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Dmodules :: Fourier

Fourier -- Fourier transform for Weyl algebra

Synopsis

Usage:
Fourier A
Inputs:
- A, a ring element, an ideal, or a matrix
Outputs:
- a ring element, an ideal, ora matrix of the same type as A -- the Fourier transform of A

Description

The Fourier transform is the automorphism of the Weyl algebra which sends x_i to D_i and D_i to -x_i.

i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]

o1 = W

o1 : PolynomialRing

i2 : L = x^2*Dy + y*Dy^2 + 3*Dx^5*Dy       

        5      2         2
o2 = 3Dx Dy + x Dy + y*Dy

o2 : W

i3 : Fourier L

       5        2    2
o3 = 3x y + y*Dx  - y Dy - 2y

o3 : W

See also

WeylAlgebra -- name for an optional argument

Ways to use `Fourier` :

Fourier(Ideal)
Fourier(Matrix)
Fourier(RingElement)