We know that a function or method will: * Return some result, or * Raise an exception if it cannot find the result But there is a third thing a function can return and that is **NotImplemented**. The simple meaning of **return NotImplemented** by...

We know that a function or method will:

- Return some result, or
- Raise an exception if it cannot find the result

But there is a third thing a function can return and that is **NotImplemented**. The simple meaning of **return NotImplemented** by a function is that the function is declaring that it cannot find the result but instead of raising the exception, it will transfer the control to another function, hoping that the other function will get the result. The other function is known as **Reflection Function**.

We will explore the whole idea in context to **Object Oriented Programming** and associated **Magic Methods** (also known as special methods or dunder methods) which are used for different special functionalities and we will just see the ones used to define the support for different operator (e.g. +,-,* etc.) for objects of one class.

Let's see this simple Point class defined for the points on **XY plane**:

```
class Point:
def __init__(self,x,y):
self.x=x
self.y=y
def __str__(self):
return f'({self.x},{self.y})'
p1=Point(3,4)
print(p1)
```

The **__str__** method is defined for the proper representation of the point object and the last **print** statement will print the point as **(3,4)**.

If we want to define a function for the addition of two point objects, it can be done as:

```
def addPoints(self,other):
return Point(self.x+other.x,self.y+other.y)
```

And then we can use it as:

```
p1=Point(3,4)
p2=Point(1,1)
p3=p1.addPoints(p2)
print(p3)
```

This will display **(4,5)** as output.

But it will be better if instead of using a custom named function like **addPoints**, we could directly apply **+** operator like we do for simple numbers and a few other data types e.g. **4+5**. At present if we use **+** operator on two point objects as:

```
p1=Point(3,4)
p2=Point(1,1)
p3=p1+p2
```

It will generate following error which is self-explanatory:

TypeError: unsupported operand type(s) for +: 'Point' and 'Point'

If we change the name of the function **addPoints** to **__add__** which is a magic method, the **+** operator applied between two point objects will call this method.
See the complete code here:

```
class Point:
def __init__(self,x,y):
self.x=x
self.y=y
def __str__(self):
return f'({self.x},{self.y})'
def __add__(self,other):
return Point(self.x+other.x,self.y+other.y)
p1=Point(3,4)
p2=Point(1,1)
p3=p1+p2
print(p3)
```

And the output will be **(4,5)**.

We have special methods for other operators too e.g. **__sub__** is for subtraction ( - ), **__mul__** is for multiplication ( * ), **__div__** is for division( / ) and a few more.

In fact, when we apply **+** operator between any data types, interpreter actually executes **__add__** method on those e.g. for **3+4**, interpreter will execute **3.__add__(4)** and the method __add__ is defined in **int** class for addition of two integers. Similarly, if **a** and **b** are two lists, **a+b** will result into **a.__add__(b)** and __add__ is defined inside **list** class as concatenation of the lists.

Now let's define **__mul__** for the **Point** class but not for the multiplication of two point objects but to multiply the Point object with a number, resulting into a new point with scaled **x** and **y** components. It will be done by adding **__mul__** method as shown here:

```
class Point:
def __init__(self,x,y):
self.x=x
self.y=y
def __str__(self):
return f'({self.x},{self.y})'
def __add__(self,other):
return Point(self.x+other.x,self.y+other.y)
def __mul__(self,num):
return Point(self.x*num,self.y*num)
p1=Point(3,4)
p2=p1*2
print(p2)
```

The output will be **(6,8)**.

But instead of **p1*2** if we execute **2*p1**, then instead of getting the same result, we get an error as:

TypeError: unsupported operand type(s) for *: 'int' and 'Point'

This is something we will resolve using the concept of **NotImplemented** and **Reflection Function**.

When a function returns **NotImplemented**, interpreter will run the **reflection** function associated with that function after **flipping** the input arguments. For example, if original function has input arguments as **a** and **b**, at returning NotImplemented, interpreter will run the associated reflection function on **b** and **a**.

Second important thing is that the reflection functions associated with different functions are predefined in Python and you cannot make some function as reflection of some other function by your own. The reflection function of **__add__** is **__radd__**, reflection function of **__mul__** is **__rmul__** and so on for different magic methods.

**So, lets see what happened when interpreter executed 2*p1 in above program.**
As described earlier that **2*p1** will result into **2.__mul__(p1)**, so interpreter will apply **__mul__** on **2** which is an integer. Therefore, interpreter will search for **__mul__** method inside **int** class. Interpreter will find the method in **int** class but that method defines multiplication between two integers and may be between an integer and some other data type but not between an integer and the Point class object. And in such cases (unsupported datatype), the **__mul__** of **int** class returns **NotImplemented**.
With NotImplemented returned, interpreter will run the **reflection method** i.e. **__rmul__** on flipped input arguments as **p1.__rmul__(2)**. And you can see that the method is applied on **p1** which is Point class object and hence interpreter will search for this method (__rmul__) in Point class and will fail since this method is not defined inside Point class. So it will return back to the original function (of int class) and will generate this error:

TypeError: unsupported operand type(s) for *: 'int' and 'Point'

The whole process is given here step by step for further clarification:

**2*p1**will result into**2.__mul__(p1)**and Interpreter searches for**__mul__**in**int**class.**__mul__**in int class returns**NotImplemeted**for unsupported types of operands.- This results into execution of reflection function as
**p1.__rmul__(2)**. - Interpreter will look for
**__rmul__**inside Point class because**p1**is Point class object. - When failed to find
**__rmul__**in Point class, interpreter will go back to int class and generate the error.

So if you have followed along these steps, you probably have figured out the solution which is that we must define **__rmul__** in **Point** class, so that **p1.__rmul__(2)** should get executed.

**What should be inside this function?**

**p1.__rmul__(2)** means that **self** is **p1** and second input argument is **2** and we need to return a new point with scaled **xy** coordinates. So, we should have **__rmul__** defined as:

```
def __rmul__(self,num):
return Point(self.x*num,self.y*num)
```

But this is exactly what **__mul__** does, and hence we can also do as:

```
def __rmul__(self,num):
return self*num
```

Above return statement with multiplication will call the **__mul__** method.
Even a better approach will be to just declare:

`__rmul__=__mul__`

Because the function are also Objects and we are saying that **__rmul__** is referring to same object as **__mul__**.
The complete code will be:

```
class Point:
def __init__(self,x,y):
self.x=x
self.y=y
def __str__(self):
return f'({self.x},{self.y})'
def __add__(self,other):
return Point(self.x+other.x,self.y+other.y)
def __mul__(self,num):
return Point(self.x*num,self.y*num)
__rmul__=__mul__
p1=Point(3,4)
p2=2*p1
print(p2)
```

And now we will get the correct output as **(6,8)**.

You can see that it is just the one last line added in Point class i.e. **__rmul__=__mul__** and it resolved a big problem. And that is all because of the power of **NotImplemented** and **Reflection Function** support of Python.

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**You can find further detail with more practice examples in this video:**

**If you need more detail on Magic Methods, you can find that in the following videos:**

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