# Orderless

is an attribute that can be assigned to a symbol f to indicate that the elements ei in expressions of the form f[e1,e2,] should automatically be sorted into canonical order. This property is accounted for in pattern matching.

# Details

• 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.
• Functions like Plus and Times are Orderless.
• 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.

# Examples

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## Basic Examples(3)

Plus sorts its arguments because it has attribute Orderless:

Any orderless function will sort its arguments:

The pattern matcher reorders arguments of Orderless functions to obtain matches:

Note that Plus itself does not reorder these particular arguments:

## Properties & Relations(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:

This sorting occurs as part of the standard evaluation process:

## Possible Issues(1)

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

Wolfram Research (1988), Orderless, Wolfram Language function, https://reference.wolfram.com/language/ref/Orderless.html.

#### Text

Wolfram Research (1988), Orderless, Wolfram Language function, https://reference.wolfram.com/language/ref/Orderless.html.

#### CMS

Wolfram Language. 1988. "Orderless." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Orderless.html.

#### APA

Wolfram Language. (1988). Orderless. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Orderless.html

#### BibTeX

@misc{reference.wolfram_2022_orderless, author="Wolfram Research", title="{Orderless}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Orderless.html}", note=[Accessed: 30-January-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_orderless, organization={Wolfram Research}, title={Orderless}, year={1988}, url={https://reference.wolfram.com/language/ref/Orderless.html}, note=[Accessed: 30-January-2023 ]}