Apparent singularities of D-finite systems. (November 2019)

• Record Type: Journal Article
• Authors: Chen, Shaoshi; Kauers, Manuel; Li, Ziming; Zhang, Yi
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 217
• Page End: 237
• Publication Date: 2019-11
• Subjects: D-finite system -- Gröbner basis -- Ordinary point -- Formal power series -- Apparent singularity -- Desingularization; 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.2019.02.009
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We generalize the notions of ordinary points and singularities from linear ordinary differential equations to D-finite systems. Ordinary points and apparent singularities of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms are presented for removing and detecting apparent singularities. In addition, an algorithm is given for computing formal power series solutions of a D-finite system at apparent singularities.