clear all
; The 3 solutions for x in the cubic equation:
0 = x^3 + a1 x^2 + a2 x + a3

q=(3a2-a1^2)/9
r=(9a1*a2-27a3-2a1^3)/54
s=(r+(q^3+r^2)^.5)^(1/3)
t=(r-(q^3+r^2)^.5)^(1/3)
real_root=s+t-a1/3
eliminate s t q r
; Next determine the other 2 roots from the real root:
other_roots=(-a1-real_root+sign*(-3*real_root^2-2*a1*real_root+a1^2-4*a2)^.5)/2
eliminate real_root
clear 2-5