112 lines
3.4 KiB
C
112 lines
3.4 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) 2011-2012 Fredrik Johansson
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******************************************************************************/
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#include "flint.h"
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#include "nmod_poly.h"
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#include "nmod_poly_mat.h"
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slong
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nmod_poly_mat_rref(nmod_poly_mat_t R, nmod_poly_t den, const nmod_poly_mat_t A)
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{
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slong i, j, k, m, n, rank;
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slong *pivots, *nonpivots;
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rank = nmod_poly_mat_fflu(R, den, NULL, A, 0);
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m = nmod_poly_mat_nrows(R);
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n = nmod_poly_mat_ncols(R);
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/* clear bottom */
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for (i = rank; i < m; i++)
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for (j = 0; j < n; j++)
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nmod_poly_zero(nmod_poly_mat_entry(R, i, j));
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/* Convert row echelon form to reduced row echelon form */
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if (rank > 1)
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{
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nmod_poly_t tmp, tmp2;
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nmod_poly_init(tmp, nmod_poly_mat_modulus(R));
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nmod_poly_init(tmp2, nmod_poly_mat_modulus(R));
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pivots = flint_malloc(sizeof(slong) * n);
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nonpivots = pivots + rank;
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/* find pivot positions */
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for (i = j = k = 0; i < rank; i++)
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{
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while (nmod_poly_is_zero(nmod_poly_mat_entry(R, i, j)))
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{
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nonpivots[k] = j;
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k++;
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j++;
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}
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pivots[i] = j;
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j++;
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}
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while (k < n - rank)
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{
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nonpivots[k] = j;
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k++;
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j++;
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}
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for (k = 0; k < n - rank; k++)
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{
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for (i = rank - 2; i >= 0; i--)
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{
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nmod_poly_mul(tmp, den, nmod_poly_mat_entry(R, i, nonpivots[k]));
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for (j = i + 1; j < rank; j++)
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{
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nmod_poly_mul(tmp2, nmod_poly_mat_entry(R, i, pivots[j]),
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nmod_poly_mat_entry(R, j, nonpivots[k]));
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nmod_poly_sub(tmp, tmp, tmp2);
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}
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nmod_poly_div(nmod_poly_mat_entry(R, i, nonpivots[k]),
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tmp, nmod_poly_mat_entry(R, i, pivots[i]));
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}
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}
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/* clear pivot columns */
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for (i = 0; i < rank; i++)
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{
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for (j = 0; j < rank; j++)
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{
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if (i == j)
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nmod_poly_set(nmod_poly_mat_entry(R, j, pivots[i]), den);
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else
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nmod_poly_zero(nmod_poly_mat_entry(R, j, pivots[i]));
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}
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}
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flint_free(pivots);
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nmod_poly_clear(tmp);
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nmod_poly_clear(tmp2);
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}
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return rank;
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}
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