.. _fmpz-mpoly-factor:

**fmpz_mpoly_factor.h** -- factorisation of multivariate polynomials over the integers
======================================================================================

Types, macros and constants
-------------------------------------------------------------------------------

.. type:: fmpz_mpoly_factor_struct

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

.. type:: fmpz_mpoly_factor_t

    An array of length 1 of ``fmpz_mpoly_factor_struct``.


Memory management
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.. function:: void fmpz_mpoly_factor_init(fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)

    Initialise ``f``.

.. function:: void fmpz_mpoly_factor_clear(fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)

    Clear ``f``.


Basic manipulation
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.. function:: void fmpz_mpoly_factor_swap(fmpz_mpoly_factor_t f, fmpz_mpoly_factor_t g, const fmpz_mpoly_ctx_t ctx)

    Efficiently swap `f` and ``g``.

.. function:: slong fmpz_mpoly_factor_length(const fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)

    Return the length of the product in `f`.

.. function:: void fmpz_mpoly_factor_get_constant_fmpz(fmpz_t c, const fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)
              void fmpz_mpoly_factor_get_constant_fmpq(fmpq_t c, const fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)

    Set `c` to the constant of `f`.

.. function:: void fmpz_mpoly_factor_get_base(fmpz_mpoly_t B, const fmpz_mpoly_factor_t f, slong i, const fmpz_mpoly_ctx_t ctx)
              void fmpz_mpoly_factor_swap_base(fmpz_mpoly_t B, fmpz_mpoly_factor_t f, slong i, const fmpz_mpoly_ctx_t ctx)

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

.. function:: slong fmpz_mpoly_factor_get_exp_si(fmpz_mpoly_factor_t f, slong i, const fmpz_mpoly_ctx_t ctx)

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

.. function:: void fmpz_mpoly_factor_sort(fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)

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


Factorisation
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    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_mpoly_factor_squarefree(fmpz_mpoly_factor_t f, const fmpz_mpoly_t A, const fmpz_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 :func:`fmpz_mpoly_factor_sort`
    and then multiply the bases with the desired exponent.

.. function:: int fmpz_mpoly_factor(fmpz_mpoly_factor_t f, const fmpz_mpoly_t A, const fmpz_mpoly_ctx_t ctx)

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

