Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05) (2005)
Sept. 25, 2005 to Sept. 29, 2005
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SYNASC.2005.3
Katsusuke Nabeshima , Johannes Kepler University
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).
K. Nabeshima, "A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields," Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05)(SYNASC), Timisoara, Romania, 2005, pp. 39-47.