Re: Bug, or what am I missing?

[Ariel Pacetti <apacetti@math.utexas.edu>]

If you look at the documentation it says:

If the exponent is not of type integer, this is treated as a 
transcendental function (see Section 3.3), and in particular has the 
effect of componentwise powering on vector or matrices.

So what it means is that what it is computing is exactly:

exp(log(-8)/3)

? exp(log(-8)/3)
%1 = 1.0000000000000000000000000000000000000 + 
1.7320508075688772935274463415058723669*I

This is not a bug, since you have 3 solutions to you problem (you are 
looking at the roots of x^3+8, and there are 3 of them), the point is that 
you have to make a choice in the answer.
It depends on which branch of the logarithm you are taking. If you start 
with a positive integer, you don't have this problem, since the first 
solution lies in the real line.

So an ugly way to get the answer you are looking for (for odd exponent 
denominators) is to add an absolute value and the sign in the final 
answer:

-(abs(8))^(1/3)

? -(abs(8)^(1/3))
%2 = -2.0000000000000000000000000000000000000

Ariel

On Wed, 14 Apr 2010, Ryan Voots wrote:

> While I find it hard to believe that you guys could have overlooked this (I
> suspect that it has got to be something I need to do or something I'm unaware
> of)
>
> ? (-8)^(1/3)
> %1 = 1.0000000000000000000000000000000000000 +
> 1.7320508075688772935274463415058723669*I
>
> I'd expect to get -2 here instead of an imaginary number.  Increasing the
> precision doesn't seem to help (just adds more digits).  Interestingly this
> number appears to be related to the correct answer.  If you take it and
> multiply by its conjugate and then take the square root you'll get close to
> the answer (just wrong sign).
>
> ? (-8)^(1/3)
> %2 = 1.000000000000000000000000000 + 1.732050807568877293527446342*I
> ? (1.000000000000000000000000000 + 1.732050807568877293527446342*I) *
> (1.000000000000000000000000000 - 1.732050807568877293527446342*I)
> %3 = 4.000000000000000000000000002 + 0.E-38*I
> ? (4.000000000000000000000000002 + 0.E-38*I)^(1/2)
> %4 = 2.000000000000000000000000001
>
> What am I missing here to be getting the correct answer?