
Re: complex conjugation by star
Posted:
Apr 20, 2014 4:47 AM


Mathematica already has a builtin Conjugate function used in the form Conjugate[z] as well as a suffix operator with a star that may be typed Esc co Esc or \[Conjugate].
You should not use ordinary lowercase i to denote the imaginary unit; type either I or Esc ii Esc. And it's best to avoid using uppercase letters A, B, G, etc., to avoid clashes with builtin Mathematica symbols.
Automatically, Mathematica will do some of what you want:
{a, b, g}\[Conjugate] (* {Conjugate[a], Conjugate[b], Conjugate[g]} *) Evaluating an expression such as Element[a, Complexes] by itself accomplishes nothing and is _not_ "remembered" in any way for further calculations. The way to indicate symbols are to be treated as reals when doing complexalgebra calculations is to use ComplexExpand. Thus:
(x + I y)\[Conjugate] // ComplexExpand (* x  I y *)
With the builtin Conjugate function, for your example with BesselJ, you'd need to use:
On Apr 18, 2014, at 1:46 AM, Brambilla Roberto Luigi (RSE) <Roberto.Brambilla@rseweb.it> wrote:
> I have defined the following useful star complexconjugation (common star exponent notation) > > f_*:=f/.Complex[u_,v_]>Complex[u,v] > > and it works fine. For example BesselJ[2,x+I y]* gives BesselJ[2,xI y] etc...(x,y defined/undefined). > Also it is listable on number lists > > {1+i2, 5+i6}* gives {1i2, 5i6} . > > Unfortunately it does not work on symbols, i.e. > A* gives A even if I have defined A as a complex number by means of Element[A, Complexes]. > Similarly if I define Element[{A,B,G}, Complexes] > > {A,B,G}* gives {A,B,G} and (A+B+G)* gives A+B+G. > > I'd like to obtain {A*,B*,G*} and A*+B*+G* ( ! ) > > Is it possible to fix this deficiency, unpleasant in manipulating general expressions where is not known > if symbols represent real or complex variables ? > > Many thanks! > Rob > > > > > RSE SpA ha adottato il Modello Organizzativo ai sensi del = D.Lgs.231/2001, inforza del quale l'assunzione di obbligazioni da parte = della Societ=E0 avviene con firma di un procuratore, munito di idonei = poteri. >
Murray Eisenberg murray@math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 240 2467240 (H) University of Massachusetts 710 North Pleasant Street Amherst, MA 010039305

