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Re: Trouble computing conjugates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88547] Re: Trouble computing conjugates
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 8 May 2008 04:12:56 -0400 (EDT)
  • References: <fvs2k5$enp$1@smc.vnet.net>


Hi Roy,

mathematica thinks the distributed form is more complicated, therefore, 

you get the undistributed form. You may tell mma to distribute by e.g.:

Refine[Conjugate[c1 u1+c2 u2]//Distribute]

hope this helps, Daniel



Roy wrote:

> I'm having trouble getting mathematica to compute complex conjugates

> of some fairly simple expressions:

> 

> If I type the following:

> 

> $Assumptions = {g \[Element] Reals, f \[Element] Reals}

> u1 = f + \[ImaginaryI] g

> u2 = f - \[ImaginaryI] g

> 

> Then the command:

> 

> Refine[Conjugate [c1 u1]]

> 

> returns:

> 

> f - \[ImaginaryI] g) Conjugate[c1]

> 

> and the command:

> 

> Refine[Conjugate[c1 u1 + u2]]

> 

> returns:

> 

> f + \[ImaginaryI] g + (f - \[ImaginaryI] g) Conjugate[c1]

> 

> as I would expect.  But the command:

> 

> Refine[Conjugate[c1 u1 + c2 u2]]

> 

> returns:

> 

> Conjugate[c2 (f - \[ImaginaryI] g) + c1 (f + \[ImaginaryI] g)]

> 

> i.e. it refuses to distribute the complex conjugate throughout the

> expression.  What I would like it to tell me is:

> 

> (f + \[ImaginaryI] g) Conjugate[c2] + (f - \[ImaginaryI] g)

> Conjugate[c1]

> 

> The closest I have been able to come to getting what I want is by

> using:

> 

> ComplexExpand[Refine[Conjugate[ c1 u1 + c2 u2]], {c1, c2}]

> 

> but this separates c1 and c2 into their real and imaginary parts.  The

> above expressions are much simpler than the ones I REALLY want

> Mathematica's help in simplifying.  If I use this ComplexExpand

> command, then I'm going to have to recombine them into complex numbers

> again, which would be very very bad.

> 

> Thanks,

> Roy

> 




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