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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/