# [Maxima] Error in (-5/3)^(1/3)

Juan Pablo Romero Bernal jromerobernal
Thu Nov 9 20:21:48 CST 2006

```Hi,

On 11/9/06, Roman <rvru at mega.ist.utl.pt> wrote:
> Hello!
>
> Maxima calculate with error the exponentiation of negative noninteger
> numbers. Maxima's method:
> (-a/b)^(c/d) (where a,b,c,d positive integer numbers)=>
> -(a^(c/d))/(b^(c/d)) is not true.
>
> Maxima 5.10.0 http://maxima.sourceforge.net
> Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL)
> Dedicated to the memory of William Schelter.
> This is a development version of Maxima. The function bug_report()
> provides bug reporting information.
> (%i1) ((-5/3)^(1/3)),numer;
> (%o1)                         - 1.185631101496688
> (%i2)
>
>
>
>
>     |\^/|     Maple 10 (IBM INTEL NT)
> ._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc.
> 2005
> <____ ____>  Waterloo Maple Inc.
>       |       Type ? for help.
> > (-5/3)^(1/3);
>                                      1/3  2/3
>                                  (-5)    3
>                                  ------------
>                                       3
> > evalf(%);
>                          0.5928155506 + 1.026786654 I
> >
>
> Is this a bug or peculiarity?

I think that the Maxima answer is correct in the real domain:

(%i13) domain;
(%o13) real
(%i14) (-5/3)^(1/3);
(%o14) -5^(1/3)/3^(1/3)
(%i15) %,numer;
(%o15) -1.185631101496687
(%i16) domain:complex;
(%o16) complex
(%i17) (-5/3)^(1/3);
(%o17) (-1)^(1/3)*5^(1/3)/3^(1/3)
(%i18) %,numer;
(%o18) 1.185631101496687*(.8660254037844386*%i+.5000000000000001)
(%i19) expand(%);
(%o19) 1.026786653413057*%i+.5928155507483438

Bye,

--
Juan Pablo Romero Bernal