An n-dimensional representation for the Dirac delta "function"

Edgardo S. Cheb-Terrab

Waterloo Maple Inc
Theoretical Physics Department, UERJ - Brazil
Centre for Experimental and Constructive Mathematics

The Dirac "function", actually a distribution, is implemented in Maple as a 
function of one variable, delta(x);.  In typical applications, however, we need 
an n-dimensional representation for it, where
`@@`(delta,n)([x[1], x[2], ..., x[k]]) = delta(x[1])*delta(x[2])*...*delta(x[k]).  
We also need a representation for the n-dimensional partial derivative of this 
more general Dirac function as well as expansion, combination, simplification, 
fourier transformation and mainly integration related procedures. These routines 
were developed and the idea is to integrate the set into a future release of the 
Maple system.