PROPER REPARAMETRIZATION FOR INHERENTLY IMPROPER UNIRATIONAL VARIETIES  

作　　者：Liyong SHEN Engwee CHIONH Xiao-Shan GAO Jia LI 

机构地区：[1]School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China [2]School of Computing, National University of Singapore, 117543, Singapore. [3]Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, ChineseAcademy of Sciences, Beijing 100190, China. [4]Beijing Electrical Science and Technology Institute, Beijing 100070, China.

出　　处：《Journal of Systems Science & Complexity》2011年第2期367-380,共14页系统科学与复杂性学报（英文版）

基　　金：This research is supported by the National Key Basic Research Project of China under Grant No. 2011CB302400 and the National Natural Science Foundation of China under Grant No. 10901163.

摘　　要：In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.

关 键 词：BKK bound chow form improper lattice supports improper rational parametrizations reparametrization support transformation. 

分 类 号：TV223[水利工程—水工结构工程] TH76[机械工程—仪器科学与技术]