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Re: Symbolic complex conjugation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89985] Re: Symbolic complex conjugation?
  • From: "David Park" <djmpark at comcast.net>
  • Date: Wed, 25 Jun 2008 06:32:05 -0400 (EDT)
  • References: <g3q7vb$aus$1@smc.vnet.net>

It was the rule matching that tripped things up.

Clear[p, pStar, a, b]
eqnp = {((dwa/2) + I (w - wa)) p - I (kappa/(2 w)) dN e == 0}
solnp = Solve[eqnp, p]
p = p /. solnp[[1]]
pStar = p /. {I -> -I}
% // FullForm

Looking at the FullForm we see that I == Complex[0,1] does not actually 
appear in the p expression. Instead we have Complex[0,-1]. So the rule does 
not match. To do complex conjugation use:

Clear[p, pStar, a, b]
eqnp = {((dwa/2) + I (w - wa)) p - I (kappa/(2 w)) dN e == 0}
solnp = Solve[eqnp, p]
p = p /. solnp[[1]]
pStar = p /. {Complex[a_, b_] -> Complex[a, -b]}

You could also use:

pStar = ComplexExpand[Conjugate[p]] // Simplify // Factor

which seems like a little more work than it ought to be.

-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"AES" <siegman at stanford.edu> wrote in message 
news:g3q7vb$aus$1 at smc.vnet.net...
> I'm sorry, but I just don't understand why the following test case works
> just fine:
>
> [In copying it, I've substituted "Isymbol" for the \[ImaginaryI] that
> actually appears in the Out[] cells.]
>
>   In[202]:= eqna={a+I b==0};
>   solna=Solve[eqna,b];
>   b=b/.solna[[1]];
>   bStar=b/.{I->-I};
>   {b, Star}
>
>   Out[205]={ -Isymbol a, Isymbol a }
>
> but the actual calculation that prompted the test case doesn't:
>
>   In[206]:= eqnp={((dwa/2)+I(w-wa))p-I (kappa/(2 w))dN e==0};
>   solnp=Solve[eqnp,p];
>   p=p/.solnp[[1]];
>   pStar=p/.{I->-I}
>
>   Out[208]= { (dN e kappa)/(w (-Isymbol dwa+2 w-2 wa)),
>                        (dN e kappa)/(w (-Isymbol dwa+2 w-2 wa)) }
>
> And actually, I guess my real concern is not understanding "how it
> happens" -- but more "how it can happen" that Mathematica can do
> something this potentially damaging to some innocent user.
> 



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