92 lines
2.5 KiB
C
92 lines
2.5 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 Fredrik Johansson
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******************************************************************************/
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#include "fmpz_mat.h"
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slong
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fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat)
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{
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slong i, j, k, n, rank, nullity;
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slong * pivots;
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slong * nonpivots;
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fmpz_mat_t tmp;
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fmpz_t den;
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n = mat->c;
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fmpz_mat_init_set(tmp, mat);
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fmpz_init(den);
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rank = fmpz_mat_rref(tmp, den, mat);
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nullity = n - rank;
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fmpz_mat_zero(res);
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if (rank == 0)
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{
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for (i = 0; i < nullity; i++)
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fmpz_one(res->rows[i] + i);
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}
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else if (nullity)
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{
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pivots = flint_malloc(rank * sizeof(slong));
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nonpivots = flint_malloc(nullity * sizeof(slong));
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for (i = j = k = 0; i < rank; i++)
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{
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while (fmpz_is_zero(tmp->rows[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 < nullity)
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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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fmpz_set(den, tmp->rows[0] + pivots[0]);
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for (i = 0; i < nullity; i++)
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{
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for (j = 0; j < rank; j++)
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fmpz_set(res->rows[pivots[j]] + i, tmp->rows[j] + nonpivots[i]);
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fmpz_neg(res->rows[nonpivots[i]] + i, den);
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}
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flint_free(pivots);
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flint_free(nonpivots);
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}
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fmpz_clear(den);
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fmpz_mat_clear(tmp);
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return nullity;
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}
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