Applying Functions to Lists and Other Expressions
In an expression like 
you are giving a list as the argument to a function. Often you need instead to apply a function directly to the elements of a list, rather than to the list as a whole. You can do this in Mathematica using Apply.
This makes each element of the list an argument of the function
.
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This gives
Times[a, b, c] which yields the product of the elements in the list.
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Here is a definition of a function that works like the built-in function
GeometricMean, written using
Apply.
| Apply[f,{a,b,...}] | apply f to a list, giving  |
| Apply[f,expr] or f@@expr | apply f to the top level of an expression |
| Apply[f,expr,{1}] or f@@@expr | apply f at the first level in an expression |
| Apply[f,expr,lev] | apply f at the specified levels in an expression |
Applying functions to lists and other expressions.
What
Apply does in general is to replace the head of an expression with the function you specify. Here it replaces
Plus by
List.
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Using
Apply without an explicit level specification replaces the top-level list with
.
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This applies
only to parts of
at level 1.
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This applies
at levels 0 through 1.
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