109 lines
2.6 KiB
C
109 lines
2.6 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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static void
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theta3_qexp(fmpz * r, slong n)
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{
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slong i, j;
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_fmpz_vec_zero(r, n);
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for (i = j = 0; j < n; i++)
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{
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fmpz_set_ui(r + j, i == 0 ? 1 : 2);
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j += 1 + 2*i;
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}
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}
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static void
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theta3_qexp_squared(fmpz * r, slong n)
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{
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slong i, j, x, y;
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_fmpz_vec_zero(r, n);
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for (x = i = 0; x < n; i++)
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{
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for (y = j = 0; x + y < n; j++)
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{
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fmpz_add_ui(r + x + y, r + x + y, (x ? 2 : 1) * (y ? 2 : 1));
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y += 2 * j + 1;
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}
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x += 2 * i + 1;
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}
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}
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void
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arith_sum_of_squares_vec(fmpz * r, ulong k, slong n)
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{
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if (k == 0 || n <= 1)
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{
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_fmpz_vec_zero(r, n);
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if (n > 0)
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fmpz_set_ui(r, 1);
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}
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else if (k == 1)
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{
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theta3_qexp(r, n);
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}
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else if (k == 2)
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{
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theta3_qexp_squared(r, n);
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}
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else if (k % 2 == 0)
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{
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fmpz * t = _fmpz_vec_init(n);
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theta3_qexp_squared(t, n);
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_fmpz_poly_pow_trunc(r, t, k / 2, n);
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_fmpz_vec_clear(t, n);
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}
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else
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{
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fmpz *t, *u;
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t = _fmpz_vec_init(n);
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u = _fmpz_vec_init(n);
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theta3_qexp_squared(t, n);
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if (k == 3)
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{
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theta3_qexp(u, n);
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_fmpz_poly_mullow(r, t, n, u, n, n);
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}
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else
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{
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_fmpz_poly_pow_trunc(u, t, (k - 1) / 2, n);
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theta3_qexp(t, n);
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_fmpz_poly_mullow(r, t, n, u, n, n);
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}
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_fmpz_vec_clear(t, n);
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_fmpz_vec_clear(u, n);
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}
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}
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