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 Σ={f(x,y),g(x,y)}Σ={f(x,y),g(x,y)} 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 Σ=0Σ=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.