       Re: Absolute value

• To: mathgroup at smc.vnet.net
• Subject: [mg110647] Re: Absolute value
• From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
• Date: Wed, 30 Jun 2010 08:04:53 -0400 (EDT)

```Hi, Mark,
the most important part you have already done, the rest may be done like this:

(* This is your starting expression *)
startingExpression =
ComplexExpand[
Abs[A1 E^(I \[Phi]1) ((1 + Cos[Sqrt c z])/2) +
AD E^(I \[Phi]D) I/Sqrt Sin[Sqrt c z] +
A2 E^(I \[Phi]2) ((Cos[Sqrt c z] - 1)/2)]^2,
TargetFunctions -> {Re, Im}];

(* Here each term, i.e. ~ A1^2, A2^2  and AD^2, is separated out *)

expr1 = startingExpression /. {A2 -> 0, AD -> 0} // Factor;
expr2 = startingExpression /. {A1 -> 0, AD -> 0} // Factor;
expr3 = startingExpression /. {A2 -> 0, A1 -> 0} // Factor;

(* done *)

finalExpression = expr1 + expr2 + expr3

1/4 A1^2 (1 + Cos[Sqrt c z])^2 (Cos[\[Phi]1]^2 + Sin[\[Phi]1]^2) +
1/4 A2^2 (-1 + Cos[Sqrt c z])^2 (Cos[\[Phi]2]^2 +
Sin[\[Phi]2]^2) +
1/2 AD^2 Sin[Sqrt c z]^2 (Cos[\[Phi]D]^2 + Sin[\[Phi]D]^2)

Have fun, Alexei

Thanks, this gave some insight. And yet I'm struggling to get it in another form. I have to work with an expression like:

FullSimplify[
Collect[ComplexExpand[
Abs[A1 E^(I \[Phi]1) ((1 + Cos[Sqrt c z])/2) +
AD E^(I \[Phi]D) I/Sqrt Sin[Sqrt c z] +
A2 E^(I \[Phi]2) ((Cos[Sqrt c z] - 1)/2)]^2,
TargetFunctions -> {Re, Im}], A1 | A2 | AD], TrigFactor]

Which does not separate A1, A2 and AD. I would like to have an output in a form like:

A1^2*f1[Cos[Sqrt c z],Sin[Sqrt c z]] + A2^2*f2[Cos[Sqrt c z],Sin[Sqrt c z]] + AD^2*f3[Cos[Sqrt c z],Sin[Sqrt c z]],

where f1, f2, and f3 are some functions of Cos[Sqrt c z] and Sin[Sqrt c z]. Is this possible?

Regards, Mark.

--
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development

IEE S.A.
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