The GetRingName(A) calling sequence returns the name of the Ore algebra A.

The GetVariable(A) calling sequence returns the independent variable on which the Ore polynomial ring A acts.

The GetSigma(A) calling sequence returns sigma for the Ore algebra A.

The GetSigmaInverse(A) calling sequence returns sigma^(-1) for the Ore algebra A.

The Getdelta(A) calling sequence returns delta for the Ore algebra A.

The GetdeltaStar(A) calling sequence returns delta^(*) for the Ore algebra A.

The GetTheta1(A) calling sequence returns theta(1) for the Ore algebra A.

For a brief review of pseudo-linear algebra (also known as Ore algebra), see OreAlgebra.

$\mathrm{with}\left(\mathrm{OreTools}\right)\:$

$\mathrm{with}\left(\mathrm{OreTools}\left[\mathrm{Properties}\right]\right)\:$

$A≔\mathrm{SetOreRing}\left(n\,'\mathrm{shift}'\right)$

$A≔\mathrm{UnivariateOreRing}\left(n\,\mathrm{shift}\right)$

$\mathrm{GetRingName}\left(A\right)$

$\mathrm{shift}$

$\mathrm{GetVariable}\left(A\right)$

$n$

$\mathrm{GetSigma}\left(A\right)\left(s\left(n\right)\,n\right)$

$s\left(n+1\right)$

$\mathrm{GetSigmaInverse}\left(A\right)\left(s\left(n\right)\,n\right)$

$s\left(n-1\right)$

$\mathrm{Getdelta}\left(A\right)\left(s\left(n\right)\,n\right)$

$0$

$\mathrm{GetdeltaStar}\left(A\right)\left(s\left(n\right)\,n\right)$

$0$

$\mathrm{GetTheta1}\left(A\right)$

$1$

The OreTools[Properties][GetRingName], OreTools[Properties][GetVariable], OreTools[Properties][GetSigma], OreTools[Properties][GetSigmaInverse], OreTools[Properties][Getdelta], OreTools[Properties][GetdeltaStar] and OreTools[Properties][GetTheta1] commands were updated in Maple 2017.