class_docstr: Class for affine connections.
  
  Parameters
  ----------
  space : Manifold object
      M in the tuple (M, g).
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docstr: Compute the covariant derivative of the curvature.
  
  For four tangent vectors at base_point :math:`P`:
  
  - :math:`H|_P = tangent\_vec\_a`,
  - :math:`X|_P = tangent\_vec\_b`,
  - :math:`Y|_P = tangent\_vec\_c`,
  - :math:`Z|_P = tangent\_vec\_d`,
  
  the covariant derivative of the curvature is defined as:
  :math:`(\nabla_H R)(X, Y) Z |_P`.
  
  Parameters
  ----------
  tangent_vec_a : array-like, shape=[..., dim]
      Tangent vector at `base_point`.
  tangent_vec_b : array-like, shape=[..., dim]
      Tangent vector at `base_point`.
  tangent_vec_c : array-like, shape=[..., dim]
      Tangent vector at `base_point`.
  tangent_vec_d : array-like, shape=[..., dim]
      Tangent vector at `base_point`.
  base_point :  array-like, shape=[..., dim]
      Point on the manifold.
  
  Returns
  -------
  curvature_derivative : array-like, shape=[..., dim]
      Tangent vector at base-point.
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code: def curvature_derivative(
      self,
      tangent_vec_a,
      tangent_vec_b,
      tangent_vec_c,
      tangent_vec_d,
      base_point=None,
  ):
      r"""Compute the covariant derivative of the curvature.
  
      For four tangent vectors at base_point :math:`P`:
  
      - :math:`H|_P = tangent\_vec\_a`,
      - :math:`X|_P = tangent\_vec\_b`,
      - :math:`Y|_P = tangent\_vec\_c`,
      - :math:`Z|_P = tangent\_vec\_d`,
  
      the covariant derivative of the curvature is defined as:
      :math:`(\nabla_H R)(X, Y) Z |_P`.
  
      Parameters
      ----------
      tangent_vec_a : array-like, shape=[..., dim]
          Tangent vector at `base_point`.
      tangent_vec_b : array-like, shape=[..., dim]
          Tangent vector at `base_point`.
      tangent_vec_c : array-like, shape=[..., dim]
          Tangent vector at `base_point`.
      tangent_vec_d : array-like, shape=[..., dim]
          Tangent vector at `base_point`.
      base_point :  array-like, shape=[..., dim]
          Point on the manifold.
  
      Returns
      -------
      curvature_derivative : array-like, shape=[..., dim]
          Tangent vector at base-point.
      """
      raise NotImplementedError(
          "The covariant derivative of the curvature is not implemented."
      )
  
imports: from abc import ABC
  import geomstats.backend
  import geomstats.errors
label_desc: Use image node_id 13 for calling the Connection obj's underlying member method code with example usage: obj.curvature_derivative(tangent_vec_a, tangent_vec_b, tangent_vec_c, tangent_vec_d, base_point) without return types