/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2009, 2008 William Hart Copyright (C) 2011 Sebastian Pancratz Copyright (C) 2011 Fredrik Johansson Copyright (C) 2012 Lina Kulakova ******************************************************************************/ ******************************************************************************* Factorisation ******************************************************************************* void fmpz_mod_poly_factor_init(fmpz_mod_poly_factor_t fac) Initialises \code{fac} for use. An \code{fmpz_mod_poly_factor_t} represents a polynomial in factorised form as a product of polynomials with associated exponents. void fmpz_mod_poly_factor_clear(fmpz_mod_poly_factor_t fac) Frees all memory associated with \code{fac}. void fmpz_mod_poly_factor_realloc(fmpz_mod_poly_factor_t fac, slong alloc) Reallocates the factor structure to provide space for precisely \code{alloc} factors. void fmpz_mod_poly_factor_fit_length(fmpz_mod_poly_factor_t fac, slong len) Ensures that the factor structure has space for at least \code{len} factors. This function takes care of the case of repeated calls by always, at least doubling the number of factors the structure can hold. void fmpz_mod_poly_factor_set(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_factor_t fac) Sets \code{res} to the same factorisation as \code{fac}. void fmpz_mod_poly_factor_print(const fmpz_mod_poly_factor_t fac) Prints the entries of \code{fac} to standard output. void fmpz_mod_poly_factor_insert(fmpz_mod_poly_factor_t fac, const fmpz_mod_poly_t poly, slong exp) Inserts the factor \code{poly} with multiplicity \code{exp} into the factorisation \code{fac}. If \code{fac} already contains \code{poly}, then \code{exp} simply gets added to the exponent of the existing entry. void fmpz_mod_poly_factor_concat(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_factor_t fac) Concatenates two factorisations. This is equivalent to calling \code{fmpz_mod_poly_factor_insert()} repeatedly with the individual factors of \code{fac}. Does not support aliasing between \code{res} and \code{fac}. void fmpz_mod_poly_factor_pow(fmpz_mod_poly_factor_t fac, slong exp) Raises \code{fac} to the power \code{exp}. int fmpz_mod_poly_is_irreducible(const fmpz_mod_poly_t f) Returns 1 if the polynomial \code{f} is irreducible, otherwise returns 0. int fmpz_mod_poly_is_irreducible_ddf(const fmpz_mod_poly_t f) Returns 1 if the polynomial \code{f} is irreducible, otherwise returns 0. Uses fast distinct-degree factorisation. int fmpz_mod_poly_is_irreducible_rabin(const fmpz_mod_poly_t f) Returns 1 if the polynomial \code{f} is irreducible, otherwise returns 0. Uses Rabin irreducibility test. int _fmpz_mod_poly_is_squarefree(const fmpz * f, slong len, const fmpz_t p) Returns 1 if \code{(f, len)} is squarefree, and 0 otherwise. As a special case, the zero polynomial is not considered squarefree. There are no restrictions on the length. int fmpz_mod_poly_is_squarefree(const fmpz_mod_poly_t f) Returns 1 if \code{f} is squarefree, and 0 otherwise. As a special case, the zero polynomial is not considered squarefree. int fmpz_mod_poly_factor_equal_deg_prob(fmpz_mod_poly_t factor, flint_rand_t state, const fmpz_mod_poly_t pol, slong d) Probabilistic equal degree factorisation of \code{pol} into irreducible factors of degree \code{d}. If it passes, a factor is placed in \code{factor} and 1 is returned, otherwise 0 is returned and the value of factor is undetermined. Requires that \code{pol} be monic, non-constant and squarefree. void fmpz_mod_poly_factor_equal_deg(fmpz_mod_poly_factor_t factors, const fmpz_mod_poly_t pol, slong d) Assuming \code{pol} is a product of irreducible factors all of degree \code{d}, finds all those factors and places them in factors. Requires that \code{pol} be monic, non-constant and squarefree. void fmpz_mod_poly_factor_distinct_deg(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_t poly, slong * const *degs) Factorises a monic non-constant squarefree polynomial \code{poly} of degree n into factors $f[d]$ such that for $1 \leq d \leq n$ $f[d]$ is the product of the monic irreducible factors of \code{poly} of degree $d$. Factors $f[d]$ are stored in \code{res}, and the degree $d$ of the irreducible factors is stored in \code{degs} in the same order as the factors. Requires that \code{degs} has enough space for $(n/2)+1 * sizeof(slong)$. void fmpz_mod_poly_factor_squarefree(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_t f) Sets \code{res} to a squarefree factorization of \code{f}. void fmpz_mod_poly_factor(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_t f) Factorises a non-constant polynomial \code{f} into monic irreducible factors choosing the best algorithm for given modulo and degree. Choise is based on heuristic measurments. void fmpz_mod_poly_factor_cantor_zassenhaus(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_t f) Factorises a non-constant polynomial \code{f} into monic irreducible factors using the Cantor-Zassenhaus algorithm. void fmpz_mod_poly_factor_kaltofen_shoup(fmpz_mod_poly_factor_t res, const fmpz_mod_poly_t poly) Factorises a non-constant polynomial \code{poly} into monic irreducible factors using the fast version of Cantor-Zassenhaus algorithm proposed by Kaltofen and Shoup (1998). More precisely this algorithm uses a ``baby step/giant step'' strategy for the distinct-degree factorization step. void fmpz_mod_poly_factor_berlekamp(fmpz_mod_poly_factor_t factors, const fmpz_mod_poly_t f) Factorises a non-constant polynomial \code{f} into monic irreducible factors using the Berlekamp algorithm.