OreTools[Properties] - Maple Programming Help

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OreTools[Properties]

 GetRingName
 return the name of the Ore algebra
 GetVariable
 return the name of the independent variable on which the Ore polynomial ring acts
 GetSigma
 return sigma
 GetSigmaInverse
 return sigma^(-1)
 Getdelta
 return delta
 GetTheta1
 return theta(1)

 Calling Sequence GetRingName(A) GetVariable(A) GetSigma(A) GetSigmaInverse(A) Getdelta(A) GetTheta1(A)

Parameters

 A - Ore algebra; to define an Ore algebra, use the SetOreRing function.

Description

 • 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 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.

Examples

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

Define the shift algebra.

 > $A≔\mathrm{SetOreRing}\left(n,'\mathrm{shift}'\right)$
 ${A}{≔}{\mathrm{UnivariateOreRing}}{}\left({n}{,}{\mathrm{shift}}\right)$ (1)

Determine the properties of the algebra.

 > $\mathrm{GetRingName}\left(A\right)$
 ${\mathrm{shift}}$ (2)
 > $\mathrm{GetVariable}\left(A\right)$
 ${n}$ (3)
 > $\mathrm{GetSigma}\left(A\right)\left(s\left(n\right),n\right)$
 ${s}{}\left({n}{+}{1}\right)$ (4)
 > $\mathrm{GetSigmaInverse}\left(A\right)\left(s\left(n\right),n\right)$
 ${s}{}\left({n}{-}{1}\right)$ (5)
 > $\mathrm{Getdelta}\left(A\right)\left(s\left(n\right),n\right)$
 ${0}$ (6)
 > $\mathrm{GetTheta1}\left(A\right)$
 ${1}$ (7)