#### Publication Year

2002

#### Keywords

Grobner, mathematics, theory, algebraic geometry

#### Disciplines

Algebraic Geometry | Mathematics

#### Abstract

Within the realm of mathematics, many problems can be translated into the solution sets of polynomial equations. A specific field of mathematics, called algebraic geometry, is devoted to studying the solution sets of such polynomial equations. More technically, algebraic geometers study the zero loci of polynomials, that is, the sets of points for which the value of a polynomial or of each of a collection of polynomials is zero. These zero loci are geometric objects called algebraic varieties, and they are not only the most basic object of algebraic geometry, but in fact the very objects on which the entire filed is based. As it turns out, a branch of computational algebra called Grobner basis theory is extremely useful in determining algebraic varieties. This paper discusses the use of an algebraic method called the Buchberger algorithm to determine a Grobner basis of an ideal, leading to the calculation of the solution set of a system of polynomial equations. It further develops the theoretical foundations of Grobner basis theory, and also discusses its application to the field of algebraic coding theory.

#### Department 1 Awarding Honors Status

Mathematics

#### Recommended Citation

Cochrane, J. S.
(2002).
*Exploring Grobner Bases: Theory and Applications* (Undergraduate honors thesis, University of Redlands).
Retrieved from https://inspire.redlands.edu/cas_honors/738