More mathematical commands via Numpy

The basic Python language doesn’t contain many more commands for doing maths than the basic arithmetical operations. If we want more complex things like trigonometric functions, we have to import a package or a module which offers those commands. For our purposes, packages and modules are essentially the same thing. There are a number of packages that provide mathematical functions. The one you will most commonly use is numpy (which stands for numerical Python). There are several ways of importing packages. For now, we’ll import numpy in the following conventional way:

import numpy as np

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 import numpy as np

ModuleNotFoundError: No module named 'numpy'

The previous cell told Python to make the numpy package available, and call it np. We could call it anything other than np, but np is a conventional name for numpy. We can now use the functions provided by numpy like so:

np.cos(0)

1.0

Note that numpy works in radians. You can get the value of pi using np.pi, so we can compute:

np.sin(np.pi / 6)

0.49999999999999994

The output of the last cell looks a bit funny - it should be 0.5 exactly. When dealing with floating point numbers, there will always be some rounding errors in the computations, and you shouldn’t rely on getting exact values. You will see more on this in further notebooks.

When we write np.cos(0), we are “calling the function np.cos with argument 0”. We will later see how to write and call our own functions.

Numpy contains many other useful mathematical functions, listed here. It’s not worth trying to remember all of them; just remember that this list exists!

We could have also imported numpy using import numpy. We would then use the functions in it by writing, for example, numpy.cos(0).

A Warning

You will occasionally see material import numpy or other modules using the following format:

from numpy import *

# now we can use the functions from numpy without putting np. before them
cos(pi)

-1.0

Do not do this. While it might seem innocuous and indeed useful at first, it is actually considered dangerous and bad practice. If you do want to be able to use things from numpy without putting np. before them, you should import them like this:

from numpy import cos, pi

cos(pi)

-1.0

Other modules

There are many other packages available in Python - far too many to list - but you can import any of them in the same way as shown above provided they are installed on your computer.

One example that we have already seen is mobilechelonian. We import this using the final syntax shown above:

from mobilechelonian import Turtle

donna = Turtle()

donna.forward(50)
donna.left(720)

Another module that you will likely make use of is math. This has some overlap with numpy.