Fourier -- Fourier transform for Weyl algebra

Synopsis

• Usage:

  Fourier A

• Inputs:
  • A, a matrix, a matrix, function, or ideal over the Weyl algebra
• Outputs:
  • a matrix, the Fourier transform of A as a matrix, function, or ideal over the Weyl algebra

Description

i1 : makeWA(QQ[x,y])

o1 = QQ[x..y, dx, dy]

o1 : PolynomialRing, 2 differential variables

i2 : L = x^2*dy + y*dy^2 + 3*dx^5*dy

        5      2         2
o2 = 3dx dy + x dy + y*dy

o2 : QQ[x..y, dx, dy]

i3 : Fourier L

       5        2    2
o3 = 3x y + y*dx  - y dy - 2y

o3 : QQ[x..y, dx, dy]

See also

• WeylAlgebra -- an optional argument