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Re: Weird result in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg76415] Re: Weird result in Mathematica 6
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 22 May 2007 02:39:14 -0400 (EDT)
• Organization: Uni Leipzig
• References: <f2rqvi$9uo$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

because you have not given an domain. But

Reduce[(z - a)/(1 - a\[Conjugate] z) == w && a a\[Conjugate] < 1 &&
   w w\[Conjugate] < 1, z, Complexes]

does this.

Regards
   Jens

Sebastian Meznaric wrote:
> I was playing around with Mathematica 6 a bit and ran this command to
> solve for the inverse of the Moebius transformation
> 
> FullSimplify[
>  Reduce[(z - a)/(1 - a\[Conjugate] z) == w && a a\[Conjugate] < 1 &&
>    w w\[Conjugate] < 1, z]]
> 
> This is what I got as a result:
> -1 < w < 1 && -1 < a < 1 && z == (a + w)/(1 + w Conjugate[a])
> 
> Why is Mathematica assuming a and w are real? The Moebius
> transformation is invertible in the unit disc regardless of whether a
> and w are real or not. Any thoughts?
> 
>