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Re: Transformation rule problem

• To: mathgroup at smc.vnet.net
• Subject: [mg58046] Re: Transformation rule problem
• From: dh <dh at metrohm.ch>
• Date: Fri, 17 Jun 2005 05:18:44 -0400 (EDT)
• References: <d8rnfg$l4b$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi Oliver,
I am not sure if I understand your question right. You want to replace 
ewvery a b by d. But what do you mean by "This replacement is required 
to work for arbitrary a and b".
Well, for the part that I understood:

You have 4 different cases: a b, a b^n, a^n b, a^n b^m
The rule for the first case is simply: a b -> d
second case: a b^n_ -> b^(n-1) d
third: a^n b -> a^(n-1) d
four: a^n b^m ->  a^Max[0, n - m] b^Max[0, m - n] d^Min[m, n]

sincerely, Daniel

Oliver Buerschaper wrote:
> 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.
> 
> Cheerio,
> Oliver
>