PIECEWISE SEMIALGEBRAIC SETS  

作　　者：Zhu, CG Wang, RH 

机构地区：[1]Dalian Univ Technol, Inst Math Sci, Dalian 116024, Peoples R China

出　　处：《Journal of Computational Mathematics》2005年第5期503-512,共10页计算数学（英文）

基　　金：Supported by the National Natural Science Foundation of China （Grant Nos. 10271022 and 60373093）.

摘　　要：Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.

关 键 词：Algebraic geometry Semialgebraic geometry Tarski-Seidenberg Principle Multivariate splines Piecewise semialgebraic sets 

分 类 号：O15[理学—数学]