import and the math module

What you will be able to do

After this lesson you can

• import a module and use its tools with a dot,
• use the main tools of math,
• choose between import math, from math import sqrt and import math as m, and
• read the two import errors.

Do not build what exists

Suppose that you need a square root. You could write a long function with a loop. Or you could use a tool that experts have already made, tested, and made fast. Python keeps such tools in modules. A module is a toolbox.

To use a toolbox, you import it. Then you reach a tool with a dot: math.sqrt(144). The dot says: "the tool sqrt that lives in the toolbox math".

Why does Python not bring every tool in from the start? Because a program that imports only what it needs starts faster, and the names do not clash. You ask for the toolbox when you need it.

Predict first: what will each line show? Then run it.

• math.sqrt(144) is 12.0. The answer is a decimal number, even for a perfect square.
• math.pi is the number pi. round(math.pi, 4) gives 3.1416.
• math.floor(7.9) rounds down to 7, and math.ceil(7.1) rounds up to 8. The names mean "the floor" and "the ceiling".
• math.factorial(5) is $5 \times 4 \times 3 \times 2 \times 1 = 120$.
• math.gcd(12, 18) is the greatest common divisor, 6.
• math.hypot(3, 4) is the long side of a right triangle with sides 3 and 4: 5.0.

Three ways to import

A fourth way, from math import *, brings in every tool, with no module name. Avoid it. You will not know where a name comes from, and a name can silently replace one of your own.

More tools, and two warnings

For a positive number, floor and trunc agree. Only below 0 do they part: math.floor(-2.3) is -3, while math.trunc(-2.3) is -2.

When the import fails

Two mistakes with modules are common. Both give a clear message.

Common mistakes

• Using a tool without importing. A NameError: name 'math' is not defined.
• Importing after the first use. The import must come first. Put all the imports at the top.
• Angles in degrees for sin, cos and tan.
• Comparing decimal numbers with ==. Use isclose.
• Naming your own file math.py. Python imports your file instead of the real module. Choose another name.

Practice

Start with two quick questions. Each New numbers gives you a fresh one, so you can practise as long as you like.

Then the labs and the problems:

1. Warm-up. Open the lab Use the math tools. You use five tools, and the checker confirms each answer.
2. Build. Open the problem Square roots and pi and the problem How many buses?
3. Stretch. Open the problem The long side of a triangle and the problem Factorial and gcd.

Remember these

• import math brings the toolbox. math.sqrt(x) uses a tool.
• ceil rounds up. floor rounds down. trunc cuts.
• sin and cos use radians. isclose compares decimal numbers.
• ModuleNotFoundError is a wrong module name. AttributeError is a wrong tool name.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is math.floor(7.9)?

2. What is math.ceil(7.1)?

3. How do you bring in only the tool sqrt?

4. Why is 0.1 + 0.2 == 0.3 false?