The geometry of algebraic systems and their exact solving using Grobner bases

Abstract

Although exact methods for solving general polynomial systems are incorporated into well-known computer algebra systems such as Derive, Maple, Mathematica, MuPad, and Reduce, only a small portion of the scientific community knows about them. This article introduces one such method - Grobner bases - for non-mathematicians in an intuitive way. Specifically, we show the analogies and differences between linear and algebraic system solving, with an emphasis on the underlying geometric aspects.