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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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