5  Dealing with values

This chapter is about values and variables, the two most central concepts in programming.

Math

Much programming is done to compute stuff. In Python, the usual math operations are done using these arithmetic operators:

Operator	Operation
+	plus
-	minus
/	division
//	integer division
*	multiplication
**	exponentiation
%	modulo (remainder)

You are probably quite familiar with these - except perhaps for integer division, exponentiation, and modulo. Let us take some of the operators for a spin. Remember to carefully write the whole thing in an empty file in VScode. Do not copy-paste. Then save the file as mathandlogic.py and run it from the terminal. Do not call your file math.py. It may bite you later. Just trust me on that one.

print("Four times two is",  4 * 2)

Notice how you can print more than one thing at a time if you put commas between the values you want to print? We can group computations using parentheses, just like in normal math. Try this:

print("10 / (2 + 3) is", 10 / (2 + 3))
print("(10 / 2) + 3 is", (10 / 2) + 3)

In addition to the regular math operators, there are a few extra operators that we call comparison operators because they are used to compare two values, e.g., two numbers.

Operator	Operation
<	less-than
>	greater-than
<=	less-than-or-equal
>=	greater-than-or-equal
==	equal
!=	not equal

Try this:

print("Is 5 greater than -2?", 5 > -2)
print("Is 5 greater or equal to -2?", 5 >= -2)
print("Is 5 less or equal to -2?", 5 <= -2)
print("Is 5 less than 7 - 2?", 5 < 7 - 2)
print("Is 5 equal to 7 - 2?", 5 == 7 - 2)

As you may have noticed, running this code and comparing things using these operators, we always produce either True or False. E.g., the following

print(5 < 7)

prints the value True because 5 is smaller than 7. True and False are special values in Python that we can use (and print if we like) just like any other Python value:

print(True)
print(False)

Exercise 5-1

Try to write and run the code below. Compare each line to what is printed when you run the code. Make sure you understand why.

print("I have", 25 + 30 / 6, "of something")
print("I have", 100 - 25 * 3 % 4, "of something else")

print("Is it true that 3 + 2 < 5 - 7?")
print(3 + 2.1 < 5.4 - 7)

print("3 + 2.1 is", 3 + 2.1)
print("5.4 - 7 is", 5.4 - 7)

print("Oh, that's why it's False.")

Exercise 5-2

An additional comparison operator even tests if something is a part of something else. That operator is called in. One use of it is to test if one string is part of another string. Try this to figure out how it works:

print("Hell" in "Hello world")
print("Hello world" in "Hello world")
print("Hello world" in "Hell")
print("lo wo" in "Hello world")
print("Artichoke" in "Hello world")

Exercise 5-3

Say the supermarket has chocolate bars for 7 kr. Write a small Python program (in a file called chocolate.py) that prints how many chocolate bars you can get for your 30 kr. You should run it like this;

For example, it could output something like this:

$ python chocolate.py

to have it print something like this:

I can buy 4.285714285714286 chocolate bars!

Exercise 5-4

We mentioned a special operator called modulo. Google it if you do not remember what it does. How about integer division. Explain both to a fellow student (or to yourself out loud).

Exercise 5-5

You obviously cannot go buy 4.3 chocolate bars in a store. You will have to settle for 4. Can you change the program you made in Section 5.0.0.3 to print the number of bars you can buy and the change you then have left? Use the modulo and integer division operators. Something like:

I can buy 4 chocolate bars, leaving me with 2 kr in change.

Exercise 5-6

What happens if you try to run the following program?

print( 1 / 0 )

If you get an error? What kind of error? Why do you think you get that error? Do you think it makes sense?

Exercise 5-7

You probably know the Pythagorean theorem for computing a right-angled triangle’s hypotenuse (the longest side). The Pythagorean theorem looks like this: \(a^2 + b^2 = c^2\). Here \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the triangle’s two legs. So if we have a triangle where \(a = 5\) and \(b = 2\) and we want to find \(c^2\) we can do this in Python:

print("The squared length of the hypotenuse is:", 5**2 + 2**2)

Exercise 5-8

However, we are rarely interested in the squared length of the hypotenuse. Can you modify the code you wrote in Section 5.0.0.7 so you compute \(c\) instead of \(c^2\)? Taking the square root of a number is the same as taking that number and exponentiating it to 0.5, so the square root of \(x\) is \(x^{0.5}\). Do you know of a Python operator that does exponentiation?

Logic

Now you know how to use the comparison operations to produce a True or False value. There are three additional operators that let you express more elaborate “True/False” statements than with the comparison operators alone. These are the logical operators: and, or and not.

Exercise 5-9

Go through the code below and see if you can figure out what each line does. Then, write the code into your editor and run it to see what happens.

print(2 < 3)
print(10 < 12)
print(8 > 100)
print(2 < 3 and 10 < 12)
print(8 > 100 and 2 < 3)
print(8 > 100 or 2 < 3)
print(not 8 > 100 and 2 < 3)
print(not 8 > 100 and not 2 > 3)

Did it do what you expected? Can you explain each line?

Exercise 5-10

When exposed to the operators and, or and not, some values are considered true and others are considered false. What happens when you put not in front of something that is considered true or false? Decide what you think and why before you write the code and try it out.

print(not True)
print(not False)
print(not 0)
print(not -4)
print(not 0.0000000)
print(not 3.14159265359)
print(not "apple")
print(not "")

From the code above, try to find out which values Python considers true and which it considers false. Can you come up with a rule?

Exercise 5-11

The logical operator and takes two values (the one to the left of the operator and the one to the right) and figures out whether both the left and the right expression are true. It boils down to this:

Left expression	Right expression	Result
True	True	True
True	False	False
False	True	False
False	False	False

Write some code to confirm that the table above is correct using Python. For example, to test the first case, do this:

print(True and True)

Exercise 5-12

Python will only do the necessary work to determine if a logical expression is true. That means that if the value left of and is considered false by Python, then there is no reason to look at the right value since it is already established that they are not both considered true. In this case the expression reduces to the left value. I.e. False and True reduces to False.

If Python considers the value left of and true, then It needs to look at the right value, too, to establish if they are both considered true. In this case, the expression reduces to the value on the right. I.e., True and False reduces to False.

A rule of thumb is that the whole expression reduces to the last value that Python needs to consider to decide if the whole expression is true or false. Use that rationale to explain how the two last combinations in Section 5.0.0.11 are evaluated.

Exercise 5-13

Like the and operator, the or operator also takes two values. However, the or operator determines whether one of the two values is true. Thus, the or operator boils down to this:

Left expression	Right expression	Result
True	True	True
True	False	True
False	True	True
False	False	False

Write some code using Python to confirm that the table above is correct. For example, to test the first case, do this:

print(True or True)

Exercise 5-14

As with the and operator, Python will not do any more work than absolutely necessary when evaluating an expression with ‘or’. So if the value left of or is considered true by Python, then there is no reason to look at the right value since it is already established that at least one of them is considered true. In this case the expression reduces to the left value. I.e. True or False reduces to True.

If the value left of or is considered false by Python, then Python still needs to look at the right value to establish if at least one of them is considered true. In this case, the expression reduces to the right value. I.e., False or True reduces to True.

Again, the whole expression reduces to the last value that Python needs to consider to decide if the whole expression is true or false. Use that same rationale to explain to yourself how the two last combinations in Section 5.0.0.13 are evaluated.

Exercise 5-15

Remember what you learned in Section 5.0.0.10 about which values are considered true and which are considered false. Combine that with what you learned in Section 5.0.0.11 and Section 5.0.0.13 about what logical expressions reduce to and see if you can figure out what is printed below and why. Use the rule-of-thumb from Section 5.0.0.14. Decide what you think before you write the code and try it out.

print(True and 4)
print(0 and 7)
print(-27 and 0.5)
print(42 and 0)
print("apple" and "orange")
print("apple" and "")
print(42 or 0)
print("apple" and "")
print("apple" or "")

If you were surprised by what was printed, maybe go back and look at Section 5.0.0.11 and Section 5.0.0.13 again.

Exercise 5-16

Recall the in operator from Section 5.0.0.2? There is also an operator called not in. I guess you can imagine what that tests. Try it out.

Variables

By now, you probably feel the first signs of brain overload. If you do not take breaks, your brain may overheat and explode - we have seen that happen. One of the nice things about the brain is that it works when you rest. Archiving and understanding a lot of new information takes time, and force-feeding your brain will not help. The last part of this chapter is very important so now might be a good time for a good long break.

This section is about variables and is where the fun begins. A variable is a way of assigning a name to a value. 8700000 is just a value, but if we assign a name to it, then it gets a special meaning:

number_of_species = 8700000
print(number_of_species)

In this case, the variable number_of_species represents the estimated number of eukaryotic species on the planet, which is 8700000. So 8700000 is the value, and “number_of_species” is the variable name. Write the code above into a file and run it. Notice how this lets us refer to the value using the variable name. What appears in the terminal when you do that? Do you see number_of_species or 8700000?

As you can see in the small program above, one of two different things happens when a variable name appears in Python code:

• Assignment: When a variable name appears to the left of an equal sign, a value is assigned to the variable. This happens in the first line where number_of_species is assigned the value 8700000.
• Substitution: In all other contexts, the variable is substituted for its value. This happens in the second line where Python substitutes the variable name number_of_species for its value 8700000 and then prints that.

That is it, but let us take the example further and create another variable to which we assign the value 1200000. That is the number of species discovered so far. Now, let us add this to the program and use it to compute the number of species we have yet to identify. Start by reading the code below super carefully. Remember that a variable is either assigned a value or substituted for the value it represents. For each occurrence of the variables below, determine if they are being assigned a value or if they are substituted for their value.

number_of_species = 8700000
number_discovered = 1200000
number_unidentified = number_of_species - number_discovered
print(number_unidentified)

Now write the code into a file and run it. Take some time to let it sink in that variables are extremely useful for two reasons:

1. Variables give meaning to a value. Without the variable name, the value of 1200000 could just as well be the number of people that live in Copenhagen. However, by giving the value a meaningful name, it becomes clear what it represents.
2. We can assign new values to variables (that is why they are called variables). For example, we can change the value of number_discovered as new species are discovered.

Your variable names can be pretty much anything, but they have to start with a letter or an underscore (_), and the rest of the name has to be either letters, numbers, or underscores. To be clear, a space is not any of those things, so do not use spaces in variable names. Above all, be careful in your choice of variable names. Variable names are case-sensitive, meaning that count and Count are different variables. Stick to lowercase variable names. That makes your code easier to read.

Exercise 5-17

For each occurrence of the variables below, determine if they are being assigned a value or if they are substituted for their value.

breeding_birds = 4
print(breeding_birds)
breeding_birds = 5
print(breeding_birds)

Exercise 5-18

For each occurrence of the variables below, determine if they are being assigned a value or if they are substituted for their value.

breeding_birds = 4
print(breeding_birds)
breeding_birds = breeding_birds + 1
print(breeding_birds)

Exercise 5-19

What happens if you take the first example in this section and swap the two lines? So, going from this:

number_of_species = 8700000
print(number_of_species)

to this:

print(number_of_species)
number_of_species = 8700000

Explain to yourself what happens in each case. What kind of error do you get with version two, and why? Remember Oath 2!

Exercise 5-20

Write the following code in a file, save it, and run it.

income = 45000
taxpercentage = 0.43
tax_amount = tax_percentage * income
income_after_tax = income - tax_amount
print('Income after tax is', income_after_tax)

You should get an error that looks at lot like this one:

Traceback (most recent call last):
  File "tax.py", line 3, in <module>
    tax_amount = tax_percentage * income
NameError: name 'tax_percentage' is not defined

It says that the error is on line 3. Can you figure out what is wrong? Hopefully, you will now appreciate how much attention to detail is required when programming. Every tiny, little symbol or character in your code is essential.

Different types of values

By now, you probably have a pretty good idea of what a value in Python is. So far, you have seen text like 'Banana', integers like 7, and numbers with a fractional part like 4.25.

In Python, a text value is a type of value called a string, which Python denotes as str (abbreviation for “string”). So 'Banana' is a string, and so is 'Banana split'. There are two types of numbers in Python. Integers (7, 42, and 3) are called int. Numbers with a fractional part (like 3.1254 and 4.0) are that are called float (an abbreviation for “floating-point number”).

As I mentioned earlier, True and False are Python values too. They are called booleans or bool, named after an English mathematician called George Boole famous for his work on logic.

So the different types of values we know so far are:

Name	Type in Python	Examples
String	str	"hello", '9'
Integer	int	0, 2721, 9
Floating-point	float	1.0, 4.4322
Boolean	bool	True, False
None	NoneType	None

In case you did not notice, I added a special type at the end that can only have the value None. I may sound a little weird, but in programming, we sometimes need a value representing nothing or None. For now, just make a mental note that None is also a Python value.

When you do computations in Python, it is no problem to mix integers and floating-point numbers. Try this:

print("What is 0.5 * 2?", 0.5 * 2)
print("What is 3 / 2?", 3 / 2)

As you can see we can also make computations using only integers that result in floating-point numbers.

Some of the math operators not only work on numbers, but they also work on strings. That way, you can add two strings together. It is no longer math, of course - but quite handy.

fruit = 'Ba' + 'na' + 'na'
print(fruit)

Exercise 5-21

If you try to combine different types of values in ways that are not allowed in Python, you will get an error. Try each of the following weird calculations, and read each error message carefully.

x = 3 - '1.5'
print(x)

x = None - 4
print(x)

Exercise 5-22

Write these two examples and compare the resulting values of x

x = '9' + '4'
print(x)

x = 9 + 4
print(x)

Exercise 5-23

Try these two examples. What happens in each case? Does it make sense?

x = '72' * 3

x = '72' * '3'

Exercise 5-24

Will this work? Use what you have learned from the other exercises and try to predict what will happen here. Then, write the code and try it out.

x = 'Ba' + 'na' * 2
print(x)

Exercise 5-25

Sometimes, you may need to change a string to a number. You can do that like this:

some_value = "42"
other_value = int(some_value)

Write some code that converts strings to numbers and numbers to strings. Remember that numeric values are either integers or float. Use int, float as in the example above. You will notice that only meaningful conversions work. E.g., this will not work: number = int('four'). To convert a number to a string, you can use str.

Having completed the above exercises, you should take note of the following four important points:

1. All Python values have a type. You know about strings, integers, floating-points, and booleans so far.
2. Math operators let you do cool things like concatenating two strings by adding them together.
3. The flip side of that cool coin is that Python will assume you know what you are doing if you add two strings ('4' + '4' is '44' not 8) or multiply a string with an integer ('4' * 4 is '4444' not 16).
4. You can change the type of a value, e.g., '4' to 4 or 1 to 1.0.
5. Python will throw a TypeError if you try to combine types values of values in ways that are not allowed.

Escape characters: An escape character is a backslash \ followed by a single character. \n and \t are the most commonly used ones.

Exercise 5-26

What do you think is printed here?

main_course = 'Duck a la Banana\n'
dessert = 'Banana split\n'
menu = main_course + dessert
print(menu)

Can you figure out what the special character \n represents?

Exercise 5-27

What do you think is printed here?

dish_one = 'Banana\t\tsplit'
dish_two = 'Chocolate\tcake'
print(dish_one)
print(dish_two)

Can you figure out what the special character \t represents?

Mixed exercises

Each chapter in the book ends with a set of mixed exercises meant to allow you to combine what you have learned so far. In this case, they are meant to train your familiarity with the following topics:

• Strings
• Math
• Logic
• Types of values
• Variables

Exercise 5-28

What happens if you try to run the following program?

print("What happens now?", 1 / )

If you get an error, why do you think you get that error?

Exercise 5-29

What happens if you try to run the following program?

print("What happens now?", 1 / 3

If you get an error, why do you think you get that error? Can you fix it? (Hint: EOF is short for End Of File)

Exercise 5-30

Determine, for each of the eight occurrences of the variable x below, where it is being assigned a value and when it is substituted for its value:

x = 1
x = x + 1
x = x + 1
x = x + 1
print(x)

Then, figure out what is printed and why (remember oath 2). What value does x represent at each occurrence in the code?

Exercise 5-31

Some comparison operators also work with strings. Consider this code:

print("apples" == "pears")

What is printed here? Write the code and see for yourself once you think you know. If you were wrong, make sure you understand why.

Exercise 5-32

Consider this code:

print('aaaaaa' < 'b')
print('a' < 'b')
print('aa' < 'ab')
print('99' > '100')
print('four bananas' > 'one banana')

What is printed here? Write the code and see for yourself once you think you know. By what rule does Python decide if one string is smaller than another? You may have a clue if you have looked something up in an encyclopedia recently. Also, try to google “ASCII table”.

Exercise 5-33

Consider this code:

print('banana' < 'Banana')

What is printed here? Write the code and see for yourself once you think you know.

Exercise 5-34

Do you think it is allowed to use relational operators on values of different types? Try these out and see for yourself:

print('Banana' > 4)

print('42' == 43) # this one is dangerous...

print(4 in '1234')

Practice reading this kind of error (TypeError).

Exercise 5-35

Can you use the in operator to test if this mini gene is part of the DNA string?

mini_gene = 'ATGTAG'
dna_string = 'GCTATGTAGGTA'

Exercise 5-36

Say you have two strings "4" and "2". What happens if you add them like this: "4" + "2". Can you convert each one to integers so you get 6 when you add them? (have a look at Section 5.0.0.25 if you do not remember).

Exercise 5-37

What happens if you run this code? Do you get an error? Do you remember why?

1value = 42

Exercise 5-38

What happens if you run this code?

print('Hi')
print('Hi')
print('Hi')

Compare this to what happens when you run this code:

print('Hi\nHi\nHi')

Do you remember what \n represents? What does it tell about what is added at the end every time you print something?

Exercise 5-39

Make three exercises for your fellow students. See if you can make them so they test the understanding of (almost) all you have learned so far.