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NoetherianOperators :: diffOp(Ring,RingElement)

diffOp(Ring,RingElement) -- create a differential operator from a Weyl algebra element

Synopsis

Description

Creates a differential operator of the ring R from an element f of a Weyl algebra of R

i1 : needsPackage "Dmodules"

o1 = Dmodules

o1 : Package
i2 : R = QQ[x,y]

o2 = R

o2 : PolynomialRing
i3 : S = makeWA R

o3 = S

o3 : PolynomialRing, 2 differential variables
i4 : D = diffOp_R(x^2 * dx + y^2 * dy^2*dx)

      2     2    2
o4 = y dx*dy  + x dx

o4 : DiffOp
i5 : ring D === R

o5 = true

The ring does not have to be specified. Note that in this case, the resulting operator will not be a differential operator of R, but that of a new ring. This ring is cached, so subsequent calls will result in operators of the same ring.

i6 : E = diffOp(x^2* dx)

      2
o6 = x dx

o6 : DiffOp
i7 : ring E === R

o7 = false
i8 : F = diffOp(dy^2)

       2
o8 = dy

o8 : DiffOp
i9 : ring E === ring F

o9 = true

See also