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Topic: complex conjugation by star
Replies: 7   Last Post: Apr 23, 2014 4:52 AM

 Messages: [ Previous | Next ]
 Bob Hanlon Posts: 906 Registered: 10/29/11
Re: complex conjugation by star
Posted: Apr 20, 2014 4:46 AM

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@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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