dc.contributor.author | Recio, Tomás | |
dc.contributor.author | Sendra Pons, Juan Rafael | |
dc.contributor.author | Villarino Cabellos, Carlos | |
dc.date.accessioned | 2021-01-13T15:47:14Z | |
dc.date.available | 2021-01-13T15:47:14Z | |
dc.date.issued | 2018-07 | |
dc.identifier.bibliographicCitation | Recio, T., Sendra, J.R. & Villarino, C. 2018, "The importance of being zero”, in Proceedings of the 2018 ISSAC, July 2018, New York, NY, United States, pp. 327-333. | |
dc.identifier.isbn | 978-1-4503-5550-6 | |
dc.identifier.uri | http://hdl.handle.net/10017/45788 | |
dc.description | 2018 International Symposium on Symbolic and Algebraic Computation (ISSAC), July 2018, New York, NY, United States | en |
dc.description.abstract | We present a deterministic algorithm for deciding if a polynomial ideal, with coefficients in an algebraically closed field K of characteristic zero, of which we know just some very limited data, namely:the number n of variables, and some upper bound for the geometric degree of its zero set in Kn, is or not the zero ideal. The algorithm performs just a finite number of decisions to check whether a point is or not in the zero set of the ideal. Moreover, we extend this technique to test, in the same fashion, if the elimination of some
variables in the given ideal yields or not the zero ideal. Finally, the role of this technique in the context of automated theorem proving of elementary geometry statements, is presented, with references to recent documents describing the excellent performance of the already existing prototype version, implemented in GeoGebra. | en |
dc.description.sponsorship | Agencia Estatal de Investigación | es_ES |
dc.format.mimetype | application/pdf | en |
dc.language.iso | eng | en |
dc.publisher | ACM Press | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights | © 2018 ACM Press | |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Zero-test | en |
dc.subject | Polynomial ideals | en |
dc.subject | Schwartz-Zippel Lemma | en |
dc.subject | Automated reasoning in geometry | en |
dc.subject | Proving by examples | en |
dc.subject | GeoGebra | en |
dc.title | The importance of being zero | en |
dc.type | info:eu-repo/semantics/conferenceObject | en |
dc.subject.eciencia | Matemáticas | es_ES |
dc.subject.eciencia | Mathematics | en |
dc.contributor.affiliation | Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas | es_ES |
dc.relation.publisherversion | https://doi.org/10.1145/3208976.3208981 | |
dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
dc.identifier.doi | 10.1145/3208976.3208981 | |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88796-P/ES/COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONES/ | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |
dc.identifier.publicationtitle | Proceedings of the 2018 International Symposium on Symbolic and Algebraic Computation | |
dc.identifier.publicationlastpage | 333 | |
dc.identifier.publicationfirstpage | 327 | |