Replace rule does not match

Question

I have the following expression

-3 I Ez Re[Ex] + 3 I Ex Re[Ez]

And I wish to write this in the form -3 Re[I Ez Conjugate[Ex]]. So I have made the rule

f_ I x_ Re[y_] - f_ I y_ Re[x_] -> f Real[I x Conjugate[y]]

But my expression does not seem to match that expression. What is wrong?

This thread: groups.google.com/group/comp.soft-sys.math.mathematica/…, should give you an exhaustive answer :) — Leonid Shifrin, Feb 10, 2012 at 12:00
@Leonid Thanks. I was starting to feel too good about the day. — Daniel Lichtblau, Feb 10, 2012 at 18:29

Mark McClure · Accepted Answer · 2012-02-10 12:54:50Z

10

Pattern matching with complex numbers is notoriously difficult because Complex numbers are atomic yet have non-trivial FullForm.

{AtomQ[-3 I], FullForm[-3 I]}

{True,Complex[0,-3]}

Examining the FullForm of your expression, perhaps you want the following.

rule = a_Complex*x_*Re[y_] + b_Complex*y_*Re[x_] :>
  Abs[a]*Re[I x Conjugate[y]] /; a == -b;
-3 I Ez Re[Ex] + 3 I Ex Re[Ez] /. rule

-3 Im[Ex Conjugate[Ez]]

answered Feb 10, 2012 at 11:57

Mark McClure

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$\begingroup$ @Mr.Wizard What is the correct way to add textual Mathematica output, as you have done in your edit? $\endgroup$
– Mark McClure
Feb 10, 2012 at 12:12
$\begingroup$ I don't know about "correct" but I am putting the output in quote blocks (which just means it starts with > Sometimes I think it looks better to combine code and quote types, which means starting each line with > followed by five spaces. I hoped you wouldn't mind my edit; I guess you don't. $\endgroup$
– Mr.Wizard
Feb 10, 2012 at 12:15
$\begingroup$ You can see the raw text of the message at any time by starting to edit it. $\endgroup$
– Mr.Wizard
Feb 10, 2012 at 12:16
$\begingroup$ @Mr.Wizard I was hoping someone would edit it so I could see formatted output. I see that R.M. has just added a further edit. I really don't think that either of these actually quite right. The standard quote block really looks more like a PrintUsage cell in Mathematica. Perhaps, this is discussion for Meta. $\endgroup$
– Mark McClure
Feb 10, 2012 at 12:54
$\begingroup$ Mark, it's already there. I am interested to know what you think looks best. $\endgroup$
– Mr.Wizard
Feb 10, 2012 at 13:01

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