Abstract
In this paper we describe comprehensive Gröbner bases over finite fields by direct product of fields. In general, representations of comprehensive Gröbner bases have some conditions on parameters. However, in finite fields we can construct comprehensive Gröbner bases without conditions by the theory of von Neumann regular rings. Our comprehensive Gröbner bases are defined as Gröbner bases in polynomial rings over commutative von Neumann regular rings, hence our comprehensive Gröbner bases have some nice properties. Our method is different from the methods of Weispfenning (CGB,CCGB), Montes (DisPGB), Sato and Suzuki (ACGB).
| Original language | English |
|---|---|
| Title of host publication | 7th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC05) |
| Editors | Petcu, D. |
| Pages | 10-17 |
| Number of pages | 8 |
| Publication status | Published - 2005 |
Fields of science
- 101 Mathematics
- 101001 Algebra
- 101005 Computer algebra
- 101009 Geometry
- 101012 Combinatorics
- 101013 Mathematical logic
- 101020 Technical mathematics