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
expression is f[x, y]
. You might use f[x, y]
to represent a mathematical function f (x, y)
. The function is named f
, and it has two arguments, x
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
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 ^
) and /
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 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.
gives the "function name" f
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 f[x, y]|
|FullForm[expr]||display an expression in the full form used by Mathematica|
Functions for manipulating expressions.