Re: (x-y) DiracDelta[x-y] does not simplify to 0

*To*: mathgroup at smc.vnet.net*Subject*: [mg56233] Re: [mg56198] (x-y) DiracDelta[x-y] does not simplify to 0*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 20 Apr 2005 05:30:06 -0400 (EDT)*References*: <200504190854.EAA02509@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 19 Apr 2005, at 17:54, Alain Cochard wrote: > > Mathematica 4.0 for Linux > Copyright 1988-1999 Wolfram Research, Inc. > -- Motif graphics initialized -- > > Considering that > > In[1]:= FullSimplify[x DiracDelta[x]] > > Out[1]= 0 > > I was surprised about this one: > > In[2]:= FullSimplify[(x-y) DiracDelta[x-y]] > > Out[2]= (x - y) DiracDelta[x - y] > > whereas: > > In[3]:= FullSimplify[(x-y) DiracDelta[x-y]/.x-y->z] > > Out[3]= 0 > > Is it simply that Mathematica is a little weak on Out[2], or does it have a > good reason for not simplifying, i.e., am I missing something at the > mathematics level? > > Thanks in advance, > Alain > > On the one hand I think the Mathematica implementation of DiracDelta (and KroneckerDelta) leaves a lot to be desired... and that is putting it mildly. (That means I have plenty of much worse examples...). On the other hand, I am not convinced that Mathematica ought to perform this sort of simplification at all. DiracDelta is a generalised function. The statement x DiracDelta[x] == 0 needs a lot of interpreting to make sense of (I prefer to think of it as nonsense). However Integrate[(x-y) DiracDelta[x-y], {x,-Infinity,Infinity}] 0 is correct. Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/andrzej/index.html http://www.mimuw.edu.pl/~akoz/

**References**:**(x-y) DiracDelta[x-y] does not simplify to 0***From:*Alain Cochard <alain@geophysik.uni-muenchen.de>