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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void
fmpz_mpoly_factor_init
(fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)¶ Initialise
f
.
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void
fmpz_mpoly_factor_clear
(fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)¶ Clear
f
.
Basic manipulation¶
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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
.
-
slong
fmpz_mpoly_factor_length
(const fmpz_mpoly_factor_t f, const fmpz_mpoly_ctx_t ctx)¶ Return the length of the product in \(f\).
-
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 \(f\).
-
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 \(A\).
-
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
.
-
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¶
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_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
fmpz_mpoly_factor_sort()
and then multiply the bases with the desired exponent.
-
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.