寻求多项式系统在开超长方体中的实零点

Finding real zeros of polynomial system in open hypercuboid

对于给定的一个n元实多项式系统P和Rn中一个开超长方体S,给出了一个有效算法,使得在ZeroR(P)∩S的每一个半代数连通分支上能找到至少一个零点。为精确起见,所找的实零点通过所谓的区间有理单元表示来描述。为处理实例,有关算法在Maple软件平台上被编制成一个通用程序。

For a system P of polynomials over R in n variables and an open hypercuboid S in Rn,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.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.