Re:complex conjugation by star

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• Subject: [mg132609] Re:complex conjugation by star
• From: "Dave Snead" <dsnead6 at charter.net>
• Date: Sun, 20 Apr 2014 04:46:55 -0400 (EDT)
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```Rob --

This will do it.
x,y are real, any others are complex.

RealQ[f_]:=MemberQ[{x,y},f}
SuperStar[f_?RealQ]:=f
SuperStar[f_?NumberQ]:=Conjugate[f]
SuperStar[f:_[___]]:=SuperStar/@f

Cheers,
Dave Snead

-----Original Message-----
From: Brambilla Roberto Luigi (RSE)
Sent: Friday, April 18, 2014 2:10 AM
To: 'Dave Snead' ; mathgroup at smc.vnet.net
Subject: [mg132609] R: complex conjugation by star

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: venerdì 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: [mg132609] 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

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