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Re: complex conjugation by star

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132613] Re: complex conjugation by star
  • From: "Kevin J. McCann" <kjm at KevinMcCann.com>
  • Date: Mon, 21 Apr 2014 05:11:04 -0400 (EDT)
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I have used the following for many years

Clear[x, aaa, bbb]
SuperStar[x_] := x /. Complex[aaa_, bbb_] -> Complex[aaa, -bbb]

(The SuperStar[x_] translates to x_^*)

No problems. Also, no highlighted asterisk.

Kevin


On 4/20/2014 4:47 AM, Murray Eisenberg wrote:
> I don't see how your definition can be valid. When I type input
>
>    f_*:=f/.Complex[u_,v_]->Complex[u,-v]
>
> I see a highlighted asterisk, indicating a syntax error.
>
>
> 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
>>
>>
>>
>>
> 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
>
>
>
>
>
>
>



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