construct the adjoint of a given Ore polynomial ring - Maple Help

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OreTools[AdjointRing] - construct the adjoint of a given Ore polynomial ring

OreTools[AdjointOrePoly] - compute the adjoint Ore polynomial in a given Ore ring

Calling Sequence

AdjointRing(A)

AdjointOrePoly(Poly, A)

Parameters

Poly

-

Ore polynomial; to define an Ore polynomial, use the OrePoly structure.

A

-

Ore ring; to define an Ore ring, use the SetOreRing function.

Description

• 

The AdjointRing(A) calling sequence constructs the adjoint of A.

• 

The AdjointOrePoly(Poly, A) calling sequence computes the adjoint Ore polynomial of the polynomial Poly in A.

• 

An Ore polynomial ring is defined vi SetOreRing. For a description of the adjoint of an Ore polynomial ring, see OreAlgebra.

Examples

withOreTools:

withOreTools[Properties]:

Define the shift polynomial ring.

A:=SetOreRingn,'shift'

A:=UnivariateOreRingn,shift

(1)

Construct the adjoint Ore polynomial ring B of A.

B:=AdjointRingA

B:=AdjUnivariateOreRingn,shift

(2)

Construct the adjoint Ore polynomial ring C of B. The ring C must be the same as A.

C:=AdjointRingB

C:=UnivariateOreRingn,shift

(3)

GetSigmaAsn,n=GetSigmaCsn,n

sn+1=sn+1

(4)

GetSigmaInverseAsn,n=GetSigmaInverseCsn,n

sn1=sn1

(5)

GetdeltaAsn,n=GetdeltaCsn,n

0=0

(6)

Define two Ore polynomials P1 and P2 in A.

P1:=OrePolyn+1,n;P2:=OrePoly1,n+1

P1:=OrePolyn+1,n

P2:=OrePoly1,n+1

(7)

Compute the adjoint operators of P1 and P2 in A.

adjP1:=AdjointOrePolyP1,A

adjP1:=OrePolyn+1,n1

(8)

adjP2:=AdjointOrePolyP2,A

adjP2:=OrePoly1,n

(9)

Multiply adjP1 and adjP2 in the adjoint B of A.

MultiplyadjP1,adjP2,B

OrePolyn+1,n2+2n1,n12

(10)

See Also

OreTools, OreTools/OreAlgebra, OreTools/OrePoly, OreTools[Properties], OreTools[SetOreRing]


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