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.. _fmpz-mod-mpoly-factor:
**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
--------------------------------------------------------------------------------
.. function:: void fmpz_mod_mpoly_factor_init(fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_ctx_t ctx)
Initialise *f*.
.. function:: void fmpz_mod_mpoly_factor_clear(fmpz_mod_mpoly_factor_t f, const fmpz_mod_mpoly_ctx_t ctx)
Clear *f*.
Basic manipulation
--------------------------------------------------------------------------------
.. function:: 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*.
.. function:: 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*.
.. function:: 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*.
.. function:: 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*.
.. function:: 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``.
.. function:: 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*.
.. function:: 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 :func:`fmpz_mod_mpoly_factor_sort`
and then multiply the bases with the desired exponent.
.. function:: 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.
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