fmpz_mod_mpoly_factor.h

Initialises f as the empty product with constant 1.

Free f, change its allocation to alloc factors, or ensure space for len factors.

Swap two factorisations, and set f to the empty product with constant 1.

Return the number of factors, and set c to the constant.

Set p to the base of index i or swap it with p, and return the exponent of index i, which must fit an slong.

Appends the factor A^e to f, swapping A into it (so A is changed).

Set A to the product represented by f (returning 0 for negative or too large exponents), and test whether f represents a.

Sort the factors by exponent and then by base, and compare two factorisations (constant, number of factors, then factor by factor).

Prints the constant followed by one line *(base)^exp per factor.

Sets f to a factorisation into variables and polynomials primitive with respect to every variable.

Set f to a factorisation with squarefree, pairwise coprime bases. With sep = 1, fmpz_mod_mpoly_factor_separable also makes each base g satisfy \partial g/\partial x_i = 0 or \gcd(g, \partial g/\partial x_i) = 1 for every variable, as nmod_mpoly_factor_separable.

Sets f to the factorisation of A into monic irreducible factors.

As fmpz_mod_mpoly_factor with only one lifting method, or the methods in the bit mask algo (MPOLY_FACTOR_USE_ZAS, MPOLY_FACTOR_USE_WANG, MPOLY_FACTOR_USE_ZIP, MPOLY_FACTOR_USE_ALL).

Initialise and clear a stack; fit_request ensures that k more objects are available and returns a pointer to them, request also reserves them, take_top reserves one fitted object, give_back releases the k most recently reserved objects, and size returns the number of reserved objects.

The degree of a; A = B + d_0 C; A = B + (d_1 x + d_0) C; A = x^k A + c; evaluation of P at \alpha, and at \pm\alpha simultaneously, using the cached powers alphapow of \alpha.

Operations on vectors of univariate polynomials: maximum degree, monic GCD of the entries (and division by it), multiplication and exact division by g, and scaling.

Start a cache c of powers of b, and set a = a \cdot b^e using and extending the cache.

As nmod_mat_is_reduced and nmod_mat_init_nullspace_tr: test whether the rows of N describe a partition of the columns, and compute a basis of the right nullspace of tmp as the rows of X.

Memory management, assignment, coefficient access, degrees in the main (gen0) and the inner (gen1) variable, conversion from univariate polynomials in either variable, and printing of dense bivariate polynomials.

Arithmetic of bivariate polynomials: products, and products and division with the inner variable truncated to order terms; exact division (returning 1 if exact); making the polynomial monic as a series in the inner variable, or removing its content g (a polynomial in the inner variable); the derivative with respect to the main variable; the substitutions x \mapsto x + \alpha and y \mapsto y + c; and swapping the variables.

Memory management of arrays of bivariate polynomials.

Conversions between polynomials in two variables of the context and dense or sparse bivariate representations.

Memory management, assignment, degrees and printing of the sparse types with one, two or three packed main variables.

Operations on fmpz_mod_mpolyn_t and conversions from and to fmpz_mod_mpoly_t (with the variable var moved into the univariate coefficients, or with a permutation and deflation of the variables).

The evaluation (reduce, at \alpha or at \pm\alpha), first-image (lift) and Chinese remaindering (crt) steps of Brown's algorithm, as for nmod_mpoly; the crt functions return whether the interpolant changed and update lastdeg.

Sparse interpolation of polynomials with known support: the monomial evaluations at powers of the evaluation points, the master polynomials \prod (z - m_i) of the monomial values (product_roots, returning the maximum number of terms), the incremental evaluation of the next image, and the solution of the transposed Vandermonde systems (returning 1 for success and 0 or -1 if the images are inconsistent).

Computes the GCD G and, if Abar and Bbar are not NULL, the cofactors of the nonzero A and B with the algorithms in the bit mask algo (MPOLY_GCD_USE_BROWN, MPOLY_GCD_USE_HENSEL, MPOLY_GCD_USE_ZIPPEL, MPOLY_GCD_USE_ZIPPEL2, MPOLY_GCD_USE_PRS or MPOLY_GCD_USE_ALL). For a word-size modulus it calls _nmod_mpoly_gcd_algo_small. Returns 1 for success.

The GCD algorithms with evaluation points in \mathbb{F}_p: Brown's dense algorithm (bivariate and multivariate), Zippel's algorithm in the variables up to var, sparse interpolation with two main variables given the leading coefficient of the GCD, and Hensel lifting. Return 1 for success, also setting the cofactors.

Get, or replace by c, the leading coefficient of a polynomial viewed as a polynomial in variable 0.

Sets f to the factorisation nf computed in the nmod_mpoly context nctx with the same modulus.

Vectors of polynomials, and conversion between B and the coefficients of its expansion in powers of xalpha = x_j - \alpha.

GCD of Alen polynomials (returning 1 for success), and exact division or multiplication of all of them by c.

Apply and undo a monomial compression computed by mpoly_compression_set, as nmod_mpoly_compression_do and nmod_mpoly_compression_undo.

As fmpz_mod_mpoly_factor_separable for a monic primitive A.

Factors the bivariate B, separable in the main variable: sets c to its content and F to its irreducible factors, by evaluation of the inner variable at a point of \mathbb{F}_p (only 0 unless allow_shift), Hensel lifting and recombination by linear algebra [Lec2006]. Returns 0 if no suitable point is found.

Bivariate (and trivariate) Hensel lifting of two or r factors modulo powers of y - \alpha, as the n_bpoly_mod versions in nmod_mpoly_factor.

Multivariate partial fractions and Hensel lifting, dense or by sparse interpolation, as the corresponding nmod_mpoly functions.

Wang's leading coefficient distribution [Wan1978], as nmod_mpoly_factor_lcc_wang.

Irreducible factorisation of a monic squarefree polynomial in at least three variables with evaluation points in \mathbb{F}_p. Return 1 for success, 0 if they ran out of evaluation points and -1 for a failure that other points would not fix.

Evaluate all but the first one or two variables, giving univariate or bivariate images.