118 lines
3.4 KiB
C
118 lines
3.4 KiB
C
|
/*=============================================================================
|
||
|
|
||
|
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
|
||
|
Copyright (C) 2012 Lina Kulakova
|
||
|
|
||
|
******************************************************************************/
|
||
|
|
||
|
#include "fmpz_mod_poly.h"
|
||
|
#include "ulong_extras.h"
|
||
|
|
||
|
int
|
||
|
fmpz_mod_poly_factor_equal_deg_prob(fmpz_mod_poly_t factor,
|
||
|
flint_rand_t state,
|
||
|
const fmpz_mod_poly_t pol, slong d)
|
||
|
{
|
||
|
fmpz_mod_poly_t a, b, c, polinv;
|
||
|
fmpz_t exp, t, p;
|
||
|
int res = 1;
|
||
|
slong i;
|
||
|
|
||
|
if (pol->length <= 1)
|
||
|
{
|
||
|
flint_printf("Exception (fmpz_mod_poly_factor_equal_deg_prob): \n");
|
||
|
flint_printf("Input polynomial is linear.\n");
|
||
|
abort();
|
||
|
}
|
||
|
|
||
|
fmpz_init_set(p, &pol->p);
|
||
|
|
||
|
fmpz_mod_poly_init(a, p);
|
||
|
|
||
|
do
|
||
|
{
|
||
|
fmpz_mod_poly_randtest(a, state, pol->length - 1);
|
||
|
} while (a->length <= 1);
|
||
|
|
||
|
fmpz_mod_poly_gcd(factor, a, pol);
|
||
|
|
||
|
if (factor->length != 1)
|
||
|
{
|
||
|
fmpz_mod_poly_clear(a);
|
||
|
return 1;
|
||
|
}
|
||
|
|
||
|
fmpz_mod_poly_init(b, p);
|
||
|
fmpz_mod_poly_init(polinv, p);
|
||
|
|
||
|
fmpz_mod_poly_reverse(polinv, pol, pol->length);
|
||
|
fmpz_mod_poly_inv_series_newton(polinv, polinv, polinv->length);
|
||
|
|
||
|
fmpz_init(exp);
|
||
|
if (fmpz_cmp_ui(p, 2) > 0)
|
||
|
{
|
||
|
/* compute a^{(p^d-1)/2} rem pol */
|
||
|
fmpz_pow_ui(exp, p, d);
|
||
|
fmpz_sub_ui(exp, exp, 1);
|
||
|
fmpz_fdiv_q_2exp(exp, exp, 1);
|
||
|
|
||
|
fmpz_mod_poly_powmod_fmpz_binexp_preinv(b, a, exp, pol, polinv);
|
||
|
}
|
||
|
else
|
||
|
{
|
||
|
/* compute b = (a^{2^{d-1}}+a^{2^{d-2}}+...+a^4+a^2+a) rem pol */
|
||
|
fmpz_mod_poly_rem(b, a, pol);
|
||
|
fmpz_mod_poly_init(c, p);
|
||
|
fmpz_mod_poly_set(c, b);
|
||
|
for (i = 1; i < d; i++)
|
||
|
{
|
||
|
/* c = a^{2^i} = (a^{2^{i-1}})^2 */
|
||
|
fmpz_mod_poly_powmod_ui_binexp_preinv(c, c, 2, pol, polinv);
|
||
|
fmpz_mod_poly_add(b, b, c);
|
||
|
}
|
||
|
fmpz_mod_poly_rem(b, b, pol);
|
||
|
fmpz_mod_poly_clear(c);
|
||
|
}
|
||
|
fmpz_clear(exp);
|
||
|
|
||
|
fmpz_init(t);
|
||
|
fmpz_sub_ui(t, &(b->coeffs[0]), 1);
|
||
|
fmpz_mod(t, t, p);
|
||
|
fmpz_mod_poly_set_coeff_fmpz(b, 0, t);
|
||
|
fmpz_clear(t);
|
||
|
|
||
|
fmpz_mod_poly_gcd(factor, b, pol);
|
||
|
|
||
|
if ((factor->length <= 1) || (factor->length == pol->length))
|
||
|
res = 0;
|
||
|
|
||
|
fmpz_mod_poly_clear(a);
|
||
|
fmpz_mod_poly_clear(b);
|
||
|
fmpz_mod_poly_clear(polinv);
|
||
|
fmpz_clear(p);
|
||
|
|
||
|
return res;
|
||
|
}
|