Built-in Mathematica Symbol

MapIndexed

MapIndexed[f, expr]
applies f to the elements of expr, giving the part specification of each element as a second argument to f.

MapIndexed[f, expr, levelspec]
applies f to all parts of expr on levels specified by levelspec.

Level -1 consists of numbers, symbols and other objects that do not have subparts.

With the option setting Heads->True, MapIndexed also applies to heads of expressions, and their parts.

MapIndexed traverses the parts of expr in a depth-first order, with leaves visited before roots. »

MapIndexed always effectively constructs a complete new expression, and then evaluates it.

#2 gives the indices of each part:

Map at level 1 (default):

Map down to level 2:

Map at level 2:

Map down to level 3:

Map onto all elements of an expression:

Map only onto the "leaves" of the expression:

Negative levels:

Different heads at each level:

Map on levels 0 through 1; the head has index {}:

MapIndexed can be used on expressions with any head:

The function can be mapped onto the heads as well:

MapIndexed works on sparse arrays:

By default, the function is not mapped onto the heads:

Map onto the heads at all levels:

Label parts by position:

Use tooltips to show part numbers of subexpressions:

Convert a list to a polynomial:

Rotate lists based on position:

Obtain a list of all parts in an expression:

Leaves are visited before roots:

Using only the first argument is equivalent to using Map: