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

• To: mathgroup at smc.vnet.net
• Subject: [mg56266] Re: (x-y) DiracDelta[x-y] does not simplify to 0
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Wed, 20 Apr 2005 05:32:19 -0400 (EDT)
• References: <d42kg5\$39t\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Alain,

may I add the strangest case I found up to now:

case wh01
In[3]:=Simplify[(x - y)*DiracDelta[x - y], {x, y}]
Out[3]=0

But also these are strange enough

case wh02
In[7]:=Simplify[(x - y)*DiracDelta[x - y], {x && y}]
Out[7]=0

case wh03
In[13]:=Simplify[(x - y)*DiracDelta[x - y], {x || y}]
Out[13]=(x - y)*DiracDelta[x - y]

case wh04
In[29]:=Simplify[I*x*DiracDelta[I*x]]
Out[29]=0

But
case wh05
In[30]:=Simplify[I*DiracDelta[I]]
Out[30]=I*DiracDelta[I]

Can't explain ...
Wolfgang

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
>
>
>      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?
>
> Alain
>
>

```

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