An alternative approach to comprehensive Gröbner bases

Authors:
Akira Suzuki;Yosuke Sato
Affiliations:
Kobe University, Japan;Ritsumeikan University, Japan
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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Abstract

We give an alternative definition of comprehensive Gröbner bases in terms of Gröbner bases in polynomial rings over commutative Von Neumann regular rings. Our comprehensive Gröbner bases are defined as Gröbner bases in polynomial rings over certain commutative Von Neumann regular rings, hence they have two important properties which do not hold in standard comprehensive Gröbner bases. One is that they have canonical forms. Another one is that we can define monomial reductions which are compatible with any instantiation.