def METHOD_NAME():
    a = (-1 + sqrt(5))/4 - I*sqrt((sqrt(5) + 5)/8)
    A = QQ.algebraic_field(a)
    a = A.unit
    _, x, y, z = ring('x y z', A)
    f1 = x**2 - 2*a**2*x + a**3*z**2 - (a**3 + a**2 + a + 1)*y + 12*a
    f2 = x**2 - 2*a**3*x + a**2*z**2 + a*y - 12*(a**3 + a**2 + a + 1)
    f3 = x**2 + 2*(a**3 + a**2 + a + 1)*x + a*z**2 + a**3*y + 12*a**2
    f4 = x**2 - 2*a*x - (a**3 + a**2 + a + 1)*z**2 + a**2*y + 12*a**3
    f = f1*f2*f3*f4
    assert efactor(f) == (1, [(f2, 1), (f1, 1), (f4, 1), (f3, 1)])