NonCommutativeMultiply
a**b**c
is a general associative, but non‐commutative, form of multiplication.
Details
- NonCommutativeMultiply has attribute Flat.
- Instances of NonCommutativeMultiply are automatically flattened, but no other simplification is performed.
- You can use NonCommutativeMultiply as a generalization of ordinary multiplication for special mathematical objects.
- NonCommutativeMultiply is the default operator used by NonCommutativeAlgebra. »
Examples
open all close allBasic Examples (1)
Applications (2)
Use NonCommutativeMultiply to represent composition in an algebra of differential operators.
The base case, where 
is a function, simply multiplies by 
:
The next two properties express linearity:
Here the operator is D. HoldPattern stops the derivative from acting on the double blank:
Composition of operators applied to an expression:
Power of an operator applied to an expression:
Apply these rules to derive the KdV equation for the Lax pair:
Build a function to expand non-commutative products. Distributivity with respect to Plus:
Handling the commutative product inside the non-commutative one:
Properties & Relations (3)
No automatic simplification rules exist for NonCommutativeMultiply:
Expand and Simplify do not operate on expressions with NonCommutativeMultiply:
NonCommutativeMultiply is the default operator used by NonCommutativeAlgebra:
Possible Issues (1)
NonCommutativeMultiply of one argument, unlike Times, stays unevaluated:
Text
Wolfram Research (1988), NonCommutativeMultiply, Wolfram Language function, https://reference.wolfram.com/language/ref/NonCommutativeMultiply.html (updated 2025).
CMS
Wolfram Language. 1988. "NonCommutativeMultiply." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/NonCommutativeMultiply.html.
APA
Wolfram Language. (1988). NonCommutativeMultiply. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonCommutativeMultiply.html