Re: complex conjugation by star

• To: mathgroup at smc.vnet.net
• Subject: [mg132608] Re: complex conjugation by star
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 20 Apr 2014 04:46:35 -0400 (EDT)
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• References: <20140418054638.0964A6A15@smc.vnet.net>

```See documentation for Conjugate.

Traditional Form (Mathematica | Preferences... | Evaluation | Format type
of new output cells: | TraditionalForm)

Clear[conjugate]

conjugate[expr_, complexExpand_: False] :=
Module[{expr2 = Conjugate /@ expr},
If[complexExpand,
Simplify[expr2,
Element[Cases[expr, _Symbol, Infinity], Reals]],
expr2]]

BesselJ[2, x + I y] // Conjugate

Conjugate[BesselJ[2, x + I y]]

BesselJ[2, x + I y] // conjugate

BesselJ[2, Conjugate[x] - I Conjugate[y]]

BesselJ[2, x + I y] // conjugate[#, True] &

BesselJ[2, x - I y]

A B C // Conjugate

Conjugate[A B C]

A B C // conjugate

Conjugate[A] Conjugate[B] Conjugate[C]

A + B + C // Conjugate

Conjugate[A + B + C]

A + B + C // conjugate

Conjugate[A] + Conjugate[B] + Conjugate[C]

Bob Hanlon

On Fri, 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
>
>

```

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