An alternative approach to comprehensive Gröbner bases

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.

REFERENCES

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• 2: Yosuke Sato, A new type of canonical Gröbner bases in polynomial rings over Von Neumann regular rings, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.317-321, August 13-15, 1998, Rostock, Germany [doi>10.1145/281508.281658]
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.5 Roots of Nonlinear Equations
          Subjects: Polynomials, methods for

Additional Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Analysis of algorithms
  I.3 COMPUTER GRAPHICS
      I.3.6 Methodology and Techniques
          Subjects: Standards

General Terms:
Algorithms, Documentation, Standardization