class_docstr: Class for the n-dimensional Poincare ball.
  
  Class for the n-dimensional Poincaré ball model. For other
  representations of hyperbolic spaces see the `Hyperbolic` class.
  
  Parameters
  ----------
  dim : int
      Dimension of the hyperbolic space.
class_docstr_tok: ["Class","for","the","n-dimensional","Poincare","ball",".","Class","for","the","n-dimensional","Poincar\u00e9","ball","model",".","For","other","representations","of","hyperbolic","spaces","see","the","`","Hyperbolic","`","class",".","Parameters","--","--","--","--","--","dim",":","int","Dimension","of","the","hyperbolic","space","."]
docstr: Test if a point belongs to the hyperbolic space.
  
  Test if a point belongs to the hyperbolic space based on
  the poincare ball representation.
  
  Parameters
  ----------
  point : array-like, shape=[..., dim]
      Point to be tested.
  atol : float, optional
      Tolerance at which to evaluate how close the squared norm
      is to the reference value.
      Optional, default: backend atol.
  
  Returns
  -------
  belongs : array-like, shape=[...,]
      Array of booleans indicating whether the corresponding points
      belong to the hyperbolic space.
docstr_tok: ["Test","if","a","point","belongs","to","the","hyperbolic","space",".","Test","if","a","point","belongs","to","the","hyperbolic","space","based","on","the","poincare","ball","representation",".","Parameters","--","--","--","--","--","point",":","array-like",",","shape=","[","...",",","dim","]","Point","to","be","tested",".","atol",":","float",",","optional","Tolerance","at","which","to","evaluate","how","close","the","squared","norm","is","to","the","reference","value",".","Optional",",","default",":","backend","atol",".","Returns","--","--","--","-","belongs",":","array-like",",","shape=","[","...",",","]","Array","of","booleans","indicating","whether","the","corresponding","points","belong","to","the","hyperbolic","space","."]
code: def belongs(self, point, atol=gs.atol):
      """Test if a point belongs to the hyperbolic space.
  
      Test if a point belongs to the hyperbolic space based on
      the poincare ball representation.
  
      Parameters
      ----------
      point : array-like, shape=[..., dim]
          Point to be tested.
      atol : float, optional
          Tolerance at which to evaluate how close the squared norm
          is to the reference value.
          Optional, default: backend atol.
  
      Returns
      -------
      belongs : array-like, shape=[...,]
          Array of booleans indicating whether the corresponding points
          belong to the hyperbolic space.
      """
      return gs.sum(point**2, axis=-1) < (1 - atol)
  
imports: import math
  import geomstats.algebra_utils
  import geomstats.backend
  from geomstats.geometry._hyperbolic import _Hyperbolic
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 3 for calling the PoincareBall obj's underlying member method code with example usage: obj.belongs(point, atol) and returns: unknown