Struggles with "simple" complex polynomials

[dpsanders]

julia> roots(x->24.109999999999996 - 70.33*x + 65.33*x^2 - 15.11*x^3 - 5.0*x^4 + 1.0*x^5, Complex(-10..10, -10..10), Krawczyk)

apparently hangs

[OlivierHnt]

Currently, provided that the derivative is explicitly prescribed, the code no longer hangs. However, it gives many trivial roots except for one which is claimed to be unique... but unfortunately even this root seems not correct 😨.

[Kolaru]

Are you sure you got the derivative right ? I made a mistake and got trivial interval like you, but then corrected it and got it to hang (max_iteration saving me again).

julia> f(x) = 24.109999999999996 - 70.33*x + 65.33*x^2 - 15.11*x^3 - 5.0*x^4 + 1.0*x^5
f (generic function with 1 method)

julia> df(x) = -70.33 + 2*65.33*x - 3*15.11*x^2 - 4*5.0*x^3 + 5.0*x^4
df (generic function with 1 method)

julia> rts = roots(f, Complex(interval(-10, 10), interval(-10, 10)) ; contractor = Krawczyk, derivative = df, max_iteration = 10000)
1852-element Vector{Root{Complex{Interval{Float64}}}}:
 Root([6.01098, 6.01099]_com_NG + im*[-7.90672e-12, 7.90672e-12]_com_NG, :unique)
 Root([-4.01975, -4.01852]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01853, -4.01728]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01729, -4.01604]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01605, -4.01478]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01479, -4.01356]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01357, -4.01232]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01233, -4.01108]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.01109, -4.00982]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.00983, -4.00858]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 Root([-4.00859, -4.00732]_com + im*[-0.00132114, 0.000989419]_com, :unknown)
 ⋮

This is quite wrong regardless.

[OlivierHnt]

Oh maybe I had made a mistake. But still, there should be a safeguard, so that even if I give a wrong derivative, it should not claim that there is a root in an interval when evaluating f on the interval does not contain 0.

[Kolaru]

Currently we do not support automatic differentiation for Complex problems, and this is working when the derivative is given, so I'm closing.