239 lines
6.6 KiB
C
239 lines
6.6 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2007 David Howden
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Copyright (C) 2007, 2008, 2009, 2010 William Hart
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Copyright (C) 2008 Richard Howell-Peak
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include <stdlib.h>
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#include "nmod_poly.h"
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#include "nmod_mat.h"
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#include "ulong_extras.h"
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#include "profiler.h"
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#include "perm.h"
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static void
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nmod_poly_to_nmod_mat_col(nmod_mat_t mat, slong col, nmod_poly_t poly)
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{
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slong i;
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for (i = 0; i < poly->length; i++)
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nmod_mat_entry(mat, i, col) = poly->coeffs[i];
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for ( ; i < mat->r; i++)
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nmod_mat_entry(mat, i, col) = UWORD(0);
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}
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static void
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nmod_mat_col_to_nmod_poly_shifted(nmod_poly_t poly, nmod_mat_t mat,
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slong col, slong * shift)
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{
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slong i, j, rows = mat->r;
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nmod_poly_fit_length(poly, rows);
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for (i = 0, j = 0; j < rows; j++)
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{
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if (shift[j])
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poly->coeffs[j] = 0;
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else
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{
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poly->coeffs[j] = nmod_mat_entry(mat, i, col);
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i++;
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}
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}
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poly->length = rows;
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_nmod_poly_normalise(poly);
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}
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static void
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__nmod_poly_factor_berlekamp(nmod_poly_factor_t factors,
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flint_rand_t state, const nmod_poly_t f)
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{
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const mp_limb_t p = nmod_poly_modulus(f);
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const slong n = nmod_poly_degree(f);
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nmod_poly_factor_t fac1, fac2;
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nmod_poly_t x, x_p;
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nmod_poly_t x_pi, x_pi2;
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nmod_poly_t Q;
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nmod_mat_t matrix;
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mp_limb_t coeff;
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slong i, nullity, col, row, *shift;
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nmod_poly_t *basis;
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if (f->length <= 2)
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{
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nmod_poly_factor_insert(factors, f, 1);
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return;
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}
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/* Step 1, we compute x^p mod f in F_p[X]/<f> */
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nmod_poly_init(x, p);
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nmod_poly_init(x_p, p);
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nmod_poly_set_coeff_ui(x, 1, 1);
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nmod_poly_powmod_ui_binexp(x_p, x, p, f);
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nmod_poly_clear(x);
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/* Step 2, compute the matrix for the Berlekamp Map */
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nmod_mat_init(matrix, n, n, p);
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nmod_poly_init(x_pi, p);
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nmod_poly_init(x_pi2, p);
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nmod_poly_set_coeff_ui(x_pi, 0, 1);
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for (i = 0; i < n; i++)
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{
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/* Q - I */
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nmod_poly_set(x_pi2, x_pi);
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coeff = nmod_poly_get_coeff_ui(x_pi2, i);
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if (coeff)
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nmod_poly_set_coeff_ui(x_pi2, i, coeff - 1);
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else
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nmod_poly_set_coeff_ui(x_pi2, i, p - 1);
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nmod_poly_to_nmod_mat_col(matrix, i, x_pi2);
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nmod_poly_mulmod(x_pi, x_pi, x_p, f);
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}
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nmod_poly_clear(x_p);
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nmod_poly_clear(x_pi);
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nmod_poly_clear(x_pi2);
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/* Row reduce Q - I */
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nullity = n - nmod_mat_rref(matrix);
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/* Find a basis for the nullspace */
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basis = (nmod_poly_t *) flint_malloc(nullity * sizeof(nmod_poly_t));
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shift = (slong *) flint_calloc(n, sizeof(slong));
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col = 1; /* first column is always zero */
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row = 0;
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shift[0] = 1;
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for (i = 1; i < nullity; i++)
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{
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nmod_poly_init(basis[i], p);
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while (nmod_mat_entry(matrix, row, col))
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{
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row++;
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col++;
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}
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nmod_mat_col_to_nmod_poly_shifted(basis[i], matrix, col, shift);
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nmod_poly_set_coeff_ui(basis[i], col, p - 1);
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shift[col] = 1;
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col++;
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}
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flint_free(shift);
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nmod_mat_clear(matrix);
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/* we are done */
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if (nullity == 1)
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{
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nmod_poly_factor_insert(factors, f, 1);
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flint_free(basis);
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}
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else
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{
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/* Generate random linear combinations */
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nmod_poly_t factor, b, power, g;
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nmod_poly_init(factor, p);
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nmod_poly_init(b, p);
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nmod_poly_init(power, p);
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nmod_poly_init(g, p);
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while (1)
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{
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do
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{
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nmod_poly_zero(factor);
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for (i = 1; i < nullity; i++)
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{
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nmod_poly_scalar_mul_nmod(b, basis[i], n_randint(state, p));
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nmod_poly_add(factor, factor, b);
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}
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nmod_poly_set_coeff_ui(factor, 0, n_randint(state, p));
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if (!nmod_poly_is_zero(factor))
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nmod_poly_make_monic(factor, factor);
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}
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while (nmod_poly_is_one(factor) || nmod_poly_is_zero(factor));
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nmod_poly_gcd(g, f, factor);
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if (nmod_poly_length(g) != 1) break;
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if (p > 3)
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nmod_poly_powmod_ui_binexp(power, factor, p >> 1, f);
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else
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nmod_poly_set(power, factor);
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power->coeffs[0] = n_addmod(power->coeffs[0], p - 1, p);
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_nmod_poly_normalise(power);
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nmod_poly_gcd(g, power, f);
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if (nmod_poly_length(g) != 1)
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break;
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}
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for (i = 1; i < nullity; i++)
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nmod_poly_clear(basis[i]);
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flint_free(basis);
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nmod_poly_clear(power);
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nmod_poly_clear(factor);
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nmod_poly_clear(b);
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if (!nmod_poly_is_zero(g))
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nmod_poly_make_monic(g, g);
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nmod_poly_factor_init(fac1);
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nmod_poly_factor_init(fac2);
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__nmod_poly_factor_berlekamp(fac1, state, g);
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nmod_poly_init(Q, p);
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nmod_poly_div(Q, f, g);
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if (!nmod_poly_is_zero(Q))
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nmod_poly_make_monic(Q, Q);
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__nmod_poly_factor_berlekamp(fac2, state, Q);
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nmod_poly_factor_concat(factors, fac1);
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nmod_poly_factor_concat(factors, fac2);
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nmod_poly_factor_clear(fac1);
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nmod_poly_factor_clear(fac2);
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nmod_poly_clear(Q);
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nmod_poly_clear(g);
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}
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}
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void
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nmod_poly_factor_berlekamp(nmod_poly_factor_t factors, const nmod_poly_t f)
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{
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flint_rand_t r;
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flint_randinit(r);
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__nmod_poly_factor_berlekamp(factors, r, f);
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flint_randclear(r);
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}
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