why defining only lt makes > operation possible?

August 25, 2022

class Node:
    def __init__(self,a,b):
        self._a=a
        self._b=b
    def __lt__(self,other):
        return self._a<other._a


a=Node(1,2)
b=Node(0,4)
print(a>b)

The code above shows True.

class Node:
    def __init__(self,a,b):
        self._a=a
        self._b=b
    def __lt__(self,other):
        return self._a<other._a
    def __eq__(self,other):
        return self._a==other._a

a=Node(1,2)
b=Node(0,4)
print(a>=b)

The code above shows TypeError: ‘<=’ not supported between instances of ‘Node’ and ‘Node.

Why defining only lt makes >(which is gt) operation possible?
why defining both lt and eq makes <= impossible?

>Solution :

The Python docs dictates:

There are no swapped-argument versions of these methods (to be used when the left argument does not support the operation but the right argument does); rather, __lt__() and __gt__() are each other’s reflection, __le__() and __ge__() are each other’s reflection, and __eq__() and __ne__() are their own reflection.

So if the left-hand-side argument doesn’t implement a comparison operator while the right-hand-side implements its reflection, that reflection is called instead. This also explains why Python doesn’t combine __lt__() and __eq__() into __le__() — it simply isn’t considered.