Effective bounds for polynomial systems defined over the rationals

Abstract

This survey paper was primarily written as as the support for a course pesented at the JNCF2025: it aims to present some material that illustrates the kind of estimates one can obtain in effective algebraic geometry, for affine polynomial equation systems defined over the rational numbers Q, and focuses on the case of finite varieties.

Survey, 19 pages. To appear in "Recent Trends of Computer Algebra", Texts & Monographs in Symbolic Computation