code: 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
      )
  
imports: from sympy.core import Lambda, Symbol, symbols
  from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r, R3_c, R3_s, R2_origin
  from sympy.diffgeom import Manifold, Patch, CoordSystem, Commutator, Differential, TensorProduct, WedgeProduct, BaseCovarDerivativeOp, CovarDerivativeOp, LieDerivative, covariant_order, contravariant_order, twoform_to_matrix, metric_to_Christoffel_1st, metric_to_Christoffel_2nd, metric_to_Riemann_components, metric_to_Ricci_components, intcurve_diffequ, intcurve_series
  from sympy.simplify import trigsimp, simplify
  from sympy.functions import sqrt, atan2, sin
  from sympy.matrices import Matrix
  from sympy.testing.pytest import raises, nocache_fail
  from sympy.testing.pytest import warns_deprecated_sympy
label_desc: Use image node_id 9 for calling a global function with example usage: test_lie_derivative() without return types