Re: Trouble computing conjugates

*To*: mathgroup at smc.vnet.net*Subject*: [mg88558] Re: Trouble computing conjugates*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Thu, 8 May 2008 04:14:58 -0400 (EDT)*Organization*: University of Bergen*References*: <fvs2k5$enp$1@smc.vnet.net>

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] For this particular example, you could manually distribute Conjugate over the sum: Refine@Distribute[Conjugate[c1 u1 + c2 u2]] FunctionExpand works, too: Conjugate[c1 u1 + c2 u2] // FunctionExpand > > 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. > I hope that FunctionExpand will work for your more complicated example. If it doesn't (or it has side effects that you want to avoid), you could experiment with something like Refine[ expr /. HoldPattern@Conjugate@Plus[terms__] :> Distribute@Conjugate@Plus[terms] ] The HoldPattern was necessary to prevent Plus[terms__] from evaluating to terms__