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/*
Copyright (C) 2014 Alex J. Best
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "fmpz_mat.h"
void fmpz_mat_snf_kannan_bachem(fmpz_mat_t S, const fmpz_mat_t A)
{
slong i, j, k, d, m, n;
fmpz_t r1g, r2g, b, u, v, g;
m = A->r;
n = A->c;
d = FLINT_MIN(m, n);
fmpz_init(r1g);
fmpz_init(r2g);
fmpz_init(b);
fmpz_init(u);
fmpz_init(v);
fmpz_init(g);
fmpz_mat_set(S, A);
for (k = 0; k != d; k++)
{
int col_done;
do
{
/* clear column */
for (i = k + 1; i != m; i++)
{
/* reduce row i - 1 with row i */
if (fmpz_is_zero(fmpz_mat_entry(S, i - 1, k)))
continue;
if (fmpz_cmpabs(fmpz_mat_entry(S, i, k),
fmpz_mat_entry(S, i - 1, k)) == 0)
{
if (fmpz_equal(fmpz_mat_entry(S, i, k),
fmpz_mat_entry(S, i - 1, k)))
{
for (j = k; j != n; j++)
fmpz_sub(fmpz_mat_entry(S, i - 1, j),
fmpz_mat_entry(S, i - 1, j),
fmpz_mat_entry(S, i, j));
}
else
{
for (j = k; j != n; j++)
fmpz_add(fmpz_mat_entry(S, i - 1, j),
fmpz_mat_entry(S, i - 1, j),
fmpz_mat_entry(S, i, j));
}
continue;
}
fmpz_xgcd(g, u, v, fmpz_mat_entry(S, i, k),
fmpz_mat_entry(S, i - 1, k));
fmpz_divexact(r2g, fmpz_mat_entry(S, i - 1, k), g);
fmpz_divexact(r1g, fmpz_mat_entry(S, i, k), g);
for (j = k; j != n; j++)
{
fmpz_mul(b, u, fmpz_mat_entry(S, i, j));
fmpz_addmul(b, v, fmpz_mat_entry(S, i - 1, j));
fmpz_mul(fmpz_mat_entry(S, i - 1, j), r1g,
fmpz_mat_entry(S, i - 1, j));
fmpz_submul(fmpz_mat_entry(S, i - 1, j), r2g,
fmpz_mat_entry(S, i, j));
fmpz_set(fmpz_mat_entry(S, i, j), b);
}
}
fmpz_mat_swap_rows(S, NULL, m - 1, k);
/* clear row */
for (j = k + 1; j != n; j++)
{
/* reduce col j with col k */
if (fmpz_is_zero(fmpz_mat_entry(S, k, j)))
continue;
if (fmpz_cmpabs(fmpz_mat_entry(S, k, k),
fmpz_mat_entry(S, k, j)) == 0)
{
if (fmpz_equal(fmpz_mat_entry(S, k, k),
fmpz_mat_entry(S, k, j)))
{
for (i = k; i != m; i++)
fmpz_sub(fmpz_mat_entry(S, i, j),
fmpz_mat_entry(S, i, j),
fmpz_mat_entry(S, i, k));
}
else
{
for (i = k; i != m; i++)
fmpz_add(fmpz_mat_entry(S, i, j),
fmpz_mat_entry(S, i, j),
fmpz_mat_entry(S, i, k));
}
continue;
}
fmpz_xgcd(g, u, v, fmpz_mat_entry(S, k, k),
fmpz_mat_entry(S, k, j));
fmpz_divexact(r2g, fmpz_mat_entry(S, k, j), g);
fmpz_divexact(r1g, fmpz_mat_entry(S, k, k), g);
for (i = k; i != m; i++)
{
fmpz_mul(b, u, fmpz_mat_entry(S, i, k));
fmpz_addmul(b, v, fmpz_mat_entry(S, i, j));
fmpz_mul(fmpz_mat_entry(S, i, j), r1g,
fmpz_mat_entry(S, i, j));
fmpz_submul(fmpz_mat_entry(S, i, j), r2g,
fmpz_mat_entry(S, i, k));
fmpz_set(fmpz_mat_entry(S, i, k), b);
}
}
col_done = 1;
for (i = 0; i != m; i++)
col_done &= (i == k) || fmpz_is_zero(fmpz_mat_entry(S, i, k));
}
while (!col_done);
if (fmpz_sgn(fmpz_mat_entry(S, k, k)) < 0)
fmpz_neg(fmpz_mat_entry(S, k, k), fmpz_mat_entry(S, k, k));
}
fmpz_clear(r2g);
fmpz_clear(r1g);
fmpz_clear(b);
fmpz_clear(u);
fmpz_clear(v);
fmpz_clear(g);
fmpz_mat_snf_diagonal(S, S);
}