NonCommutativePolynomialQ[expr,vars,alg]
tests whether expr is a polynomial in vars over the non-commutative algebra alg.


NonCommutativePolynomialQ
NonCommutativePolynomialQ[expr,vars,alg]
tests whether expr is a polynomial in vars over the non-commutative algebra alg.
Details

- NonCommutativePolynomialQ is used to test whether an expression is a polynomial over a non-commutative algebra.
- NonCommutativePolynomialQ gives True if vars includes all variables in expr other than the commutative and 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.
- NonCommutativePolynomialQ threads over lists in the first argument.
Examples
open all close allBasic Examples (2)
Scope (5)
Test whether an expression is a polynomial over an algebra with symbolic property names:
Test whether an expression is a polynomial over an algebra of square matrices with Dot product:
Test whether an expression is a polynomial over an algebra of linear endomorphisms with Composition:
NonCommutativePolynomialQ threads over lists in the first argument:
Scalar arguments to algebra operations are interpreted as scalar multiples of the multiplicative unity:
Properties & Relations (2)
Use NonCommutativeVariables to find variables in a non-commutative polynomial:
The input expression is a non-commutative polynomial in the retuned variables:
Unlike in the commutative case, the expression is not a polynomial in proper subsets of its variables:
Use PolynomialQ to test for commutative polynomials:
In the commutative case, the expression is a polynomial in proper subsets of its variables:
Related Guides
History
Text
Wolfram Research (2025), NonCommutativePolynomialQ, Wolfram Language function, https://reference.wolfram.com/language/ref/NonCommutativePolynomialQ.html.
CMS
Wolfram Language. 2025. "NonCommutativePolynomialQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonCommutativePolynomialQ.html.
APA
Wolfram Language. (2025). NonCommutativePolynomialQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonCommutativePolynomialQ.html
BibTeX
@misc{reference.wolfram_2025_noncommutativepolynomialq, author="Wolfram Research", title="{NonCommutativePolynomialQ}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/NonCommutativePolynomialQ.html}", note=[Accessed: 04-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_noncommutativepolynomialq, organization={Wolfram Research}, title={NonCommutativePolynomialQ}, year={2025}, url={https://reference.wolfram.com/language/ref/NonCommutativePolynomialQ.html}, note=[Accessed: 04-August-2025]}