Normal projection： deterministic and probabilistic algorithms

作     者：Dongmei LI Jinwang LIU Weijun LIU 

作者机构：Department of Mathematics and Computing Sciences Hunan University of Scienceand Technology Xiangtan 411201 China Department of Mathematics and Statistics Central South University Changsha 410083 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2014年第9卷第1期

页      面：93-99页

核心收录：

学科分类：07[理学] 08[工学] 070102[理学-计算数学] 0701[理学-数学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Acknowledgements the article and made The authors are thankful to numerous helpful suggestions the referees for their carefully reading This work was partially supported by the National Natural Science Foundation of China (Nos. 11071062  11271208)  the Natural Science Foundation of Hunan Province (14JJ6027)  and the Scientific Research ~nd of Education Department of Hunan Province (10A033  12C0130) 

主　　题：Normal projection primary decomposition of ideal deterministic algorithm 

摘      要：We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature.