The OrePoly Structure - Maple Programming Help

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The OrePoly Structure

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An Ore polynomial is represented by an OrePoly structure. It consists of the constructor OrePoly with a sequence of coefficients starting with the one of degree zero. For example, in the differential case with the differential operator D, OrePoly(2/x, x, x+1, 1) represents the operator 2/x+xD+(x+1)D^2+D^3.

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

Examples

withOreTools:

Define the differential algebra.

ASetOreRingx,'differential'

A:=UnivariateOreRingx,differential

(1)

PolyOrePoly23x+1x24+27x,2x4+27x,1

Poly:=OrePoly23x+1x24+27x,2x4+27x,1

(2)

ApplyPoly,fx,A

23x+1fxx24+27x2ⅆⅆxfxx4+27x+ⅆ2ⅆx2fx

(3)

Define the shift algebra.

ASetOreRingn,'shift'

A:=UnivariateOreRingn,shift

(4)

PolyOrePoly1,2,2,1

Poly:=OrePoly1,2,2,1

(5)

ApplyPoly,sn,A

sn2sn+12sn+2+sn+3

(6)

Define the q-shift algebra.

ASetOreRingx,q,'qshift'

A:=UnivariateOreRingx,qshift

(7)

PolyOrePolyq1qx,1

Poly:=OrePolyqqx+1,1

(8)

ApplyPoly,sx,A

qqx+1sx+sqx

(9)

See Also

OreTools

OreTools/Apply

OreTools/OreAlgebra

OreTools/SetOreRing

 


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