Re: Why is this so?
- To: mathgroup at smc.vnet.net
- Subject: [mg15339] Re: Why is this so?
- From: "Donald E. Niman" <donald.e.niman at safetran.com>
- Date: Fri, 8 Jan 1999 04:15:26 -0500
- Organization: Safetran Systems Corporation
- References: <76pq9g$e0n@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
A cube root of x has three possible results. For a Real x, there is
one real cube root and two imaginary cube roots. For x>0 Mathematica
chooses the Real cube root. For x<0, it chooses an imaginary cube
root. (I am not sure why but I have a suspicion that does this
deliberately.) See the Mathematica Book, 3.2.7. The Plot[] function
obviously chokes on the complex number.
In order to get the plot that I think you are expecting, try this:
f[x_]:=Sign[x]Abs[x^(1/3)];
Plot[f[x],{x,-125,125}];
Maybe there is a more elegant way to do this...?
Also, for (-125)^(1/3), you can see the cube roots by doing a
Solve[x^3 == -125, x] (* to find the three solutions *)
N[%] (* to see the numerical results *)
{{x->-5.},{x->2.5 + 4.33013 I},{x->2.5 -4.33013 I}}
In case something works differently for you, I am using Mathematica Pro
3.0.1 on Windows NT 4.0.
I hope this helps...
Chester Lin wrote:
>
> The following in/out does not make sense to me:
>
> Clear[f, x]
> f[x_] := x^(1/3)
> Plot[f[x], {x, -125, 125}]
>
> Plot::plnr : f[x] is not a machine-size real number at x = -125..
> Plot::plnr : f[x] is not a machine-size real number at x = -114.858.
> Plot::plnr : f[x] is not a machine-size real number at x = -103.798.
> General::stop :
> Further output of Plot::plnr will be suppressed during this
> calculation.
>
> Isn't it true that (-125)^(1/3) == -5?
>
> Why do I get this strange result?
>
> I am using Mathematica 3.01 for Students on Macintosh.
>
> Thanks for any info.
>
> Chester Lin
> chester at nicco.sscnet.ucla.edu
--
Donald E. Niman Software Engineer Research and
Development Vital Systems Safetran Systems Corporation Rancho
Cucamonga, CA