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

• To: mathgroup at smc.vnet.net
• Subject: [mg56225] Re: [mg56198] (x-y) DiracDelta[x-y] does not simplify to 0
• From: yehuda ben-shimol <bsyehuda at gmail.com>
• Date: Wed, 20 Apr 2005 05:29:55 -0400 (EDT)
• References: <200504190854.EAA02509@smc.vnet.net>
• Reply-to: yehuda ben-shimol <bsyehuda at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

As I remember, DiracDelta is singular and has a meaning only under integration.
Anyway the properties of the DiracDelta are kept by Mathematica
i.e.,
Integrate[(x - y)DiracDelta[x - y], {x, -1, 1}, {y, -1, 1}]
returns 0 as expected
yehuda

On 4/19/05, Alain Cochard <alain at geophysik.uni-muenchen.de> 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
> 
>

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