Finding Real Zeros Of A Polynomial System In A Closed Hypercuboid

For a system P of polynomials in n variables and a closed hypercuboid S in Rn, we present an algorithm for finding at least one real zero in each semi-algebraically connected component of ZeroR(P)∩S, where ZeroR(P) is the set of zeros of P in R". In order to represent accurately the resulting real zeros, we adopt the so-called rational univariate representations. Furthermore, we give another algorithm for deciding whether the resulting points belong to the hypercuboid S. With the aid of the computer algebraic system Maple, these algorithms are made into a general program.In the forth chapter, as an application of our algorithms, we investigate the systems of sine (cosine)-polynomial equations, and establish an algorithm. In order to illustrate our algorithms, several examples are provided in this paper.