class_docstr: Class for Riemannian and pseudo-Riemannian metrics.
  
  The associated Levi-Civita connection on the tangent bundle.
class_docstr_tok: ["Class","for","Riemannian","and","pseudo-Riemannian","metrics",".","The","associated","Levi-Civita","connection","on","the","tangent","bundle","."]
docstr: Compute inner coproduct between two cotangent vectors at base point.
  
  This is the inner product associated to the cometric matrix.
  
  Parameters
  ----------
  cotangent_vec_a : array-like, shape=[..., dim]
      Cotangent vector at `base_point`.
  cotangent_vet_b : array-like, shape=[..., dim]
      Cotangent vector at `base_point`.
  base_point : array-like, shape=[..., dim]
      Point on the manifold.
  
  Returns
  -------
  inner_coproduct : float
      Inner coproduct between the two cotangent vectors.
docstr_tok: ["Compute","inner","coproduct","between","two","cotangent","vectors","at","base","point",".","This","is","the","inner","product","associated","to","the","cometric","matrix",".","Parameters","--","--","--","--","--","cotangent_vec_a",":","array-like",",","shape=","[","...",",","dim","]","Cotangent","vector","at","`","base_point","`",".","cotangent_vet_b",":","array-like",",","shape=","[","...",",","dim","]","Cotangent","vector","at","`","base_point","`",".","base_point",":","array-like",",","shape=","[","...",",","dim","]","Point","on","the","manifold",".","Returns","--","--","--","-","inner_coproduct",":","float","Inner","coproduct","between","the","two","cotangent","vectors","."]
code: def inner_coproduct(
      self, cotangent_vec_a, cotangent_vec_b, base_point
  ):
      """Compute inner coproduct between two cotangent vectors at base point.
  
      This is the inner product associated to the cometric matrix.
  
      Parameters
      ----------
      cotangent_vec_a : array-like, shape=[..., dim]
          Cotangent vector at `base_point`.
      cotangent_vet_b : array-like, shape=[..., dim]
          Cotangent vector at `base_point`.
      base_point : array-like, shape=[..., dim]
          Point on the manifold.
  
      Returns
      -------
      inner_coproduct : float
          Inner coproduct between the two cotangent vectors.
      """
      vector_2 = gs.einsum(
          "...ij,...j->...i",
          self.cometric_matrix(base_point),
          cotangent_vec_b,
      )
      return gs.dot(cotangent_vec_a, vector_2)
  
imports: from abc import ABC
  import joblib
  import geomstats.backend
  import geomstats.geometry
  from geomstats.geometry.connection import Connection
  from geomstats.vectorization import check_is_batch
label_desc: Use image node_id 9 for calling the RiemannianMetric obj's underlying member method code with example usage: obj.inner_coproduct(cotangent_vec_a, cotangent_vec_b, base_point) and returns: gs