The OrePoly Structure
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.
For a brief review of pseudo-linear algebra (also known as Ore algebra), see OreAlgebra.
Examples
withOreTools:
Define the differential algebra.
A≔SetOreRingx,differential
A≔UnivariateOreRingx,differential
Poly≔OrePoly23x+1x24+27x,−2x4+27x,1
ApplyPoly,fx,A
23x+1fxx24+27x−2ⅆⅆxfxx4+27x+ⅆ2ⅆx2fx
Define the shift algebra.
A≔SetOreRingn,shift
A≔UnivariateOreRingn,shift
Poly≔OrePoly1,−2,−2,1
ApplyPoly,sn,A
sn−2sn+1−2sn+2+sn+3
Define the q-shift algebra.
A≔SetOreRingx,q,qshift
A≔UnivariateOreRingx,qshift
Poly≔OrePoly−q1−qx,1
Poly≔OrePoly−q−qx+1,1
ApplyPoly,sx,A
−q−qx+1sx+sqx
See Also
OreTools
OreTools/Apply
OreTools/OreAlgebra
OreTools/SetOreRing
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