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MathGroup Archive 2005

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Re: Problem with D and Abs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60982] Re: [mg60970] Problem with D and Abs
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 6 Oct 2005 04:08:24 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Use the second argument to ComplexExpand

D[
    ComplexExpand[
      Abs[(Conjugate[s11]*gs)/
              (1 + Abs[s11]^2*(-1 + gs)) - a0/(1 + ni)] -
        Sqrt[ni*(1 - Abs[a0]^2 + ni)]/(1 + ni),
      {a0, s11}],
    gs] // Simplify


Bob Hanlon

> 
> From: Daniele Lupo <danwolf80_no_spam_ at libero.it>
To: mathgroup at smc.vnet.net
> Date: 2005/10/05 Wed AM 02:28:21 EDT
> Subject: [mg60982] [mg60970] Problem with D and Abs
> 
> Hi to all.
> 
> I've a problem with this expression:
> 
> \!\(Abs[\(Conjugate[s11]\ g\_s\)\/\(1 + Abs[s11]\^2\ \((\(-1\) + g\_s)\)\)
> - \
> Ã\_0\/\(1 + N\_i\)] - \@\(N\_i\ \((1 - Abs[Ã\_0]\^2 + N\_i)\)\)\/\(1 +
> N\_i\)\
> \)
> 
> 
> I want to have derivative in gs. If I use D, I obtain a strange result,
> that invoke Abs'[...], that's not correct, naturally.
> 
> I've tried to use PiecewiseExpand, but I've a problem. In this expression,
> \!\(g\_s\) and \!\(N\_i\) are real, while \!\(Ã\_0\) and s11 are complexes.
> I don't know how to create an expansion that consider some symbol as 
real,
> and some other as complex.
> 
> How can I do it?
> 
> Thanks for your answers.
> 
> Daniele
> 
> PS I'm using version 5.1, WinXP
> 
> 


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