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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105050] Re: [mg105018] How to instruct Math to take a certain (e.g. real) type of results
  • From: "David Park" <djmpark at comcast.net>
  • Date: Thu, 19 Nov 2009 05:23:08 -0500 (EST)
  • References: <19419730.1258547128749.JavaMail.root@n11>

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
solution.

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
True


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


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


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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