寻求多项式系统在闭超长方体上的实零点

Finding real zeros of polynomial system in closed hypercuboid

对于给定的一个n元多项式系统P和Rn中一个闭超长方体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实零点。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。同时给出了另一算法,可用来检验所得的实零点是否属于闭超长方体S。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 in n variables and a closed hypercuboid Rn in,an algorithm is presented to find at least one real zero in each semi-algebraically connected component of ZeroR（P）∩S.In order to represent accurately the resulting real zeros,the so-called rational univariate representations are adopted.Furthermore,another algorithm is provided to decide 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.