       Re: Problem with D and Abs

• To: mathgroup at smc.vnet.net
• Subject: [mg60977] Re: [mg60970] Problem with D and Abs
• From: Andrzej Kozlowski <andrzej at yhc.att.ne.jp>
• Date: Thu, 6 Oct 2005 04:08:20 -0400 (EDT)
• References: <200510050628.CAA10385@smc.vnet.net>
• Reply-to: Andrzej Kozlowski <andrzej at akikoz.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 5 Oct 2005, at 15:28, Daniele Lupo wrote:

> 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?
>
>
> Daniele
>
> PS I'm using version 5.1, WinXP
>
>

Try

D[ComplexExpand[Abs[(Conjugate[s11]*Subscript[g, s])/
((Subscript[g, s] - 1)*Abs[s11]^2 + 1) -
Subscript[Ã, 0]/(Subscript[N, i] + 1)] -
Sqrt[Subscript[N, i]*(-Abs[Subscript[Ã, 0]]^2 +
Subscript[N, i] + 1)]/(Subscript[N, i] + 1),
{s11, Subscript[Ã, 0]}], Subscript[g, s]]

Andrzej Kozlowski

```

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