112 lines
3.2 KiB
C
112 lines
3.2 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 "nmod_poly.h"
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#include "ulong_extras.h"
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void
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nmod_poly_powpowmod(nmod_poly_t res, const nmod_poly_t pol,
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ulong exp, ulong exp2, const nmod_poly_t f)
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{
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nmod_poly_t pow;
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ulong i;
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nmod_poly_init_preinv(pow, f->mod.n, f->mod.ninv);
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nmod_poly_powmod_ui_binexp(pow, pol, exp, f);
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nmod_poly_set(res, pow);
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if (!nmod_poly_equal(pow, pol))
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for (i = 1; i < exp2; i++)
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nmod_poly_powmod_ui_binexp(res, res, exp, f);
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nmod_poly_clear(pow);
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}
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int
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nmod_poly_is_irreducible_rabin(const nmod_poly_t f)
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{
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if (nmod_poly_length(f) > 2)
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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_t a, x, x_p;
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nmod_poly_init(a, p);
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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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/* Compute x^q mod f */
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nmod_poly_powpowmod(x_p, x, p, n, f);
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if (!nmod_poly_is_zero(x_p))
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nmod_poly_make_monic(x_p, x_p);
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/* Now do the irreducibility test */
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if (!nmod_poly_equal(x_p, x))
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{
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nmod_poly_clear(a);
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nmod_poly_clear(x);
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nmod_poly_clear(x_p);
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return 0;
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}
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else
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{
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n_factor_t factors;
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slong i;
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n_factor_init(&factors);
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n_factor(&factors, n, 1);
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for (i = 0; i < factors.num; i++)
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{
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nmod_poly_powpowmod(a, x, p, n / factors.p[i], f);
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nmod_poly_sub(a, a, x);
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if (!nmod_poly_is_zero(a))
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nmod_poly_make_monic(a, a);
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nmod_poly_gcd(a, a, f);
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if (a->length != 1)
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{
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nmod_poly_clear(a);
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nmod_poly_clear(x);
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nmod_poly_clear(x_p);
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return 0;
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}
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}
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}
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nmod_poly_clear(a);
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nmod_poly_clear(x);
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nmod_poly_clear(x_p);
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}
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return 1;
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}
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