Relaxed Hensel lifting of triangular sets

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.