151 lines
4.2 KiB
C
151 lines
4.2 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_factor_squarefree(nmod_poly_factor_t res, const nmod_poly_t f)
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{
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nmod_poly_t f_d, g, g_1;
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mp_limb_t p;
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slong deg, i;
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if (f->length <= 1)
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{
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res->num = 0;
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return;
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}
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if (f->length == 2)
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{
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nmod_poly_factor_insert(res, f, 1);
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return;
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}
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p = nmod_poly_modulus(f);
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deg = nmod_poly_degree(f);
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/* Step 1, look at f', if it is zero then we are done since f = h(x)^p
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for some particular h(x), clearly f(x) = sum a_k x^kp, k <= deg(f) */
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nmod_poly_init(g_1, p);
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nmod_poly_init(f_d, p);
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nmod_poly_init(g, p);
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nmod_poly_derivative(f_d, f);
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/* Case 1 */
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if (nmod_poly_is_zero(f_d))
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{
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nmod_poly_factor_t new_res;
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nmod_poly_t h;
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nmod_poly_init(h, p);
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for (i = 0; i <= deg / p; i++) /* this will be an integer since f'=0 */
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{
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nmod_poly_set_coeff_ui(h, i, nmod_poly_get_coeff_ui(f, i * p));
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}
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/* Now run square-free on h, and return it to the pth power */
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nmod_poly_factor_init(new_res);
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nmod_poly_factor_squarefree(new_res, h);
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nmod_poly_factor_pow(new_res, p);
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nmod_poly_factor_concat(res, new_res);
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nmod_poly_clear(h);
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nmod_poly_factor_clear(new_res);
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}
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else
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{
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nmod_poly_t h, z;
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nmod_poly_gcd(g, f, f_d);
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nmod_poly_div(g_1, f, g);
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i = 1;
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nmod_poly_init(h, p);
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nmod_poly_init(z, p);
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/* Case 2 */
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while (!nmod_poly_is_one(g_1))
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{
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nmod_poly_gcd(h, g_1, g);
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nmod_poly_div(z, g_1, h);
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/* out <- out.z */
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if (z->length > 1)
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{
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nmod_poly_factor_insert(res, z, 1);
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nmod_poly_make_monic(res->p + (res->num - 1),
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res->p + (res->num - 1));
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if (res->num)
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res->exp[res->num - 1] *= i;
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}
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i++;
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nmod_poly_set(g_1, h);
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nmod_poly_div(g, g, h);
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}
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nmod_poly_clear(h);
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nmod_poly_clear(z);
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nmod_poly_make_monic(g, g);
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if (!nmod_poly_is_one(g))
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{
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/* so now we multiply res with square-free(g^1/p) ^ p */
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nmod_poly_t g_p; /* g^(1/p) */
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nmod_poly_factor_t new_res_2;
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nmod_poly_init(g_p, p);
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for (i = 0; i <= nmod_poly_degree(g) / p; i++)
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nmod_poly_set_coeff_ui(g_p, i, nmod_poly_get_coeff_ui(g, i*p));
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nmod_poly_factor_init(new_res_2);
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/* square-free(g^(1/p)) */
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nmod_poly_factor_squarefree(new_res_2, g_p);
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nmod_poly_factor_pow(new_res_2, p);
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nmod_poly_factor_concat(res, new_res_2);
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nmod_poly_clear(g_p);
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nmod_poly_factor_clear(new_res_2);
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}
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}
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nmod_poly_clear(g_1);
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nmod_poly_clear(f_d);
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nmod_poly_clear(g);
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}
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