class_docstr: Class for Lie groups.
  
  In this class, point_type ('vector' or 'matrix') will be used to describe
  the format of the points on the Lie group.
  If point_type is 'vector', the format of the inputs is
  [..., dimension], where dimension is the dimension of the Lie group.
  If point_type is 'matrix' the format of the inputs is
  [..., n, n] where n is the parameter of GL(n) e.g. the amount of rows
  and columns of the matrix.
  
  Parameters
  ----------
  dim : int
      Dimension of the Lie group.
  lie_algebra : MatrixLieAlgebra
      Lie algebra for matrix groups.
      Optional, default: None.
  
  Attributes
  ----------
  lie_algebra : MatrixLieAlgebra or None
      Tangent space at the identity.
docstr: Compute the push-forward map by the left/right translation.
  
  Compute the push-forward map, of the left/right translation by the
  point. It corresponds to the tangent map, or differential of the
  group multiplication by the point or its inverse. For groups with a
  vector representation, it is only implemented at identity, but it can
  be used at other points by passing `inverse=True`. This method wraps
  the jacobian translation which actually computes the matrix
  representation of the map.
  
  Parameters
  ----------
  point : array-like, shape=[..., {dim, [n, n]]
      Point.
  left: bool
      Whether to calculate the differential of left or right
      translations.
      Optional, default: True.
  inverse : bool,
      Whether to inverse the jacobian matrix. If True, the push forward
      by the translation by the inverse of point is returned.
      Optional, default: False.
  
  Returns
  -------
  tangent_map : callable
      Tangent map of the left/right translation by point. It can be
      applied to tangent vectors.
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code: def tangent_translation_map(self, point, left=True, inverse=False):
      r"""Compute the push-forward map by the left/right translation.
  
      Compute the push-forward map, of the left/right translation by the
      point. It corresponds to the tangent map, or differential of the
      group multiplication by the point or its inverse. For groups with a
      vector representation, it is only implemented at identity, but it can
      be used at other points by passing `inverse=True`. This method wraps
      the jacobian translation which actually computes the matrix
      representation of the map.
  
      Parameters
      ----------
      point : array-like, shape=[..., {dim, [n, n]]
          Point.
      left: bool
          Whether to calculate the differential of left or right
          translations.
          Optional, default: True.
      inverse : bool,
          Whether to inverse the jacobian matrix. If True, the push forward
          by the translation by the inverse of point is returned.
          Optional, default: False.
  
      Returns
      -------
      tangent_map : callable
          Tangent map of the left/right translation by point. It can be
          applied to tangent vectors.
      """
      if self.default_point_type == "matrix":
          if inverse:
              point = self.inverse(point)
          if left:
              return lambda tangent_vec: Matrices.mul(
                  point, tangent_vec
              )
          return lambda tangent_vec: Matrices.mul(tangent_vec, point)
  
      jacobian = self.jacobian_translation(point, left)
      if inverse:
          jacobian = gs.linalg.inv(jacobian)
      return lambda tangent_vec: gs.einsum(
          "...ij,...j->...i", jacobian, tangent_vec
      )
  
imports: import abc
  import geomstats.backend
  from geomstats.geometry.invariant_metric import InvariantMetric
  from geomstats.geometry.manifold import Manifold
  from geomstats.geometry.matrices import Matrices
label_desc: Use image node_id 7 for calling the LieGroup obj's underlying member method code with example usage: obj.tangent_translation_map(point, left, inverse) and returns: function, function, function