Exemple #1
0
long
nmod_poly_mat_nullspace(nmod_poly_mat_t res, const nmod_poly_mat_t mat)
{
    long i, j, k, m, n, rank, nullity;
    long * pivots;
    long * nonpivots;
    nmod_poly_mat_t tmp;
    nmod_poly_t den;

    m = mat->r;
    n = mat->c;

    nmod_poly_init(den, nmod_poly_mat_modulus(mat));
    nmod_poly_mat_init_set(tmp, mat);
    rank = nmod_poly_mat_rref(tmp, den, NULL, tmp);
    nullity = n - rank;

    nmod_poly_mat_zero(res);

    if (rank == 0)
    {
        for (i = 0; i < nullity; i++)
            nmod_poly_one(res->rows[i] + i);
    }
    else if (nullity)
    {
        pivots = flint_malloc(rank * sizeof(long));
        nonpivots = flint_malloc(nullity * sizeof(long));

        for (i = j = k = 0; i < rank; i++)
        {
            while (nmod_poly_is_zero(tmp->rows[i] + j))
            {
                nonpivots[k] = j;
                k++;
                j++;
            }
            pivots[i] = j;
            j++;
        }
        while (k < nullity)
        {
            nonpivots[k] = j;
            k++;
            j++;
        }

        nmod_poly_set(den, tmp->rows[0] + pivots[0]);

        for (i = 0; i < nullity; i++)
        {
            for (j = 0; j < rank; j++)
                nmod_poly_set(res->rows[pivots[j]] + i,
                              tmp->rows[j] + nonpivots[i]);
            nmod_poly_neg(res->rows[nonpivots[i]] + i, den);
        }

        flint_free(pivots);
        flint_free(nonpivots);
    }

    nmod_poly_clear(den);
    nmod_poly_mat_clear(tmp);
    return nullity;
}
Exemple #2
0
int
nmod_poly_mat_inv(nmod_poly_mat_t Ainv, nmod_poly_t den,
                    const nmod_poly_mat_t A)
{
    slong n = nmod_poly_mat_nrows(A);

    if (n == 0)
    {
        nmod_poly_one(den);
        return 1;
    }
    else if (n == 1)
    {
        nmod_poly_set(den, E(A, 0, 0));
        nmod_poly_one(E(Ainv, 0, 0));
        return !nmod_poly_is_zero(den);
    }
    else if (n == 2)
    {
        nmod_poly_mat_det(den, A);

        if (nmod_poly_is_zero(den))
        {
            return 0;
        }
        else if (Ainv == A)
        {
            nmod_poly_swap(E(A, 0, 0), E(A, 1, 1));
            nmod_poly_neg(E(A, 0, 1), E(A, 0, 1));
            nmod_poly_neg(E(A, 1, 0), E(A, 1, 0));
            return 1;
        }
        else
        {
            nmod_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
            nmod_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
            nmod_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
            nmod_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
            return 1;
        }
    }
    else
    {
        nmod_poly_mat_t LU, I;
        slong * perm;
        int result;

        perm = _perm_init(n);
        nmod_poly_mat_init_set(LU, A);
        result = (nmod_poly_mat_fflu(LU, den, perm, LU, 1) == n);

        if (result)
        {
            nmod_poly_mat_init(I, n, n, nmod_poly_mat_modulus(A));
            nmod_poly_mat_one(I);
            nmod_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
            nmod_poly_mat_clear(I);
        }
        else
            nmod_poly_zero(den);

        if (_perm_parity(perm, n))
        {
            nmod_poly_mat_neg(Ainv, Ainv);
            nmod_poly_neg(den, den);
        }

        _perm_clear(perm);
        nmod_poly_mat_clear(LU);
        return result;
    }
}