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MathGroup Archive 2006

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Re: Why is the negative root?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69479] Re: [mg69474] Why is the negative root?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 14 Sep 2006 06:54:46 -0400 (EDT)
  • References: <200609130803.EAA18412@smc.vnet.net>

On 13 Sep 2006, at 17:03, p-valko at tamu.edu wrote:

> (Reduce[{z^3-z^2- b z-1==0, b>0, z>0}, z] //ToRadicals)/.b->3.//Chop
>
> gives a negativ z:
>
> z == - 0.414214
>
> What am I doing wrong?
>
> Regards
> Peter
>

Why do you need to use ToRadicals here? There is no point in it and,  
in fact you, are only asking for trouble. I am not sure why  
Mathematica even tries to convert Root objects with parameters to  
radicals, since it can't be done reliably due to branching problems  
and is of no practical use whatever, but at least the Help tells you  
that:

â?¼ If Root objects in expr contain parameters, ToRadicals[expr] may  
yield a result that is not equal to expr for all values of the  
parameters.

And, of course, if you do not use ToRadicals, there is no problem:

Reduce[{z^3 - z^2 - b*z - 1 == 0, b > 0, z > 0}, z] /. b -> 3

z == 1 + Sqrt[2]


Andrzej Kozlowski
Tokyo, Japan


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