NonCommutativeVariables
NonCommutativeVariables[poly,alg]
gives a list of all noncommutative variables in a polynomial poly over an algebra alg.
Details
- NonCommutativeVariables gives a list of variables in a polynomial over a non-commutative algebra.
- The returned list does not include commutative or scalar variables of the algebra alg.
- alg can be a NonCommutativeAlgebra object, {Dot,n}, Composition, TensorProduct or NonCommutativeMultiply. If the algebra argument is omitted, NonCommutativeAlgebra with the default property values is used.
- NonCommutativeVariables goes inside lists in the first argument.
Examples
open all close allBasic Examples (2)
Scope (5)
Variables of a polynomial over an algebra with symbolic property names:
Variables of a polynomial over an algebra of square matrices with Dot product:
Variables of a polynomial over an algebra of linear endomorphisms with Composition:
NonCommutativeVariables goes inside lists in the first argument:
Variables are any expressions found inside algebra operations that are not specified to be scalars:
Scalar arguments to algebra operations are interpreted as scalar multiples of the multiplicative unity:
Properties & Relations (2)
Find variables in a non-commutative polynomial:
The input expression is a non-commutative polynomial in the returned variables:
Unlike in the commutative case, the expression is not a polynomial in proper subsets of its variables:
Use Variables to find variables in commutative polynomials:
Text
Wolfram Research (2025), NonCommutativeVariables, Wolfram Language function, https://reference.wolfram.com/language/ref/NonCommutativeVariables.html.
CMS
Wolfram Language. 2025. "NonCommutativeVariables." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonCommutativeVariables.html.
APA
Wolfram Language. (2025). NonCommutativeVariables. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonCommutativeVariables.html