Tracking p-adic precision

Xavier Caruso (1) , David Roe (2) , Tristan Vaccon (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 University of Calgary

We present a new method to propagate $p$-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy application to the stable computation of the SOMOS 4 sequence.

Mots clés: ultrametric fields; precision

Domaines: Théorie des nombres [math.NT]; Calcul formel [cs.SC]

Xavier Caruso, David Roe, Tristan Vaccon. Tracking p-adic precision. LMS Journal of Computation and Mathematics, 2014, 17 (SI), pp.274-294. ⟨10.1112/S1461157014000357⟩. ⟨hal-00952952⟩