Abstract
dc:description.abstractThe theory of Gröbner bases has become a useful tool in computational commutative algebra. In this paper, we outline some basic results, as they are found in [1], including the concepts of terms ordering, multivariable polynomial division, Gröbner bases, Buchberger's algorithm, and syzygy modules. Specially, we present several equivalent definitions for Gröbner bases and prove how to compute a Gröbner basis for an ideal I of A = k[x1, x2, • • • , xn] generated by {fl, f2, • • • , f8} through Buchberger's algorithm. As an application of Gröbner bases, we present a standard method (see [1]) to compute the syzygy module of a set {f1, f2, • • • , f8} of polynomials, illustrated with original examples. Finally, we implement these examples on the computer using the Mathematica package of [4].
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Discipline thesis:degree_discipline
- Department of Mathematics and Computer Science
- Year
- 1995
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Zhao, Yonggan
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Repository record dc:identifier
- https://digitalcommons.wku.edu/theses/924
- OAI identifier oai:identifier
- oai:digitalcommons.wku.edu:theses-1927