Polynomial Roots With Multiplicities

Specific Domains Numerics
3

If you know you have multiplicities and you have real coefficients, the PolynomialZeros package has a multroot function that can work for this example:

using Polynomials, PolynomialsZeros
julia> p = Poly([1, 0, -4, 0, 6, 0, -4, 0, 1.0])
Poly(1.0 - 4.0*x^2 + 6.0*x^4 - 4.0*x^6 + 1.0*x^8)

julia> PolynomialZeros.MultRoot.multroot(p)
[ Info: The multiplicity count may be in error--the initial guess for the roots failed to improve when refined along the pejorative manifold.
([-1.0, 1.0], [4, 4])
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