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

*To*: mathgroup at smc.vnet.net*Subject*: [mg56296] Re: (x-y) DiracDelta[x-y] does not simplify to 0*From*: Alain Cochard <alain at geophysik.uni-muenchen.de>*Date*: Thu, 21 Apr 2005 05:36:15 -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 writes: > 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 I have not much experience with delta functions with complex numbers, so I don't have an opinion on wh04 and wh05, but I indeed find wh01->03 funny. Hope some will tell us what's going on. Alain