Machine learning parameter systems, Noether normalisations and quasi-stable positions
| dc.date.accessioned | 2024-07-05T09:22:39Z | |
| dc.date.available | 2024-07-05T09:22:39Z | |
| dc.date.issued | 2024-06-25 | |
| dc.description.sponsorship | Gefördert im Rahmen des Projekts DEAL | |
| dc.identifier | doi:10.17170/kobra-2024070510466 | |
| dc.identifier.uri | http://hdl.handle.net/123456789/15897 | |
| dc.language.iso | eng | |
| dc.relation.doi | doi:10.1016/j.jsc.2024.102345 | |
| dc.relation.issupplementedby | doi:10.5281/zenodo.12114165 | |
| dc.rights | Namensnennung 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
| dc.subject | Quasi-stable ideals | eng |
| dc.subject | Noether normalisation | eng |
| dc.subject | Systems of parameters | eng |
| dc.subject | Pommaret bases | eng |
| dc.subject | Machine learning | eng |
| dc.subject | Multi-class classification | eng |
| dc.subject.ddc | 510 | |
| dc.subject.swd | Maschinelles Lernen | ger |
| dc.subject.swd | Parameteridentifikation | ger |
| dc.subject.swd | Noether-Theorem | ger |
| dc.title | Machine learning parameter systems, Noether normalisations and quasi-stable positions | eng |
| dc.type | Aufsatz | |
| dc.type.version | publishedVersion | |
| dcterms.abstract | We discuss the use of machine learning models for finding “good coordinates” for polynomial ideals. Our main goal is to put ideals into quasi-stable position, as this generic position shares most properties of the generic initial ideal, but can be deterministically reached and verified. Furthermore, it entails a Noether normalisation and provides us with a system of parameters. Traditional approaches use either random choices which typically destroy all sparsity or rather simple human heuristics which are only moderately successful. Our experiments show that machine learning models provide us here with interesting alternatives that most of the time make nearly optimal choices. | eng |
| dcterms.accessRights | open access | |
| dcterms.creator | Hashemi, Amir | |
| dcterms.creator | Mirhashemi, Mahshid | |
| dcterms.creator | Seiler, Werner M. | |
| dcterms.source.articlenumber | Article 102345 | |
| dcterms.source.identifier | eissn:1095-855X | |
| dcterms.source.journal | Journal of Symbolic Computation | eng |
| dcterms.source.volume | Volume 126 | |
| kup.iskup | false |