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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) 2010,2011 Fredrik Johansson
******************************************************************************/
#include "fmpz_mat.h"
void
_fmpz_mat_det_cofactor_2x2(fmpz_t det, fmpz ** const x)
{
fmpz_t t;
fmpz_init(t);
fmpz_mul (t, &x[0][0], &x[1][1]);
fmpz_submul(t, &x[0][1], &x[1][0]);
fmpz_set(det, t);
fmpz_clear(t);
}
void
_fmpz_mat_det_cofactor_3x3(fmpz_t det, fmpz ** const x)
{
fmpz_t a, t;
fmpz_init(a);
fmpz_init(t);
fmpz_mul (a, &x[1][0], &x[2][1]);
fmpz_submul(a, &x[1][1], &x[2][0]);
fmpz_mul (t, a, &x[0][2]);
fmpz_mul (a, &x[1][2], &x[2][0]);
fmpz_submul(a, &x[1][0], &x[2][2]);
fmpz_addmul(t, a, &x[0][1]);
fmpz_mul (a, &x[1][1], &x[2][2]);
fmpz_submul(a, &x[1][2], &x[2][1]);
fmpz_addmul(t, a, &x[0][0]);
fmpz_set(det, t);
fmpz_clear(a);
fmpz_clear(t);
}
void
_fmpz_mat_det_cofactor_4x4(fmpz_t det, fmpz ** const x)
{
fmpz_t a, b, t;
fmpz_init(a);
fmpz_init(b);
fmpz_init(t);
fmpz_mul (a, &x[0][3], &x[1][2]);
fmpz_submul(a, &x[0][2], &x[1][3]);
fmpz_mul (b, &x[2][1], &x[3][0]);
fmpz_submul(b, &x[2][0], &x[3][1]);
fmpz_mul(t, a, b);
fmpz_mul (a, &x[0][1], &x[1][3]);
fmpz_submul(a, &x[0][3], &x[1][1]);
fmpz_mul (b, &x[2][2], &x[3][0]);
fmpz_submul(b, &x[2][0], &x[3][2]);
fmpz_addmul(t, a, b);
fmpz_mul (a, &x[0][2], &x[1][1]);
fmpz_submul(a, &x[0][1], &x[1][2]);
fmpz_mul (b, &x[2][3], &x[3][0]);
fmpz_submul(b, &x[2][0], &x[3][3]);
fmpz_addmul(t, a, b);
fmpz_mul (a, &x[0][3], &x[1][0]);
fmpz_submul(a, &x[0][0], &x[1][3]);
fmpz_mul (b, &x[2][2], &x[3][1]);
fmpz_submul(b, &x[2][1], &x[3][2]);
fmpz_addmul(t, a, b);
fmpz_mul (a, &x[0][0], &x[1][2]);
fmpz_submul(a, &x[0][2], &x[1][0]);
fmpz_mul (b, &x[2][3], &x[3][1]);
fmpz_submul(b, &x[2][1], &x[3][3]);
fmpz_addmul(t, a, b);
fmpz_mul (a, &x[0][1], &x[1][0]);
fmpz_submul(a, &x[0][0], &x[1][1]);
fmpz_mul (b, &x[2][3], &x[3][2]);
fmpz_submul(b, &x[2][2], &x[3][3]);
fmpz_addmul(t, a, b);
fmpz_set(det, t);
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(t);
}
void
fmpz_mat_det_cofactor(fmpz_t det, const fmpz_mat_t A)
{
slong dim = A->r;
switch (dim)
{
case 0: fmpz_one(det); break;
case 1: fmpz_set(det, A->rows[0]); break;
case 2: _fmpz_mat_det_cofactor_2x2(det, A->rows); break;
case 3: _fmpz_mat_det_cofactor_3x3(det, A->rows); break;
case 4: _fmpz_mat_det_cofactor_4x4(det, A->rows); break;
default:
flint_printf("Exception (fmpz_mat_det_cofactor). dim > 4 not implemented.");
abort();
}
}
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