Parallel computation of real solving bivariate polynomial systems by zero-matching method

We present a new algorithm for solving the real roots of a bivariate polynomial system R 1⁄4 ff ðx; yÞ; gðx; yÞg with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for the bivariate polynomial system when the system is non-zero. Moreover, the multiplicities of the roots of R 1⁄4 0 can be obtained by the associated quotient ring technique and a given neighborhood. From this approach, the parallelization of the method arises naturally. By using a multidimensional matching method this principle can be generalized to the multivariate equation systems. 2013 Elsevier Inc. All rights reserved.