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dc.contributor.authorMontes, Antonio
dc.contributor.authorRecio Muñiz, Tomás 
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2014-10-06T09:53:59Z
dc.date.available2014-10-06T09:53:59Z
dc.date.issued2014-10
dc.identifier.issn0378-4754
dc.identifier.issn1872-7166
dc.identifier.otherMTM2011-25816-C02-02
dc.identifier.urihttp://hdl.handle.net/10902/5301
dc.description.abstractIn this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of equations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we describe, through a relevant example, how the Gröbner cover algorithm is particularly well suited to obtain the missing hypotheses for a given geometric statement to hold true. We deal with the following problem: to describe the triangles that have at least two bisectors of equal length. The case of two inner bisectors is the well known, XIX century old, Steiner–Lehmus theorem, but the general case of inner and outer bisectors has been only recently addressed. We show how the Gröbner cover method automatically provides, while yielding more insight than through any other method, the conditions for a triangle to have two equal bisectors of whatever kind.es_ES
dc.format.extent25 p.es_ES
dc.language.isoenges_ES
dc.publisherElsevieres_ES
dc.rights© 2014 Elsevier B.V. This is the author’s version of a work that was accepted for publication in Mathematics and Computer in Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematics and Computer in Simulation, Vol. 104, Pp. 67-81, DOI:10.1016/j.matcom.2013.06.006es_ES
dc.sourceMathematics and Computer in Simulation, Vol. 104, Pp. 67-81es_ES
dc.subject.otherAutomatic discoveryes_ES
dc.subject.otherAutomatic deductiones_ES
dc.subject.otherElementarygeometryes_ES
dc.subject.otherComprehensive Gröbner systemes_ES
dc.subject.otherGröbner coveres_ES
dc.titleGeneralizing the Steiner–Lehmus theorem using the Gröbner coveres_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttp://dx.doi.org/10.1016/j.matcom.2013.06.006es_ES
dc.rights.accessRightsopenAccesses_ES
dc.identifier.DOI10.1016/j.matcom.2013.06.006
dc.type.versionacceptedVersiones_ES


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