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

• To: mathgroup at smc.vnet.net
• Subject: [mg56262] Re: (x-y) DiracDelta[x-y] does not simplify to 0
• From: "Dr. Wolfgang Hintze \(SBS\)" <wolfgang.hintze at siemens.com>
• Date: Wed, 20 Apr 2005 05:32:06 -0400 (EDT)
• References: <d42kg5\$39t\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I was even more surprised by this:

In[3]:= Simplify[(x - y)*DiracDelta[x - y], {x, y}]
Out[3]=0

As I don't know what {x,y} means here.
I found it by playing around with the more meaningful {x>y},{x<y},{x==y}
Wolfgang

"Alain Cochard" <alain at geophysik.uni-muenchen.de> wrote in message
news:d42kg5\$39t\$1 at smc.vnet.net...
> 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
>
>
>      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?
>