Computer Science for STEM: The PreTeXt Interactive Edition

It is important to understand that each of the functions we write can be used and called from other functions we write. This is one of the most important ways that computer scientists take a large problem and break it down into a group of smaller problems. This process of breaking a problem into smaller subproblems is called functional decomposition.

Here’s a simple example of functional decomposition using two functions. The first function called square simply computes the square of a given number. The second function called sum_of_squares makes use of square to compute the sum of three numbers that have been squared.

Even though this is a pretty simple idea, in practice this example illustrates many very important Python concepts, including local and global variables along with parameter passing. Note that when you step through this example, codelens bolds line 1 and line 5 as the functions are defined. The body of square is not executed until it is called from the sum_of_squares function for the first time on line 6. Also notice that when square is called there are two groups of local variables, one for square and one for sum_of_squares. As you step through you will notice that x, and y are local variables in both functions and may even have different values. This illustrates that even though they are named the same, they are in fact, very different.

So far, it may not be clear why it is worth the trouble to create all of these new functions. Actually, there are a lot of reasons, but this example demonstrates two: