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#pragma once
/* #[ License : */
/*
* Copyright (C) 1984-2026 J.A.M. Vermaseren
* When using this file you are requested to refer to the publication
* J.A.M.Vermaseren "New features of FORM" math-ph/0010025
* This is considered a matter of courtesy as the development was paid
* for by FOM the Dutch physics granting agency and we would like to
* be able to track its scientific use to convince FOM of its value
* for the community.
*
* This file is part of FORM.
*
* FORM 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 3 of the License, or (at your option) any later
* version.
*
* FORM 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 FORM. If not, see <http://www.gnu.org/licenses/>.
*/
/* #] License : */
#include <vector>
#include <string>
// First prime modulo which factorization is tried. Too small results
// in more unsuccessful attempts; too large is slower.
const int POLYFACT_FIRST_PRIME = 17;
// Fraction of [1,p) that is used for substitutions of variables. Too
// small results in more unsuccessful attempts; too large is slower.
const int POLYFACT_IDEAL_FRACTION = 5;
// Number of ideals that are tried before failure due to unlucky
// choices is accepted.
const int POLYFACT_MAX_IDEAL_TRIES = 3;
// Number of confirmations for the minimal number of factors before
// Hensel lifting is started.
const int POLYFACT_NUM_CONFIRMATIONS = 3;
// Maximum number of equations for predetermination of coefficients
// for multivariate Hensel lifting
const int POLYFACT_MAX_PREDETERMINATION = 10000;
class poly;
class factorized_poly {
/* Class for representing a factorized polynomial
* The polynomial is given by: PRODUCT(factor[i] ^ power[i])
*/
public:
std::vector<poly> factor;
std::vector<int> power;
void add_factor(const poly &f, int p=1);
const std::string tostring () const;
friend std::ostream& operator<< (std::ostream &out, const poly &p);
};
std::ostream& operator<< (std::ostream &out, const factorized_poly &a);
namespace polyfact {
// factorization routine
const factorized_poly factorize (const poly &a);
// methods for squarefree factorization
const factorized_poly squarefree_factors (const poly &a);
const factorized_poly squarefree_factors_Yun (const poly &a);
const factorized_poly squarefree_factors_modp (const poly &a);
// methods for choosing suitable reductions
const std::vector<poly> factorize_squarefree (const poly &a, const std::vector<int> &x);
WORD choose_prime (const poly &a, const std::vector<int> &x, WORD p=0);
WORD choose_prime_power (const poly &a, WORD p);
const std::vector<int> choose_ideal (const poly &a, int p, const factorized_poly &lc, const std::vector<int> &x);
// methods for univariate factorization
const std::vector<std::vector<WORD> > Berlekamp_Qmatrix (const poly &a);
const std::vector<poly> Berlekamp_find_factors (const poly &a, const std::vector<std::vector<WORD> > &Q);
const std::vector<poly> combine_factors (const poly &a, const std::vector<poly> &f);
// methods for Hensel lifting
const std::vector<poly> extended_gcd_Euclidean_lifted (const poly &a, const poly &b);
const std::vector<poly> solve_Diophantine_univariate (const std::vector<poly> &a, const poly &b);
const std::vector<poly> solve_Diophantine_multivariate (const std::vector<poly> &a, const poly &b, const std::vector<int> &x, const std::vector<int> &c, int d);
const std::vector<poly> lift_coefficients (const poly &a, const std::vector<poly> &f);
const std::vector<poly> lift_variables (const poly &a, const std::vector<poly> &f, const std::vector<int> &x, const std::vector<int> &c, const std::vector<poly> &lc);
void predetermine (int dep, const std::vector<std::vector<int> > &state, std::vector<std::vector<std::vector<int> > > &terms, std::vector<int> &term, int sumdeg=0);
}
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