KMS Chongqing Institute of Green and Intelligent Technology, CAS
| Full Rank Representation of Real Algebraic Sets and Applications | |
Chen, Changbo1,2; Wu, Wenyuan1,2 ; Feng, Yong1,2
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| 2017 | |
| 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. |
| 语种 | 英语 |
| DOI | 10.1007/978-3-319-66320-3_5 |
| 会议(录)名称 | 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017
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| 页码 | 51-65 |
| 通讯作者 | Wu, Wenyuan (wuwenyuan@cigit.ac.cn) |
| 收录类别 | EI |
| 会议地点 | Beijing, China |
| 会议日期 | September 18, 2017 - September 22, 2017 |
