WOLFRAM LANGUAGE TUTORIAL

Expressions as Trees

Here is an expression in full form.
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Out[1]//FullForm=
TreeForm prints out expressions to show their "tree" structure.
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Out[2]//TreeForm=

You can think of any Wolfram Language 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.
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Out[3]//TreeForm=
Here is a more complicated expression.
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Out[4]=
The tree for this expression has several levels.
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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.