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MathGroup Archive 2005

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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
> 
> 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
> 
> 


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