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

• To: mathgroup at smc.vnet.net
• Subject: [mg56300] Re: (x-y) DiracDelta[x-y] does not simplify to 0
• From: Peter Pein <petsie at arcor.de>
• Date: Thu, 21 Apr 2005 05:36:18 -0400 (EDT)
• References: <d42kg5\$39t\$1@smc.vnet.net> <d45agf\$ieu\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Dr. Wolfgang Hintze wrote:
> 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
>> -- 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
>>
>>
>
>
FullSimplify[expr,lst] simplifies expr assuming all element of lst being
True:

In[1]:= FullSimplify[{a, b, c}, {a, c}]
Out[1]= {True, b, True}

and (True - True) evaluates to 0 (strange, isn't it? IMHO this
shouldn't) eval to anything other than \$Failed)
--
Peter Pein
Berlin

```

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