Date: Thu, 8 Aug 2002 20:26:05 +0200
From: Daniel Duparc <daniel.duparc at free>
On 08 Aug 2002 13:31:57 -0400
HJSTEIN@bloomberg.com (Harvey J. Stein) wrote:
> Daniel Duparc <daniel.duparc@FREE.FR> writes:
>
> > (C1) rectform((-1)^(1/6));
> >
> > %I SQRT(3)
> > (D1) -- + -------
> > 2 2
>
> It shouldn't really do this given that there are 6 possible answers.
> At a minimum, a well defined result (such as the number with the smallest
> nonnegative angle) should be part of the spec for rectform(), but this
> isn't possible for arbitrary expressions.
>
You are true, but it is not that simple (it should
give, in general cases, an answer in the form RootOf(something), but
the "something" is quickly hard to manage, as one can see
with Maple.
However one can have everything now by Maxima in this
simple case:
(C1) solve(x^6+1,x);
1/6 1/6 1/6 1/6
(- 1) SQRT(3) %I + (- 1) (- 1) SQRT(3) %I - (- 1)
(D1) [x = ------------------------------, x = ------------------------------,
2 2
1/6 1/6
1/6 (- 1) SQRT(3) %I + (- 1)
x = - (- 1) , x = - ------------------------------,
2
1/6 1/6
(- 1) SQRT(3) %I - (- 1) 1/6
x = - ------------------------------, x = (- 1) ]
2
(C2) d1[2];
1/6 1/6
(- 1) SQRT(3) %I - (- 1)
(D2) x = ------------------------------
2
(C3) rectform(d2);
%I SQRT(3)
(D3) x = -- - -------
2 2
(C4) rectform(d1[6]);
%I SQRT(3)
(D4) x = -- + -------
2 2
(C5) rectform(d1[1]);
(D5) x = %I
(C6)
etc...
Best regards.
--
Daniel Duparc <daniel.duparc@free.fr>
29 av. de la Commune de Paris
94400 Vitry sur Seine (France)