181 lines
5.5 KiB
C
181 lines
5.5 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
|
|
Copyright (C) 2013 Mike Hansen
|
|
|
|
******************************************************************************/
|
|
|
|
|
|
#ifdef T
|
|
|
|
#include "templates.h"
|
|
|
|
#include "ulong_extras.h"
|
|
|
|
void
|
|
TEMPLATE(T, poly_factor_squarefree) (TEMPLATE(T, poly_factor_t) res,
|
|
const TEMPLATE(T, poly_t) f,
|
|
const TEMPLATE(T, ctx_t) ctx)
|
|
{
|
|
TEMPLATE(T, poly_t) f_d, g, g_1, r;
|
|
TEMPLATE(T, t) x;
|
|
fmpz_t p;
|
|
slong deg, i, p_ui;
|
|
|
|
if (f->length <= 1)
|
|
{
|
|
res->num = 0;
|
|
return;
|
|
}
|
|
|
|
if (f->length == 2)
|
|
{
|
|
TEMPLATE(T, poly_factor_insert) (res, f, 1, ctx);
|
|
return;
|
|
}
|
|
|
|
fmpz_init(p);
|
|
fmpz_set(p, TEMPLATE(T, ctx_prime) (ctx));
|
|
|
|
deg = TEMPLATE(T, poly_degree) (f, ctx);
|
|
|
|
/* 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) */
|
|
|
|
TEMPLATE(T, init) (x, ctx);
|
|
TEMPLATE(T, poly_init) (g_1, ctx);
|
|
TEMPLATE(T, poly_init) (f_d, ctx);
|
|
TEMPLATE(T, poly_init) (g, ctx);
|
|
TEMPLATE(T, poly_derivative) (f_d, f, ctx);
|
|
|
|
/* Case 1 */
|
|
if (TEMPLATE(T, poly_is_zero) (f_d, ctx))
|
|
{
|
|
TEMPLATE(T, poly_factor_t) new_res;
|
|
TEMPLATE(T, poly_t) h;
|
|
|
|
/* We can do this since deg is a multiple of p in this case */
|
|
p_ui = fmpz_get_ui(p);
|
|
|
|
TEMPLATE(T, poly_init) (h, ctx);
|
|
|
|
for (i = 0; i <= deg / p_ui; i++) /* this will be an integer since f'=0 */
|
|
{
|
|
TEMPLATE(T, poly_get_coeff) (x, f, i * p_ui, ctx);
|
|
TEMPLATE(T, pth_root) (x, x, ctx);
|
|
TEMPLATE(T, poly_set_coeff) (h, i, x, ctx);
|
|
}
|
|
|
|
/* Now run squarefree on h, and return it to the pth power */
|
|
TEMPLATE(T, poly_factor_init) (new_res, ctx);
|
|
|
|
TEMPLATE(T, poly_factor_squarefree) (new_res, h, ctx);
|
|
TEMPLATE(T, poly_factor_pow) (new_res, p_ui, ctx);
|
|
|
|
TEMPLATE(T, poly_factor_concat) (res, new_res, ctx);
|
|
TEMPLATE(T, poly_clear) (h, ctx);
|
|
TEMPLATE(T, poly_factor_clear) (new_res, ctx);
|
|
}
|
|
else
|
|
{
|
|
TEMPLATE(T, poly_t) h, z;
|
|
|
|
TEMPLATE(T, poly_init) (r, ctx);
|
|
|
|
TEMPLATE(T, poly_gcd) (g, f, f_d, ctx);
|
|
TEMPLATE(T, poly_divrem) (g_1, r, f, g, ctx);
|
|
|
|
i = 1;
|
|
|
|
TEMPLATE(T, poly_init) (h, ctx);
|
|
TEMPLATE(T, poly_init) (z, ctx);
|
|
|
|
/* Case 2 */
|
|
while (g_1->length > 1)
|
|
{
|
|
TEMPLATE(T, poly_gcd) (h, g_1, g, ctx);
|
|
TEMPLATE(T, poly_divrem) (z, r, g_1, h, ctx);
|
|
|
|
/* out <- out.z */
|
|
if (z->length > 1)
|
|
{
|
|
TEMPLATE(T, poly_factor_insert) (res, z, 1, ctx);
|
|
TEMPLATE(T, poly_make_monic) (res->poly + (res->num - 1),
|
|
res->poly + (res->num - 1), ctx);
|
|
if (res->num)
|
|
res->exp[res->num - 1] *= i;
|
|
}
|
|
|
|
i++;
|
|
TEMPLATE(T, poly_set) (g_1, h, ctx);
|
|
TEMPLATE(T, poly_divrem) (g, r, g, h, ctx);
|
|
}
|
|
|
|
TEMPLATE(T, poly_clear) (h, ctx);
|
|
TEMPLATE(T, poly_clear) (z, ctx);
|
|
TEMPLATE(T, poly_clear) (r, ctx);
|
|
|
|
TEMPLATE(T, poly_make_monic) (g, g, ctx);
|
|
|
|
if (g->length > 1)
|
|
{
|
|
/* so now we multiply res with squarefree(g^1/p) ^ p */
|
|
TEMPLATE(T, poly_t) g_p; /* g^(1/p) */
|
|
TEMPLATE(T, poly_factor_t) new_res_2;
|
|
|
|
TEMPLATE(T, poly_init) (g_p, ctx);
|
|
|
|
p_ui = fmpz_get_ui(p);
|
|
|
|
for (i = 0; i <= TEMPLATE(T, poly_degree) (g, ctx) / p_ui; i++)
|
|
{
|
|
TEMPLATE(T, poly_get_coeff) (x, g, i * p_ui, ctx);
|
|
TEMPLATE(T, pth_root) (x, x, ctx);
|
|
TEMPLATE(T, poly_set_coeff) (g_p, i, x, ctx);
|
|
}
|
|
|
|
TEMPLATE(T, poly_factor_init) (new_res_2, ctx);
|
|
|
|
/* squarefree(g^(1/p)) */
|
|
TEMPLATE(T, poly_factor_squarefree) (new_res_2, g_p, ctx);
|
|
TEMPLATE(T, poly_factor_pow) (new_res_2, p_ui, ctx);
|
|
|
|
TEMPLATE(T, poly_factor_concat) (res, new_res_2, ctx);
|
|
TEMPLATE(T, poly_clear) (g_p, ctx);
|
|
TEMPLATE(T, poly_factor_clear) (new_res_2, ctx);
|
|
}
|
|
}
|
|
|
|
fmpz_clear(p);
|
|
TEMPLATE(T, clear) (x, ctx);
|
|
TEMPLATE(T, poly_clear) (g_1, ctx);
|
|
TEMPLATE(T, poly_clear) (f_d, ctx);
|
|
TEMPLATE(T, poly_clear) (g, ctx);
|
|
}
|
|
|
|
|
|
#endif
|