Test whether an expression is a polynomial over a non-commutative algebra:

The variable list needs to contain all non-commutative variables:

The variable list does not need to contain the commutative or scalar variables of the algebra:

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:

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:

An expression may only be a polynomial in all non-commutative variables it involves:

Unlike in the commutative case, the expression is not a polynomial in proper subsets of its variables: