Certifying Zeros of Polynomial Systems Using Interval Arithmetic

We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has built-in function certify , which proves the correctness of an isolated nonsingular solution to square system polynomial equations. The implementation rests on Krawczyk’s method. demonstrate that it dramatically outperforms earlier approaches certification. see this contribution powerful new geometry, can make default and not just option.