Lesson 3: Variables, operators, and types

(c) 2019 Justin Bois. With the exception of pasted graphics, where the source is noted, this work is licensed under a Creative Commons Attribution License CC-BY 4.0. All code contained herein is licensed under an MIT license.

This document was prepared at Caltech with financial support from the Donna and Benjamin M. Rosen Bioengineering Center.

This lesson was generated from an Jupyter notebook. You can download the notebook here.

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Whether you are programming in Python or pretty much any other language, you will be working with variables. While the precise definition of a variable will vary from language to language, we'll focus on Python variables here. Like many of the concepts in this bootcamp, though, the knowledge you gain about Python variables will translate to other languages.

We will talk more about objects later, but a variable, like everything in Python, is an object. For now, you can think of it this way. The following can be properties of a variable:

1. The type of variable. E.g., is it an integer, like 2, or a string, like 'Hello, world.'?
2. The value of the variable.

Depending on the type of the variable, you can do different things to it and other variables of similar type. This, as with most things, is best explored by example. We'll go through some of the properties of variables and things you can do to them in this tutorial.

We will work through this and the rest of the tutorials for the first day of the bootcamp using Jupyter notebooks. So, launch and notebook, and we'll get rolling!

Determining the type

First, we will use Python's built-in type() function to determine the type of some variables.

type(2)

int

type(2.3)

float

type('Hello, world.')

str

The type function told us that 2 is an int (short for integer), 2.3 is a float (short for floating point number, basically a real number that is not an integer), and 'Hello, world.' is a str (short for string). Note that the single quotes around the characters indicate that it is a string. So, '1' is a string, but 1 is an integer.

Note that we can also express floats using scientific notation; $4.5\times 10^{-7}$ is expressed as 4.5e-7.

type(4.5e-7)

float

A note on strings

We just saw that strings can be enclosed in single quotes. In Python, we can equivalently enclose them in double quotes. E.g.,

'my string'

and

"my string"

are the same thing. We can also denote a string with triple quotes. So,

"""my string"""
'''my string'''
"my string"
'my string'

are all the same thing. The difference with triple quotes is that it allows a string to extend over multiple lines.

# A multi-line string
my_str = """It was the best of times,
it was the worst of times..."""

print(my_str)

It was the best of times,
it was the worst of times...

Note, though, we cannot do this with single quotes.

# This is a SyntaxError
my_str = 'It was the best of times,
it was the worst of times...'

  File "<ipython-input-6-2cc9f4015bb6>", line 2
    my_str = 'It was the best of times,
                                       ^
SyntaxError: EOL while scanning string literal

Operators

Operators allow you to do things with variables, like add them. They are represented by special symbols, like + and *. For now, we will focus on arithmetic operators. Python's arithmetic operators are

action	operator
addition	+
subtraction	-
multiplication	*
division	/
raise to power	**
modulo	%
floor division	//

Warning: Do not use the ^ operator to raise to a power. That is actually the operator for bitwise XOR, which we will not cover in the bootcamp. Observe firey death if you use these inappropriately:

10^200

194

Instead of raising 10 to the 200th power, Python performed a bitwise XOR as illustrated below:

a	Binary	Decimal
Input	00001010	10
Input	11001000	200
Output	11000010	194

Note: if you want to see how a decimal number is represented in binary, you can use the following:

'{0:b}'.format(194)

'11000010'

Operations on integers

Let's see how these operators work on integers.

2 + 3

5

2 - 3

-1

2 * 3

6

2 / 3

0.6666666666666666

2**3

8

2 % 3

2

2 // 3

0

This is what we would expect. An import note, though. If you are using Python 2, division of integers defaults to floor division. Some legacy code is written in Python 2, though it officially sunsets on New Years Day.

Operations on floats

Let's try floats.

2.1 + 3.2

5.300000000000001

Wait a minute! We know 2.1 + 3.2 = 5.3, but Python gives 5.300000000000001. This is due to the fact that floating point numbers are stored with a finite number of binary bits. There will always be some rounding errors. This means that as far as the computer is concerned, it cannot tell you that 2.1 + 3.2 and 5.3 are equal. This is important to remember when dealing with floats, as we will see in the next lesson.

2.1 - 3.2

-1.1

# Very very close to zero because of finite precision
5.3 - (2.1 + 3.2)

-8.881784197001252e-16

2.1 * 3.2

6.720000000000001

2.1 / 3.2

0.65625

2.1**3.2

10.74241047739471

2.1 % 3.2

2.1

2.1 // 3.2

0.0

Aside from the floating point precision issue I already pointed out, everything is like we would expect. Note, though, that we cannot divide by zero.

2.1 / 0.0

---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
<ipython-input-24-2f8acfa4b142> in <module>
----> 1 2.1 / 0.0

ZeroDivisionError: float division by zero

We can't do it with ints, either.

2 / 0

---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
<ipython-input-25-8b4ac6d3a3e1> in <module>
----> 1 2 / 0

ZeroDivisionError: division by zero

Operations on integers and floats

This proceeds as we think it should.

2.1 + 3

5.1

2.1 - 3

-0.8999999999999999

2.1 * 3

6.300000000000001

2.1 / 3

0.7000000000000001

2.1**3

9.261000000000001

2.1 % 3

2.1

2.1**3

9.261000000000001

And again we have the rounding errors, but everything is otherwise intuitive.

Operations on strings

Now let's try some of these operations on strings. This idea of applying mathematical operations to strings seems strange, but let's just mess around and see what we get.

'Hello, ' + 'world.'

'Hello, world.'

Ah! Adding strings together concatenates them! This is also intuitive. How about subtracting strings?

'Hello, ' - 'world'

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-34-75667588e15f> in <module>
----> 1 'Hello, ' - 'world'

TypeError: unsupported operand type(s) for -: 'str' and 'str'

That stands to reason. Subtracting strings does not make sense. Python was kind enough to give us a nice error message saying that we can't have a str and a str operand type for the subtraction operation. It also makes sense that we can't do multiplication, raising of power, etc., with two strings. How about multiplying a string by an integer?

'Hello, world.' * 3

'Hello, world.Hello, world.Hello, world.'

Yes, this makes sense! Multiplication by an integer is the same thing as just adding multiple times, so Python concatenates the string several times.

As a final note on operators with strings, watch out for this:

'4' + '2'

'42'

The result is not 6, but it is a string containing the characters '4' and '2'.

Order of operations

The order of operations is also as we would expect. Exponentiation comes first, followed by multiplication and division, floor division, and modulo. Next comes addition and subtraction. In order of precedence, our arithmetic operator table is

precedence	operators
1	**
2	*, /, //, %
3	+, -

You can also group operations with parentheses. Operations within parentheses is are always evaluated first. Let's practice.

1 + 4**2

17

1 + 4/2

3.0

1**3 + 2**3 + 3**3 + 4**3

100

(1 + 2 + 3 + 4)**2

100

Interestingly, we also demonstrated that the sum of the first $n$ cubes is equal to the sum of the first $n$ integers squared. Fun!

Variables and assignment operators

So far, we have essentially just used Python as an oversized desktop calculator. We would really like to be able to think about our computational problems symbolically. We mentioned variables at the beginning of the tutorial, but in practice we were just using numbers and strings directly. We would like to say that a variable, a, represents an integer and another variable b represents another integer. Then, we could do things like add a and b. So, we see immediately that the variables have to have a type associated with them so the Python interpreter knows what to do when we use operators with them. A variable should also have a value associated with it, so the interpreter knows, e.g., what to add.

In order to create, or instantiate, a variable, we can use an assignment operator. This operator is the equals sign. So, let's make variables a and b and add them.

a = 2
b = 3
a + b

5

Great! We get what we expect! And we still have a and b.

a, b

(2, 3)

Now, we might be tempted to say, "a is two." No. a is not two. a is a variable that has a value of 2. A variable in Python is not just its value. A variable also carries with it a type. It also has more associated with it under the hood of the interpreter that we will not get into. So, you can think about a variable as a map to an address in RAM (called a pointer in computer-speak) that stores information, including a type and a value.

Assignment/increment operators

Now, let's say we wanted to update the value of a by adding 4.1 to it. Python will do some magic for us.

print(type(a), a)

a = a + 4.1

print(type(a), a)

<class 'int'> 2
<class 'float'> 6.1

We see that a was initially an integer with a value of 2. But we added 4.1 to it, so the Python interpreter knew to change its type to a float and update its value.

This operation of updating a value can also be accomplished with an increment operator.

a = 2
a += 4.1
a

6.1

The += operator told the interpreter to take the value of a and add 4.1 to it, changing the type of a in the intuitive way if need be. The other six arithmetic operators have similar constructions, -=, *=, /=, //=, %=, and **=.

a = 2
a **= 3
a

8

Type conversion

Suppose you have a variable of one type, and you want to convert it to another. For example, say you have a string, '42', and you want to convert it to an integer. This would happen if you were reading information from a text file, which by definition is full of strings, and you wanted to convert some string to a number. This is done as follows.

my_str = '42'
my_int = int(my_str)
print(my_int, type(my_int))

42 <class 'int'>

Conversely, we can convert an int back to a str.

str(my_int)

'42'

When converting a float to an int, the interpreter does not round the result, but gives the floor.

int(2.9)

2

Also consider our string concatenation warning/example from above:

print('4' + '2')
print(int('4') + int('2'))

42
6

Computing environment

%load_ext watermark
%watermark -v -p jupyterlab

CPython 3.7.3
IPython 7.1.1

jupyterlab 0.35.5