Re: complex conjugation by star

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• Subject: [mg132610] Re: complex conjugation by star
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 20 Apr 2014 04:47:15 -0400 (EDT)
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```Mathematica already has a built-in 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 lower-case i to denote the imaginary unit; type either I or Esc ii Esc. And it's best to avoid using upper-case letters A, B, G, etc., to avoid clashes with built-in 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 complex-algebra calculations is to use ComplexExpand. Thus:

(x + I y)\[Conjugate] // ComplexExpand
(* x - I y *)

With the built-in 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 at rse-web.it> wrote:

> I have defined the following useful star complex-conjugation (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,x-I y]  etc...(x,y defined/undefined).
> Also it is listable on number lists
>
> {1+i2, 5+i6}*  gives  {1-i2, 5-i6} .
>
> 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 at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 240 246-7240 (H)
University of Massachusetts
710 North Pleasant Street
Amherst, MA 01003-9305

```

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