Certification of roots
General Tech QA/Testing 2 years ago
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Best Answer
2 years ago
I have a system of two bivariate polynomials of degree 3 and would like to find its roots. With the help of resultants I project the system first at x-axis, then at y-axis, thus obtaining two univariate polynomial of degree 9 (Bezout's theorem). I know how to find the roots (or more precisely: the isolating intervals) of a univariate polynomial with arbitrary precision but I dont know how to make sure ("to certify") that a root of the first polynomial is also a root of the second polynomial.
How to find such pairs of intervals of these two univariate polynomials that will surely be also the roots of the original polynomial system?