return empty MultiIndex for symmetrical difference on equal MultiInde…

…xes (#16486)

(cherry picked from commit d31ffdb)

doc/source/whatsnew/v0.20.2.txt

@@ -41,6 +41,7 @@ Bug Fixes
 - Silenced a warning on some Windows environments about "tput: terminal attributes: No such device or address" when
   detecting the terminal size. This fix only applies to python 3 (:issue:`16496`)
 - Bug in using ``pathlib.Path`` or ``py.path.local`` objects with io functions (:issue:`16291`)
+- Bug in ``Index.symmetric_difference()`` on two equal MultiIndex's, results in a TypeError (:issue `13490`)
 - Bug in ``DataFrame.update()`` with ``overwrite=False`` and ``NaN values`` (:issue:`15593`)
 - Passing an invalid engine to :func:`read_csv` now raises an informative
   ``ValueError`` rather than ``UnboundLocalError``. (:issue:`16511`)

pandas/core/indexes/multi.py

@@ -414,6 +414,12 @@ def view(self, cls=None):
         return result
 
     def _shallow_copy_with_infer(self, values=None, **kwargs):
+        # On equal MultiIndexes the difference is empty.
+        # Therefore, an empty MultiIndex is returned GH13490
+        if len(values) == 0:
+            return MultiIndex(levels=[[] for _ in range(self.nlevels)],
+                              labels=[[] for _ in range(self.nlevels)],
+                              **kwargs)
         return self._shallow_copy(values, **kwargs)
 
     @Appender(_index_shared_docs['_shallow_copy'])

pandas/tests/indexes/test_base.py

@@ -188,7 +188,6 @@ def test_constructor_ndarray_like(self):
         # it should be possible to convert any object that satisfies the numpy
         # ndarray interface directly into an Index
         class ArrayLike(object):
-
             def __init__(self, array):
                 self.array = array
 
@@ -246,7 +245,6 @@ def test_index_ctor_infer_nan_nat(self):
                      [np.timedelta64('nat'), np.nan],
                      [pd.NaT, np.timedelta64('nat')],
                      [np.timedelta64('nat'), pd.NaT]]:
-
             tm.assert_index_equal(Index(data), exp)
             tm.assert_index_equal(Index(np.array(data, dtype=object)), exp)
 

pandas/tests/indexing/test_multiindex.py

@@ -697,6 +697,17 @@ def test_multiindex_slice_first_level(self):
                                 index=range(30, 71))
         tm.assert_frame_equal(result, expected)
 
+    def test_multiindex_symmetric_difference(self):
+        # GH 13490
+        idx = MultiIndex.from_product([['a', 'b'], ['A', 'B']],
+                                      names=['a', 'b'])
+        result = idx ^ idx
+        assert result.names == idx.names
+
+        idx2 = idx.copy().rename(['A', 'B'])
+        result = idx ^ idx2
+        assert result.names == [None, None]
+
 
 class TestMultiIndexSlicers(object):