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MathGroup Archive 2006

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Re: Simplifying algebraic expressions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66926] Re: Simplifying algebraic expressions
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Sun, 4 Jun 2006 01:10:07 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 6/3/06 at 3:25 AM, murray at math.umass.edu (Murray Eisenberg) wrote:

>I think the original poster's intention was to ask how to make
>Mathematica make the following simplifications:

>   (-1)^(2 x + 3 y)
>   ((-1)^(2x)) * ((-1)^(3y))
>   (((-1)^2)^x) * ((-1)^(3y))
>   (1^x) * (-1)^(3y)
>   1 * (-1)^(3y)
>   (-1)^(3y)

>Of course this is valid only in special circumstances, even when x
>and y are real and positive.

Yes, I realized that was the case after I saw the response others made. And I also focused on the expression for the exponent without really considering it was (-1) raised to some power. In any case, you are certainly correct in saying the simplification is only valid for special cases.

The desired simplification can be done with pattern matching as follows:

In[2]:=
(-1)^(2*x + 3*y) /. (-1)^((a_)*(m_) + (b_)*(n_)) :> 
   ((-1)^a)^m*((-1)^b)^n

Out[2]=
(-1)^y

But I don't know that this is any simpler than the suggestion Andrezj made. And using pattern matching in this way really isn't mathematics per se. That is there is nothing done to ensure the substitutions are valid.
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