# fmpz_mod_mpoly_factor.h – factorisation of multivariate polynomials over the integers mod n

## Types, macros and constants

type fmpz_mod_mpoly_factor_struct

  A struct for holding a factored polynomial over the integers mod n. There is a single constant and a product of bases to corresponding exponents.

type fmpz_mod_mpoly_factor_t

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

## Memory management

void fmpz_mod_mpoly_factor_init(fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_ctx_t ctx)

  Initialise f.

void fmpz_mod_mpoly_factor_clear(fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_ctx_t ctx)

  Clear f.

## Basic manipulation

void fmpz_mod_mpoly_factor_swap(fmpz_mod_mpoly_factor_t f, fmpz_mod_mpoly_factor_t g, const fmpz_mod_mpoly_ctx_t ctx)

  Efficiently swap f and g.

slong fmpz_mod_mpoly_factor_length(const fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_ctx_t ctx)

  Return the length of the product in f.

void fmpz_mod_mpoly_factor_get_constant_fmpz(fmpz_t c, const fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_ctx_t ctx)

  Set c to the constant of f.

void fmpz_mod_mpoly_factor_get_base(fmpz_mod_mpoly_t B, const fmpz_mod_mpoly_factor_t f, slong i, const fmpz_mod_mpoly_ctx_t ctx)
void fmpz_mod_mpoly_factor_swap_base(fmpz_mod_mpoly_t B, fmpz_mod_mpoly_factor_t f, slong i, const fmpz_mod_mpoly_ctx_t ctx)

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

slong fmpz_mod_mpoly_factor_get_exp_si(fmpz_mod_mpoly_factor_t f, slong i, const fmpz_mod_mpoly_ctx_t ctx)

  Return the exponent of the term of index i in f. It is assumed to fit an `slong`.

void fmpz_mod_mpoly_factor_sort(fmpz_mod_mpoly_factor_t f, const fmpz_mod_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 fmpz_mod_mpoly_factor_squarefree(fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_t A, const fmpz_mod_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 `fmpz_mod_mpoly_factor_sort()` and then multiply the bases with the desired exponent.

int fmpz_mod_mpoly_factor(fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_t A, const fmpz_mod_mpoly_ctx_t ctx)

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