Dissertation/ Thesis
Effective computation of base points of two-dimensional ideals
| Τίτλος: | Effective computation of base points of two-dimensional ideals |
|---|---|
| Συγγραφείς: | Blanco Fernández, Guillem |
| Συνεισφορές: | Alberich-Carramiñana, Maria, Àlvarez Montaner, Josep, Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72], Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I, Álvarez Montaner, Josep, Alberich Carramiñana, Maria |
| Πηγή: | Digital.CSIC. Repositorio Institucional del CSIC instname Consejo Superior de Investigaciones Científicas (CSIC) Recercat. Dipósit de la Recerca de Catalunya UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | Universidad Politécnica de Cataluña, 2015. |
| Έτος έκδοσης: | 2015 |
| Θεματικοί όροι: | Geometry, Algebraic, Algebraic, Base points, Two-dimensional ideal, Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry, Puiseux series, 14 Algebraic geometry::14Q Computational aspects in algebraic geometry [Classificació AMS], Geometry, Matemàtiques i estadística::Geometria::Geometria algebraica [Àrees temàtiques de la UPC], Geometria algèbrica, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, Equisingularity |
| Περιγραφή: | 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. Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística. Departament de Matemàtica Aplicada I. Treball Final de Màster: Master of Science in Advanced Mathematics and Mathematical Engineering. |
| Τύπος εγγράφου: | Master thesis |
| Περιγραφή αρχείου: | application/pdf |
| Σύνδεσμος πρόσβασης: | http://hdl.handle.net/10261/155302 http://hdl.handle.net/2117/78812 https://hdl.handle.net/2117/78812 |
| Rights: | CC BY NC SA |
| Αριθμός Καταχώρησης: | edsair.dedup.wf.002..8f5eb0655a8fc9c2c165b8b85d1cf9d1 |
| Βάση Δεδομένων: | OpenAIRE |
| Η περιγραφή δεν είναι διαθέσιμη |