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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) 2012 Lina Kulakova
Copyright (C) 2013 Martin Lee
******************************************************************************/
#undef ulong
#define ulong ulongxx/* interferes with system includes */
#include <math.h>
#undef ulong
#include <gmp.h>
#define ulong mp_limb_t
#include "fmpz_mod_poly.h"
int fmpz_mod_poly_is_irreducible_ddf(const fmpz_mod_poly_t poly)
{
fmpz_mod_poly_t f, v, vinv, reducedH0, tmp;
fmpz_mod_poly_t *h, *H, *I;
slong i, j, l, m, n, d;
fmpz_t p;
double beta;
int result = 1;
n = fmpz_mod_poly_degree(poly);
if (n < 2)
return 1;
if (!fmpz_mod_poly_is_squarefree(poly))
return 0;
beta = 0.5 * (1. - (log(2) / log(n)));
l = ceil(pow(n, beta));
m = ceil(0.5 * n / l);
/* initialization */
fmpz_init(p);
fmpz_set(p, &poly->p);
fmpz_mod_poly_init(f, p);
fmpz_mod_poly_init(v, p);
fmpz_mod_poly_init(vinv, p);
fmpz_mod_poly_init(reducedH0, p);
fmpz_mod_poly_init(tmp, p);
if (!(h = flint_malloc((2 * m + l + 1) * sizeof(fmpz_mod_poly_struct))))
{
flint_printf("Exception (fmpz_mod_poly_is_irreducible_ddf): \n");
flint_printf("Not enough memory.\n");
abort();
}
H = h + (l + 1);
I = H + m;
for (i = 0; i < l + 1; i++)
fmpz_mod_poly_init(h[i], p);
for (i = 0; i < m; i++)
{
fmpz_mod_poly_init(H[i], p);
fmpz_mod_poly_init(I[i], p);
}
fmpz_mod_poly_make_monic(v, poly);
fmpz_mod_poly_reverse (vinv, v, v->length);
fmpz_mod_poly_inv_series_newton (vinv, vinv, v->length);
/* compute baby steps: h[i]=x^{p^i}mod v */
fmpz_mod_poly_set_coeff_ui(h[0], 1, 1);
for (i = 1; i < l + 1; i++)
fmpz_mod_poly_powmod_fmpz_binexp_preinv(h[i], h[i - 1], p, v, vinv);
/* compute coarse distinct-degree factorisation */
fmpz_mod_poly_set(H[0], h[l]);
fmpz_mod_poly_set(reducedH0, H[0]);
d = 1;
for (j = 0; j < m; j++)
{
/* compute giant steps: H[i]=x^{p^(li)}mod v */
if (j > 0)
{
fmpz_mod_poly_rem (reducedH0, reducedH0, v);
fmpz_mod_poly_rem (tmp, H[j-1], v);
fmpz_mod_poly_compose_mod_brent_kung_preinv(H[j], tmp, reducedH0,
v, vinv);
}
/* compute interval polynomials */
fmpz_mod_poly_set_coeff_ui(I[j], 0, 1);
for (i = l - 1; (i >= 0) && (2*d <= v->length - 1); i--, d++)
{
fmpz_mod_poly_rem(tmp, h[i], v);
fmpz_mod_poly_sub(tmp, H[j], tmp);
fmpz_mod_poly_mulmod_preinv (I[j], tmp, I[j], v, vinv);
}
/* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */
/* F_j is stored on the place of I_j */
fmpz_mod_poly_gcd(I[j], v, I[j]);
if (I[j]->length > 1)
{
result = 0;
break;
}
}
fmpz_clear(p);
fmpz_mod_poly_clear(f);
fmpz_mod_poly_clear(reducedH0);
fmpz_mod_poly_clear(v);
fmpz_mod_poly_clear(vinv);
fmpz_mod_poly_clear(tmp);
for (i = 0; i < l + 1; i++)
fmpz_mod_poly_clear(h[i]);
for (i = 0; i < m; i++)
{
fmpz_mod_poly_clear(H[i]);
fmpz_mod_poly_clear(I[i]);
}
flint_free(h);
return result;
}
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