code: def test_ordered_api(self):
      # GH 9347
      cat1 = Categorical(list("acb"), ordered=False)
      tm.assert_index_equal(cat1.categories, Index(["a", "b", "c"]))
      assert not cat1.ordered
  
      cat2 = Categorical(
          list("acb"), categories=list("bca"), ordered=False
      )
      tm.assert_index_equal(cat2.categories, Index(["b", "c", "a"]))
      assert not cat2.ordered
  
      cat3 = Categorical(list("acb"), ordered=True)
      tm.assert_index_equal(cat3.categories, Index(["a", "b", "c"]))
      assert cat3.ordered
  
      cat4 = Categorical(
          list("acb"), categories=list("bca"), ordered=True
      )
      tm.assert_index_equal(cat4.categories, Index(["b", "c", "a"]))
      assert cat4.ordered
  
imports: import re
  import numpy
  import pytest
  from pandas.compat import PY311
  from pandas import Categorical, CategoricalIndex, DataFrame, Index, Series, StringDtype
  import pandas._testing
  from pandas.core.arrays.categorical import recode_for_categories
label_desc: Use image node_id 2 for calling the TestCategoricalAPI obj's underlying member method code with example usage: obj.test_ordered_api() without return types