A sharp bound on the number of real intersection points of a sparse plane curve with a line. (July 2017)

• Record Type: Journal Article
• Authors: Bihan, Frédéric; El Hilany, Boulos
• Is Part Of: Journal of symbolic computation. Volume 81(2017)
• Page Start: 88
• Page End: 96
• Publication Date: 2017-07
• Subjects: 14T05; Sparse varieties -- Fewnomials; 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.2016.12.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We prove that the number of real intersection points of a real line with a real plane curve defined by a polynomial with at most t monomials is either infinite or does not exceed 6 t − 7 . This improves a result by M. Avendaño. Furthermore, we prove that this bound is sharp for t = 3 with the help of Grothendieck's dessins d'enfant.