A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases

Authors:
Akira Suzuki;Yosuke Sato
Affiliations:
Kobe University, Kobe, Japan;Tokyo University of Science, Tokyo, Japan
Venue:
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Year:
2006

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Abstract

We introduce a simple algorithm to compute comprehensive Gröbner bases. It requires only computations of reduced Gröbner bases in polynomial rings over ground fields. It is so simple that we can easily implement it on any computer algebra system that has a routine to compute reduced Gröbner bases. Our implementations on several computer algebra systems show that it is also sufficiently fast comparing with other existing algorithms.