2.1.1 Everything Is an Expression

Mathematica handles many different kinds of things: mathematical formulas, lists and graphics, to name a few. Although they often look very different, Mathematica represents all of these things in one uniform way. They are all expressions.

A prototypical example of a Mathematica expression is f[x, y]. You might use f[x, y] to represent a mathematical function . The function is named f, and it has two arguments, x and y.

You do not always have to write expressions in the form f[x, y, ... ]. For example, x + y is also an expression. When you type in x + y, Mathematica converts it to the standard form Plus[x, y]. Then, when it prints it out again, it gives it as x + y.

The same is true of other "operators", such as ^ (Power) and / (Divide).

In fact, everything you type into Mathematica is treated as an expression.

x + y + z	Plus[x, y, z]
x y z	Times[x, y, z]
x^n	Power[x, n]
{a, b, c}	List[a, b, c]
a -> b	Rule[a, b]
a = b	Set[a, b]

You can see the full form of any expression by using FullForm[expr].

The object f in an expression f[x, y, ... ] is known as the head of the expression. You can extract it using Head[expr]. Particularly when you write programs in Mathematica, you will often want to test the head of an expression to find out what kind of thing the expression is.

Head[expr]	give the head of an expression: the f in f[x, y]
FullForm[expr]	display an expression in the full form used by Mathematica