Finding Real Zeros Of A Polynomial System In An Open Hypercuboid

For a system P of polynomials over R in n variables and an open hypercuboid S in R", where R is the field of real numbers, we present an algorithm for finding at least one real zero in each semi-algebraically connected component of ZeroR (P)∩S。In order to represent accurately the resulting real zeros, we adopt the so-called rational univariate representations。With the aid of the computer algebraic system Maple, these algorithms are made into a general program。...