.

type nmod_mpoly_factor_t

  An array of length \(1\) of `nmod_mpoly_factor_struct`.

## Memory management

void nmod_mpoly_factor_init(nmod_mpoly_factor_t f, const nmod_mpoly_ctx_t ctx)

  Initialise f.

void nmod_mpoly_factor_clear(nmod_mpoly_factor_t f, const nmod_mpoly_ctx_t ctx)

  Clear f.

## Basic manipulation

void nmod_mpoly_factor_swap(nmod_mpoly_factor_t f, nmod_mpoly_factor_t g, const nmod_mpoly_ctx_t ctx)

  Efficiently swap f and g.

slong nmod_mpoly_factor_length(const nmod_mpoly_factor_t f, const nmod_mpoly_ctx_t ctx)

  Return the length of the product in f.

ulong nmod_mpoly_factor_get_constant_ui(const nmod_mpoly_factor_t f, const nmod_mpoly_ctx_t ctx)

  Return the constant of f.

void nmod_mpoly_factor_get_base(nmod_mpoly_t p, const nmod_mpoly_factor_t f, slong i, const nmod_mpoly_ctx_t ctx)
void nmod_mpoly_factor_swap_base(nmod_mpoly_t p, nmod_mpoly_factor_t f, slong i, const nmod_mpoly_ctx_t ctx)

  Set (resp. swap) B to (resp. with) the base of the term of index \(i\) in A.

slong nmod_mpoly_factor_get_exp_si(nmod_mpoly_factor_t f, slong i, const nmod_mpoly_ctx_t ctx)

  Return the exponent of the term of index \(i\) in A. It is assumed to fit an `slong`.

void nmod_mpoly_factor_sort(nmod_mpoly_factor_t f, const nmod_mpoly_ctx_t ctx)

  Sort the product of f first by exponent and then by base.

## Factorisation

> A return of \(1\) indicates that the function was successful. Otherwise, the return is \(0\) and f is undefined. None of these functions multiply f by A: f is simply set to a factorisation of A, and thus these functions should not depend on the initial value of the output f.

int nmod_mpoly_factor_squarefree(nmod_mpoly_factor_t f, const nmod_mpoly_t A, const nmod_mpoly_ctx_t ctx)

  Set f to a factorization of A where the bases are primitive and pairwise relatively prime. If the product of all irreducible factors with a given exponent is desired, it is recommended to call `nmod_mpoly_factor_sort()` and then multiply the bases with the desired exponent.

int nmod_mpoly_factor(nmod_mpoly_factor_t f, const nmod_mpoly_t A, const nmod_mpoly_ctx_t ctx)

  Set f to a factorization of A where the bases are irreducible.