# fmpq_mpoly_factor.h – factorisation of multivariate polynomials over the rational numbers

## Types, macros and constants

type fmpq_mpoly_factor_struct

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

type fmpq_mpoly_factor_t

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

## Memory management

void fmpq_mpoly_factor_init(fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)

  Initialise f.

void fmpq_mpoly_factor_clear(fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)

  Clear f.

## Basic manipulation

slong fmpq_mpoly_factor_length(const fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)

  Return the length of the product in f.

void fmpq_mpoly_factor_get_constant_fmpq(fmpq_t c, const fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)

  Set c to the constant of f.

void fmpq_mpoly_factor_get_base(fmpq_mpoly_t B, const fmpq_mpoly_factor_t f, slong i, const fmpq_mpoly_ctx_t ctx)
void fmpq_mpoly_factor_swap_base(fmpq_mpoly_t B, fmpq_mpoly_factor_t f, slong i, const fmpq_mpoly_ctx_t ctx)

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

slong fmpq_mpoly_factor_get_exp_si(fmpq_mpoly_factor_t f, slong i, const fmpq_mpoly_ctx_t ctx)

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

void fmpq_mpoly_factor_sort(fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)

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

int fmpq_mpoly_factor_make_monic(fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)
int fmpq_mpoly_factor_make_integral(fmpq_mpoly_factor_t f, const fmpq_mpoly_ctx_t ctx)

  Make the bases in f monic (resp. integral and primitive with positive leading coefficient). Return \(1\) for success, \(0\) for failure.

## 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. The normalization of the factors is not yet specified: use `fmpq_mpoly_factor_make_monic()` or `fmpq_mpoly_factor_make_integral()` for common normalizations.

int fmpq_mpoly_factor_squarefree(fmpq_mpoly_factor_t f, const fmpq_mpoly_t A, const fmpq_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 `fmpq_mpoly_factor_sort()` and then multiply the bases with the desired exponent.

int fmpq_mpoly_factor(fmpq_mpoly_factor_t f, const fmpq_mpoly_t A, const fmpq_mpoly_ctx_t ctx)

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