[Date Index] [Thread Index] [Author Index]

Re: Mathematica strange behaviour finding a cubic root

• To: mathgroup at smc.vnet.net
• Subject: [mg129120] Re: Mathematica strange behaviour finding a cubic root
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 17 Dec 2012 02:53:26 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net
• References: <20121216060645.D7C256924@smc.vnet.net>

The possibly unexpected results your seeing are because, by definition, 
Mathematica gives the _principal_ roots with such fractional powers. In 
particular, a power b^(m/n) with b < 0, m an even positive integer, and 
n an odd positive integer will be non-real complex.

To force Mathematica to return the real cube-roots, etc., there are 
several approaches. The simplest, now with Mathematica 9, is to use 
Surd:

   Surd[-1/2, 3]^2
2^(-2/3)

(where I'm showing the InputForm of the output).


On Dec 16, 2012, at 1:06 AM, sergio_r at mail.com wrote:

>
> How can I make Mathematica provides the same answer for
> (-1/2)^(2/3) = ((-1/2)^2)^(1/3) ?
>
> What follows is a Mathematica session:
>
> In[1]:= (-1/2)^(2/3)
>
>           1  2/3
> Out[1]= (-(-))
>           2
>
> In[2]:= N[%]
>
> Out[2]= -0.31498 + 0.545562 I
>
> In[3]:= ((-1/2)^2)^(1/3)
>
>         -(2/3)
> Out[3]= 2
>
> In[4]:= N[%]
>
> Out[4]= 0.629961
>
>
> Sergio

---
Murray Eisenberg                                    murray at math.umass.edu
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
710 North Pleasant Street                         fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Mathematica strange behaviour finding a cubic root
    • From: sergio_r@mail.com