x_and_d {weyl}

Generating elements for the first Weyl algebra

Description

Variables x and d correspond to operator \(x\) and \(\partial_x\); they are provided for convenience. These elements generate the one-dimensional Weyl algebra.

Note that a similar system for multivariate Weyl algebras is not desirable. We might want to consider the Weyl algebra generated by \(\left\lbrace x,y,z,\partial_x,\partial_y,\partial_z\right\rbrace\) and correspondingly define R variables x,y,z,dx,dy,dz. But then variable x is ambiguous: is it a member of the first Weyl algebra or the third?

Usage

data(x_and_d)

Author(s)

Robin K. S. Hankin

Examples

d
x

.[d,x]   # dx-xd==1

d^3 * x^4

(1-d*x*d)*(x^2-d^3)