Applying Functions to Lists

Many computations are conveniently specified in terms of applying functions in parallel to many elements in a list. Mathematica provides a suite of elegant functional programming constructs for doing this. In Mathematica, mathematical functions are automatically taken to be "listable", so that they are always applied to every element in a list.

Map (/@ ) — map a function over a list, at specified levels

Apply (@@ , @@@ ) — apply a function to a list, at specified levels

MapIndexed — map a function, including index information

MapAt — map a function at particular positions

Scan — scan over every element of a list, applying a function

FoldList — successively apply a function, "folding in" elements from a list

ComposeList   ▪ Outer   ▪ Inner   ▪ Accumulate   ▪ Differences   ▪ Ratios

MapThread — map a function across corresponding elements in multiple lists

Thread — "thread" a function across lists that appear in its arguments

Listable — attribute for any function to automatically thread over lists

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