Built-in Mathematica Symbol

Ordering

Ordering[list]
gives the positions in list at which each successive element of Sort[list] appears.

Ordering[list, n]
gives the positions in list at which the first n elements of Sort[list] appear.

Ordering[list, -n]
gives the positions of the last n elements of Sort[list].

Ordering[list, n, p]
uses Sort[list, p].

In a numerical list Ordering[list, n] gives the positions of the n smallest elements. Ordering[list, -n] gives the positions of the n largest elements.

If there are several smallest elements in list, Ordering[list, 1] will give only the position of the one that appears first.

Ordering[list, All, p] gives the position at which all elements of list appear in Sort[list, p].

Find the ordering that sorts a list:

Apply the ordering:

Find the positions of the 4 smallest elements in a list:

Find the position of the largest element:

Find the ordering that sorts a list:

Apply the ordering:

Find the positions of the 4 smallest elements in a list:

Find the position of the largest element:

Find positions of elements from the 4

smallest to the largest:

Find positions of elements in Sort[list, Greater]:

Use expressions with any head:

Find a permutation that sorts a list:

Apply the permutation:

Find the inverse of a permutation:

Sort a list of lists with respect to a particular position:

The same as Sort, but Ordering keeps the original ordering when elements are the same:

Using Ordering this way is much faster for large sets of lists:

Find the position of the maximum element:

list[[Ordering[list]]] is equivalent to Sort[list]: