Get determinant expression for matrix of arbitrary size.

determinant.py

# Get determinant expression for a matrix.

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


def DetExpr(m):
    """
    :param m: Minor submatrix.
    :return: Expression of minor determinant
    """
    if len(m) == 1:
        return m[0][0]
    res = "("
    for i in range(0, len(m)):
        if i % 2 == 1:
            res += " - "
        elif i > 1:
            res += " + "
        res += m[i][0] + "*" + DetExpr(Minor(m, i))
    res += ")"
    return res


M = []
SIZE = 4
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(DetExpr(M))

Sample output for 4x4 matrix:
(a00*(a11*(a22*a33 - a32*a23) - a21*(a12*a33 - a32*a13) + a31*(a12*a23 - a22*a13)) - a10*(a01*(a22*a33 - a32*a23) - a21*(a02*a33 - a32*a03) + a31*(a02*a23 - a22*a03)) + a20*(a01*(a12*a33 - a32*a13) - a11*(a02*a33 - a32*a03) + a31*(a02*a13 - a12*a03)) - a30*(a01*(a12*a23 - a22*a13) - a11*(a02*a23 - a22*a03) + a21*(a02*a13 - a12*a03)))