Re: Conjugate of symbolic expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg108098] Re: [mg108034] Conjugate of symbolic expressions
- From: Joe Gwinn <joegwinn at comcast.net>
- Date: Mon, 8 Mar 2010 06:14:22 -0500 (EST)
- References: <28745811.1267954710914.JavaMail.root@n11>
David,
At 9:30 AM -0500 3/7/10, David Park wrote:
>
>Have you tried ComplexExpand? It assumes that all symbols are Reals, unless
>specified otherwise. Also check its TargetFunctions option.
I had tried ComplexExpand some time ago and had forgotten it, because
it too overachieved, yielding trig.
A number of people have suggested it in response to my query, so I
tried it again.
I just tried TargetFunctions, but Exp isn't an allowed function, and
{Re,Im} allowed the trig answers.
What seems to work is ComplexExpand[]//TrigToExp.
Thanks,
Joe
>David Park
>djmpark at comcast.net
>http://home.comcast.net/~djmpark/
>
>
>
>
>From: Joseph Gwinn [mailto:joegwinn at comcast.net]
>
>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