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Re: Replace not spotting a replacement

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103427] Re: Replace not spotting a replacement
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Mon, 21 Sep 2009 05:51:51 -0400 (EDT)
  • References: <h94vil$nfi$1@smc.vnet.net>

On 2009.09.20. 12:19, claranet news wrote:
> Hi Folks,
>
> Seems the replace function is being a bit dim here.  This fails:
>
> Sqrt[2 \[Pi]] \[Tau]^(3/2) /. Sqrt[ 2 \[Pi] \[Tau]] ->  \[Mu]
>
> Apologies if this is an FAQ - I couldn't see anything about it.  What do I
> need to do here to coerce Mathematica into making this replacement? I tried using the
> Collect function on tau first, but that didn't seem to work.  I also tried
> re-writing the replacement rule as
>
> Sqrt[2 \[Pi]] \[Tau]^(3/2) /. Sqrt[ 2 \[Pi] ] t^(1/2) ->  \[Mu]
>
> But still no joy.
>

Hi,

ReplaceAll does structural replacements only, it does not take into 
account any mathematical relations.  (a+b+c /. a+c->d only works because 
Plus has the attributes Flat and Orderless.  It is still merely a 
structural replacement, not a mathematical one).  In other words, for 
ReplaceAll to work, the part of the expression to be replaced must be 
written exactly as it appears.

I think the replacement you want to do is not clearly defined 
mathematically.  I know you want mu tau as the result, but I'm not sure 
how to formulate the problem in a clear way to the computer.  If we're 
taking mathematical relations into account, it could just as well return 
mu^3/(2Pi).  Here's how to eliminate a variable completely:

Solve[e == Sqrt[2 \[Pi]] \[Tau]^(3/2) &&
   Sqrt[2 \[Pi] \[Tau]] == \[Mu], e, \[Tau]]


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