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How to instruct Math to take a certain (e.g. real) type of results

• To: mathgroup at smc.vnet.net
• Subject: [mg105018] How to instruct Math to take a certain (e.g. real) type of results
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Wed, 18 Nov 2009 06:57:41 -0500 (EST)

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.
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• Follow-Ups:
  • Re: How to instruct Math to take a certain (e.g. real)
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: How to instruct Math to take a certain (e.g. real)
    • From: Daniel Lichtblau <danl@wolfram.com>