APC_Australia_Issue_442_June_2017

howto » coding masterclass
Doing maths with Python
Not great with numbers? Don’t worry, Python is. Darren Yates delves
into Python’s module of mathematical functions to begin solving
almost any problem.
There’s a lot of talk about
STEM (Science, Technology,
Engineering, Mathematics)
education in schools at the
moment. A recent Federal
Government report found that school
enrolments in these subjects are at
20-year lows (tinyurl.com/lxduqto).
Given how crucial these areas are to
our future, the report is alarming.
If we had to pick which of these
areas was most important, we think
the choice is easy — mathematics.
Why? Without mathematics, the other
three areas couldn’t exist (tinyurl.com/
lywfnro). But while maths isn’t
everyone’s cuppa, it’s something
computers excel at and Python is
loaded with functions and modules
designed to help solve practical
maths problems.
THE ‘BIG FOUR’
Starting at the very beginning,
the four basic maths functions
or ‘operators’ are addition (+),
subtraction (-), multiplication (*)
and division (/). You can try these out
in the Python Shell:
print(2+5)
print(18/3)
print(15.2-6.4)
print(5.4*3)
ARITHMETIC PRECEDENCE
You don’t have to be on LinkedIn,
Twitter or Facebook for long before
you get the inevitable maths
brainteaser quiz that goes something
like this:
4 + 10 / 2 – 2 x 3 = ?
Getting the right answer relies on
knowing what’s called ‘arithmetic
precedence’ or ‘order of operations’
— either way, it’s the order in which
the operators must be calculated.
That basic order is division (/) and
multiplication (x), followed by
addition (+) and subtraction (-).
You can create a Direct
Digital Synthesis table
with Python code.
Get Python
Grab the latest version of Python
for your operating system
(Windows, Linux, Mac OS X) from
www.python.org/downloads
We’re using the latest version 3.x, so
choose that rather than version 2.x.
You may even remember ‘BODMAS’
from school — Brackets, Orders, then
Division, Multiplication, Addition,
Subtraction as before.
In this example, we start with 4,
but instead of adding ‘10’, we have to
calculate the division operator first,
so 10/2 = 5. Add the ‘5’ to the ‘4’ and you
get 9. Continuing on, we can’t subtract
the ‘2’ as the following multiplication
operator takes precedence, so we get
2 x 3 = 6. Now we subtract the ‘6’ from
‘9’ and get 3. Try this out in Python
Shell:
print (4 + 10 / 2 – 2 * 3)
And you should end up with ‘3.0’.
COMPUTERS CAN’T ADD UP?
We give computers a lot of credit
for working out all sorts of problems,
but there are limitations — and those
limitations are easier to see than you
might expect. We store numbers in
variables of a particular datatype —
whole numbers or ‘integers’ are stored
in ‘integer’ variables, decimal or ‘real’
numbers are stored in ‘floating-point’
variables.
Fire up Python Shell again and try
out the following:
106 www.apcmag.com
Calculate the 3dB
cut-off frequency of an
RC filter using the Math
module.
print(0.1 + 0.1 + 0.1 + 0.1 +
0.1 + 0.1 + 0.1 + 0.1 + 0.1 +
0.1)
The answer you’d expect is ‘1.0’.
The answer you’ll get is
‘0.9999999999999999’, which
obviously isn’t the same thing. Now
instead of assuming computers are
stupid and can’t add up, the reason for
this has to do with the way computers
store real numbers. The basic problem
is that, while we talk and think in
decimal numbers (factors of 10 or