When you write Python programs with basic data types, without thinking you use operators to add, subtract, multiply, and divide values, to compare values, and to apply all kinds of standard functionalities. Such interactions are not defined by default for classes you define yourself, but Python allows you to specify what should happen when one applies such an interaction to instances of your class. This is called “operator overloading.”

For instance, suppose that you define a class that represents quaternions.¹¹ You know that adding and multiplying quaternions are well-defined operations. Therefore, you might want to define what happens when you combine two of your quaternions with a $+$ operator. Python allows you to specify that. In fact, Python allows you to specify what the $+$ operator does for any of your new classes.

Isn’t that great? You can define a class Student, and then define that if you add two students together with a $+$ operator, that their ages are added up. Wonderful, isn’t it? No, it isn’t. It obviously makes no sense to add up two students. You might start thinking about what a natural interpretation of adding up two students would entail, but the answer is that everything that you can come up with is far-fetched. You should not define an addition operator for classes which have no natural addition defined. This is one of the dangers of operator overloading: if you apply it without thinking, you get nonsensical programs.

Still, operator overloading has powerful applications. In the rest of this chapter I will introduce some of the most common applications of operator overloading.

By the way, operator overloading is a typical example of “polymorphism,” a concept that allows a function to have different results depending on the type of its arguments. Polymorphism is often hailed as one of the powerful features of object orientation.