Relaxed Hensel lifting of triangular sets

摘要

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 competithie and compare favorably on some examples. (C) 2014 Elsevier Ltd. All rights reserved.