88 lines
2.3 KiB
C
88 lines
2.3 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) 2010 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "arith.h"
|
|
#include "fmpz.h"
|
|
|
|
/* note: destroys factors! */
|
|
void
|
|
_arith_divisor_sigma(fmpz_t res, const fmpz_factor_t factors, ulong k)
|
|
{
|
|
slong i;
|
|
fmpz * p;
|
|
fmpz_t r;
|
|
|
|
fmpz_one(res);
|
|
|
|
if (factors->num == 0)
|
|
return;
|
|
|
|
fmpz_init(r);
|
|
|
|
if (k == 0)
|
|
{
|
|
for (i = 0; i < factors->num; i++)
|
|
{
|
|
fmpz_set_ui(r, factors->exp[i] + UWORD(1));
|
|
fmpz_mul(res, res, r);
|
|
}
|
|
return;
|
|
}
|
|
else
|
|
{
|
|
for (i = 0; i < factors->num; i++)
|
|
{
|
|
p = factors->p + i;
|
|
fmpz_set(p, factors->p + i);
|
|
fmpz_pow_ui(p, p, k);
|
|
fmpz_pow_ui(r, p, factors->exp[i] + UWORD(1));
|
|
fmpz_sub_ui(r, r, UWORD(1));
|
|
fmpz_sub_ui(p, p, UWORD(1));
|
|
fmpz_divexact(p, r, p);
|
|
}
|
|
|
|
_fmpz_vec_prod(res, factors->p, factors->num);
|
|
}
|
|
|
|
fmpz_clear(r);
|
|
}
|
|
|
|
void
|
|
arith_divisor_sigma(fmpz_t res, const fmpz_t n, ulong k)
|
|
{
|
|
fmpz_factor_t factors;
|
|
|
|
if (fmpz_is_zero(n))
|
|
{
|
|
fmpz_zero(res);
|
|
return;
|
|
}
|
|
|
|
fmpz_factor_init(factors);
|
|
fmpz_factor(factors, n);
|
|
_arith_divisor_sigma(res, factors, k);
|
|
fmpz_factor_clear(factors);
|
|
}
|