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Re: Simplification de formule/ Simplification of formula

• To: mathgroup at smc.vnet.net
• Subject: [mg124418] Re: Simplification de formule/ Simplification of formula
• From: Tomas Garza <tgarza10 at msn.com>
• Date: Thu, 19 Jan 2012 05:09:15 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201181104.GAA16719@smc.vnet.net>

Not a very nice formula, but you may play around, e.g. the following looks slightly better:
In[1]:= FullSimplify[ TrigExpand[-((DK Pv2 Cos[a2 - alpha3] Cos[aV2] Sin[a2 - aV2])/(DK Cos[a2 - alpha3] -         KF Sin[a2 - alpha3])) + (KF Pv2 Cos[aV2] Sin[a2 - alpha3] Sin[       a2 - aV2])/(DK Cos[a2 - alpha3] -       KF Sin[a2 - alpha3]) - (DG3 P3 Sin[alpha3] Sin[       a2 - aV2])/(DK Cos[a2 - alpha3] -       KF Sin[a2 - alpha3]) - (DK FV2 Pv2 Cos[a2 - alpha3] Cos[       a2 - aV2] Sin[       aV2])/(L2 (DK Cos[a2 - alpha3] -     KF Sin[a2 - alpha3])) + (FV2 KF Pv2 Cos[a2 - aV2] Sin[       a2 - alpha3] Sin[       aV2])/(L2 (DK Cos[a2 - alpha3] -         KF Sin[a2 - alpha3])) - (KF Pv2 Cos[a2 - alpha3] Sin[       a2 - aV2] Sin[aV2])/(DK Cos[a2 - alpha3] -       KF Sin[a2 - alpha3]) + (FV2 KF Pv2 Cos[a2 - alpha3] Sin[     a2 - aV2] Sin[       aV2])/(L2 (DK Cos[a2 - alpha3] -         KF Sin[a2 - alpha3])) - (DK Pv2 Sin[a2 - alpha3] Sin[       a2 - aV2] Sin[aV2])/(DK Cos[a2 - alpha3] -       KF Sin[a2 - alpha3]) + (DK FV2 Pv2 Sin[a2 - alpha3] Sin[       a2 - aV2] Sin[       
 a!
V2])/(L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]))]]
Out[1]= -(FV2 KF Pv2 Cos[2 a2 - alpha3] - KF L2 Pv2 Cos[alpha3] -     FV2KF Pv2 Cos[2 a2 - alpha3 - 2 aV2] +     KF L2 Pv2 Cos[2 a2 - alpha3 - 2 aV2] +     DG3 L2 P3 Cos[a2 - alpha3 - aV2] -     DG3 L2 P3 Cos[a2 + alpha3 - aV2] + DK FV2 Pv2 Sin[2 a2 - alpha3] +     DK L2 Pv2 Sin[alpha3] +     DK (-FV2 + L2) Pv2 Sin[      2 a2 - alpha3 - 2 aV2])/(2 L2 (DK Cos[a2 - alpha3] -       KF Sin[a2 - alpha3]))
You are left with just one denominator and nine terms in the numerator :( 
-Tomas

> Date: Wed, 18 Jan 2012 06:04:01 -0500
> From: nicodumonastal at gmail.com
> Subject: Simplification de formule/ Simplification of formula
> To: mathgroup at smc.vnet.net
>
>
> Hi !
>
> I want to simplify this formula :
>
> -((DK Pv2 Cos[a2 - alpha3] Cos[aV2] Sin[a2 - aV2])/(
>   DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) + (
>  KF Pv2 Cos[aV2] Sin[a2 - alpha3] Sin[a2 - aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) - (
>  DG3 P3 Sin[alpha3] Sin[a2 - aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) - (
>  DK FV2 Pv2 Cos[a2 - alpha3] Cos[a2 - aV2] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) + (
>  FV2 KF Pv2 Cos[a2 - aV2] Sin[a2 - alpha3] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) - (
>  KF Pv2 Cos[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) + (
>  FV2 KF Pv2 Cos[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) - (
>  DK Pv2 Sin[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) + (
>  DK FV2 Pv2 Sin[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])).
>
> By manually regrouping the terms, the denominator disappears for a
> large number of fraction but I'm not able to reproduce this result
> with Simplify or others Mathematica tools to handle formula. Any
> suggestion of how I could do that with Mathematica ?
> Thank you for your help !
>
>
>
>
>
>
>
>
>
> Bonjour,
>
> Je souhaite simplifier cette formule :
>
> -((DK Pv2 Cos[a2 - alpha3] Cos[aV2] Sin[a2 - aV2])/(
>   DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) + (
>  KF Pv2 Cos[aV2] Sin[a2 - alpha3] Sin[a2 - aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) - (
>  DG3 P3 Sin[alpha3] Sin[a2 - aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) - (
>  DK FV2 Pv2 Cos[a2 - alpha3] Cos[a2 - aV2] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) + (
>  FV2 KF Pv2 Cos[a2 - aV2] Sin[a2 - alpha3] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) - (
>  KF Pv2 Cos[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) + (
>  FV2 KF Pv2 Cos[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])) - (
>  DK Pv2 Sin[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3]) + (
>  DK FV2 Pv2 Sin[a2 - alpha3] Sin[a2 - aV2] Sin[aV2])/(
>  L2 (DK Cos[a2 - alpha3] - KF Sin[a2 - alpha3])).
>
> En regroupant les bons termes le d=E9nominateur se simplifie pour un
> grand nombres de fractions mais je n'arrive pas a ce r=E9sultat avec les
> outils de simplification (FullSimplify ou Simplify) ou les outils de
> manipulations de formule. Est ce que vous auriez une id=E9e de comment
> faire comme pr=E9ciser certains "assumption" dans Simplify ?
> Merci de votre aide.
>

• References:
  • Simplification de formule/ Simplification of formula
    • From: Nicolas Simon <nicodumonastal@gmail.com>