118 lines
3.4 KiB
C
118 lines
3.4 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 "fmpz_mod_poly.h"
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#include "ulong_extras.h"
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int
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fmpz_mod_poly_factor_equal_deg_prob(fmpz_mod_poly_t factor,
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flint_rand_t state,
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const fmpz_mod_poly_t pol, slong d)
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{
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fmpz_mod_poly_t a, b, c, polinv;
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fmpz_t exp, t, p;
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int res = 1;
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slong i;
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if (pol->length <= 1)
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{
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flint_printf("Exception (fmpz_mod_poly_factor_equal_deg_prob): \n");
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flint_printf("Input polynomial is linear.\n");
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abort();
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}
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fmpz_init_set(p, &pol->p);
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fmpz_mod_poly_init(a, p);
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do
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{
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fmpz_mod_poly_randtest(a, state, pol->length - 1);
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} while (a->length <= 1);
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fmpz_mod_poly_gcd(factor, a, pol);
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if (factor->length != 1)
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{
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fmpz_mod_poly_clear(a);
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return 1;
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}
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fmpz_mod_poly_init(b, p);
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fmpz_mod_poly_init(polinv, p);
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fmpz_mod_poly_reverse(polinv, pol, pol->length);
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fmpz_mod_poly_inv_series_newton(polinv, polinv, polinv->length);
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fmpz_init(exp);
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if (fmpz_cmp_ui(p, 2) > 0)
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{
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/* compute a^{(p^d-1)/2} rem pol */
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fmpz_pow_ui(exp, p, d);
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fmpz_sub_ui(exp, exp, 1);
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fmpz_fdiv_q_2exp(exp, exp, 1);
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fmpz_mod_poly_powmod_fmpz_binexp_preinv(b, a, exp, pol, polinv);
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}
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else
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{
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/* compute b = (a^{2^{d-1}}+a^{2^{d-2}}+...+a^4+a^2+a) rem pol */
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fmpz_mod_poly_rem(b, a, pol);
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fmpz_mod_poly_init(c, p);
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fmpz_mod_poly_set(c, b);
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for (i = 1; i < d; i++)
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{
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/* c = a^{2^i} = (a^{2^{i-1}})^2 */
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fmpz_mod_poly_powmod_ui_binexp_preinv(c, c, 2, pol, polinv);
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fmpz_mod_poly_add(b, b, c);
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}
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fmpz_mod_poly_rem(b, b, pol);
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fmpz_mod_poly_clear(c);
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}
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fmpz_clear(exp);
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fmpz_init(t);
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fmpz_sub_ui(t, &(b->coeffs[0]), 1);
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fmpz_mod(t, t, p);
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fmpz_mod_poly_set_coeff_fmpz(b, 0, t);
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fmpz_clear(t);
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fmpz_mod_poly_gcd(factor, b, pol);
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if ((factor->length <= 1) || (factor->length == pol->length))
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res = 0;
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fmpz_mod_poly_clear(a);
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fmpz_mod_poly_clear(b);
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fmpz_mod_poly_clear(polinv);
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fmpz_clear(p);
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return res;
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}
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