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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