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


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
>>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
>>
>>
> 
> 
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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