Re: FullSimplify doesn't simplify
- To: mathgroup at smc.vnet.net
- Subject: [mg32778] Re: FullSimplify doesn't simplify
- From: "John Doty" <jpd at w-d.org>
- Date: Sat, 9 Feb 2002 05:11:54 -0500 (EST)
- References: <a404nb$bqk$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <a404nb$bqk$1 at smc.vnet.net>, "Ken Morgan" <kmorga51 at calvin.edu>
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?
Sure:
In[1]:= (x y)^n == (x^n)(y^n)/.{x->-1,y->-1,n->1/2}
Out[1]= False
It's true in some common special cases:
In[2]:= FullSimplify[(x y)^n == (x^n)(y^n), Element[n,Integers]]
Out[2]= True
In[3]:= FullSimplify[(x y)^n == (x^n)(y^n), X>=0 && y>=0]
Out[3]= True
If you like living dangerously you can use PowerExpand:
In[4]:= PowerExpand[(x y)^n == (x^n)(y^n)]
Out[4]= True
Beware, however, that PowerExpand's transformations are not valid in
general.
--
| John Doty "You can't confuse me, that's my job."
| Home: jpd at w-d.org
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