achrzesz wrote :
SAGE:
sage: s=solve(3*x^3-9*x+10==0,x,solution_dict=True)
sage: [n(t[x]) for t in s]
[1.06780542232902 - 1.84949324407141*I,
0.0277635108030695 + 1.24902476648341*I,
-1.09556893313209 + 0.600468477588001*I]
# WRONG!
sage: s=solve(3*x^3-9*x+10==0,x,
solution_dict=True,to_poly_solve='force')
sage: [n(t[x]) for t in s]
[1.06780542232902 - 0.648556288895405*I,
-2.13561076604555,
1.06780538302277 + 0.648556231003039*I]
# POOR PRECISION
MAXIMA:
sage: maxima_console()
(%i1) expand(float(solve(3*x^3-9*x+10=0,x)));
(%o1) [x = 1.067805422329021 - .6485562888954052 %i,
x = .6485562888954052 %i + 1.067805422329021,
x = - 2.135610844658043]
#O.K.
There are recent messages about this equation at maxima mailling list :
http://www.math.utexas.edu/pipermail/maxima/2011/024170.html
A conclusion is in this sage-devel/sage-support message :
http://groups.google.com/group/sage-devel/browse_thread/thread/be4f78d55df1cd9b?fwc=1
There is a sequence of 2 unfair calculus.
A/ (-1)^(1/3) remains (-1)^(1/3)
in Sage and in Maxima with the option domain:complex sent from Sage to
Maxima in solve.
Maxima is right because solve select domain:real by default.
B/ Sage sees N((-1)^(1/3)) as complex number : so it get complex exp(I*pi/3)
Maxima sees (-1)^(1/3) as a real negative number.
F. who doesn't know how many bug there is ? 1 or 2, where ? in A/, in
B/, or in A/ and B/.
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