docstr: Integrability tensor derivatives is alternate in pre-shape.
  
  For two horizontal vector fields :math:`X,Y` the integrability
  tensor (hence its derivatives) is alternate:
  :math:`\nabla_X ( A_Y Z + A_Z Y ) = 0`.
code: def test_integrability_tensor_derivative_is_alternate(
      self, n_points, atol
  ):
      r"""Integrability tensor derivatives is alternate in pre-shape.
  
      For two horizontal vector fields :math:`X,Y` the integrability
      tensor (hence its derivatives) is alternate:
      :math:`\nabla_X ( A_Y Z + A_Z Y ) = 0`.
      """
      base_point = self.data_generator.random_point(n_points)
      horizontal_vec_x = self._get_horizontal_vec(base_point)
      horizontal_vec_y = self._get_horizontal_vec(base_point)
      horizontal_vec_z = self._get_horizontal_vec(base_point)
      nabla_x_y = self._get_nabla_x_y(
          horizontal_vec_x, horizontal_vec_y, base_point
      )
      nabla_x_z = self._get_nabla_x_y(
          horizontal_vec_x, horizontal_vec_z, base_point
      )
  
      (
          nabla_x_a_y_z,
          a_y_z,
      ) = self.bundle.integrability_tensor_derivative(
          horizontal_vec_x,
          horizontal_vec_y,
          nabla_x_y,
          horizontal_vec_z,
          nabla_x_z,
          base_point,
      )
      (
          nabla_x_a_z_y,
          a_z_y,
      ) = self.bundle.integrability_tensor_derivative(
          horizontal_vec_x,
          horizontal_vec_z,
          nabla_x_z,
          horizontal_vec_y,
          nabla_x_y,
          base_point,
      )
  
      shape = (
          (n_points,) + self.total_space.shape
          if n_points > 1
          else self.total_space.shape
      )
      expected = gs.zeros(shape)
  
      result = nabla_x_a_y_z + nabla_x_a_z_y
      self.assertAllClose(result, expected, atol=atol)
  
      result = a_y_z + a_z_y
      self.assertAllClose(result, expected, atol=atol)
  
imports: import pytest
  import geomstats.backend
  from geomstats.geometry.matrices import Matrices
  from geomstats.test.random import KendalShapeRandomDataGenerator, get_random_times
  from geomstats.test.vectorization import generate_vectorization_data
  from geomstats.test_cases.geometry.base import LevelSetTestCase
  from geomstats.test_cases.geometry.fiber_bundle import FiberBundleTestCase
  from geomstats.test_cases.geometry.quotient_metric import QuotientMetricTestCase
  from geomstats.vectorization import get_batch_shape
label_desc: Use image node_id 13 for calling the PreShapeSpaceBundleTestCase obj's underlying member method code with example usage: obj.test_integrability_tensor_derivative_is_alternate(n_points, atol) without return types