NonCommutativeAlgebra

NonCommutativeAlgebra[alg]
NonCommutativeAlgebra[spec]

represents a non-commutative algebra. alg can name a supported special algebra, while spec can provide generators, relations, operation names and ordering settings.

The resulting object can be passed to NonCommutativeExpand, NonCommutativeCollect and related functions.

Example

Create an algebra using the default non-commutative multiplication:

alg = NonCommutativeAlgebra[];
NonCommutativeExpand[(a + 2 b) ** (3 a + 4 b), alg]

See the official Wolfram Language reference for the complete specification format.