On the computation of p-adic Gröbner bases

  • Tristan Vaccon (Université de Limoges, Limoges, France)
E1 05 (Leibniz-Saal)


Gröbner bases are a multi-purpose tool for ideal arithmetic in polynomial algebras: membership testing, intersection, elimination... In this talk, I will present various approaches on how to compute Gröbner bases over the p-adics. I will focus on strategies to compute 'shape position' bases, which are often applied for system solving.

The main problem with effective computation over the p-adics, finite precision, will be discussed. Handling it will lead us to a pleasant excursion through tropical Gröbner bases and Tate algebras.

Various joint works with X.Caruso, Y.Ishihara, G.Renault, T.Verron and K.Yokoyama will be invoked.


Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Enis Kaya

University of Groningen

Avinash Kulkarni

Dartmouth College

Antonio Lerario


Mima Stanojkovski

RWTH Aachen and Max Planck Institute for Mathematics in the Sciences