MPSolve (Multiprecision Polynomial SOLVEr) provides an easy-to-use universal blackbox for solving polynomials and secular equations. Its features include arbitrary precision approximation and guaranteed inclusion radii for the results. It can exploit polynomial structures, taking advantage of sparsity as well as coefficients in a particular domain (i.e., integers or rationals), and can be specialized for specific classes of polynomials.
https://ui.adsabs.harvard.edu/abs/2000NuAlg..23..127B and https://dl.acm.org/doi/abs/10.1016/j.cam.2013.04.037