Everything Is an Expression
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
. You might use
to represent a mathematical function
. The function is named
, and it has two arguments,
You do not always have to write expressions in the form
. For example,
is also an expression. When you type in
converts it to the standard form Plus
. Then, when it prints it out again, it gives it as
The same is true of other "operators", such as
In fact, everything you type into Mathematica
is treated as an expression.
Some examples of Mathematica expressions.
You can see the full form of any expression by using FullForm[expr]
This is the full form of the expression.
Here is another expression.
Its full form has several nested pieces.
The object f
in an expression
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.
gives the "function name"
gives the name of the "operator".
You can distinguish different kinds of numbers by their heads.
|Head[expr]||give the head of an expression: the f in |
|FullForm[expr]||display an expression in the full form used by Mathematica|
Functions for manipulating expressions.