Why this recent change about (-1)^(1/3) ?

Francois,

Thanks for your email and your interest in Maxima.

I am not sure what exactly the problem is you're having.  Are the roots
incorrect in some versions of Maxima?  Keep in mind that there are many ways
of expressing the same number, e.g. 2*(sqrt(2)-1) == 2^(3/2)-2 ==
2/(sqrt(2)+1), and many tools within Maxima for changing the form of
expressions, including ratsimp, radcan, factor,
block([algebraic:true],ratsimp(...)), etc.

By the way, when showing algebraic results in email, please use
display2d:false -- the 2-diimensional display in general isn't legible, and
is cannot be re-entered into Maxima for testing.

Thanks,

             -s



On Wed, Feb 16, 2011 at 09:23, Francois Maltey <fmaltey at nerim.fr> wrote:

> Hello,
>
> I discover Maxima and compare it to Sage or Maple.
>
> I feel that Maxima changes about (-1)^(1/3).
>
> My old maxima is 5.13.0 from an Ubuntu box and is fine,
> but a more recent maxima in Sage is less nice.
> Is there a reason ?
>
> First the (-1)^(1/3)=-1 in the old maxima, and the solve after is right.
>
> (%i2) (-1)^(1/3) ;
> (%o2)                                 - 1
>
> (%i4) solve (3*x^3-9*x+10, x) ;
>                                      sqrt(3) %i   1
>                                    - ---------- - -
>             1/3  sqrt(3) %i   1          2        2
> (%o4) [x = - 3    (---------- - -) - ----------------,
>                      2        2           1/3
>                                          3
>                  sqrt(3) %i   1
>                  ---------- - -
>                      2        2    1/3    sqrt(3) %i   1          1/3    1
>            x = - -------------- - 3    (- ---------- - -), x = - 3    -
> ----]
>                        1/3                    2        2
> 1/3
>                       3                                                 3
>
> Now I call a more recent maxima built in Sage 4.6.1 at 2011-01-11
> This maxima seems to be a 5.22.1 but I'm not sure.
> I don't know how Sage works, I only find this library in Sage.
> The (-1)^(1/3) remains and the solve result is a little too long.
>
> sage: maxima ('(-1)^(1/3)')
> (-1)^(1/3)
> sage: maxima ()')
> [ x=3^(1/3)*(sqrt(3)*%i/2-1/2)/(-1)^(1/3) +
> (-1)^(1/3)*(-sqrt(3)*%i/2-1/2)/3^(1/3),
> x=(-1)^(1/3)*(sqrt(3)*%i/2-1/2)/3^(1/3) +
> 3^(1/3)*(-sqrt(3)*%i/2-1/2)/(-1)^(1/3),
> x=3^(1/3)/(-1)^(1/3)+(-1)^(1/3)/3^(1/3)]
>
> Is there a reason ?
> F. from France.
>
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