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MathGroup Archive 2005

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RealValued functions and derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63332] RealValued functions and derivatives
  • From: "Fabrice Bonjean" <bonjean at esr.org>
  • Date: Sat, 24 Dec 2005 07:18:57 -0500 (EST)
  • Organization: Earth & Space Research
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,
With my version 4 of Mathematica, I cannot prescribe the derivatives, 
and the partial derivatives, of a function f to be real valued when f is 
real valued in the first place:

Im[x]=0;Im[y]=0;
RealValued[f]
From here, f'[x] or the partial derivatives of f will not be recognized 
as real entities in any expressions involving them so that, for example, 
Im[f'[x]] is not zero.

The same question was posted twice on 1998 and 2004 by others, but the 
answer, although helpful, is not satisfying enough to me. It suggests 
using the trick of "a posteriori" forcing derivatives to be real, by 
applying ComplexExpand to any expression.
1) This does not seem to work with PARTIAL derivatives
2) I find cumbersome or time-consuming employing such a trick in a 
symbolic math software.

Does the latest version still have this problem? Otherwise, is there a 
more comprehensive solution to this problem than the one above 
(complement package, etc ...)?

Thanks for any help,
Fabrice Bonjean



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