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MathGroup Archive 1998

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Re: Re: Very strange Bug !?

  • To: mathgroup at
  • Subject: [mg13306] Re: [mg13154] Re: [mg13037] Very strange Bug !?
  • From: Sean Ross <seanross at>
  • Date: Fri, 17 Jul 1998 03:19:07 -0400
  • References: <>
  • Sender: owner-wri-mathgroup at

Hugh Walker wrote:
> On 7Jul98 M Blle Ramquet <MN.Ramquet at> wrote:
> " I just discovered something that amazed me. If you type
> N[(-1)^{1/3}], it gives an imaginary answer !!! I've tried it out with
> an old local release but it is still the same. Of course the problem is
> the same for all cubic root of any negative number... I know that
> purely, the root of a negative real is not well defined ... but anyway
> it is commonly accepted that (-1)^{1/3} is -1 !!!
>   Can any guru of mathematica help me to sort out this mess ?"
> ***********************
> I find, using v. 3.0, the (expected) Mathematica result
> (-1)^(1/3) -> (-1)^(1/3)
> and also the principal value
> (-1)^(1/3)//ComplexExpand -> (1/2) + I Sqrt[3]/2
> I also get
> (-1)^(1/3)//N -> 0,5 + I 0,866025
> These conform with what I understand about the rules of complex
> arithmetic.
> Hugh Walker
> Professsor Emeritus
> University of Houston
> Gnarly Oaks

Most humans I have talked to, when faced with choosing a "standard" root
out of a choice of several, would choose the one on the real axis. 
Mathematica does not do this.  Its standard root, if it can only return
one, is the one in the first quadrant.  If you want to see all the
roots, use the command Roots.  You can also use the package RealOnly
and you will only get real roots.

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