fq_nmod_mpoly_factor.h – factorisation of multivariate polynomials over finite fields of word-sized characteristic

Types, macros and constants

type fq_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 fq_nmod_mpoly_factor_t

An array of length 1 of fq_nmod_mpoly_factor_struct.

Memory management

void fq_nmod_mpoly_factor_init(fq_nmod_mpoly_factor_t f, const fq_nmod_mpoly_ctx_t ctx)

Initialise f.

void fq_nmod_mpoly_factor_clear(fq_nmod_mpoly_factor_t f, const fq_nmod_mpoly_ctx_t ctx)

Clear f.

Basic manipulation

void fq_nmod_mpoly_factor_swap(fq_nmod_mpoly_factor_t f, fq_nmod_mpoly_factor_t g, const fq_nmod_mpoly_ctx_t ctx)

Efficiently swap \(f\) and g.

slong fq_nmod_mpoly_factor_length(const fq_nmod_mpoly_factor_t f, const fq_nmod_mpoly_ctx_t ctx)

Return the length of the product in \(f\).

void fq_nmod_mpoly_factor_get_constant_fq_nmod(fq_nmod_t c, const fq_nmod_mpoly_factor_t f, const fq_nmod_mpoly_ctx_t ctx)

Set \(c\) to the the constant of \(f\).

void fq_nmod_mpoly_factor_get_base(fq_nmod_mpoly_t p, const fq_nmod_mpoly_factor_t f, slong i, const fq_nmod_mpoly_ctx_t ctx)

void fq_nmod_mpoly_factor_swap_base(fq_nmod_mpoly_t p, fq_nmod_mpoly_factor_t f, slong i, const fq_nmod_mpoly_ctx_t ctx)

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

slong fq_nmod_mpoly_factor_get_exp_si(fq_nmod_mpoly_factor_t f, slong i, const fq_nmod_mpoly_ctx_t ctx)

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

void fq_nmod_mpoly_factor_sort(fq_nmod_mpoly_factor_t f, const fq_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 fq_nmod_mpoly_factor_squarefree(fq_nmod_mpoly_factor_t f, const fq_nmod_mpoly_t A, const fq_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 recommend to call fq_nmod_mpoly_factor_sort() and then multiply the bases with the desired exponent.

int fq_nmod_mpoly_factor(fq_nmod_mpoly_factor_t f, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_ctx_t ctx)

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