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
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
