✦ LIBER ✦
A new notion of reduction: Generating universal Gröbner bases of ideals in K[x, y]
✍ Scribed by W. Herfort; H. Penz
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 996 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0747-7171
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✦ Synopsis
In this paper a new notion of reduction depending on an arbitrary non-empty set ORD of term orderings on a polynomial ring is introduced. A general Buchberger algorithm based on this notion is devised. For a single element set ORD it specializes to the ordinary Buehberger algorithm. For ORD being the set of all term orderings a particular universal Gr~Sbner basis is constructed. We only deal with the ease K[x,y] since for higher dimensions we have not been able to prove that the generalized algorithm stops after a finite number of steps. Some reasons for understanding the underlying difticulties are given.