109 lines
2.6 KiB
C
109 lines
2.6 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) 2011 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "arith.h"
|
|
|
|
static void
|
|
theta3_qexp(fmpz * r, slong n)
|
|
{
|
|
slong i, j;
|
|
|
|
_fmpz_vec_zero(r, n);
|
|
|
|
for (i = j = 0; j < n; i++)
|
|
{
|
|
fmpz_set_ui(r + j, i == 0 ? 1 : 2);
|
|
j += 1 + 2*i;
|
|
}
|
|
}
|
|
|
|
static void
|
|
theta3_qexp_squared(fmpz * r, slong n)
|
|
{
|
|
slong i, j, x, y;
|
|
|
|
_fmpz_vec_zero(r, n);
|
|
|
|
for (x = i = 0; x < n; i++)
|
|
{
|
|
for (y = j = 0; x + y < n; j++)
|
|
{
|
|
fmpz_add_ui(r + x + y, r + x + y, (x ? 2 : 1) * (y ? 2 : 1));
|
|
y += 2 * j + 1;
|
|
}
|
|
x += 2 * i + 1;
|
|
}
|
|
}
|
|
|
|
void
|
|
arith_sum_of_squares_vec(fmpz * r, ulong k, slong n)
|
|
{
|
|
if (k == 0 || n <= 1)
|
|
{
|
|
_fmpz_vec_zero(r, n);
|
|
if (n > 0)
|
|
fmpz_set_ui(r, 1);
|
|
}
|
|
else if (k == 1)
|
|
{
|
|
theta3_qexp(r, n);
|
|
}
|
|
else if (k == 2)
|
|
{
|
|
theta3_qexp_squared(r, n);
|
|
}
|
|
else if (k % 2 == 0)
|
|
{
|
|
fmpz * t = _fmpz_vec_init(n);
|
|
|
|
theta3_qexp_squared(t, n);
|
|
_fmpz_poly_pow_trunc(r, t, k / 2, n);
|
|
_fmpz_vec_clear(t, n);
|
|
}
|
|
else
|
|
{
|
|
fmpz *t, *u;
|
|
t = _fmpz_vec_init(n);
|
|
u = _fmpz_vec_init(n);
|
|
|
|
theta3_qexp_squared(t, n);
|
|
|
|
if (k == 3)
|
|
{
|
|
theta3_qexp(u, n);
|
|
_fmpz_poly_mullow(r, t, n, u, n, n);
|
|
}
|
|
else
|
|
{
|
|
_fmpz_poly_pow_trunc(u, t, (k - 1) / 2, n);
|
|
theta3_qexp(t, n);
|
|
_fmpz_poly_mullow(r, t, n, u, n, n);
|
|
}
|
|
|
|
_fmpz_vec_clear(t, n);
|
|
_fmpz_vec_clear(u, n);
|
|
}
|
|
}
|