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