摘要
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.
出处
《南昌大学学报(理科版)》
CAS
北大核心
2013年第1期6-11,16,共7页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(11161034)
江西省教育厅基金资助项目(Gjj12012)
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
Polynomial system
Real zero
Hypercuboid
Rational univariate representation
Semi-algebraically connected component
Strictly critical point
The Wu method