ALL: Add flint

2014-05-19 00:03:37 +02:00
parent a15ef46ea6
commit d51d8e3652
3752 changed files with 446416 additions and 0 deletions
--- a/external/flint-2.4.3/nmod_poly_mat/rref.c
+++ b/external/flint-2.4.3/nmod_poly_mat/rref.c
@@ -0,0 +1,111 @@
+/*=============================================================================
+
+    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) 2011-2012 Fredrik Johansson
+
+******************************************************************************/
+
+#include "flint.h"
+#include "nmod_poly.h"
+#include "nmod_poly_mat.h"
+
+slong
+nmod_poly_mat_rref(nmod_poly_mat_t R, nmod_poly_t den, const nmod_poly_mat_t A)
+{
+    slong i, j, k, m, n, rank;
+    slong *pivots, *nonpivots;
+
+    rank = nmod_poly_mat_fflu(R, den, NULL, A, 0);
+    m = nmod_poly_mat_nrows(R);
+    n = nmod_poly_mat_ncols(R);
+
+    /* clear bottom */
+    for (i = rank; i < m; i++)
+        for (j = 0; j < n; j++)
+            nmod_poly_zero(nmod_poly_mat_entry(R, i, j));
+
+    /* Convert row echelon form to reduced row echelon form */
+    if (rank > 1)
+    {
+        nmod_poly_t tmp, tmp2;
+        nmod_poly_init(tmp, nmod_poly_mat_modulus(R));
+        nmod_poly_init(tmp2, nmod_poly_mat_modulus(R));
+
+        pivots = flint_malloc(sizeof(slong) * n);
+        nonpivots = pivots + rank;
+
+        /* find pivot positions */
+        for (i = j = k = 0; i < rank; i++)
+        {
+            while (nmod_poly_is_zero(nmod_poly_mat_entry(R, i, j)))
+            {
+                nonpivots[k] = j;
+                k++;
+                j++;
+            }
+            pivots[i] = j;
+            j++;
+        }
+        while (k < n - rank)
+        {
+            nonpivots[k] = j;
+            k++;
+            j++;
+        }
+
+        for (k = 0; k < n - rank; k++)
+        {
+            for (i = rank - 2; i >= 0; i--)
+            {
+                nmod_poly_mul(tmp, den, nmod_poly_mat_entry(R, i, nonpivots[k]));
+
+                for (j = i + 1; j < rank; j++)
+                {
+                    nmod_poly_mul(tmp2, nmod_poly_mat_entry(R, i, pivots[j]),
+                        nmod_poly_mat_entry(R, j, nonpivots[k]));
+                    nmod_poly_sub(tmp, tmp, tmp2);
+                }
+
+                nmod_poly_div(nmod_poly_mat_entry(R, i, nonpivots[k]),
+                    tmp, nmod_poly_mat_entry(R, i, pivots[i]));
+            }
+        }
+
+        /* clear pivot columns */
+        for (i = 0; i < rank; i++)
+        {
+            for (j = 0; j < rank; j++)
+            {
+                if (i == j)
+                    nmod_poly_set(nmod_poly_mat_entry(R, j, pivots[i]), den);
+                else
+                    nmod_poly_zero(nmod_poly_mat_entry(R, j, pivots[i]));
+            }
+        }
+
+        flint_free(pivots);
+        nmod_poly_clear(tmp);
+        nmod_poly_clear(tmp2);
+    }
+
+    return rank;
+}
+