Mostra el registre d'ítem simple
Effective computation of base points of two-dimensional ideals
dc.contributor | Álvarez Montaner, Josep |
dc.contributor | Alberich Carramiñana, Maria |
dc.contributor.author | Blanco Fernández, Guillem |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2015-11-05T10:31:27Z |
dc.date.available | 2015-11-05T10:31:27Z |
dc.date.issued | 2015-10 |
dc.identifier.uri | http://hdl.handle.net/2117/78812 |
dc.description.abstract | This 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.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica |
dc.subject.lcsh | Geometry, Algebraic |
dc.subject.other | Equisingularity |
dc.subject.other | Base points |
dc.subject.other | Puiseux series |
dc.subject.other | Two-dimensional ideal |
dc.title | Effective computation of base points of two-dimensional ideals |
dc.type | Master thesis |
dc.subject.lemac | Geometria algèbrica |
dc.subject.ams | Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry |
dc.identifier.slug | FME-1192 |
dc.rights.access | Open Access |
dc.date.updated | 2015-10-30T06:39:02Z |
dc.audience.educationlevel | Màster |
dc.audience.mediator | Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística |
dc.audience.degree | MÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010) |