Resultant elimination via implicit equation interpolation (Q1691953)

Solving multivariate polynomial systems is a fundamental problem in Engineering and Science and many methods have developed hitherto. Elimination method via resultants is undoubtably one of the most known but it implies difficult symbolic tasks as computations of determinants of matrices whose elements are all polynomials, and factorizations of multivariate polynomials. In this paper, to overcome these problems, they combine multivariate rational function interpolation with resultant elimination to compute a kind of implicit equation, taking advantages of the good specialization of resultants. The efficiency of the method described in the article is showed in the fifth section on three unsolved combinatorial geometric problems.