Think Python for CS114 2 Variables, expressions and statements 4 Adding new functions

Chapter 3 Built-in Functions

In the context of programming, a function is a named sequence of statements that performs a computation. When you define a function, you specify the name and the sequence of statements. Later, you can “call” the function by name.

3.1 Function calls

We have already seen one example of a function call:

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>>> type(42)

The name of the function is type. The expression in parentheses is called the argument of the function. The result, for this function, is some information about the type of the argument.

It is common to say that a function “takes” an argument and “returns” a result. The result is also called the return value.

(Reminder: do not use the type function except while debugging.)

Python provides functions that convert values from one type to another. The int function takes any value and converts it to an integer, if it can, or complains otherwise:

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>>> int('32')

>>> int('Hello')

ValueError: invalid literal for int(): Hello

int can convert floating-point values to integers, but it doesn’t round off; it chops off the fraction part:

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>>> int(3.99999)

>>> int(-2.3)

-2

float converts integers and strings to floating-point numbers:

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>>> float(32)

32.0

>>> float('3.14159')

3.14159

Finally, str converts its argument to a string:

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>>> str(32)

'32'

>>> str(3.14159)

'3.14159'

3.2 Math functions

Python has a math module that provides most of the familiar mathematical functions. A module is a file that contains a collection of related functions.

Before we can use the functions in a module, we have to import it with an import statement:

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>>> import math

This statement creates a module object named math. If you display the module object, you get some information about it:

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>>> math

The module object contains the functions and variables defined in the module. To access one of the functions, you have to specify the name of the module and the name of the function, separated by a dot (also known as a period). This format is called dot notation.

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>>> ratio = signal_power / noise_power

>>> decibels = 10 * math.log10(ratio)

>>> radians = 0.7

>>> height = math.sin(radians)

The first example uses math.log10 to compute a signal-to-noise ratio in decibels (assuming that signal_power and noise_power are defined). The math module also provides log, which computes logarithms base e.

The second example finds the sine of radians. The variable name radians is a hint that sin and the other trigonometric functions (cos, tan, etc.) take arguments in radians. To convert from degrees to radians, divide by 180 and multiply by $\pi$ :

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>>> degrees = 45

>>> radians = degrees / 180.0 * math.pi

>>> math.sin(radians)

0.707106781187

The expression math.pi gets the variable pi from the math module. Its value is a floating-point approximation of $\pi$ , accurate to about 15 digits.

If you know trigonometry, you can check the previous result by comparing it to the square root of two, divided by two:

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>>> math.sqrt(2) / 2.0

0.707106781187