THE GEOMETRY OF ALGEBRAIC SYSTEMS AND THEIR EXACT SOLVING USING GROEBNER BASES

摘要

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 aims to introduce 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. In the next issue, we will provide more details about Grobner bases along with some surprising applications.