code: def test_lie_bracket_jacobi_identity(self, n_points, atol):
      identity = repeat_point(self.space.identity, n_points)
      tangent_vec_a = self.data_generator.random_tangent_vec(identity)
      tangent_vec_b = self.data_generator.random_tangent_vec(identity)
      tangent_vec_c = self.data_generator.random_tangent_vec(identity)
  
      lhs = self.space.lie_bracket(
          self.space.lie_bracket(tangent_vec_a, tangent_vec_b),
          tangent_vec_c,
      )
      rhs_1 = self.space.lie_bracket(
          tangent_vec_a,
          self.space.lie_bracket(tangent_vec_b, tangent_vec_c),
      )
      rhs_2 = -self.space.lie_bracket(
          tangent_vec_b,
          self.space.lie_bracket(tangent_vec_a, tangent_vec_c),
      )
      rhs = rhs_1 + rhs_2
  
      self.assertAllClose(lhs, rhs, atol=atol)
  
imports: import pytest
  import geomstats.backend
  from geomstats.test.vectorization import generate_vectorization_data
  from geomstats.test_cases.geometry.manifold import ManifoldTestCase
  from geomstats.test_cases.geometry.mixins import GroupExpTestCaseMixins
  from geomstats.vectorization import repeat_point
label_desc: Use image node_id 15 for calling the _LieGroupTestCaseMixins obj's underlying member method code with example usage: obj.test_lie_bracket_jacobi_identity(n_points, atol) without return types