Numbers
There’s nothing magical about numbers in Python, and we’ve already discovered how we perform operations on them.
>>> (2*(1 + 3) - 5)/0.5
2
>>> 11 % 4
3
The only thing to keep in mind is that Python has a few different types of numbers, and they can behave differently.
>>> 10/3
3
>>> 10.0/3.0
3.3333333333333335
Interesting. Something different happens when we use numbers with and without
decimal places! This occurs because numbers given with decimal places, like
3.14 are floats, while those without, like 3, are integers.
For historical reasons, dividing two integers in Python 2 returns an integer, where the intermediate result is always rounded down. Division using at least one float gives us the more intuitive answer.
In Python 3, division with integers works the same way as with floats. You can ask to have this behaviour in Python 2.
>>> from __future__ import division
>>> 3/4
0.75
>>> 3.0/4.0
0.75
Because the default behaviour in Python 2 is quite unintuitive, we recommend
using the from __future__ import division line everywhere. We’ll come to what exactly this
line is doing shortly.
If you do want a rounding division, you then can ask for it explicitly with
the // operation:
>>> 10/3
3.3333333333333335
>>> 10//3
3
Operators
This behaviour can be explained in terms of operators and the double-underscore methods. You can see that numbers have two methods for division:
>>> dir(1)
[...,
'__floordiv__',
...
'__truediv__',
...]
In Python 2, the / operator corresponded to the __floordiv__ method when
used with integers, but the __truediv__ operator when used with floats. In
Python 3, and when using the from __future__ import division line, the /
operator always uses the __truediv__ method.
Python also lets you manipulate complex numbers, using j to represent the
complex term.
>>> a = 1 + 4j
>>> b= 4 - 1j
>>> a - b
(-3+5j)
Complex numbers are objects, of course, and have some useful functions and properties attached to them.
>>> a.conjugate()
(1-4j)
>>> a.imag
4.0
>>> a.real
1.0
Somewhat confusingly, computing the magnitude of a complex number can be done
with the abs method, which is available globally.
>>> abs(a)
4.123105625617661
>>> import math
>>> math.sqrt(a.real**2 + a.imag**2)
4.123105625617661
This also demonstrates the ** operator, which for real numbers corresponds to
exponentiation.
Each type of number can be created literally, like we’ve been doing, by just typing the number into your shell or source code, and by using the correspond methods.
>>> int()
0
>>> float()
0.0
>>> complex()
0j