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MathGroup Archive 2005

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Re: Transformation rule problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58158] Re: Transformation rule problem
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 20 Jun 2005 05:21:36 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <d8rnfg$l4b$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <d8rnfg$l4b$1 at smc.vnet.net>,
 Oliver Buerschaper <groo137vy at yahoo.co.uk> wrote:

> I'm stuck with a problem concerning transformation rules and was 
> wondering whether somebody could give me a hint on this. I wouldn't 
> mind a complete solution either ;-) Here's the problem:
> 
> In a sum like for example
> 
> a^2 b^4 + a^3 b + a^5 + a^5 b
> 
> I'd like to replace every instance of the product (a b) by a different 
> expression, let's call it d. Thus my result should look like
> 
> d^2 b^2 + a^2 d + a^5 + a^4 d
> 
> This replacement is required to work for arbitrary a and b (especially 
> when they're functions). I've already tried some simple transformation 
> rules but they couldn't do the job.

Others have shown how to do this using replacement rules. For this type 
of problem though, I think that PolynomialReduce is the right tool:

  PolynomialReduce[a^2 b^4 + a^3 b + a^5 + a^5 b, a b - d, 
    {a, b}] // Last

Cheers,
Paul

-- 
Paul Abbott                                      Phone: +61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul
        http://InternationalMathematicaSymposium.org/IMS2005/


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