code: def test_reciprocal_real_rv_transform(self):
      # 1 / Cauchy(mu, sigma) = Cauchy(mu / (mu^2 + sigma ^2), sigma / (mu ^ 2, sigma ^ 2))
      test_value = [-0.5, 0.9]
      test_rv = Cauchy.dist(1, 2, size=(2,)) ** (-1)
  
      np.testing.assert_allclose(
          logp(test_rv, test_value).eval(),
          sp.stats.cauchy(1 / 5, 2 / 5).logpdf(test_value),
      )
      np.testing.assert_allclose(
          logcdf(test_rv, test_value).eval(),
          sp.stats.cauchy(1 / 5, 2 / 5).logcdf(test_value),
      )
      with pytest.raises(NotImplementedError):
          icdf(test_rv, test_value)
  
imports: import numpy
  import pytensor
  import pytensor.tensor
  import pytest
  import scipy
  import scipy.special
  from pytensor.graph.basic import equal_computations
  from pymc.distributions.continuous import Cauchy, ChiSquared
  from pymc.logprob.basic import conditional_logp, icdf, logcdf, logp
  from pymc.logprob.transforms import ArccoshTransform, ArcsinhTransform, ArctanhTransform, ChainedTransform, CoshTransform, ErfcTransform, ErfcxTransform, ErfTransform, ExpTransform, LocTransform, LogTransform, ScaleTransform, SinhTransform, TanhTransform, Transform
  from pymc.logprob.utils import ParameterValueError
  from pymc.testing import Rplusbig, Vector, assert_no_rvs
  from tests.distributions.test_transform import check_jacobian_det
label_desc: Use image node_id 2 for calling the TestPowerRVTransform obj's underlying member method code with example usage: obj.test_reciprocal_real_rv_transform() without return types