Operators¶

assignment
math
logic
comparison
identity
membership

Operators are special symbols in Python that carry out arithmetic or logical computation.

Assignment Operator¶

Python uses = for assignment.

my_var = 1

Math Operators¶

+, -, *, / for addition, subtraction, multiplication, & division
** for exponentiation & % for modulus (remainder)
// for floor division (integer division)

Python uses the mathematical operators +, -, *, / for 'sum', 'substract', 'multiply', and 'divide', repsectively.

print(2 + 3)

div_result = 4 / 2 
print(div_result)
type(div_result)

2.0

float

Order of Operations¶

Mathematical operators follow the rules for order of operations.

follow the rules for order of operations.
parentheses specify which order you want to occur first

order_operations = 3 + 16 / 2
print(order_operations)

11.0

To specify that you want the addition to occur first, you would use parentheses.

specify_operations = (3 + 16) / 2
print(specify_operations)

9.5

Clicker #1¶

What would be the value stored in my_value?

Note: Best to think about it before running the code to ensure you understand.

my_value = (3 + 2) + 16 / (4 / 2) 
my_value

13.0

A) 7.0
B) 10.5
C) 13.0
D) 20.0
E) Produces an error

More Math¶

Python also has ** for exponentiation and % for remainder (called modulus). These also return numbers.

# 2 to the power 3
2 ** 3

# remainder of 17 divided by 7
17 % 7

Clicker #2¶

What would be the value stored in remainder?

remainder = 16 % 5
remainder

A) 0
B) 1
C) 3
D) 3.2
E) Produces an error

Clicker #3¶

What would be the value stored in modulo_time?

modulo_time = 4 * 2 % 5
modulo_time

A) 0
B) 1
C) 3
D) 3.2
E) Produces an error

Remainder¶

How to get Python to tell you the integer and the remainder when dividing?

The way I first thought of involved a package and we haven’t talked about those yet…

a = 17 // 7
b = 17 % 7

print(a, 'remainder', b)

2 remainder 3

// is an operator for floor division (integer division)

Clicker #4¶

What value is stored in math_out from the code below?

math_out = 32 / (1 + 3) ** 2 
math_out

2.0

A) 2
B) 16
C) 64
D) This code will fail

Logical (Boolean) operators¶

use Boolean logic
logical operators: and, or, and not

Booleans are named after the British mathematician - George Boole. He first formulated Boolean algebra, which are a set of rules for how to reason with and combine these values. This is the basis of all modern computer logic.

Python has and, or and not for boolean logic. These operators return booleans.

and : True if both are true
or : True if at least one is true
not : True only if false

True and True

True

True or True

True

True and not False

True

not False

True

# two nots cancel one another out
not (not True)

True

Capitalization matters¶

# this will give you an error
# 'TRUE' is not a boolean
# 'True' is
TRUE and TRUE

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-65-9b3f2ee967bc> in <module>()
      2 # 'TRUE' is not a boolean
      3 # 'True' is
----> 4 TRUE and TRUE

NameError: name 'TRUE' is not defined

Clicker #5¶

How will the following boolean expression evaluate:

True and False

False

A) True
B) False
C) None
D) This code will fail

Short-circuit evaluation¶

The second argument is evaluated only if the first argument does not definitively determine the value of the expression.

# python stops after False
# no need to check second expression
# since first is False
False and print("Hi")

False

# Continues to evaluate the expression
True and print("Hi")

Hi

# evaluates print statement before and
print("Hi") and False

Hi

Clicker #6¶

How will the following boolean expression evaluate?

True and not True or False

False

A) True
B) False
C) None
D) This code will fail

Clicker #7¶

How will the following boolean expression evaluate:

True and not False

True

A) True
B) False
C) None
D) This code will fail

Comparison Operators¶

Python has comparison operators ==, !=, <, >, <=, and >= for value comparisons. These operators return booleans.

== : values are equal
!= : values are not equal
< : value on left is less than value or right
> : value on left is greater than value on right
<= : value on left is less than or equal to value on right
>= : value on left is greater than or equal to value on the right

a = 12
b = 13
a > b

False

True == True

True

True != False

True

'aa' == 'aa'

True

12 <= 13

True

Clicker #8¶

Assume you’re writing a videogame that will only slay the dragon only if our magic lightsabre sword is charged to 90 or higher and we have 100 or more energy units in our protective shield.

Start with the code in the following cell. Replace --- with values that will evaluate to True when the cell is run (and slay the dragon!).

A) I did it!
B) I tried but am stuck.
C) I’m unsure where to start

## EDIT CODE HERE
sword_charge = 90
shield_energy = 100

alias_a = sword_charge

(sword_charge >= 90) and (shield_energy >= 100)

True

Understanding Boolean logic¶

When first learning booleans, we sometimes think we know what we’re asking the computer to do, but our logic can be flawed.

Let’s look at an example that could trip you up now.

Python considers empty strings as having boolean value of False. Non-empty string as having boolean value of True.

empty_string = ''
bool(empty_string)

False

nonempty_string = 'string has something in it'
bool(nonempty_string)

True

For and operator if left value is True, then right value is checked and returned. If left value is False, then that left value is returned.

True and False

False

bool('a')

True

'a' and 'b'

'b'

'b' and 'a'

'a'

Clicker Question #9¶

What would the following code cell return?

'' and 'a'

''

False and 'a'

False

not True and 'a'

False

A) ‘’
B) ‘a’
C) True
D) False

# the left value in parentheses is True
'a' == ('b' and 'a')

True

'b' and 'a'

'a'

'a' and 'b'

'b'

# the left value in parentheses is True
'a' == ('a' and 'b')

False

# the left value in parentheses is False
'a' == ('' and 'a')

False

# what we actually wanted python to do
# to look at a in a and b
'a' == 'a' and 'a' == 'b' 

False

For or operator if left value is True, then it is returned, otherwise if left value is False, then right value is returned.

'a' or 'b'

'a'

# empty string evaluates as False
'' or 'b'

'b'

False or False

False

'' or ''

''

'b' or ''

'b'

'a' == ('a' or 'b')

True

'b' == ('a' or 'b')

False

'b' == 'a' or 'b' == 'b'

True

Clicker Question #10¶

What would the following code cell return?

'a' == ('' or 'a')

True

A) ‘’
B) ‘a’
C) True
D) False

Identity Operators¶

Identity operators are used to check if two values (or variables) are located on the same part of the memory.

Python uses is and is not to compare identity. These operators return booleans.

is : True if both refer to the same object
is not : True if they do not refer to the same object

a = 927
b = a
c = 927

print(a is b)
print(c is a)

True
False

Two variables that are equal does not imply that they are identical.

If we wanted that second statement to evaluate as True we could use is not…

# make a True statement
print(c is not a)

True

# testing for value equality
a == b == c

True

Clicker #11¶

Using the variables provded below and identity operators replace --- with code such that true_variable will return True and false_variable will return False.

A) I did it!
B) I tried but am stuck.
C) I’m unsure where to start

z = 5
x = '5'
c = 'Hello'
d = c
e = [1, 2, 3]
f = [1, 2, 3]

# EDIT CODE HERE
true_variable = c is d 
false_variable = z is x

print(true_variable, false_variable)

True False

Delving Deeper: Identity Operators¶

A new object is created each time we have a variable that makes reference to it, but there are few notable exceptions:

some simple strings
Integers between -5 and 256 (inclusive)
empty immutable containers (e.g. tuples) - we’ll get to these later

While these may seem random, they exist for memory optimization in Python implementation.

Shorter and less complex strings are “interned” (share the same space in memory).

The rules behind this are a bit fuzzy, so we’ll just go through a few examples here. But, if you want to read more about string interning and how Python handles this, you can read more here.

simple_string = 'string'
simple_string2 = 'string'

simple_string is simple_string2

True

print(id(simple_string), id(simple_string2))

4429063032 4429063032

longer_string = 'really long string that just keeps going'
longer_string2 = 'really long string that just keeps going'

longer_string is longer_string2

False

print(id(longer_string), id(longer_string2))

4461758576 4461758192

d = 5
e = 5

print(id(d), id(e))

4426314944 4426314944

print(d is e)

True

Python implementation front loads an array of integers between -5 to 256, so these objects already exist.

# Python doesn't create a new object here
j = 5
k = 5
l = 'Hello'
m = 'Hello'

true_variable_integer = j is k
true_variable_string = l is m

print(true_variable_integer, true_variable_string)

True True

# Python DOES create a new object here
n = 975 #greater than 256
o = 975
p = 'Hello!' #that exclamation point makes it more complex
q = 'Hello!'

false_variable_integer = n is o
false_variable_string = p is q

print(false_variable_integer, false_variable_string)

False False

Clicker #12¶

Using the variables provded below and identity operators replace --- with code such that true_variable will return True and false_variable will return False.

A) I did it!
B) I tried but am stuck.
C) I’m unsure where to start

a = 5
b = 5
c = b
d = 'Hello!'
e = 'Hello!'
f = 567
g = 567

# EDIT CODE HERE
true_variable = a is b
false_variable = f is g

print(true_variable, false_variable)

True False

Membership Operators¶

Python uses in and not in to compare membership. These operators return booleans.

Membership operators are used to check whether a value or variable is found in a sequence.

Here, we’ll just be checking for value membership in strings. But, we’ll discuss lists, tuples, sets, and dictionaries soon.

in : True if value is found in the sequence
not in : True if value is not found in the sequence

x = 'I love COGS18!'
print('l' in x)

True

print('L' in x)

False

print('COGS' in x)

True

print('CSOG' in x)

False

print(' ' in x)

True

String Concatenation¶

Operators sometimes do different things on different types of variables. For example, + on strings does concatenation.

'COGS' + ' 18'

'COGS 18'

'a' + 'b' + 'c'

'abc'

Chaining Operators¶

Operators and variables can also be chained together into arbitrarily complex expressions.

# Note that you can use parentheses to chunk sections
(13 % 7 >= 7) and ('COGS' + '18' == 'COGS18')

False

(13 % 7 >= 7)

False

('COGS' + '18' == 'COGS18')

True

Clicker #13¶

How will the following expression evaluate:

2**2 >= 4 and 13%3 > 1

a) True
b) False
c) None
d) This code will fail

Introductory Python

Operators

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