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/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2007 David Howden
Copyright (C) 2007, 2008, 2009, 2010 William Hart
Copyright (C) 2008 Richard Howell-Peak
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include "nmod_poly.h"
#include "ulong_extras.h"
void
nmod_poly_factor_squarefree(nmod_poly_factor_t res, const nmod_poly_t f)
{
nmod_poly_t f_d, g, g_1;
mp_limb_t p;
slong deg, i;
if (f->length <= 1)
{
res->num = 0;
return;
}
if (f->length == 2)
{
nmod_poly_factor_insert(res, f, 1);
return;
}
p = nmod_poly_modulus(f);
deg = nmod_poly_degree(f);
/* Step 1, look at f', if it is zero then we are done since f = h(x)^p
for some particular h(x), clearly f(x) = sum a_k x^kp, k <= deg(f) */
nmod_poly_init(g_1, p);
nmod_poly_init(f_d, p);
nmod_poly_init(g, p);
nmod_poly_derivative(f_d, f);
/* Case 1 */
if (nmod_poly_is_zero(f_d))
{
nmod_poly_factor_t new_res;
nmod_poly_t h;
nmod_poly_init(h, p);
for (i = 0; i <= deg / p; i++) /* this will be an integer since f'=0 */
{
nmod_poly_set_coeff_ui(h, i, nmod_poly_get_coeff_ui(f, i * p));
}
/* Now run square-free on h, and return it to the pth power */
nmod_poly_factor_init(new_res);
nmod_poly_factor_squarefree(new_res, h);
nmod_poly_factor_pow(new_res, p);
nmod_poly_factor_concat(res, new_res);
nmod_poly_clear(h);
nmod_poly_factor_clear(new_res);
}
else
{
nmod_poly_t h, z;
nmod_poly_gcd(g, f, f_d);
nmod_poly_div(g_1, f, g);
i = 1;
nmod_poly_init(h, p);
nmod_poly_init(z, p);
/* Case 2 */
while (!nmod_poly_is_one(g_1))
{
nmod_poly_gcd(h, g_1, g);
nmod_poly_div(z, g_1, h);
/* out <- out.z */
if (z->length > 1)
{
nmod_poly_factor_insert(res, z, 1);
nmod_poly_make_monic(res->p + (res->num - 1),
res->p + (res->num - 1));
if (res->num)
res->exp[res->num - 1] *= i;
}
i++;
nmod_poly_set(g_1, h);
nmod_poly_div(g, g, h);
}
nmod_poly_clear(h);
nmod_poly_clear(z);
nmod_poly_make_monic(g, g);
if (!nmod_poly_is_one(g))
{
/* so now we multiply res with square-free(g^1/p) ^ p */
nmod_poly_t g_p; /* g^(1/p) */
nmod_poly_factor_t new_res_2;
nmod_poly_init(g_p, p);
for (i = 0; i <= nmod_poly_degree(g) / p; i++)
nmod_poly_set_coeff_ui(g_p, i, nmod_poly_get_coeff_ui(g, i*p));
nmod_poly_factor_init(new_res_2);
/* square-free(g^(1/p)) */
nmod_poly_factor_squarefree(new_res_2, g_p);
nmod_poly_factor_pow(new_res_2, p);
nmod_poly_factor_concat(res, new_res_2);
nmod_poly_clear(g_p);
nmod_poly_factor_clear(new_res_2);
}
}
nmod_poly_clear(g_1);
nmod_poly_clear(f_d);
nmod_poly_clear(g);
}
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