Efficient Algorithms for MultiPolynomial Resultant

The multipolynomial resultant of a set of equations is fundamental in quantifier elimination over the elementary theory of real and algebraically closed fields. Earlier algorithms for resultant computation and symbolic elimination are considered slow in practice. In this paper we present efficient algorithms to compute multi-polynomial resultants and demonstrates their use for polynomial manipulation and symbolic applications. The algorithms utilize the linear algebra formulation of the resultants and combine its multivariate interpolation and modular arithmetic for fast computation. It is currently being implemented as part of a package and we discuss its performance as well.