Re: FullSimplify doesn't simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg32787] Re: [mg32762] FullSimplify doesn't simplify*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sat, 9 Feb 2002 23:39:33 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I hope everybody ignored my message below since almost everything in it was complete nonsense. Perhaps I am getting too old for this sort of thing. Andrzej On Friday, February 8, 2002, at 09:46 PM, Andrzej Kozlowski wrote: > Actually there are two different questions here. Let's start with the > second. > > > In[9]:= > ComplexExpand[(-I)^I] > > Out[9]= > E^(Pi/2) > > In[10]:= > ComplexExpand[(-1)^I] > > Out[10]= > E^(-Pi) > > In[11]:= > ComplexExpand[I^I] > > Out[11]= > E^(-Pi/2) > > > So (-1 * I)^I != (-1)^I * (I)^I > > You can also verify this using FullSimplify: > > In[12]:= > FullSimplify[(-1*I)^I==(-1)^I*(I)^I] > > Out[12]= > False > > However this is not the reason why Mathematica does not simplify in > your case! To see that consider: > > In[13]:= > FullSimplify[(x*y)^n,Element[n,Reals]] > > Out[13]= > (x*y)^n > > However the identity is indeed valid for real exponents. > > The point is that Simplify (and FullSimplify) will not in general use > transformations involving symbolic powers (except for a few of the > simplest ones that are universally true and are usually applied even > without without Simplify, e.g. > In[14]:= > (2*a)^y > > Out[14]= > 2^y*a^y > ). The reason is that the general algorithms on which these > transformations depend are essentially algebraic, which means they work > on polynomials and rational functions and some special functions like > trigonometric functions etc. > > > On Friday, February 8, 2002, at 05:49 PM, Ken Morgan wrote: > >> Does anyone know why Mathematica doesn't simplify the following to >> True? >> >> >> In[1] := FullSimplify[(x y)^n == (x^n)(y^n)] >> >> Out[1] := (x y)^n == (x^n)(y^n) >> >> Are there cases where this is not true? >> >> >> Thanks, >> Ken Morgan >> kmorga51 at calvin.edu >> >> >> >> > > laton.c.u-tokyo.ac.jp/andrzej/