Relaxed Hensel lifting of triangular sets

Romain Lebreton (1, 2)

1 University of Waterloo [Waterloo]
2 ECO - Exact Computing

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. Our new relaxed algorithm is competitive and compare favorably on some examples.

Keywords: p-Adic integer; Univariate representation; Triangular set; Relaxed algorithm; Polynomial system solving; Online algorithm; Power series

Domains: Algebraic Geometry [math.AG]

Romain Lebreton. Relaxed Hensel lifting of triangular sets. Journal of Symbolic Computation, 2015, Effective Methods in Algebraic Geometry, 68, pp.230-258. ⟨10.1016/j.jsc.2014.09.012⟩. ⟨hal-01022876⟩