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Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05)
A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields
Timisoara, Romania
September 25-September 29
ISBN: 0-7695-2453-2
ASCII Text
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Katsusuke Nabeshima, "A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields," Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on, pp. 39-47, Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05), 2005.
 
 
BibTex
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@article{ 10.1109/SYNASC.2005.3,
author = {Katsusuke Nabeshima},
title = {A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields},
journal ={Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on},
volume = {0},
year = {2005},
isbn = {0-7695-2453-2},
pages = {39-47},
doi = {http://doi.ieeecomputersociety.org/10.1109/SYNASC.2005.3},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - CONF
JO - Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on
TI - A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields
SN - 0-7695-2453-2
SP39
EP47
A1 - Katsusuke Nabeshima,
PY - 2005
KW - null
VL - 0
JA - Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on
ER -
 
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).
Citation:
Katsusuke Nabeshima, "A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields," synasc, pp.39-47, Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05), 2005
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