WOLFRAM

Wolfram Language & System Documentation Center

Anticommutator[x,y]

gives the anticommutator x**y+y**x of x and y.

Anticommutator[x,y,alg]

gives the anticommutator of x and y in the noncommutative algebra alg.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

Anticommutator

Anticommutator[x,y]

gives the anticommutator x**y+y**x of x and y.

Anticommutator[x,y,alg]

gives the anticommutator of x and y in the noncommutative algebra alg.

Details

Examples

open all close all

Basic Examples  (2)

The anticommutator of x and y over an algebra with the default operations:

Wolfram Language code: Anticommutator[x, y]

The anticommutator of x and y over an algebra with symbolic operations:

Wolfram Language code: alg = NonCommutativeAlgebra[<|"Multiplication" -> mult, "Addition" -> add|>]; Anticommutator[x, y, alg]

Scope  (4)

The anticommutator of x and y over the algebra of square matrices with Dot product:

Wolfram Language code: Anticommutator[x, y, {Dot, n}]

The anticommutator of x and y over the algebra of linear endomorphisms with Composition:

Wolfram Language code: Anticommutator[x, y, Composition]

Traditional form of Anticommutator[x,y]:

Wolfram Language code: Anticommutator[x, y]

Reducing modulo the anticommutator of two variables commutes the variables and adjusts term signs:

Wolfram Language code: NonCommutativePolynomialReduce[x**y**x**y**x + 2y**y**x**x**y**y, {Anticommutator[x, y]}, {y, x}][[2]]

Properties & Relations  (2)

Reducing modulo the anticommutator of two variables commutes the variables and adjusts term signs:

Wolfram Language code: NonCommutativePolynomialReduce[2x**y**x + 3x**x**y**x**x**y**y, {Anticommutator[x, y]}, {y, x}][[2]]

Commutator gives the commutator of two elements of an algebra:

Wolfram Language code: Commutator[x, y]
Wolfram Research (2025), Anticommutator, Wolfram Language function, https://reference.wolfram.com/language/ref/Anticommutator.html.

Text

Wolfram Research (2025), Anticommutator, Wolfram Language function, https://reference.wolfram.com/language/ref/Anticommutator.html.

CMS

Wolfram Language. 2025. "Anticommutator." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Anticommutator.html.

APA

Wolfram Language. (2025). Anticommutator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Anticommutator.html

BibTeX

@misc{reference.wolfram_2026_anticommutator, author="Wolfram Research", title="{Anticommutator}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/Anticommutator.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_anticommutator, organization={Wolfram Research}, title={Anticommutator}, year={2025}, url={https://reference.wolfram.com/language/ref/Anticommutator.html}, note=[Accessed: 13-June-2026]}