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

Synopsis

• Function: diffOp

• Usage:

  diffOp_R f

  diffOp(f, R)

  diffOp f

• Inputs:
  • R, a ring
  • f, a ring element, of a WeylAlgebra of R
• Outputs:
  • a differential operator
• Consequences:

  • if called without a specified ring (i.e. diffOp f), creates a new ring by discarding the $dx$-variables and caches it in the Weyl algebra
  • if such a ring had been previously cached, the cached ring will be used.

Description

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

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

• DiffOp -- differential operator
• diffOp(HashTable) -- create a differential operator