An example vector class for illustrating useful dunder methods.

Vector.py

class Vector():
    def __new__(cls, x, y):
        print("__new__ was invoked")
        instance = object.__new__(cls)
        return instance

    def __init__(self, x, y):
        print("__init__ was invoked")
        self.x = x
        self.y = y

    def __repr__(self):
        return f"Vector({self.x}, {self.y})"

    def __str__(self):
        return f"{self.x}x + {self.y}y"

    def __len__(self):
        return int((self.x*self.x +self.y*self.y)**(1/2))

    def __getitem__(self, key):
        if key < 0 or key > 1:
            raise IndexError("Index out of range! Should either be 0 or 1.")
        elif key:
            return self.y
        else:
            return self.x

    def __setitem__(self, key, val):
        if key < 0 or key > 1:
            raise IndexError("Index out of range! Should either be 0 or 1.")
        elif key:
            self.y = val
        else:
            self.x = val

    def __call__(self):
        print(f"Vector({self.x}, {self.y}) was called.")
        return (self.x*self.x +self.y*self.y)**(1/2)
        
    def __add__(self, other):
        if type(other) is not Vector:
            raise TypeError('other should be an object of class Vector')
        return Vector(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        if type(other) is not Vector:
            raise TypeError('other should be an object of class Vector')
        return Vector(self.x - other.x, self.y - other.y)

    def __mul__(self, other):
        if type(other) is not Vector:
            raise TypeError('other should be an object of class Vector')
        return self.x * other.x + self.y * other.y

    def __lt__(self, other):
        if type(other) is not Vector:
            raise TypeError('other should be an object of class Vector')
        return self() < other()

    def __gt__(self, other):
        if type(other) is not Vector:
            raise TypeError('other should be an object of class Vector')
        return self() > other()
    
    def __eq__(self, other):
        if type(other) is not Vector:
            raise TypeError('other should be an object of class Vector')
        return self.x == other.x and self.y == other.y