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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.