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JuliaHomotopyContinuation / HomotopyContinuation.jl

A Julia package for solving systems of polynomials via homotopy continuation.
https://www.JuliaHomotopyContinuation.org
MIT License
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verify_solution_completeness / distinct_certificates / certification fix #431

Closed saschatimme closed 3 years ago

saschatimme commented 3 years ago

This adds back the verify_solution_completeness routine which was already in HC v1. This should be the last missing functionality from v1.

On the way I found that we had no function to get the certificates corresponding to distinct solutions. So I added distinct_certificates.

I also observed that our epsilon inflation procedure could fail if a coordinate of the true solution is 0 since we considered only a relative value for the inflation. I improved the situation by requiring that we inflate at least by eps(prec) * prec^(-1/4).