Further Examples: Apply (@@)

This substitutes New for Old at the head of the expression using the shorthand notation for Apply. (Neither New nor Old has a built-in meaning in Mathematica.)

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This is the same thing.

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The head of a product is Times.

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The head of a list is List.

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You can see heads explicitly using FullForm.

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This substitutes Times for List.

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This changes a line into a polygon.

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This constructs a list of circles from a list of pairs of centers and radii.

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Here is another way to write the previous expression.

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Here, Apply replaces heads in subexpressions at level .

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Here is a list.

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This defines a function ff that permutes mm.

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The permutation can be written as a list of ordered pairs.

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Another way to write the permutation is as a list of rules.

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These rules can be represented more compactly as a list of cycles.

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This defines the function CyclesfromRules that finds all cycles from a list of rules.

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Here are the cycles of ff using CyclesfromRules.

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