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Re:complex conjugation by star
*To*: mathgroup at smc.vnet.net
*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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*References*: <20140418054638.0964A6A15@smc.vnet.net> <0CA7E131846E455799C2D385BDCCFB98@DV73080US> <F6CF125F5777F04CB8B97E5FFA0BD1B6101C676B@GIUDECCA.ricerca.lan>
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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