1.2 Expressions
An expression is a written combination of data with operations to perform on that data. That sounds quite formal, so imagine a mathematical formula like:
15 × 62 + 3 × 6 – 4 .
This expression contains six pieces of data: 15, 6, 2, 3, 6, and 4. There are five operations: multiplication, exponentiation, addition, multiplication, and subtraction. If I rewrite this using symbols often used in programming languages, it is:
15 * 6**2 + 3 * 6 - 4
See that repeated 6? Suppose I want to consider different numbers in its place. I can write the formula:
15 × x2 + 3 × x – 4
and the corresponding code expression:
15 * x**2 + 3 * x - 4
If I give x the value 6, I get the original expression. If I give it the value 11, I calculate:
15 * 11**2 + 3 * 11 - 4
We call x a variable and the process of giving it a value assignment. The expression
x = 11
means “assign the value 11 to x and wherever you see x, substitute in 11.” There is nothing special about x. I could have used y or something descriptive like kilograms.
An expression can contain multiple variables.
Exercise 1.3
In the expression
a * x**2 + b * x + c ,
what would you assign to a, b, c, and x to get
7 * 3**2 + 2 * 3 + 1 ?
What assignments would you do for
(-1)**2 + 9 * (-1) - 1 ?
The way we write data, operations, variables, names, and words together with the rules for combining them is called a programming language’s syntax. The syntax must be unambiguous and allow you to express your intentions elegantly. In this chapter, we do not focus on syntax but more on the ideas and the meaning, the semantics, of what programming languages can do. In Chapter 2, Working with Expressions, we begin to explore the syntax and features of Python.
We’re not limited to arithmetic in programming. Given two numbers x and y, if I saw maximum(x, y), I would expect it to return the larger value. Here “maximum” is the name of a function. We can write our own or use functions created, tested, optimized, and stored in libraries by others.