Grobner bases were introduced by Bruno Buchberger in 1965. Since that time, they have been used with considerable success in several area of Mathematics, and are the subject of much current research. The most important aspect of Grobner bases is that they can be computed. Such computations bring a wealth of examples to theoretical research, and allow some important result to be applied. This thesis develops the algebraic concept needed to understand Grobner bases. The presentation focuses on the role of monomial ideals. Grobner bases are seen to provide an effective means of computing in the factor rings of multivariable polynomials. The theory is applied to rewriting of polynomial equations and to integer programming.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/291493 |
| Date | January 1998 |
| Creators | Moelich, Mark Christopher, 1962- |
| Contributors | Grove, Larry C. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Thesis-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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