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complex conjugation by star

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132604] complex conjugation by star
  • From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
  • Date: Fri, 18 Apr 2014 01:46:38 -0400 (EDT)
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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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