File: det_cofactor.c

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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();
    }
}