There are 3 cube roots. Maple gives one. Maxima gives another (the
real-valued one). Neither one is entirely correct.
If Maxima gave the same one as Maple, someone would report it as a bug.
Someone who had not yet learned about complex numbers, perhaps.
The message about sqrt(x^2) is relevant here.
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-
> bounces at math.utexas.edu] On Behalf Of Daniel Lakeland
> Sent: Thursday, November 09, 2006 4:58 PM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] Error in (-5/3)^(1/3)
>
>
> > (%i1) ((-5/3)^(1/3)),numer;
> > (%o1) - 1.185631101496688
> > (%i2)
> >
> >
> >
> > *Maples's answer:*
>
> > > (-5/3)^(1/3);
> > 1/3 2/3
> > (-5) 3
> > ------------
> > 3
> > > evalf(%);
> > 0.5928155506 + 1.026786654 I
> > >
> >
> > Is this a bug or peculiarity?
>
> Is this a branch cut issue? Maple seems to be doing:
>
> exp(c/d * log(-a/b))
>
> which is, I think, the definition of generalized exponentiation.
>
> it seems as if maxima at some point is doing (-5)^(1/3) = - (5^1/3)
> which is where things go wrong?
>
>
>
> --
> Daniel Lakeland
> dlakelan at street-artists.org
> http://www.street-artists.org/~dlakelan
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima