ENH: Implement subtraction for object-dtype Index

doc/source/whatsnew/v0.24.0.txt

@@ -310,6 +310,7 @@ Other API Changes
 - Invalid construction of ``IntervalDtype`` will now always raise a ``TypeError`` rather than a ``ValueError`` if the subdtype is invalid (:issue:`21185`)
 - Trying to reindex a ``DataFrame`` with a non unique ``MultiIndex`` now raises a ``ValueError`` instead of an ``Exception`` (:issue:`21770`)
 - :meth:`PeriodIndex.tz_convert` and :meth:`PeriodIndex.tz_localize` have been removed (:issue:`21781`)
+- :class:`Index` subtraction will attempt to operate element-wise instead of raising ``TypeError`` (:issue:`19369`)
 
 .. _whatsnew_0240.deprecations:
 

pandas/core/indexes/base.py

@@ -2630,8 +2630,10 @@ def __iadd__(self, other):
         return self + other
 
     def __sub__(self, other):
-        raise TypeError("cannot perform __sub__ with this index type: "
-                        "{typ}".format(typ=type(self).__name__))
+        return Index(np.array(self) - other)
+
+    def __rsub__(self, other):
+        return Index(other - np.array(self))
 
     def __and__(self, other):
         return self.intersection(other)

pandas/tests/indexes/test_base.py

@@ -871,6 +871,18 @@ def test_sub(self):
         pytest.raises(TypeError, lambda: index - index.tolist())
         pytest.raises(TypeError, lambda: index.tolist() - index)
 
+    def test_sub_object(self):
+        # GH#19369
+        from decimal import Decimal
+        index = pd.Index([Decimal(1), Decimal(2)])
+        expected = pd.Index([Decimal(0), Decimal(1)])
+
+        result = index - Decimal(1)
+        tm.assert_index_equal(result, expected)
+
+        result = index - pd.Index([Decimal(1), Decimal(1)])
+        tm.assert_index_equal(result, expected)
+
     def test_map_identity_mapping(self):
         # GH 12766
         # TODO: replace with fixture