fq_zech_mpoly_factor.h

Initialise f as the empty product with constant 1, free it, change its allocation to alloc factors, or ensure space for len factors.

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

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

Set f to the factorisation of A into monic irreducible factors, with the constant equal to the leading coefficient of A, using all methods, one lifting method, or the methods in the bit mask algo (see fq_nmod_mpoly_factor_algo). The computation is done by fq_nmod_mpoly_factor_algo after conversion. Return 1 for success.

Memory management, assignment, coefficient access, the degrees in the main (0) and inner (1) variable, and conversion from univariate polynomials in either variable.

Arithmetic of bivariate polynomials: products and divisions, possibly truncated to order terms in the inner variable; exact division (returning 1 if exact); removal of the content g; the derivative with respect to the main variable; and the shifts x \mapsto x + \alpha and y \mapsto y + c.

Memory management, consistency checks, degrees and printing of the other types.

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

Test whether A involves only the variable of index var, convert such a polynomial to an fq_zech_poly (returning 0 otherwise), and set A to a univariate polynomial in that variable.

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}_q (only 0 unless allow_shift), Hensel lifting and recombination by linear algebra [Lec2006]. Returns 0 if no suitable point exists.

Hensel lifting of a factorisation modulo y - \alpha into two or r factors, up to degree degree_inner in y. Return 1 for success.

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

Sets g to the GCD of the coefficients of A and returns 1 for success.

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

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

Wang's leading coefficient distribution [Wan1978].

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

Evaluate the monomials of a polynomial at given values of some variables, and evaluate all but the first one or two variables to get univariate or bivariate images.

Steps x to the next element of \mathbb{F}_q in a fixed enumeration; returns 0 when it wraps around.