Expressions

We have dealt quite a bit with expressions

e.g.

Lists...

Plots...

Equations...

Functions

Rules

More complicated expressions

Let’s return to our quadratic equation

We can decompose it into atoms:

We see that this expression is created using nested symbols and numbers

The nested structure can be visualized intuitively using TreeForm

Extracting parts of expressions

We can programmatically extract parts of expressions:

Recall:

The root of the expression tree can be obtained by calling Head

This is always the same thing as getting the 0th index:

The “levels” of this tree can be extracted using Level

More sophisticated expressions

Holding expressions

Consider the expression

Mathematica evaluates our input expression and converts it to a canonical form

If we want to maintain the original expression in unevaluated form, use Hold

Hold can be released using ReleaseHold