Re: Transformation rule problem

• To: mathgroup at smc.vnet.net
• Subject: [mg58044] Re: Transformation rule problem
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Fri, 17 Jun 2005 05:18:41 -0400 (EDT)
• Organization: Universitaet Hannover
• References: <d8rnfg\$l4b\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Oliver Buerschaper schrieb:
> Hi there,
>
> 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.

a^2 b^4 + a^3 b + a^5 + a^5 b/.
{Power[a, m___ : 1] *Power[b, n___ : 1] :>
Power[d, Min[m,n]]*Power[a, m - Min[m, n]] *Power[b, n - Min[m, n]]}