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Topic: complex conjugation by star
Replies: 7   Last Post: Apr 23, 2014 4:52 AM

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Brambilla Roberto Luigi (RSE)

Posts: 25
Registered: 2/21/12
R: complex conjugation by star
Posted: Apr 20, 2014 4:46 AM
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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@charter.net]
Inviato: venerd=EC 18 aprile 2014 09:30
A: Brambilla Roberto Luigi (RSE); mathgroup@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
Subject: 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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