Gröbner bases for polynomial systems with parameters

• Verfasst von: Montes, Antonio [VerfasserIn]
• Verfasst von: Wibmer, Michael [VerfasserIn]
• Titel: Gröbner bases for polynomial systems with parameters
• Verf.angabe: Antonio Montes, Michael Wibmer
• E-Jahr: 2010
• Jahr: 22 June 2010
• Umfang: 35 S.
• Fussnoten: Gesehen am 03.05.2023
• Titel Quelle: Enthalten in: Journal of symbolic computation
• Ort Quelle: Amsterdam : Elsevier, 1985
• Jahr Quelle: 2010
• Band/Heft Quelle: 45(2010), 12, Seite 1391-1425
• ISSN Quelle: 1095-855X
• DOI: doi:10.1016/j.jsc.2010.06.017
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Canonical
• Sach-SW: Comprehensive
• Sach-SW: Gröbner cover
• Sach-SW: Locally closed sets
• Sach-SW: Parameters
• Sach-SW: Reduced
• K10plus-PPN: 1844476081

Abstract

Gröbner bases are the computational method par excellence for studying polynomial systems. In the case of parametric polynomial systems one has to determine the reduced Gröbner basis in dependence of the values of the parameters. In this article, we present the algorithm GröbnerCover which has as inputs a finite set of parametric polynomials, and outputs a finite partition of the parameter space into locally closed subsets together with polynomial data, from which the reduced Gröbner basis for a given parameter point can immediately be determined. The partition of the parameter space is intrinsic and particularly simple if the system is homogeneous.