Gröbner bases for polynomial systems with parameters
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...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
22 June 2010
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| In: |
Journal of symbolic computation
Year: 2010, Volume: 45, Issue: 12, Pages: 1391-1425 |
| ISSN: | 1095-855X |
| DOI: | 10.1016/j.jsc.2010.06.017 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jsc.2010.06.017 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0747717110000970 
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| Author Notes: | Antonio Montes, Michael Wibmer |
| Summary: | 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. |
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| Item Description: | Gesehen am 03.05.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1095-855X |
| DOI: | 10.1016/j.jsc.2010.06.017 |