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 >>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