This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 MATHEMATICA TUTORIAL

# Expressions as Trees

Here is an expression in full form.
 Out[1]//FullForm=
TreeForm prints out expressions to show their "tree" structure.
 Out[2]//TreeForm=
You can think of any Mathematica expression as a tree. In the expression above, the top node in the tree consists of a Plus. From this node come two "branches", and . From the node, there are then two branches, and , which can be viewed as "leaves" of the tree.
This matrix is a simple tree with just two levels.
 Out[3]//TreeForm=
Here is a more complicated expression.
 Out[4]=
The tree for this expression has several levels. The representation of the tree here was too long to fit on a single line, so it had to be broken onto two lines.
 Out[5]//TreeForm=
The indices that label each part of an expression have a simple interpretation in terms of trees. Descending from the top node of the tree, each index specifies which branch to take in order to reach the part you want.