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

• To: mathgroup at smc.vnet.net
• Subject: [mg96766] Re: [mg96749] Re: question related to (-1)^(1/3)
• From: patapon <lxguard-hw at yahoo.com.cn>
• Date: Tue, 24 Feb 2009 05:46:25 -0500 (EST)
• References: <gnqo3c$c95$1@smc.vnet.net> <200902231004.FAA28251@smc.vnet.net>

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
>
> On Feb 22, 7:33 am, "=D2=BB=D2=B6=D6=AA=C7=EF" <lxguard... at yahoo.com.cn> =
> wrote:
> > I have tried expression:
> > RecurrenceTable[{x[n + 1] == -x[n]^(1/3), x[0] == 1},
> >   x, {n, 1, 200}] // N
> >
> > Mathematica produce
> >  {-1., -0.5 - 0.866025 I, -0.766044 + 0.642788 I, -0.686242 -
> >   0.727374 I, -0.71393 + 0.700217 I, -0.704818 - 0.709389 I,
> > ...
> >
> > But it should be {1, -1, 1, -1, ... }
> >
> > If you try  (-1)^(1/3)
> >
> > In[10]:= (-1)^(1/3)
> >
> > Out[10]= (-1)^(1/3)
> >
> > In[11]:= % // N
> >
> > Out[11]= 0.5 + 0.866025 I
>
>
>

• Follow-Ups:
  • Re: Re: Re: question related to (-1)^(1/3)
    • From: Murray Eisenberg <murray@math.umass.edu>

• References:
  • Re: question related to (-1)^(1/3)
    • From: "Sjoerd C. de Vries" <sjoerd.c.devries@gmail.com>