Python Programming

So we have called built-in functions. But what if we want to define our own functions?

Easy. Let’s say we want to define a function that squares a number, \(f(x) = x^2\).

In Python, this is how you do it:

def f(x):
    return x**2

Using your newly minted function is simply a matter of calling it as usual:

y = f(3)
print(y)

Let us dissect our codes.

def is a keyword to indicate a function definition.

f is the name of the function. You should probably give a more semantically meaningful name like square! Function names are usually verbs.

x is called the parameter of the function. These are variables that have not yet been defined. Again, use a semantically meaningful name when relevant. You can name it x if this is a mathematical function, of course!

During the function call f(3), the argument 3 is assigned to the parameter x in the function. The program will then execute the body of your function definition and return an object (including None).

If you do not include a return statement, the function will automatically return None.

Note the distinction between the terms parameter and argument. In analogy to variable assignments, parameter is the variable name, and argument is the concrete value/object referred to by the variable.

You can make a call to another function from inside a function definition.

def f(x):
    return x**2

def g(x):
    return f(x)**2 + 0.5 * f(6)

y = g(4)

Of course, you can have multiple parameters.

def compute_something(x, y, z):
    a = x + 2 * y
    a = z * a + 3 * x
    return a

results = compute_something(1, 3, 2)
print(results)

Although you can only return one object, that object can be a sequence (e.g. tuple), so technically you can return more than one object!

def do_more(x, y):
    return (2*y, x+y)

results = do_more(1, 2)
print(type(results))

x, y = do_more(1, 2)
print(type(x))
print(type(y))