class_docstr: Class for the n-dimensional Hyperbolic space.
  
  This class is a common interface to the different models of hyperbolic
  geometry:
  
  - the hyperboloid, embedded in Minkowski space of dimension dim + 1 as the set of
    points whose squared norm is equal to -1. This representation is called
    `extrinsic` here.
  - the Poincare ball, the open ball of the Euclidean space of dimension dim.
  - the Poincare half-space, the open space of points of the Euclidean
    space of  dimension dim, whose last coordinate is positive.
  
  Parameters
  ----------
  dim : int
      Dimension of the hyperbolic space.
  default_coords_type : str, {'extrinsic', 'ball', 'half-space'}
      Default coordinates to represent points in hyperbolic space.
      Optional, default: 'extrinsic'.
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docstr: Instantiate class that corresponds to the default_coords_type.
docstr_tok: ["Instantiate","class","that","corresponds","to","the","default_coords_type","."]
code: def __new__(cls, dim, default_coords_type="extrinsic", equip=True):
      """Instantiate class that corresponds to the default_coords_type."""
      errors.check_parameter_accepted_values(
          default_coords_type,
          "default_coords_type",
          ["extrinsic", "ball", "half-space"],
      )
      if default_coords_type == "extrinsic":
          return Hyperboloid(dim, equip=equip)
      if default_coords_type == "ball":
          return PoincareBall(dim, equip=equip)
      return PoincareHalfSpace(dim, equip=equip)
  
imports: import geomstats.errors
  from geomstats.geometry.hyperboloid import Hyperboloid
  from geomstats.geometry.poincare_ball import PoincareBall
  from geomstats.geometry.poincare_half_space import PoincareHalfSpace
label_desc: Use image node_id 1 for calling the Hyperbolic obj's underlying member method code with example usage: obj.__new__(cls, dim, default_coords_type, equip) and returns: PoincareHalfSpace, Hyperboloid, PoincareBall