MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Question about composing a complex function.


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


  • Prev by Date: Re: Question on Compile[]
  • Next by Date: Re: contains 208,987,640 decimal digits (was: Fibonachi[5,000,000] contains 1044938 decimal digits)
  • Previous by thread: Question about composing a complex function.
  • Next by thread: Limits of DSolve ?