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 > >