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MathGroup Archive 2006

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Re: How do I create a parametric expression?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68608] Re: How do I create a parametric expression?
  • From: axlq at spamcop.net (axlq)
  • Date: Fri, 11 Aug 2006 04:40:47 -0400 (EDT)
  • References: <200608090819.EAA21141@smc.vnet.net> <ebec2n$lic$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <ebec2n$lic$1 at smc.vnet.net>,
gardyloo  <gardyloo at mail.wsu.edu> wrote:
>   I think this question comes up pretty often on the list; it seems to
>be one of the harder things to do (or do well, and consistently) with
>Mathematica. Usually, it seems that people have to delve into the
>FullForm expressions, which can be a huge pain.

Yes, from the responses posted to my original query, it seems
that there is no straightforward way to do it than by making
substitutions one step at a time.

Yours is the most efficient suggestion yet, doing most of it in one
step:

>In[9]:=
>expr //. {(a^2 + (q - z)^2)^(n_) -> R^(2*n)}
>
>Out[9]=
>
>-((1/(8*Pi*R^5*w))*((1 + 2*n)*
>    ((a^4*k^2 + a^2*(-1 + k^2*(q - z)^2) + 2*(q - z)^2)*
>      Cos[k*R] - k*R*(a^2 - 2*(q - z)^2)*Sin[k*R])*
>    Sin[((1 + 2*n)*Pi*z)/L]))

...and as others have suggested, replacing (q-z)^2 by R^2-a^2 takes
it a bit further.

-Alex


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