Lecture Notes 04: Python Basics

Python Expressions

Expressions are combinations of variables and values that must be "resolved" and turned into a combined value before the statement is completely executed.

12 + 6
x = 5
y = 2
z = x + y
w = x + 1 + y + 123 + z
print(x)
print(y)
print(z)
print(w)

1. 12 + 6     : this expression resolves to an 18 but is not saved in a variable;
2. x = 5      : the right-hand-side of the "=" sign (value 6) is a 'trivial' expression, since it is already a value);
3. y = 2      : same as above;
4. z = x + y      : here, the expression that needs resolving is x + y; it will resolve to the value 7
5. w = x + 1 + y + 123 + z     : again, the expression is on the right-hand side of the "=" sign; this one combines numbers and variables.

Basic Operations

An operator is a symbol that indicates a transformation on one or more entities called operands.

There are unary operators that apply to a single element, and binary operators that require two such entities to operate on.

The following are the basic arithmetic operations you might find in an expression:

1. Addition: y = x + 7    it may contain constants (7) or variables.
2. Subtraction: z = y - 2   it may contain constants (2) or variables
3. Multiplication: m = x * 5    it may contain constants (5) or variables
4. Division: n = m / 5    it may contain constants (5) or variables
5. Integer Division: n = n // 2    it may contain constants (2) or variables; same as floor(n/2)
6. Exponentiation(Power): p = n ** 2    it may contain constants (2) or variables; same as \(n^2\)
7. Modular arithmetic (Modulo): q = 9 % 3    it may contain constants (3) or variables
   This is the same as: integer remainder of 9/3

• P: stands for Parentheses; what is surrounded by praentheses is resolved first (inside out if many are present)
• E: stands for Exponents; apply exponents before the operations mentioned below;
• MD: stands for Multiplication and Division (if many, solve from left to right);
• AS: stands for Addition and Subtraction (if many, solve from left to right);

Strange Operator: Integer Division //

(In the following explanation, we use "=" as "equals")

When we divide two numbers, we might have a perfect fit between the numerator and the denominator
For example:    \(x = 8/4\)   (which has a quotient of 2)

OR, we could have a quotient AND a remainder
For example:   \(x = 9/4\)   (which has a quotient of 2 AND a remainder of 1)

IF   \(n / d = q \)   with a remainder of   \(r\)

we can reorder this as:   \( d*q + r = n\)

Example: since   \(17 / 5 = 3 \)   with a remainder of 2, then
\(5*3 + 2 = 17 \)

What integer division does is ignore the remainder.
So, the operation: \(17 // 5 = 3 \)

This is the same as \( \texttt{floor(17/5)} \)
(This is equivalent to rounding down, or in the direction of \(-\infty\))

Activity 3 [2 minutes]:

Strange Operator: Modulo %

We have the same approach as before:
Example: since   \(17 / 5 = 3 \)   with a remainder of 2, then
\(5*3 + 2 = 17 \)

What modulo does is ignore the quotient and it "returns" the remainder.
So, the operation: \(17 % 5 = 2 \)

Note that Python chooses to return a remainder (modulo result) with the same sign as the denominator!

Another way to think about it is this:

if we want to know \(17 % 5\), we can first obtain \(17 // 5\), which is \(\mathbf{3}\),
and then see what the remainder would be if substitute that as the quotient:
\(17 = \mathbf{3} \cdot 5 + x \)
Whatever \(x\) must be here is the correct remainder. In this case, it is 2 because \(17 = 3 \cdot 5 + \mathbf{2} \)

Activity 4 [1 minute]:

Integers and Floats

For numeric assignments, you'll see two main types:

• Integers (no decimal expansion) : like x = 5
• Floats (with decimals; AKA "floating point numbers") : like q = 3.141592
  The float is represented internally by three elements, the significant, the base, and the exponent:
  
  
  

Built-In functions for numbers

The following are built-in functions that work with numbers.

• abs(x) # return the absolute value of x
• int(x) # return x parsed as an int
• float(x) # return x parsed as a float
• max(…) # return the largest of a list of numbers
• min(…) # return the smallest of a list of numbers
• round(x[, n])
  # return x rounded to n digits after the decimal point.
  #If n is omitted, it returns the nearest integer value
• sum(…) # return the sum of a list of numbers

Terminology: "return":

Terminology: "parse":

The int function

The float function

The str function

The ord function

The chr function

Input

A program may accept input from the keyboard, and print it or use it to make decisions.

In python, the way to tell the program to "read input from the keyboard at this point", is to
use the input() built-in function.

At the point where that statement is executed, the program makes sure to "read characters from input until it detects a 'newline'".

If you want the program to display a prompt for the user that asks for input, you may add a little message inside the parentheses:
input("Please Write your name and then press 'return': ")

The usual way to use input is by assigning what the user inputs into a variable and using that variable later in the code.

Note that, the input function reads input as text!

If we want to have the input interpreted as a number, we need to use the built-in functions (int, float) to get Python to do this.

Display: AKA Output (to the console)

We've been working with the print function in order to get something displayed on the console.

Let's see a couple variations on its use:
We will implement these in this template.

You'll see the following output in the console:

Homework