Computing the intersections of three conics according to their Jacobian curve. (March 2016)

• Record Type: Journal Article
• Authors: Feng, Ruyong; Shen, Li-Yong
• Is Part Of: Journal of symbolic computation. Volume 73(2016)
• Page Start: 175
• Page End: 191
• Publication Date: 2016-03
• Subjects: Algebraic condition -- Conic -- Intersection -- Jacobian curve -- Singularity; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.06.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this study, we describe the intersection of three conics based on the singularities of their corresponding Jacobian curve. In particular, we show that certain singular points and sub-lines of the Jacobian curve are the precise common points and common tangent lines of the conics, respectively. Based on our results, these points or the tangent line can be computed as the singularities of the Jacobian curve. These results facilitate investigations of the relationships between a net of conics and their Jacobian curve.