BUILT-IN MATHEMATICA SYMBOL

Ordering

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

Ordering

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

Ordering

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

Ordering

uses Sort

.

MORE INFORMATION

In a numerical list Ordering gives the positions of the n smallest elements. Ordering gives the positions of the n largest elements.

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

is the same as Sort[list].

Ordering is equivalent to Take.

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

Ordering can be used on expressions with any head, not only List.

EXAMPLES

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Basic Examples (3)

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:

In[1]:=

Out[1]=

Apply the ordering:

In[2]:=

Out[2]=

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

In[1]:=

Out[1]=

Find the position of the largest element:

In[1]:=

Out[1]=

Scope (2)

Find positions of elements from the 4

smallest to the largest:

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

Generalizations & Extensions (1)

Use expressions with any head:

Applications (3)

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:

Properties & Relations (2)

Find the position of the maximum element:

is equivalent to Sort[list]: