Unirational differential curves and differential rational parametrizations. (May 2021)

• Record Type: Journal Article
• Authors: Fu, Lei; Li, Wei
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 539
• Page End: 562
• Publication Date: 2021-05
• Subjects: Unirational differential curve -- Proper differential rational parametrization -- Differential resultants -- Implicitization; 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.2020.08.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential curves. Then we show that the implicitization problem of proper linear differential rational parametric equations can be solved by means of differential resultants. Furthermore, for linear differential curves, we give an algorithm to determine whether an implicitly given linear differential curve is unirational, and in the affirmative case, to compute a proper differential rational parametrization for the differential curve.