flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2014 Alex J. Best
    Copyright (C) 2017 Tommy Hofmann

    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 "ulong_extras.h"
#include "nmod_mat.h"
#include "fmpz.h"
#include "fmpz_mat.h"

static void
_fmpz_mat_hnf_transform_naive(fmpz_mat_t H, fmpz_mat_t U, const fmpz_mat_t A)
{
    slong i, j, m, n;
    fmpz_mat_t A2, H2;

    m = fmpz_mat_nrows(A);
    n = fmpz_mat_ncols(A);

    fmpz_mat_init(A2, m, n + m);
    fmpz_mat_init(H2, m, n + m);

    /* append an identity matrix to the right of A */
    for (i = 0; i < m; i++)
    {
        for (j = 0; j < n; j++)
            fmpz_set(fmpz_mat_entry(A2, i, j), fmpz_mat_entry(A, i, j));
        fmpz_one(fmpz_mat_entry(A2, i, n + i));
    }

    fmpz_mat_hnf(H2, A2);

    /* recover H and U */
    for (i = 0; i < m; i++)
    {
        for (j = 0; j < n; j++)
            fmpz_set(fmpz_mat_entry(H, i, j), fmpz_mat_entry(H2, i, j));
        for (j = n; j < n + m; j++)
            fmpz_set(fmpz_mat_entry(U, i, j - n), fmpz_mat_entry(H2, i, j));
    }

    fmpz_mat_clear(A2);
    fmpz_mat_clear(H2);
}

void
fmpz_mat_hnf_transform(fmpz_mat_t H, fmpz_mat_t U, const fmpz_mat_t A)
{
    slong m, n, r, p;
    nmod_mat_t Amod;
    flint_rand_t state;

    m = fmpz_mat_nrows(A);
    n = fmpz_mat_ncols(A);

    if (n > m)
        _fmpz_mat_hnf_transform_naive(H, U, A);
    else
    {
        flint_rand_init(state);
        p = n_randprime(state, NMOD_MAT_OPTIMAL_MODULUS_BITS, 1);
        nmod_mat_init(Amod, m, n, p);

        fmpz_mat_get_nmod_mat(Amod, A);
        r = nmod_mat_rref(Amod);

        nmod_mat_clear(Amod);

        flint_rand_clear(state);

        if (r == n) /* Full column rank */
            fmpz_mat_hnf_minors_transform(H, U, A);
        else
            _fmpz_mat_hnf_transform_naive(H, U, A);
    }
}