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TitleRelaxed Hensel lifting of triangular sets
Author(s) Romain Lebreton
TypeArticle in Journal
AbstractAbstract 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 the C++ library Geomsolvex of Mathemagix (van der Hoeven et al., 2002). Our new relaxed algorithm is competitive and compare favorably on some examples.
KeywordsPolynomial system solving, Online algorithm, Relaxed algorithm, Triangular set, Univariate representation, p-Adic integer, Power series
URL http://www.sciencedirect.com/science/article/pii/S0747717114000807
JournalJournal of Symbolic Computation
Volume68, Part 2
Pages230 - 258
NoteEffective Methods in Algebraic Geometry
Translation No
Refereed No