The type CommAlgebra checks if the algebra A is an algebra of commutative polynomials, as declared by Ore_algebra[poly_algebra] (or Ore_algebra[skew_algebra] with no commutation and commutative parameters only).

The type SkewAlgebra checks if the algebra A is built by using Ore_algebra[skew_algebra] with commutations of the form

for constants p, r, and s only.  This is the case for the commutation types delta, diff, euler, shift, and their dual forms.

The type SkewParamAlgebra checks if the algebra A is built by using Ore_algebra[skew_algebra] with commutations of the form

for constants p, q, r, and s with at least one commutation with .  This is the case for the commutation types qdelta, qdiff, qdilat, qshift, `shift+qshift`, and their dual forms.

The type OreAlgebra checks if the algebra A is any of the above.

The type SkewPolynomial checks if the membership of the polynomial P in the algebra A.  When this algebra allows rational function coefficients, a polynomial with rational function coefficients is a member of the algebra.