This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Map

 Map or applies f to each element on the first level in expr. Mapapplies f to parts of expr specified by levelspec.
• Map uses standard level specifications:
 n levels 1 through n Infinity levels 1 through Infinity {n} level n only {n1,n2} levels through
• The default value for levelspec in Map is .
• A positive level n consists of all parts of expr specified by n indices.
• A negative level -n consists of all parts of expr with depth n.
• Level -1 consists of numbers, symbols, and other objects that do not have subparts.
• Level 0 corresponds to the whole expression.
• With the option setting Heads->True, Map includes heads of expressions and their parts.
• Map always effectively constructs a complete new expression and then evaluates it.
• If expr is a SparseArray object, Map applies f to the values or subarrays that appear in expr.
Alternative input form:
Use explicit pure functions:
Map at top level:
Map at level 2:
Map at levels 1 and 2:
 Out[1]=

Alternative input form:
 Out[1]=

Use explicit pure functions:
 Out[1]=
 Out[2]=

Map at top level:
 Out[1]=
Map at level 2:
 Out[2]=
Map at levels 1 and 2:
 Out[3]=
 Scope   (6)
Map at level 1 (default):
Map down to level 2:
Map at level 2:
Map on levels 0 through 2:
Map down to level 3:
Map on all levels, starting at level 1:
Map also at level 0:
Negative levels:
Positive and negative levels can be mixed:
Include heads in the levels specified:
Map can be used on expressions with any head:
The function can be mapped onto the heads as well:
Functions with attribute Listable are mapped automatically:
Map can be used on sparse arrays:
 Options   (1)
By default, the function is not mapped onto the heads:
 Applications   (3)
Reverse all sublists:
Add the same vector to every vector in a list:
Frame integers that are prime:
Leaves are visited before roots:
A function of several arguments can be mapped with MapThread:
MapIndexed passes the index of an element to the mapped function:
MapAll is equivalent to a specific level specification in Map:
Scan does the same as Map, but without returning a result:
Map by default starts at level 1, so does not apply the function to the whole expression:
Show nesting structure of an expression: