Relaxed Hensel lifting of triangular sets. (May 2015) - Lebreton, Romain
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.