@article{0199cc2f482a4940abd34124ea9e2296,
title = "Apparent singularities of D-finite systems",
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.",
keywords = "Apparent singularity, D-finite system, Desingularization, Formal power series, Gr{\"o}bner basis, Ordinary point",
author = "Shaoshi Chen and Manuel Kauers and Ziming Li and Yi Zhang",
note = "Funding Information: In this work, S. Chen was supported in part by the NSFC grants (No. 11501552, 11688101, 11871067) and by the Frontier Key Project (QYZDJ-SSW-SYS022) and the Fund of the Youth Innovation Promotion Association, CAS. M. Kauers was supported in part by the Austrian Science Fund (FWF): F50-04 and Y464-N18. Z. Li was supported in part by the NSFC grants: 11771433, 11871067. Y. Zhang was supported in part by the Austrian Science Fund (FWF): Y464-N18 and P29467-N32. Funding Information: In this work, S. Chen was supported in part by the NSFC grants (No. 11501552 , 11688101 , 11871067 ) and by the Frontier Key Project ( QYZDJ-SSW-SYS022 ) and the Fund of the Youth Innovation Promotion Association, CAS . M. Kauers was supported in part by the Austrian Science Fund (FWF): F50-04 and Y464-N18 . Z. Li was supported in part by the NSFC grants: 11771433 , 11871067 . Y. Zhang was supported in part by the Austrian Science Fund (FWF): Y464-N18 and P29467-N32 . Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",
year = "2019",
month = nov,
day = "1",
doi = "10.1016/j.jsc.2019.02.009",
language = "English",
volume = "95",
pages = "217--237",
journal = "Journal of Symbolic Computation",
issn = "0747-7171",
}