Re: Full simplify problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg122272] Re: Full simplify problem*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 23 Oct 2011 06:22:52 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j7u59t$u$1@smc.vnet.net>

On Oct 22, 1:18 pm, "A. Lapraitis" <ffcita... at gmail.com> wrote: > Hello, > > Could anyone explain why the following does not give zero? > > In[72]:= Assuming[ > x == y + z, > FullSimplify[ > E^x - E^(y + z) > ] > ] > > Out[72]= E^x - E^(y + z) > > Thanks! Wow! This is rather strange! Here is some similar examples In[31]:= Assuming[x - y == 0, FullSimplify[E^x - E^(y + z)]] (*works*) Out[31]= E^y*(1 - E^z) In[36]:= Assuming[x - y == 2, FullSimplify[E^x - E^(y + z)]](*not works*) Out[36]= E^x - E^(y + z) In[37]:= Assuming[x == y, FullSimplify[E^x - E^(y + z)]] (*works*) Out[37]= E^y*(1 - E^z) In[30]:= Assuming[x == 2*y, FullSimplify[E^x - E^(y + z)]] (*not works*) Out[30]= E^x - E^(y + z) Somehow FullSimplify need some push in order to simplify your expression and similar ones. I don't claim this is a normal behavior, I don't have any explanation for it, I don't know what I would do if I didn't have some knowledge of Mathematica but I found the following workaround (not trivial indeed) for your example: In[69]:= Assuming[x == y + z, FullSimplify[E^x - E^(y + z), ComplexityFunction -> (If[Head[#1] === Power, 1, 0] & )]] Out[69]= 0 This does the same In[70]:= Assuming[x == y + z, FullSimplify[E^x - E^(y + z), ComplexityFunction -> (Count[{#1}, _Power, Infinity] & )]] Out[70]= 0 (You can use the option ComplexityFunction to specify different simplicity criteria. Here the goal is to avoid Power if possible. Remember that Head[Exp[z]] is Power and FullForm[Exp[z]] is Power[E,z].) I would also add that for my similar examples mentioned above a workaround could be: In[80]:= TrigToExp[Assuming[x == 2*y, FullSimplify[E^x - E^(y + z), ComplexityFunction -> (Count[{#1}, _Power, Infinity] & )]]] Out[80]= E^(2*y) - E^(y + z) In[82]:= TrigToExp[Assuming[x - y == 2, FullSimplify[E^x - E^(y + z), ComplexityFunction -> (Count[{#1}, _Power, Infinity] & )]]] Out[82]= E^(2 + y) - E^(y + z) Best Regards Dimitris