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


Mathematica 4.0 for Linux
Copyright 1988-1999 Wolfram Research, Inc.
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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 mma 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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