The Chinese remainder problem, multivariate interpolation, and Gröbner bases
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Aspect graphs of algebraic surfaces
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Solving the load flow problem using Gröbner basis
ACM SIGSAM Bulletin
On the stability of Groübner bases under specializations
Journal of Symbolic Computation
Algebraic solution of the load-flow problem for a 4-nodes electrical network
Selected papers from the 1996 or 1997 IMACS-ACA conference on Non-standard applications of computer algebra
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
Canonical comprehensive Gröbner bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
On systems of algebraic equations with parametric exponents
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
A speed-up of the algorithm for computing comprehensive Gröbner systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Component-level parallelization of triangular decompositions
Proceedings of the 2007 international workshop on Parallel symbolic computation
A Study on Gröbner Basis with Inexact Input
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Comprehensive Gröbner bases and regular rings
Journal of Symbolic Computation
Hilbert stratification and parametric gröbner bases
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
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Comprehensive Gröbner bases for parametric polynomial ideals were introduced, constructed, and studied by the author in 1992. Since then the construction has been implemented in the computer algebra systems ALDES/SAC-2, MAS, REDUCE and MAPLE. A comprehensive Gröbner basis is a finite subset G of a parametric polynomial ideal I such that σ(G) constitutes a Gröbner basis of the ideal generated by σ(I) under all specializations σ of the parameters in arbitrary fields. This concept has found numerous applications. In contrast to reduced Gröbner bases, however, no concept of a canonical comprehensive Gröbner basis was known that depends only on the ideal and the term order. In this note we find such a concept under very general assumptions on the parameter ring. After proving the existence and essential uniqueness of canonical comprehensive Gröbner bases in a non-constructive way, we provide a corresponding construction for the classical case, where the parameter ring is a multivariate polynomial ring. It proceeds via the construction of a canonical faithful Gröbner system. Some simple examples illustrate the features of canonical comprehensive Gröbner bases. Besides their theoretical importance, canonical comprehensive Gröbner bases are also of potential interest for efficiency reasons as indicated by the research of A. Montes.