Relaxed Hensel lifting of triangular sets. (May 2015)

• Record Type: Journal Article
• Authors: Lebreton, Romain
• Is Part Of: Journal of symbolic computation. Volume 68:Part 2(2015)
• Page Start: 230
• Page End: 258
• Publication Date: 2015-05
• Subjects: Polynomial system solving -- Online algorithm -- Relaxed algorithm -- Triangular set -- Univariate representation -- p-Adic integer -- Power series; 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.2014.09.012
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we present a new lifting algorithm for triangular sets over general p -adic rings. Our contribution is to give, for any p -adic triangular set, a shifted algorithm of which the triangular set is a fixed point. Then we can apply the relaxed recursive p -adic framework and deduce a relaxed lifting algorithm for this triangular set. We compare our algorithm to the existing technique and report on implementations inside theC++ libraryGeomsolvex ofMathemagix (van der Hoeven et al., 2002 ). Our new relaxed algorithm is competitive and compare favorably on some examples.