Minimal canonical comprehensive Gröbner systems

This is the continuation of Montes’ paper “On the canonical discussion of polynomial systems with parameters”. In this paper, we define the Minimal Canonical Comprehensive Gröbner System of a parametric ideal and fix under which hypothesis it exists and is computable. An algorithm to obtain a canoni...

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Veröffentlicht in:Journal of symbolic computation Jg. 44; H. 5; S. 463 - 478
Hauptverfasser: Manubens, Montserrat, Montes, Antonio
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.05.2009
Schlagworte:
13 Commutative rings and algebras
13F Arithmetic rings and other special rings
13P Computational aspects of commutative algebra
68 Computer science
68W Algorithms
Algorismes
Algorithms
Canonical
Classificació AMS
Commutative algebra
Comprehensive Gröbner system
Constructible sets
Generalized canonical specification
Investigació operativa
Matemàtiques i estadística
Minimal
Programació matemàtica
Reduced specification
Àlgebra commutativa
Àrees temàtiques de la UPC
Reduced specification
Generalized canonical specification
Constructible sets
Canonical
Comprehensive Gröbner system
Minimal
ISSN:0747-7171, 1095-855X
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Beschreibung
Zusammenfassung:This is the continuation of Montes’ paper “On the canonical discussion of polynomial systems with parameters”. In this paper, we define the Minimal Canonical Comprehensive Gröbner System of a parametric ideal and fix under which hypothesis it exists and is computable. An algorithm to obtain a canonical description of the segments of the Minimal Canonical CGS is given, thus completing the whole MCCGS algorithm (implemented in Maple and Singular). We show its high utility for applications, such as automatic theorem proving and discovering, and compare it with other existing methods. A way to detect a counterexample to deny its existence is outlined, although the high number of tests done give evidence of the existence of the Minimal Canonical CGS.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2007.07.022