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

If you are willing to permute the Mathematica multi-valued solutions and
match them up for the various terms, then you can verify the z == 0

w1^3 == -8 + z;
sols1 = Solve[%, w1]
w2^3 == 8 + z;
sols2 = RotateLeft[Solve[%, w2]]
w3^3 == z;
sols3 = Solve[%, w3]

sols1 /. z -> 0 
sols2 /. z -> 0 
sols3 /. z -> 0 

(w1 /. sols1) + (w2 /. sols2) == (w3 /. sols3) /. z -> 0

David Park
djmpark at  

From: Alexei Boulbitch [mailto:Alexei.Boulbitch at] 

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

ZAE Weiergewan
11, rue Edmond Reuter
L-5326 Contern

Phone: +352 2454 2566
Fax:   +352 2454 3566


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