PhD Seminar • Computer Algebra | Symbolic Computation • P-adic Algorithm to Find a Basis of Bivariate Primary Components

Please note: This PhD seminar will be given online.

Catherine St-Pierre, PhD candidate
David R. Cheriton School of Computer Science

Supervisor: Professor Éric Schost

Inspired by the characterization of Gröbner cells from Conca and Valla [2007], we will present a quadratically convergent p-adic algorithm that we developed to find a basis of a primary component of a zero-dimensional ideal I ⊂ K[x,y], where K is a rational function field (or rationals). We will also discuss the probability of finding a “good prime” for the p-adic expansion and bound the growth of the coefficients in a basis.