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Re: Re: Re: question related to (-1)^(1/3)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96827] Re: [mg96765] Re: [mg96749] Re: question related to (-1)^(1/3)
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 25 Feb 2009 04:08:53 -0500 (EST)
  • Reply-to: hanlonr at cox.net

As pointed out previously, you do not want x^(1/3) (which is by definition a complex number for negative x), you want the real solution to y^3 == x. The real solution to this equation is Sign[x]*Abs[x]^(1/3)

Assuming[{Element[x, Reals]},
 Simplify[Reduce[
   (Sign[x]*Abs[x]^(1/3))^3 == x]]]

True

r[x_] := Sign[x]*Abs[x]^(1/3)

Plot[r[x], {x, -8, 8}]


Bob Hanlon

---- Xiang Liu <liuxiang77 at yahoo.com.cn> wrote: 

=============
I just want to get the real solution of (-1)^(1/3).
BTW, I have read the tutorial but I am still confused with its explanation.
But that is not important, I just feel it is inconvenient for the following
problem:

RecurrenceTable[{x[n + 1] == -x[n]^(1/3), x[0] == 1},  x, {n, 1, 200}] // N

I consider there should be a way to limit the output in the domain real.
for example, in MAXIMA

(%i1) domain;
(%o1) real
(%i2) (-1)^(1/3);
(%o2) -1
(%i3) domain:complex;
(%o3) complex
(%i4) (-1)^(1/3),numer;
(%o4) 0.86602540378444*%i+0.5

On Mon, Feb 23, 2009 at 6:04 PM, Sjoerd C. de Vries <
sjoerd.c.devries at gmail.com> wrote:

> This misunderstanding pops up over and over again in this group.
> Please type tutorial/FunctionsThatDoNotHaveUniqueValues in the search
> bar of the mathematica doc centre.
>
> Cheers -- Sjoerd




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