def test_correct_arguments():
raises(ValueError, lambda: R2.e_x(R2.e_x))
raises(ValueError, lambda: R2.e_x(R2.dx))
raises(ValueError, lambda: Commutator(R2.e_x, R2.x))
raises(ValueError, lambda: Commutator(R2.dx, R2.e_x))
raises(ValueError, lambda: Differential(Differential(R2.e_x)))
raises(ValueError, lambda: R2.dx(R2.x))
raises(ValueError, lambda: LieDerivative(R2.dx, R2.dx))
raises(ValueError, lambda: LieDerivative(R2.x, R2.dx))
raises(ValueError, lambda: CovarDerivativeOp(R2.dx, []))
raises(ValueError, lambda: CovarDerivativeOp(R2.x, []))
a = Symbol('a')
raises(ValueError, lambda: intcurve_series(R2.dx, a, R2_r.point([1, 2])))
raises(ValueError, lambda: intcurve_series(R2.x, a, R2_r.point([1, 2])))
raises(ValueError, lambda: intcurve_diffequ(R2.dx, a, R2_r.point([1, 2])))
raises(ValueError, lambda: intcurve_diffequ(R2.x, a, R2_r.point([1, 2])))
raises(ValueError, lambda: contravariant_order(R2.e_x + R2.dx))
raises(ValueError, lambda: covariant_order(R2.e_x + R2.dx))
raises(ValueError, lambda: contravariant_order(R2.e_x * R2.e_y))
raises(ValueError, lambda: covariant_order(R2.dx * R2.dy))
def test_lie_derivative():
assert LieDerivative(R2.e_x, R2.y) == R2.e_x(R2.y) == 0
assert LieDerivative(R2.e_x, R2.x) == R2.e_x(R2.x) == 1
assert LieDerivative(R2.e_x, R2.e_x) == Commutator(R2.e_x, R2.e_x) == 0
assert LieDerivative(R2.e_x, R2.e_r) == Commutator(R2.e_x, R2.e_r)
assert LieDerivative(R2.e_x+R2.e_y, R2.x) == 1
assert LieDerivative(R2.e_x, TensorProduct(R2.dx, R2.dy))(R2.e_x, R2.e_y) == 0
def test_commutator():
assert Commutator(R2.e_x, R2.e_y) == 0
assert Commutator(R2.x * R2.e_x, R2.x * R2.e_x) == 0
assert Commutator(R2.x * R2.e_x, R2.x * R2.e_y) == R2.x * R2.e_y
c = Commutator(R2.e_x, R2.e_r)
assert c(R2.x) == R2.y * (R2.x**2 + R2.y**2)**(-1) * sin(R2.theta)