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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) 2010, 2013 Fredrik Johansson
******************************************************************************/
#include "arith.h"
void arith_stirling_number_1u_vec_next(fmpz * row,
const fmpz * prev, slong n, slong klen)
{
slong k;
if (klen > n) fmpz_one(row + n);
if (n != 0 && klen != 0) fmpz_zero(row);
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
{
fmpz_mul_ui(row + k, prev + k, n - UWORD(1));
fmpz_add(row + k, prev + k - 1, row + k);
}
for (k = n + 1; k < klen; k++)
fmpz_zero(row + k);
}
void arith_stirling_number_1_vec_next(fmpz * row,
const fmpz * prev, slong n, slong klen)
{
slong k;
if (klen > n) fmpz_one(row + n);
if (n != 0 && klen != 0) fmpz_zero(row);
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
{
fmpz_mul_ui(row + k, prev + k, n - UWORD(1));
fmpz_sub(row + k, prev + k - 1, row + k);
}
for (k = n + 1; k < klen; k++)
fmpz_zero(row + k);
}
void arith_stirling_number_2_vec_next(fmpz * row,
const fmpz * prev, slong n, slong klen)
{
slong k;
if (klen > n) fmpz_one(row + n);
if (n != 0 && klen != 0) fmpz_zero(row);
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
{
fmpz_mul_ui(row + k, prev + k, k);
fmpz_add(row + k, prev + k - 1, row + k);
}
for (k = n + 1; k < klen; k++)
fmpz_zero(row + k);
}
void
arith_stirling_matrix_1u(fmpz_mat_t mat)
{
slong n;
if (fmpz_mat_is_empty(mat))
return;
for (n = 0; n < mat->r; n++)
arith_stirling_number_1u_vec_next(mat->rows[n],
mat->rows[n - (n != 0)], n, mat->c);
}
void
arith_stirling_matrix_1(fmpz_mat_t mat)
{
slong n;
if (fmpz_mat_is_empty(mat))
return;
for (n = 0; n < mat->r; n++)
arith_stirling_number_1_vec_next(mat->rows[n],
mat->rows[n - (n != 0)], n, mat->c);
}
void
arith_stirling_matrix_2(fmpz_mat_t mat)
{
slong n;
if (fmpz_mat_is_empty(mat))
return;
for (n = 0; n < mat->r; n++)
arith_stirling_number_2_vec_next(mat->rows[n],
mat->rows[n - (n != 0)], n, mat->c);
}
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