Thesis Title
Date of Graduation
Summer 2014
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Kishor Shah
Abstract
We study Groebner bases and their applications in our thesis. We give a detailed proof of Dickson's Lemma, closely following the proof in Cox, Little, and O'Shea's Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. We then provide a geometric proof of this lemma, in the case of two variables, using our own ideas. We use Buchberger's Algorithm to produce a Groebner basis given any set of generators for an ideal I. We also consider the problem of solving systems of polynomial equations using various methods. These methods include finding a reduced Groebner basis to form a modified system, computing the resultant to eliminate a variable, and using various commands in Wolfram Mathematica 9.0. We also show the relationships between elimination theory and Groebner bases.
Keywords
monomial order, Dickson's Lemma, polynomial division, S-polynomial, Groebner basis, Buchberger's criterion, Buchberger's Algorithm, elimination theory, resultant, Mathematica
Subject Categories
Mathematics
Copyright
© Amy Eva Fitzpatrick
Recommended Citation
Fitzpatrick, Amy Eva, "Groebner Bases" (2014). MSU Graduate Theses. 1655.
https://bearworks.missouristate.edu/theses/1655
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