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dc.contributorÁlvarez Montaner, Josep
dc.contributorAlberich Carramiñana, Maria
dc.contributor.authorBlanco Fernández, Guillem
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2015-11-05T10:31:27Z
dc.date.available2015-11-05T10:31:27Z
dc.date.issued2015-10
dc.identifier.urihttp://hdl.handle.net/2117/78812
dc.description.abstractThis works focus on computational aspects of the theory of singularities of plane algebraic curves. We show how to use the Puiseux factorization of a curve, computed through the Newton-Puiseux algorithm, to study the equisingularity type of a curve. We present a novel version of the Newton-Puiseux algorithm that can compute all the Puiseux factorization of any arbitrary polynomial, removing the restriction of reduced inputs. Next, we introduce the theory of infinitely near points and the concept of base points of an ideal. Finally, we develop a novel algorithm that, using our novel version of the Newton-Puiseux algorithm, computes the weighted cluster of base points of any two dimensional ideal from any set of generators.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
dc.subject.lcshGeometry, Algebraic
dc.subject.otherEquisingularity
dc.subject.otherBase points
dc.subject.otherPuiseux series
dc.subject.otherTwo-dimensional ideal
dc.titleEffective computation of base points of two-dimensional ideals
dc.typeMaster thesis
dc.subject.lemacGeometria algèbrica
dc.subject.amsClassificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry
dc.identifier.slugFME-1192
dc.rights.accessOpen Access
dc.date.updated2015-10-30T06:39:02Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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