96 lines
2.5 KiB
C
96 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 <stdlib.h>
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#include <gmp.h>
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#include "flint.h"
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#include "nmod_mat.h"
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slong
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nmod_mat_nullspace(nmod_mat_t X, const nmod_mat_t A)
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{
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slong i, j, k, m, n, rank, nullity;
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slong * p;
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slong * pivots;
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slong * nonpivots;
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nmod_mat_t tmp;
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m = A->r;
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n = A->c;
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p = flint_malloc(sizeof(slong) * FLINT_MAX(m, n));
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nmod_mat_init_set(tmp, A);
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rank = nmod_mat_rref(tmp);
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nullity = n - rank;
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nmod_mat_zero(X);
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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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nmod_mat_entry(X, i, i) = UWORD(1);
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}
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else if (nullity)
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{
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pivots = p; /* length = rank */
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nonpivots = p + rank; /* length = nullity */
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for (i = j = k = 0; i < rank; i++)
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{
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while (nmod_mat_entry(tmp, i, j) == UWORD(0))
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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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for (i = 0; i < nullity; i++)
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{
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for (j = 0; j < rank; j++)
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{
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mp_limb_t c = nmod_mat_entry(tmp, j, nonpivots[i]);
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nmod_mat_entry(X, pivots[j], i) = nmod_neg(c, A->mod);
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}
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nmod_mat_entry(X, nonpivots[i], i) = UWORD(1);
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}
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}
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flint_free(p);
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nmod_mat_clear(tmp);
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return nullity;
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}
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