The documentation for functools.total_ordering states that rich comparison can be enabled on a class by specifying an __eq__ method, and one of __lt__(), __le__(), __gt__(), or __ge__().  If these instructions are followed, this results in an incorrect evaluation of the not equal operator:

Here's an example:

    from functools import total_ordering

    @total_ordering
    class Value(object):

        def __init__(self, value):
            self.value = value
    
        def __eq__(self, other):
            return self.value == other.value
    
        def __lt__(self, other):
            return self.value < other.value

 
    >>> a = Value(3)
    >>> b = Value(3)
    >>> a == b
    True
    >>> a != b
    True

I've tested this on 2.7.10.
 
Either the documentation or the behaviour should be corrected.

https://docs.python.org/2/library/functools.html#functools.total_ordering

This is due to the fact that Python 3 added the ability to define only __eq__ and get a free __ne__ defined. If my memory serves me right, functools.total_ordering was added in 3.2 and then backported to 2.x - where the relationship with __eq__ and __ne__ is not present. total_ordering doesn't do anything to touch __ne__ as it expects Python itself to do so (which it doesn't in 2.x).

The docs are correct but are apparently misleading ("rich comparison methods" means all six comparison methods while "rich comparison ordering methods" means only the four that provide order).  That said, I think it would be perfectly reasonable to amend the code to supply __ne__ if it is missing.  That would be reduce the likelihood of bugs arising when supplied only __eq__ and one of the four ordering methods but not __ne__.

Now defined __ne__ always silently overridden.

This doesn't work with new-style classes that always have __ne__ inherited from object.

I afraid that the only way to fix this issue is to backport Python 3 behavior of default __ne__, automatically fallback to __eq__.

In Python 2.7, __ne__ isn't inherited from object.

Oh, sorry. Then the patch LGTM.

Nick, I'm inclined to put this in.  Only bugs can come out of the current arrangement.   Do you have any further thoughts?

Sorry for the delayed review. I agree it makes sense to fix this for 2.7, and the proposed solution looks good to me.

However, the latest patch looks it was only partway through editing - the additional test cases seem to be copies of the existing test cases, rather than new scenarios.

Ping.

Serhiy, do you want to bring this to fruition?

New changeset d94a65a0694a188713f91ba7c9fffded090247dc by Serhiy Storchaka in branch '2.7':
bpo-25732: Make functools.total_ordering implementing __ne__. (#3748)
https://github.com/python/cpython/commit/d94a65a0694a188713f91ba7c9fffded090247dc

I committed the patch from Raymond's name, but GitHub set me as the author of the commit. :(