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Mathematica > Core Language > Defining Variables and Functions > Attributes > Orderless >

BUILT-IN MATHEMATICA SYMBOL

Orderless

Orderless
is an attribute that can be assigned to a symbol f to indicate that the elements

in expressions of the form

should automatically be sorted into canonical order. This property is accounted for in pattern matching.

The Orderless attribute for a function corresponds to the mathematical property of commutativity.

Functions with the Orderless attribute use canonical order as described in the notes for Sort.

For an object that represents a matrix or a tensor, the Orderless attribute represents symmetry among indices.

In matching patterns with Orderless functions, all possible orders of arguments are tried.

The Orderless attribute must be assigned before defining any values for an Orderless function.

Out[1]=

Out[2]=

Out[2]=

All possible argument orderings are tried to match a definition for an orderless function:

Elements of an expression whose head is orderless are sorted into standard order:

Pattern matching with orderless functions can lead to a large number of possible cases: