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Canonical comprehensive Gröbner bases by Volker Weispfenning is a Computer Science article available to read on EtoBox.
What is Canonical comprehensive Gröbner bases about?
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. We also prove corresponding results for canonical comprehensive Gröbner bases relative to specializations in a
Who reads Canonical comprehensive Gröbner bases?
It is typically read by researchers, students, and practitioners in Computer Science.
- Author
- Volker Weispfenning
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0747-7171)
- Published
- 2003
- Language
- EN
- Field
- Computer Science (Physical Sciences)