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

作　　者：曾广兴[1] 胡兴[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2013年第3期205-214,227,共11页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11161034);江西省教育厅科技项目(GJJ12012)

摘　　要：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.

关 键 词：多项式系统 实零点 超长方体 有理单元表示 半代数连通分支 严格的临界点 吴方法 

分 类 号：O153[理学—数学]