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How do I create a parametric expression?

• To: mathgroup at smc.vnet.net
• Subject: [mg68537] How do I create a parametric expression?
• From: axlq at spamcop.net (axlq)
• Date: Wed, 9 Aug 2006 04:19:05 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I'm trying to figure out how to simplify a large expression so that it's
expressed in terms of a sub-expression that's factored into the larger
one.

My expression looks like this:

-((1 + 2*n)*((a^4*k^2 + a^2*(-1 + k^2*(q - z)^2) + 2*(q - z)^2)
   *Cos[k*Sqrt[a^2 + (q - z)^2]] - k*(a^2 - 2*(q - z)^2)
     *Sqrt[a^2 + (q - z)^2]*Sin[k*Sqrt[a^2 + (q - z)^2]])
       *Sin[((1 + 2*n)*Pi*z)/L])/(8*Pi*w*(a^2 + (q - z)^2)^(5/2))

Now, I *know* there are places in there were Sqrt[a^2+(q-z)^2] occurs,
either by itself or raised to various powers.  If I want to define

R:=Sqrt[a^2+(q-z)^2]

...then how can I make Mathematica re-state my expression in terms
of R?  The ReplaceRepated[] function doesn't seem to do the job.

I need to do this because I am translating the expressions into
Visual Basic code for an Excel application, and it would be nice to
find groupings of terms repeated throughout the expression that I
need to calculate only once.

-Alex

• Follow-Ups:
  • Re: How do I create a parametric expression?
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: How do I create a parametric expression?
    • From: gardyloo <gardyloo@mail.wsu.edu>
  • Re: How do I create a parametric expression?
    • From: "Chris Chiasson" <chris@chiasson.name>