304 lines
8.5 KiB
C
304 lines
8.5 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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Copyright (C) 2012 Lina Kulakova
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******************************************************************************/
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#include <stdlib.h>
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#include "fmpz_mod_poly.h"
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#include "fmpz_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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fmpz_mod_poly_to_fmpz_mat_col(fmpz_mat_t mat, slong col, fmpz_mod_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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fmpz_set(fmpz_mat_entry(mat, i, col), poly->coeffs + i);
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for (; i < mat->r; i++)
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fmpz_zero(fmpz_mat_entry(mat, i, col));
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}
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static void
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fmpz_mat_col_to_fmpz_mod_poly_shifted(fmpz_mod_poly_t poly, fmpz_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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fmpz_mod_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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fmpz_zero(poly->coeffs + j);
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else
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{
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fmpz_set(poly->coeffs + j, fmpz_mat_entry(mat, i, col));
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i++;
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}
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}
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_fmpz_mod_poly_set_length(poly, rows);
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_fmpz_mod_poly_normalise(poly);
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}
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static void
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__fmpz_mod_poly_factor_berlekamp(fmpz_mod_poly_factor_t factors,
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flint_rand_t state, const fmpz_mod_poly_t f)
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{
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const slong n = fmpz_mod_poly_degree(f);
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fmpz_mod_poly_factor_t fac1, fac2;
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fmpz_mod_poly_t x, x_p;
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fmpz_mod_poly_t x_pi, x_pi2;
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fmpz_mod_poly_t Q, r;
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fmpz_mat_t matrix;
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fmpz_t coeff, p, q, mul, pow;
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slong i, nullity, col, row;
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slong *shift, *perm;
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fmpz_mod_poly_t *basis;
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if (f->length <= 2)
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{
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fmpz_mod_poly_factor_insert(factors, f, 1);
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return;
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}
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fmpz_init(coeff);
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fmpz_init(mul);
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fmpz_init_set(p, &f->p);
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/* q = p - 1 */
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fmpz_init_set(q, p);
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fmpz_sub_ui(q, q, 1);
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fmpz_mod(q, q, p);
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/* pow = (p-1)/2 */
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fmpz_init(pow);
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if (fmpz_cmp_ui(p, 3) > 0)
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{
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fmpz_set(pow, q);
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fmpz_divexact_ui(pow, pow, 2);
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}
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/* Step 1, compute x^p mod f in F_p[X]/<f> */
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fmpz_mod_poly_init(x, p);
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fmpz_mod_poly_init(x_p, p);
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fmpz_mod_poly_set_coeff_ui(x, 1, 1);
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fmpz_mod_poly_powmod_fmpz_binexp(x_p, x, p, f);
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fmpz_mod_poly_clear(x);
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/* Step 2, compute the matrix for the Berlekamp Map */
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fmpz_mat_init(matrix, n, n);
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fmpz_mod_poly_init(x_pi, p);
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fmpz_mod_poly_init(x_pi2, p);
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fmpz_mod_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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fmpz_mod_poly_set(x_pi2, x_pi);
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fmpz_mod_poly_get_coeff_fmpz(coeff, x_pi2, i);
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if (!fmpz_is_zero(coeff))
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{
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fmpz_sub_ui(coeff, coeff, 1);
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fmpz_mod(coeff, coeff, p);
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fmpz_mod_poly_set_coeff_fmpz(x_pi2, i, coeff);
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}
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else
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{
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fmpz_mod_poly_set_coeff_fmpz(x_pi2, i, q);
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}
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fmpz_mod_poly_to_fmpz_mat_col(matrix, i, x_pi2);
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fmpz_mod_poly_mulmod(x_pi, x_pi, x_p, f);
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}
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fmpz_mod_poly_clear(x_p);
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fmpz_mod_poly_clear(x_pi);
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fmpz_mod_poly_clear(x_pi2);
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/* Row reduce Q - I */
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perm = _perm_init(n);
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nullity = n - fmpz_mat_rref_mod(perm, matrix, p);
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_perm_clear(perm);
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/* Find a basis for the nullspace */
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basis =
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(fmpz_mod_poly_t *) flint_malloc(nullity * sizeof(fmpz_mod_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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fmpz_mod_poly_init(basis[i], p);
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while (!fmpz_is_zero(fmpz_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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fmpz_mat_col_to_fmpz_mod_poly_shifted(basis[i], matrix, col, shift);
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fmpz_mod_poly_set_coeff_fmpz(basis[i], col, q);
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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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fmpz_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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fmpz_mod_poly_factor_insert(factors, f, 1);
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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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fmpz_mod_poly_t factor, b, power, g;
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fmpz_mod_poly_init(factor, p);
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fmpz_mod_poly_init(b, p);
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fmpz_mod_poly_init(power, p);
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fmpz_mod_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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fmpz_mod_poly_zero(factor);
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for (i = 1; i < nullity; i++)
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{
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fmpz_randm(mul, state, p);
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fmpz_mod_poly_scalar_mul_fmpz(b, basis[i], mul);
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fmpz_mod_poly_add(factor, factor, b);
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}
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fmpz_randm(coeff, state, p);
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fmpz_mod_poly_set_coeff_fmpz(factor, 0, coeff);
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if (!fmpz_mod_poly_is_zero(factor))
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fmpz_mod_poly_make_monic(factor, factor);
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}
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while (fmpz_mod_poly_is_zero(factor) ||
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(factor->length < 2 && fmpz_is_one(factor->coeffs)));
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fmpz_mod_poly_gcd(g, f, factor);
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if (fmpz_mod_poly_length(g) != 1)
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break;
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if (fmpz_cmp_ui(p, 3) > 0)
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fmpz_mod_poly_powmod_fmpz_binexp(power, factor, pow, f);
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else
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fmpz_mod_poly_set(power, factor);
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fmpz_add(power->coeffs, power->coeffs, q);
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fmpz_mod(power->coeffs, power->coeffs, p);
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_fmpz_mod_poly_normalise(power);
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fmpz_mod_poly_gcd(g, power, f);
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if (fmpz_mod_poly_length(g) != 1)
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break;
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}
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fmpz_mod_poly_clear(power);
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fmpz_mod_poly_clear(factor);
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fmpz_mod_poly_clear(b);
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if (!fmpz_mod_poly_is_zero(g))
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fmpz_mod_poly_make_monic(g, g);
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fmpz_mod_poly_factor_init(fac1);
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fmpz_mod_poly_factor_init(fac2);
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__fmpz_mod_poly_factor_berlekamp(fac1, state, g);
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fmpz_mod_poly_init(Q, p);
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fmpz_mod_poly_init(r, p);
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fmpz_mod_poly_divrem(Q, r, f, g);
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fmpz_mod_poly_clear(r);
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if (!fmpz_mod_poly_is_zero(Q))
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fmpz_mod_poly_make_monic(Q, Q);
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__fmpz_mod_poly_factor_berlekamp(fac2, state, Q);
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fmpz_mod_poly_factor_concat(factors, fac1);
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fmpz_mod_poly_factor_concat(factors, fac2);
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fmpz_mod_poly_factor_clear(fac1);
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fmpz_mod_poly_factor_clear(fac2);
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fmpz_mod_poly_clear(Q);
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fmpz_mod_poly_clear(g);
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}
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for (i = 1; i < nullity; i++)
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fmpz_mod_poly_clear(basis[i]);
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flint_free(basis);
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fmpz_clear(coeff);
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fmpz_clear(p);
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fmpz_clear(q);
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fmpz_clear(mul);
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fmpz_clear(pow);
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}
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void
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fmpz_mod_poly_factor_berlekamp(fmpz_mod_poly_factor_t factors,
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const fmpz_mod_poly_t f)
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{
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slong i;
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flint_rand_t r;
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fmpz_mod_poly_t v;
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fmpz_mod_poly_factor_t sq_free;
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fmpz_mod_poly_init(v, &f->p);
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fmpz_mod_poly_make_monic(v, f);
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/* compute squarefree factorisation */
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fmpz_mod_poly_factor_init(sq_free);
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fmpz_mod_poly_factor_squarefree(sq_free, v);
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/* run Berlekamp algorithm for all squarefree factors */
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flint_randinit(r);
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for (i = 0; i < sq_free->num; i++)
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{
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__fmpz_mod_poly_factor_berlekamp(factors, r, sq_free->poly + i);
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}
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flint_randclear(r);
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/* compute multiplicities of factors in f */
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for (i = 0; i < factors->num; i++)
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factors->exp[i] = fmpz_mod_poly_remove(v, factors->poly + i);
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fmpz_mod_poly_clear(v);
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fmpz_mod_poly_factor_clear(sq_free);
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}
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