![Algorithms and Complexity in Algebraic Geometry_hi-res logo](/sites/default/files/styles/workshop_banner_sm_1x/public/2023-01/Algorithms%20and%20Complexity%20in%20Algebraic%20Geometry_hi-res.jpg?h=450de763&itok=r3pqykMn)
Abstract
We present an algorithm for solving bivariate polynomial systems with coefficients in $\mathbb{Q}$ with essentially optimal bit complexity. The core of the algorithm is a classical Newton iteration procedure. New ingredients are needed, though, such as Kedlaya-Umans' modular composition algorithm and deflation techniques due to Lecerf.
Joint work with Esmaeil Mehrabi.