Re: Numerical expression
- To: mathgroup at smc.vnet.net
- Subject: [mg128825] Re: Numerical expression
- From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
- Date: Thu, 29 Nov 2012 06:03:26 -0500 (EST)
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Hy Massimo, let us define the 3-order unity-roots w0 = 1 w1 = Exp[I 2 \[Pi]/3] w2 = Exp[I 4 \[Pi]/3] and the following subexpressions h1=(9 (3)^(1/2) + 4 (23)^(1/2))^(1/3) h2=(9 (3)^(1/2) - 4 (23)^(1/2))^(1/3) then your expression will be ee=(h1+h2)/3^(1/2) ee//N= 2.32666 + 0.765945 I Using unity-roots this correspond to the choice of unity-roots ee=(w0*h1+w0*h2)/3^(1/2) ee//N= 2.32666 + 0.765945 I but if you use another (of the 9 possible) choice of unity roots you can obtain 1. By trials ee=(w1*h1+w0*h2)/3^(1/2) ee//N=1+(3.30384*10^-16 I) Other combinations give other values. Bye Rob -----Messaggio originale----- Da: Dana DeLouis [mailto:dana01 at me.com] Inviato: mercoled=EC 28 novembre 2012 9.17 A: mathgroup at smc.vnet.net Oggetto: Re: Numerical expression > ( ( 9(3)^1/2+4(23)^1/2)^1/3 + (9(3)^1/2+4(23)^1/2)^1/3 ) / (3)^1/2) Hi. Just to add to the others, if we "Assume" the following k = (9*Sqrt[3] + 4*Sqrt[23])^ (1 / 3) ; // Or... k=k//FullSimplify Sqrt[1/2 (13+Sqrt[69])] Then what you have is: (k+k) / Sqrt[3.] 3.76887 // Which matches what others have mentioned: For this to equal 1, then k would have to equal Sqrt[3] / 2 Perhaps your equation for the k part is off a little. ?? = = = = = = = = = = HTH :>) Dana DeLouis Mac & Mathematica 8 = = = = = = = = = = On Sunday, November 25, 2012 11:29:24 PM UTC-5, Massimo wrote: > How could I handle in Mathematica this expression? > > > > ( ( 9(3)^1/2+4(23)^1/2)^1/3 + (9(3)^1/2+4(23)^1/2)^1/3 ) / (3)^1/2) > > > > With a lot of trouble I have found out that is equal 1, > > but how to get it with Mathematica? > > > > Thanks very much. > > > > > > > > __________ Informazioni da ESET Smart Security, versione del database = delle firme digitali 7729 (20121125) __________ > > > > Il messaggio =EF=BF=BD stato controllato da ESET Smart Security. > > > > www.nod32.it RSE SpA ha adottato il Modello Organizzativo ai sensi del D.Lgs.231/2001, in= forza del quale l'assunzione di obbligazioni da parte della Societ=E0 avvie= ne con firma di un procuratore, munito di idonei poteri. RSE adopts a Compliance Programme under the Italian Law (D.Lgs.231/2001). Ac= cording to this RSE Compliance Programme, any commitment of RSE is taken by= the signature of one Representative granted by a proper Power of Attorney.= Le informazioni contenute in questo messaggio di posta elettronica sono ris= ervate e confidenziali e ne e' vietata la diffusione in qualsiasi modo o for= ma. Qualora Lei non fosse la persona destinataria del presente messaggio, La= invitiamo a non diffonderlo e ad eliminarlo, dandone gentilmente comunicazi= one al mittente. The information included in this e-mail and any attachments= are confidential and may also be privileged. If you are not the correct rec= ipient, you are kindly requested to notify the sender immediately, to cancel= it and not to disclose the contents to any other person.
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- Re: Numerical expression
- From: Dana DeLouis <dana01@me.com>
- Re: Numerical expression