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The changeset ef2b2ddd27c8 restricted the argument of Path.with_suffix() too much, and caused some strange behavior.
Case 1: removing suffix completely is disallowed now.
The following code worked before the fix:
>>> pathlib.PurePath('a', 'b.c').with_suffix('')
PurePosixPath('a/b')
but now fails with ValueError:
>>> pathlib.PurePath('a', 'b.c').with_suffix('')
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
 File "/home/july/source/python/Lib/pathlib.py", line 760, in with_suffix
 raise ValueError("Invalid suffix %r" % (suffix))
ValueError: Invalid suffix ''
It was the only one obvious way of removing the suffix, and I think it should remain so. (BTW: There is a XXX note in the code questioning if Path.with_suffix(None) should remove the suffix.)
Case 2: while the output is now always a correct Path, the suffix can still contain separator.
The following code produced incorrect path before the fix:
>>> pathlib.PurePath('a', 'b.c').with_suffix('./.s/.')
PurePosixPath('a/b./.s/.')
>>> _.parts
('a', 'b./.s/.')
Now, the produced path is correct, but the code itself is still allowed:
>>> pathlib.PurePath('a', 'b.c').with_suffix('./.s/.')
PurePosixPath('a/b.s')
while I would expect it to fail with ValueError.
Attached: proposed test patch.

Proposed patch attached.

Thank you! Unfortunately, it is too late for 3.4, but I will make sure the fix is included in 3.4.1 (and 3.5).

New changeset 0d84855861ff by Antoine Pitrou in branch '3.4':
Issue #20639: calling Path.with_suffix('') allows removing the suffix again.
http://hg.python.org/cpython/rev/0d84855861ff 

Sorry for the delay! The patch is now applied. Thank you for contributing!