fq_nmod_mpoly_factor.h

Initialise f as the empty product with constant 1, and free it.

Change the allocation of f to alloc factors, or ensure space for len factors.

Swap two factorisations, copy b into a, and set a 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 (despite the const in the prototype, fq_nmod_mpoly_factor_swap_base modifies f), and return the exponent of index i, which must fit an slong.

Append the factor A^e to f, copying A.

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, fq_nmod_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 over \mathbb{F}_q.

As fq_nmod_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).

Sum, difference and product; product and division with remainder with the inner variable truncated to order terms; exact division (returning 1 if exact); and removal of the content g (a polynomial in the inner variable).

Convert between a polynomial in the variables varx (main) and vary only and a dense bivariate polynomial.

Factor the bivariate B, separable in the main variable: set c to its content and F to its irreducible factors. The smprime version evaluates the inner variable at a point of \mathbb{F}_q (only 0 unless allow_shift), lifts by Hensel lifting and recombines by linear algebra [Lec2006], returning 0 if no point works; the lgprime version reduces the inner variable modulo irreducible polynomials over \mathbb{F}_q (working over \mathbb{F}_{q^n}) and always succeeds.

Hensel lifting of a factorisation of a bivariate (trivariate for n_fq_polyu3_hlift) polynomial A modulo y - \alpha into two factors B0, B1 or r factors B, up to degree degree_inner in y; the cubic version evaluates and interpolates in the other variable. Return 1 for success.

Consistency checks and printing of sparse polynomials with n_fq coefficients.

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.

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

Apply and undo a monomial compression computed by mpoly_compression_set.

Multivariate partial fractions and Hensel lifting, as the corresponding nmod_mpoly functions.

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

As fq_nmod_mpoly_factor_separable for a monic primitive A.

Irreducible factorisation of a monic squarefree polynomial in at least three variables, given for the Wang and Zippel methods the factorisation lcAfac of the leading coefficient lcA in variable 0. The smprime versions use evaluation points in \mathbb{F}_q; the lgprime versions map A into \mathbb{F}_{q^n} with the embeddings of fq_nmod_mpoly.h, factor there and multiply together the factors in each orbit of the Frobenius automorphism c \mapsto c^q of \mathbb{F}_{q^n} over \mathbb{F}_q. Return 1 for success, 0 if they ran out of evaluation points or extensions, 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.