Re: How to instruct Math to take a certain (e.g. real)

*To*: mathgroup at smc.vnet.net*Subject*: [mg105059] Re: [mg105018] How to instruct Math to take a certain (e.g. real)*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Thu, 19 Nov 2009 05:24:49 -0500 (EST)*Reply-to*: hanlonr at cox.net

Your equation does not have a solution eq = (-8 + y)^(1/3) + (8 + y)^(1/3) == y^(1/3); Reduce[eq, y] False Solve[eq, y] {} Apparently, you are looking for the solution of a different equation f[x_] := Sign[x]*Abs[x]^(1/3) eq2 = f[-8 + y] + f[8 + y] == f[y]; sol = {Reduce[eq2, y, Reals] // ToRadicals // ToRules} {{y -> 0}, {y -> -12*Sqrt[3/7]}, {y -> 12*Sqrt[3/7]}} eq2 /. sol // FullSimplify {True,True,True} eq /. sol {False,False,False} There is a legacy RealOnly add-on package at http : // library.wolfram.com/infocenter/MathSource/6771/ Bob Hanlon ---- Alexei Boulbitch <Alexei.Boulbitch at iee.lu> wrote: ============= Dear Community, I came to a problem, that I cannot check the solution y=0 of equation In[345]:= eq = (-8 + y)^(1/3) + (8 + y)^(1/3) == y^(1/3); eq /. y -> 0 Out[346]= False just because the expression In[347]:= eq[[1]] /. y -> 0 Out[347]= 2 + 2 (-1)^(1/3) Mathematica does not interpret as zero. And if I ask it to give a numerical answer In[348]:= 2 + 2 (-1.)^(1/3) Out[348]= 3.+ 1.73205 \[ImaginaryI] It returns the complex root out of the three possible. My question is the following: 1) How should I instruct Mathematica to take a certain root that I want of say, (-1)^(1/3)? 2) I think there is a general possibility instruct Mathematica that all calculations should be done on reals only. Is it right? Thank you, Alexei -- Alexei Boulbitch, Dr., habil. Senior Scientist IEE S.A. ZAE Weiergewan 11, rue Edmond Reuter L-5326 Contern Luxembourg Phone: +352 2454 2566 Fax: +352 2454 3566 Website: 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.