class_docstr: Class for the n-dimensional Poincare half-space.
  
  Class for the n-dimensional Poincaré half space model. For other
  representations of hyperbolic spaces see the `Hyperbolic` class.
  
  Parameters
  ----------
  dim : int
      Dimension of the hyperbolic space.
code: def __init__(self, dim, equip=True):
      super().__init__(
          dim=dim,
          embedding_space=Euclidean(dim),
          default_coords_type="half-space",
          equip=equip,
      )
  
imports: import math
  import geomstats.backend
  from geomstats.geometry._hyperbolic import _Hyperbolic
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.poincare_ball import PoincareBall
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 1 to create a new PoincareHalfSpace object from inherited base classes: _Hyperbolic, VectorSpaceOpenSet with example: obj = PoincareHalfSpace(dim, equip)