BUG: Fix Index.equals with string vs object dtype (#61099)

Author: MayurKishorKumar

pandas/core/indexes/base.py

@@ -5470,6 +5470,15 @@ def equals(self, other: Any) -> bool:
         if len(self) != len(other):
             # quickly return if the lengths are different
             return False
+        
+        if (
+            (isinstance(self.dtype, StringDtype)
+            or is_object_dtype(self.dtype)) 
+            and 
+            (isinstance(other.dtype, StringDtype)
+            or is_object_dtype(other.dtype))
+            ):
+            return array_equivalent(self.astype("object")._values, other.astype("object")._values)
 
         if (
             isinstance(self.dtype, StringDtype)

pandas/tests/indexes/test_base.py

@@ -1717,3 +1717,34 @@ def test_is_monotonic_pyarrow_list_type():
     idx = Index([[1], [2, 3]], dtype=pd.ArrowDtype(pa.list_(pa.int64())))
     assert not idx.is_monotonic_increasing
     assert not idx.is_monotonic_decreasing
+
+def test_index_equals_string_vs_object():
+    # GH 61099
+    idx1 = pd.Index(['a', 'b', 'c'])
+    idx2 = pd.Index(['a', 'b', 'c'], dtype='string')
+    assert idx1.equals(idx2)
+    assert idx2.equals(idx1)
+
+def test_compare_string_vs_object_index_equality():
+    # GH 61099
+    s1 = pd.Series([1, 2, 3], index=['a', 'b', 'c'])  # dtype=object
+    s2 = pd.Series([0, 1, 2], index=pd.Index(['a', 'b', 'c'], dtype='string'))  # dtype=string
+    result = s1 > s2
+    expected = pd.Series([True, True, True], index=['a', 'b', 'c'])
+    pd.testing.assert_series_equal(result, expected)
+
+def test_align_string_vs_object_index():
+    # GH 61099
+    s1 = pd.Series([1, 2, 3], index=['a', 'b', 'c'])  # object
+    s2 = pd.Series([1, 2, 3], index=pd.Index(['a', 'b', 'c'], dtype='string'))  # string
+    s1_aligned, s2_aligned = s1.align(s2)
+    assert list(s1_aligned.index) == list(s2_aligned.index)
+
+def test_comparison_without_manual_casting():
+    # GH 61099
+    s1 = pd.Series([1, 2, 3], index=['a', 'b', 'c'])  # object index
+    s2 = pd.Series([1, 2, 3], index=pd.Index(['a', 'b', 'c'], dtype='string'))
+    # Should not raise
+    result = s1 == s2
+    expected = pd.Series([True, True, True], index=['a', 'b', 'c'])
+    pd.testing.assert_series_equal(result, expected)