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

• To: mathgroup at smc.vnet.net
• Subject: [mg56198] (x-y) DiracDelta[x-y] does not simplify to 0
• From: Alain Cochard <alain at geophysik.uni-muenchen.de>
• Date: Tue, 19 Apr 2005 04:54:54 -0400 (EDT)
• Reply-to: alain at geophysik.uni-muenchen.de
• Sender: owner-wri-mathgroup at wolfram.com

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 mma 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

• Follow-Ups:
  • Re: (x-y) DiracDelta[x-y] does not simplify to 0
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: (x-y) DiracDelta[x-y] does not simplify to 0
    • From: yehuda ben-shimol <bsyehuda@gmail.com>