On Mar 7, 2:12 am, Joseph Gwinn <joegw...@comcast.net> wrote: > I have been using Mathematica 7 to do the grunt work in solving some > transmission-line problems, using the exponential form of the equations. > > A typical form would be S1 = Exp[k1*x + I*omega*(t+tau)], describing signal one, > where K1 is the attenuation in nepers per meter, I is the square root of minus > one, omega is the angular frequency in radians per second, t is time and tau is > a fixed time delay, t and tau being in seconds. > > Often I need the complex conjugate of S1, so I write Conjugate[S1]. The problem > is that Mathematica does nothing useful, leaving the explicit Conjugate in the > output expression, which after a very few steps generates a mathematically > correct but incomprehensible algebraic hairball. > > Clearly Mathematica feels that it lack sufficient information to proceed. In > particular, it has no way to know that all variables are real until explicitly > told. > > One way to solve this problem is > FullSimplify[Conjugate[S1],Element[_Symbol,Reals]], and this often works. > > But equally often, it works too well, yielding the trignometric expansion of the > desired exponential-form answer. Nor is it clear why it sometimes works and > sometimes works too well. > > Using Simplify instead of FullSimplify doesn't seem to work at all. > > So my questions are: > > 1. What controls FullSimplify's behaviour here? > > 2. What other ways are there to cause Mathematica to apply the Conjugate > without holding back? > > Thanks, > > Joe Gwinn
I struggled with Mathematica's sometimes obscure treatment of complex numbers and one morning several years ago after massive coffee fortification, I managed to force output sensible to mere humans. The expressions below work for individual complex expresssions and also (massive) Jones matrices.
It looks pretty clumsy, but it is very fast and always gives intelligible results. It works with all versions of Mathematica from 5.2 through 7. Drop me a line and I'll send you a notebook with some optical circuits.