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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: Re:complex conjugation by star
Posted: Apr 23, 2014 4:52 AM
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Hi Dave,

very good! It is what I wanted!

By your trick is possible to define reals:

realList = {A, B, G, x, y};

RealQ[f_] := MemberQ[realList, f]

So that, correctly, if

P=AZ +BY +Gy+xU;

P* gives

Gy+xU*+BY*+AZ*

But Conjugate[P] don't works since it simply echoes

Conjugate[Ux+Gy+BY+AZ]. So better the star suffix!

Fine! Many thanks! Roberto

-----Messaggio originale-----
Da: Dave Snead [mailto:dsnead6@charter.net]
Inviato: domenica 20 aprile 2014 10:47
A: mathgroup@smc.vnet.net
Oggetto: Re:complex conjugation by star

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@smc.vnet.net<mailto:mathgroup@smc.vnet.net>

Subject: 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@charter.net]<mailto:[mailto:dsnead6@charter.n=
et]>

Inviato: venerd=EC 18 aprile 2014 09:30

A: Brambilla Roberto Luigi (RSE); mathgroup@smc.vnet.net<mailto:mathgroup@sm=
c.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 ex=
ponent 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 ex=
pressions where is not known if symbols represent real or complex variables=
?



Many thanks!

Rob









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