Grobner Bases and Ideals of Points

The main point of this thesis is an introduction to the theory of Grobner bases. The concept of Grobner basis and construction of the Grobner basis by Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we study some nice and useful properties of Grobner bases, such as a uniqueness of reduced Grobner basis and existence of a Grobner basis.In Chapter 3, we explore the Buchberger-Moller algorithm to construct Grobner bases and return a set of polynomials whose residue classes form a basis of a quotient of a polynomial ring. Also, we survey a generalized Buchberger-Moller algorithm to determine directly a Grobner basis for the intersection of a finite number of ideals.In Chapter 4, we conclude this paper with some applications of Grobner bases.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.available

2006

Author dc:creator

• Chang, Eun R

Contributors dc:contributor

• Dr. James K. Deveney

• theory
• Buchberger's Algorithm
• polynomials
• algorithm
• Physical Sciences and Mathematics

Statement dc:rights

• © The Author

Identifier

https://scholarscompass.vcu.edu/etd/1214

OAI identifier oai:identifier

oai:scholarscompass.vcu.edu:etd-2213