Re: Re: Complex Oddity

*To*: mathgroup at smc.vnet.net*Subject*: [mg57651] Re: [mg57631] Re: Complex Oddity*From*: Pratik Desai <pdesai1 at umbc.edu>*Date*: Fri, 3 Jun 2005 05:33:34 -0400 (EDT)*References*: <d79enu$lbl$1@smc.vnet.net><d7hahj$3q6$1@smc.vnet.net> <200506020917.FAA11965@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

jfeth at azlink.com wrote: >I use Jones matrices to evaluate optical circuits and always need to >find the intensity of two interfering electric fields. The intensity >(or brightness) of a field is found as a positive real value from a >complex field as the field times the complex conjugate of the field. >As you can see below, Mathematica gives yet another complex value when >one does this straightforward multiplication instead of the real value >that, I might add, is drilled into all students at the first glimpse of > root(-1). For several weeks I struggled to use Mathematica in my >circuit evaluation until one inspired Saturday, after several pots of >coffee, dumb luck and iteration brought forth Intensity[expr_]:= below. > I don't know why it works, I don't know how it works, and I >don't know another way to do the job, but, even as ugly as it is, at >least it works and it works very quickly. Importantly, it also gives >me answers as cosines with arguments that are (real)sums and >differences of characteristic delays, misalignments, and phase >modulation terms. > >f=E^(I*d) > >In[1]:= >f*Conjugate[f] > >Out[1]= > E^ (I*d - I*Conjugate[d]) > >In[2]:= >Intensity[expr_]:= >TrigReduce[ExpToTrig[expr*TrigToExp[ComplexExpand[Conjugate[ExpToTrig[expr]]]]]] > >In[3]:= >Intensity[f] > >Out[3]= >1 > >With this solution in hand, as an optical engineer, I now have the >luxury of wondering 1) exactly what mathematical elegance (or utility) >is gained by Mathematica's assumption that every variable is always >complex, and 2) why there is apparently no way in Mathematica to >globally define a variable as a real number (i.e., its own conjugate). > >Regards, > >John Feth > > >John Reed wrote: > > >>Thanks to all who explained what is happening and how to work this problem >>correctly. Now I know one facet of working with complex numbers. I don't >>feel much better about this however. I received one e-mail that said this >>was my fault for not reading the documentation closely enough. This problem >>came up in the book "Mathematica for Physics" second edition by Zimmerman >>and Olness. They solve a problem using the Complex[a_,b_]->a rule, ( see >>page 91) but not the b part. The b part was my idea. Now I know why they >>didn't solve for the imaginary part this way. They get the imaginary part >>by subtracting the real part from the complex expression and dividing by I. >>How many other gotchas are hidden in the code, waiting to bite the unwary >>and relatively new user? What documentation tells about this kind of a >>problem or do I just have to find them for myself by hopefully catching the >>errors as they occur? >> >>John Reed >> >> >> > > > I have also struggled with the very same questions, I have found the TagSet defination invaluable here is how I would deal with your problem TagSet[d, Im[d], 0]; TagSet[d, Re[d], d]; TagSet[d, Conjugate[d], d]; f[d_] := E^(I*d) f[d]*Conjugate[f[d]] >>1 The fundamental question remains why does Mathematica treat all variables as complex, well the simple answer may be WHY NOT!!. You can always tell mathematica which variables are real/complex, by giving them thier identity(shown above) which is the way it is supposed to work, isn't it? :-) Best Regards Pratik Desai -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134

**References**:**Re: Complex Oddity***From:*jfeth@azlink.com