This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
Wolfram Research, Inc.

Manipulating Expressions like ListsLevels in Expressions

2.1.6 Expressions as Trees

Here is an expression in full form.

In[1]:= FullForm[x^3 + (1 + x)^2]

Out[1]//FullForm=

TreeForm prints out expressions to show their "tree" structure.

In[2]:= TreeForm[x^3 + (1 + x)^2]

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", x^3 and (1 + x)^2. From the x^3 node, there are then two branches, x and 3, which can be viewed as "leaves" of the tree.

This matrix is a simple tree with just two levels.

In[3]:= TreeForm[{{a, b}, {c, d}}]

Out[3]//TreeForm=

Here is a more complicated expression.

In[4]:= {{a b, c d^2}, {x^3 y^4}}

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.

In[5]:= TreeForm[%]

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.

Manipulating Expressions like ListsLevels in Expressions