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Topic: Conjugate of symbolic expressions
Replies: 7   Last Post: Mar 10, 2010 1:44 AM

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 Joseph Gwinn Posts: 114 Registered: 2/23/05
Re: Conjugate of symbolic expressions
Posted: Mar 9, 2010 6:26 AM

In article <hn2m1k\$3pc\$1@smc.vnet.net>, AES <siegman@stanford.edu> wrote:

> In article <hmvqlg\$1gg\$1@smc.vnet.net>,
> Joseph Gwinn <joegwinn@comcast.net> wrote:
>

> > 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].

>
> You don't know what a firestorm you may ignite with this query.

No incoming fire so far, but lots of helpful advice. Most people suggested
ComplexExpand, which also reverts to trig seemingly at random, but what does
solve my immediate problem is:

ComplexExpand[...]//TrigToExp.

> How would you do this on paper? All the other factors in your
> expression you know are going to be purely real, so you really
> just want to change I to -I, right? (How else does one take a
> CC in the real world?)

All parameters and variables are real. This is known from the physics.

> And so in Mathematica you might write
>
> S1Complex = S1 /. {I -> -I}
>
> If you try this, you'll find that sometimes it works just fine -- and
> sometimes it doesn't -- and Mathematica gives you no warning
> anywhere in the elementary discussions of /. or -> or I that you
> shouldn't do this, or why you shouldn't.

What's there for Mathematica to complain about? It did _exactly_ as instructed,
human!

> So don't do it this way (but don't expect a lot of sympathy from
> this group for people doing elementary phasor analyses like
> you're doing, who are misled by this line of thinking).

I did think of this, but am generically afraid of using syntactic rewrite rules
on mathematical expressions unless I have been able to prove the semantic
(mathematical) correctness of the transform when applied over all possible
expressions, however complex.

It isn't enough that the rewrite rule work with the expression as presented, as
Mathematica will translate the expression into various internal representations,
and these representations vary seemingly at random.

Joe Gwinn

Date Subject Author
3/7/10 Joseph Gwinn
3/8/10 AES
3/9/10 Joseph Gwinn
3/8/10 sjoerd.c.devries@gmail.com
3/8/10 Bob Hanlon
3/8/10 John Feth
3/9/10 Joseph Gwinn
3/10/10 Kevin J. McCann