$p$-adic algorithm to find a basis of bivariate ideals and primary components

par Mme Catherine St-Pierre (University of Waterloo)

vendredi 10 juin 2022, 15:00 → 16:00 Europe/Paris

https://bbb.unilim.fr/b/vac-m6r-7dv

Inspired by the characterization of a Gröbner cell from Conca and Valla (2007), we will present a quadratically convergent $p$-adic algorithm that we developed to find a basis of a bivariate zero dimensional ideal. We will show how get an equivalent conclusion for a primary component of an ideal associated to an isolated point in $V(I)$. We will also discuss the probability of finding a good prime for the $p$-adic expansion and a bound on the growth of coefficients in a basis.

This is a joint work with Éric Schost.