Re: Question about composing a complex function.

*To*: mathgroup at smc.vnet.net*Subject*: [mg49781] Re: [mg49765] Question about composing a complex function.*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 31 Jul 2004 03:14:00 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

What's missing is to tell Mathematica that r is real! T[z_] := w + r^2/(Conjugate[z] - Conjugate[w]) Simplify[T[T[z]], Element[r , Reals]] z Of course this will look nicer if you use an actual "element of" symbol to write the condition in Simplify's second argument. Or, if you wish: Simplify[T[T[z]], r > 0] z (The definition of T will look more like traditional math notation if you use David Park's Cardano2 package so that you can notate the conjugates by putting bars over z and w in the denominator of the second term defining T.) Gilmar Rodr?guez Pierluissi wrote: > Dear Mathematica Group: > Let |z-w|=r^2 be a circle with radius r and center w in the complex > plane C. > The function T(z) = w + (r^2/Conjugate(z)-Conjugate(w)) with w,z > Complex and r Real, > takes the interior of that circle to its exterior, and viceversa, > leaving the boundary of the circle fixed. > Also T(T(z)) = z, i.e. T(T(z)) acts like the identity function I(z)=z. > If I (refering to myself) define: > T[z_] := w + (r^2/(Conjugate(z)-Conjugate(w))) > and evaluate: > Simplify[T[T[z]]] > or: > Composition[T,T] > why can't Mathematica give the answer directly; namely, z ? > What I'm I missing? > Thank you for your help! > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305