2.1.6 Expressions as Trees| Here is an expression in full form. | |
In[1]:=
FullForm[x^3 + (1 + x)^2]
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Out[1]//FullForm=
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| TreeForm prints out expressions to show their "tree" structure. | |
In[2]:=
TreeForm[x^3 + (1 + x)^2]
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Out[2]//TreeForm=
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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}}]
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Out[3]//TreeForm=
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| Here is a more complicated expression. | |
In[4]:=
{{a b, c d^2}, {x^3 y^4}}
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Out[4]=
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| 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=
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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.
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