Re: complex conjugation by star

*To*: mathgroup at smc.vnet.net*Subject*: [mg132610] Re: complex conjugation by star*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sun, 20 Apr 2014 04:47:15 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20140418054638.0964A6A15@smc.vnet.net>

Mathematica already has a built-in Conjugate function used in the form Conjugate[z] as well as a suffix operator with a star that may be typed Esc co Esc or \[Conjugate]. You should not use ordinary lower-case i to denote the imaginary unit; type either I or Esc ii Esc. And it's best to avoid using upper-case letters A, B, G, etc., to avoid clashes with built-in Mathematica symbols. Automatically, Mathematica will do some of what you want: {a, b, g}\[Conjugate] (* {Conjugate[a], Conjugate[b], Conjugate[g]} *) Evaluating an expression such as Element[a, Complexes] by itself accomplishes nothing and is _not_ "remembered" in any way for further calculations. The way to indicate symbols are to be treated as reals when doing complex-algebra calculations is to use ComplexExpand. Thus: (x + I y)\[Conjugate] // ComplexExpand (* x - I y *) With the built-in Conjugate function, for your example with BesselJ, you'd need to use: On Apr 18, 2014, at 1:46 AM, Brambilla Roberto Luigi (RSE) <Roberto.Brambilla at rse-web.it> wrote: > 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 > > > > > RSE SpA ha adottato il Modello Organizzativo ai sensi del = D.Lgs.231/2001, inforza del quale l'assunzione di obbligazioni da parte = della Societ=E0 avviene con firma di un procuratore, munito di idonei = poteri. > Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 240 246-7240 (H) University of Massachusetts 710 North Pleasant Street Amherst, MA 01003-9305

**References**:**complex conjugation by star***From:*"Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla@rse-web.it>