Get determinant expression for a 4x4 matrix

determinant.py

# Get determinant expression for a matrix.
# Works for 4x4 matrix only because Rule of Sarrus is used. Can be adapted for any size by using
# recursive algorithm.

M = []
SIZE = 4


def Minor(rowIdx):
    """
    :param rowIdx: Row index for minor submatrix. Assuming column 0.
    :return: Minor submatrix.
    """
    m = []
    for i in range(0, SIZE):
        if i == rowIdx:
            continue
        row = [M[i][j] for j in range(1, SIZE)]
        m.append(row)
    return m


def MinorDet(m):
    """
    :param m: Minor submatrix.
    :return: Expression of minor determinant, defined by Rule of Sarrus.
    """
    return (m[0][0] + "*" + m[1][1] + "*" + m[2][2] + " + " +
            m[0][1] + "*" + m[1][2] + "*" + m[2][0] + " + " +
            m[0][2] + "*" + m[1][0] + "*" + m[2][1] + " - " +
            m[2][0] + "*" + m[1][1] + "*" + m[0][2] + " - " +
            m[2][1] + "*" + m[1][2] + "*" + m[0][0] + " - " +
            m[2][2] + "*" + m[1][0] + "*" + m[0][1])


for i in range(0, SIZE):
    # Members naming is defined here
    row = ["a" + str(i) + str(j) for j in range(0, SIZE)]
    M.append(row)


print(M[0][0] + " * (" + MinorDet(Minor(0)) + ") -\n" +
      M[1][0] + " * (" + MinorDet(Minor(1)) + ") +\n" +
      M[2][0] + " * (" + MinorDet(Minor(2)) + ") -\n" +
      M[3][0] + " * (" + MinorDet(Minor(3)) + ")\n")

Result for used naming:
a00 * (a11*a22*a33 + a12*a23*a31 + a13*a21*a32 - a31*a22*a13 - a32*a23*a11 - a33*a21*a12) -
a10 * (a01*a22*a33 + a02*a23*a31 + a03*a21*a32 - a31*a22*a03 - a32*a23*a01 - a33*a21*a02) +
a20 * (a01*a12*a33 + a02*a13*a31 + a03*a11*a32 - a31*a12*a03 - a32*a13*a01 - a33*a11*a02) -
a30 * (a01*a12*a23 + a02*a13*a21 + a03*a11*a22 - a21*a12*a03 - a22*a13*a01 - a23*a11*a02)

Use with caution since such operations order may lose precision. Check this variant for more safe solution: https://gist.github.com/vagran/385b5df652d3401b544a231c09abbece