Full Rank Representation of Real Algebraic Sets and Applications

doi:10.1007/978-3-319-66320-3_5

CORC > 重庆绿色智能技术研究院 > 中国科学院重庆绿色智能技术研究院 > 自动推理与认知研究中心

	Full Rank Representation of Real Algebraic Sets and Applications
	Chen, Changbo 1,2; Wu, Wenyuan1,2 ; Feng, Yong1,2
	2017
会议日期	September 18, 2017 - September 22, 2017
会议地点	Beijing, China
DOI	10.1007/978-3-319-66320-3_5
页码	51-65
通讯作者	Wu, Wenyuan (wuwenyuan@cigit.ac.cn)
英文摘要	We introduce the notion of the full rank representation of a real algebraic set, which represents it as the projection of a union of real algebraic manifolds VR(Fi) of Rm, m ≥ n, such that the rank of the Jacobian matrix of each Fiat any point of VR(Fi) is the same as the number of polynomials in F:i. By introducing an auxiliary variable, we show that a squarefree regular chain T can be transformed to a new regular chain C having various nice properties, such as the Jacobian matrix of C attains full rank at any point of VR(C). Based on a symbolic triangular decomposition approach and a numerical critical point technique, we present a hybrid algorithm to compute a full rank representation. As an application, we show that such a representation allows to better visualize plane and space curves with singularities. Effectiveness of this approach is also demonstrated by computing witness points of polynomial systems having rank-deficient Jacobian matrices. © 2017, Springer International Publishing AG.
会议录	19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017
语种	英语
电子版国际标准刊号	16113349
ISSN号	03029743
内容类型	会议论文
源URL	[http://119.78.100.138/handle/2HOD01W0/4700]
专题	自动推理与认知研究中心中国科学院重庆绿色智能技术研究院
作者单位	1.Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, China; 2.University of Chinese Academy of Sciences, Beijing, China
推荐引用方式 GB/T 7714	Chen, Changbo,Wu, Wenyuan,Feng, Yong. Full Rank Representation of Real Algebraic Sets and Applications[C]. 见:. Beijing, China. September 18, 2017 - September 22, 2017.