Workshop
On the computation of p-adic Gröbner bases
- Tristan Vaccon (Université de Limoges)
Abstract
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.
