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,  # WRONG!
-1.09556893313209 + 0.600468477588001*I]    #


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,                                    # POOR
PRECISION
 1.06780538302277 + 0.648556231003039*I] #


sage: x=CC[x].0
sage: p=3*x^3-9*x+10
sage: p.roots(multiplicities=False)
[-2.13561084465804,                                  #
1.06780542232902 - 0.648556288895405*I,  # O.K
1.06780542232902 + 0.648556288895405*I] #


sage: CF=ComplexField(128)              # FOR COMPARISON
sage: x=CF[x].0
sage: p=3*x^3-9*x+10
sage: p.roots(multiplicities=False)
[-2.1356108446580430871649905855660713838,
1.0678054223290215435824952927830356919 -
0.64855628889540511607544685008848221185*I,
1.0678054223290215435824952927830356919 +
0.64855628889540511607544685008848221185*I]

Andrzej Chrzeszczyk

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