BUILT-IN MATHEMATICA SYMBOL

MapIndexed

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

MapIndexed

applies f to all parts of expr on levels specified by levelspec.

MORE INFORMATION

MapIndexed uses standard level specifications:

	n	levels through n
	Infinity	levels through Infinity
	{n}	level n only
	{n₁,n₂}	levels through

The default value for levelspec in MapIndexed 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 consists of numbers, symbols, and other objects that do not have subparts.

Level corresponds to the whole expression.

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.

EXAMPLES

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Basic Examples (3)

gives the indices of each part:

In[1]:=

Out[1]=

gives the indices of each part:

In[1]:=

Out[1]=

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (6)

Map at level

(default):

Map down to level

:

Map at level

:

Map down to level

:

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

through

; the head has index

:

Generalizations & Extensions (3)

MapIndexed can be used on expressions with any head:

The function can be mapped onto the heads as well:

MapIndexed works on sparse arrays:

Options (2)

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

Map onto the heads at all levels:

Applications (5)

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:

Properties & Relations (2)

Leaves are visited before roots:

Using only the first argument is equivalent to using Map: