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 Fax: +352 2454 3566 Mobile: +49 (0) 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu www.iee.lu -- This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you are not the intended recipient and have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal from your system. Thank you for your co-operation.