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[2] c z])/2) +
AD E^(I \[Phi]D) I/Sqrt[2] Sin[Sqrt[2] c z] +
A2 E^(I \[Phi]2) ((Cos[Sqrt[2] 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[2] c z])^2 (Cos[\[Phi]1]^2 + Sin[\[Phi]1]^2) +
1/4 A2^2 (-1 + Cos[Sqrt[2] c z])^2 (Cos[\[Phi]2]^2 +
Sin[\[Phi]2]^2) +
1/2 AD^2 Sin[Sqrt[2] 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[2] c z])/2) +
AD E^(I \[Phi]D) I/Sqrt[2] Sin[Sqrt[2] c z] +
A2 E^(I \[Phi]2) ((Cos[Sqrt[2] 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[2] c z],Sin[Sqrt[2] c z]] + A2^2*f2[Cos[Sqrt[2] c z],Sin[Sqrt[2] c z]] + AD^2*f3[Cos[Sqrt[2] c z],Sin[Sqrt[2] c z]],
where f1, f2, and f3 are some functions of Cos[Sqrt[2] c z] and Sin[Sqrt[2] c z]. Is this possible?
Regards, Mark.
--
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development
IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 CONTERN
Luxembourg
Tel: +352 2454 2566
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Mobile: +49 (0) 151 52 40 66 44
e-mail: alexei.boulbitch at iee.lu
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