Subject: Why this recent change about (-1)^(1/3) ?
From: Francois Maltey
Date: Wed, 16 Feb 2011 15:23:44 +0100
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 ('solve (3*x^3-9*x+10,x)')
[ 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.