Re: Weird result in Mathematica 6

*To*: mathgroup at smc.vnet.net*Subject*: [mg76430] Re: [mg76393] Weird result in Mathematica 6*From*: Carl Woll <carlw at wolfram.com>*Date*: Tue, 22 May 2007 02:47:07 -0400 (EDT)*References*: <200705211001.GAA10071@smc.vnet.net>

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? > > From the help: Reduce[expr,vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex. You can try adding a domain specification: In[144]:= FullSimplify[ Reduce[(z - a)/(1 - Conjugate[a] z) == w && a Conjugate[a] < 1 && w Conjugate[w] < 1, z, Complexes]] Out[144]= -1 < Re[w] < 1 && -Sqrt[1 - Re[w]^2] < Im[w] < Sqrt[ 1 - Re[w]^2] && -1 < Re[a] < 1 && -Sqrt[1 - Re[a]^2] < Im[a] < Sqrt[ 1 - Re[a]^2] && z == (a + w)/(w Conjugate[a] + 1) Carl Woll Wolfram Research

**References**:**Weird result in Mathematica 6***From:*Sebastian Meznaric <meznaric@gmail.com>