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MathGroup Archive 2002

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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
| Work: jpd at space.mit.edu


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