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R: complex conjugation by star

• To: mathgroup at smc.vnet.net
• Subject: [mg132607] R: complex conjugation by star
• From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
• Date: Sun, 20 Apr 2014 04:46:13 -0400 (EDT)
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Dear Dave,
many thanks again.
Now I have the problem to tell Mathematica that same variables are reals  and have not to be 'starred' so that
(x+Iy+z)* is not  x*+Iy*+z* but x-Iy+z*  (if x and y are reals and z unknown. Command   like Element[x, Reals]
does not work. 
Sincerely yours Roberto

-----Messaggio originale-----
Da: Dave Snead [mailto:dsnead6 at charter.net] 
Inviato: venerd=EC 18 aprile 2014 09:30
A: Brambilla Roberto Luigi (RSE); mathgroup at smc.vnet.net
Oggetto: Re: complex conjugation by star

Rob --

This will give you what you want:

SuperStar[f_?NumberQ]:=Conjugate[f]
SuperStar[f:_[___]]:=SuperStar/@f

Cheers,
Dave Snead

-----Original Message-----
From: Brambilla Roberto Luigi (RSE)
Sent: Thursday, April 17, 2014 10:46 PM
To: mathgroup at smc.vnet.net
Subject: [mg132607] complex conjugation by star

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

• References:
  • complex conjugation by star
    • From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla@rse-web.it>