Full Rank Representation of Real Algebraic Sets and Applications
文献类型：会议论文
| 作者 | Chen, Changbo1,2; Wu, Wenyuan1,2 ; Feng, Yong1,2
|
| 出版日期 | 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 |
| 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. |
入库方式： OAI收割
来源：重庆绿色智能技术研究院
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