On the simplification of the coefficients of a parametrization
| dc.contributor.author | Andradas Heranz, Carlos | |
| dc.contributor.author | Recio, Tomas | |
| dc.contributor.author | Tabera, Luis F. | |
| dc.contributor.author | Sendra, J. Rafael | |
| dc.date.accessioned | 2023-06-20T00:08:45Z | |
| dc.date.available | 2023-06-20T00:08:45Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | Let K subset of R be a computable field. We present an algorithm to decide whether a proper rational parametrization of a ruled surface, with coefficients in K((i), can be properly reparametrized over a real (i.e. embedded in R) finite field extension of K. Moreover, in the affirmative case, the algorithm provides a proper parametrization with coefficients in a real extension of K of degree at most 2. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Educacion y Ciencia | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14730 | |
| dc.identifier.doi | 10.1016/j.jsc.2008.09.001 | |
| dc.identifier.issn | 0747-7171 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0747717108001338 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42076 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of Symbolic Computation | |
| dc.language.iso | eng | |
| dc.page.final | 210 | |
| dc.page.initial | 192 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2005-02865 | |
| dc.relation.projectID | MTM2005-08690-CO2-01/02 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Parametric varieties | |
| dc.subject.keyword | Field of definition | |
| dc.subject.keyword | Simplification of parametrizations | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On the simplification of the coefficients of a parametrization | |
| dc.type | journal article | |
| dc.volume.number | 44 | |
| dcterms.references | Alonso, C., 1994. Desarrollo, análisis e implementación de algoritmos para la manipulación de variedades paraméricas. Ph.D. Thesis. Universidad de Cantabria. Alonso, C., Gutiérrez, J., Recio, T., 1996. A rational function decomposition algorithm using near-separated polynomials. Extracta Math. 11 (3), 475479. Andradas, C., Recio, T., Sendra, J.R., 1997. A relatively optimal rational space curve reparametrization algorithm through canonical divisors. In: Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI). ACM, New York, pp. 349355 (electronic). Andradas, C., Recio, T., Sendra, J.R., 1999. Base field restriction techniques for parametric curves. In: Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation (Vancouver, BC). ACM, New York, pp. 1722 (electronic). Cox, D., Little, J., O'Shea, D., 1997. Ideals, varieties, and algorithms. In: Undergraduate Texts in Mathematics, 2nd ed. Springer- Verlag, New York. Pérez-Díaz, S., Schicho, J., Sendra, J.R., 2002. Properness and inversion of rational parametrizations of surfaces. Appl. Algebra Engrg. Comm. Comput. 13 (1), 2951. Pérez-Díaz, S., Sendra, J.R., 2004. Computation of the degree of rational surface parametrizations. J. Pure Appl. Algebra 193 (13), 99121. Recio, T., Sendra, J.R., 1997a. Real reparametrizations of real curves. J. Symbolic Comput. 23 (23), 241254. Recio, T., Sendra, J.R., 1997b. A really elementary proof of real Lüroth's theorem. Rev. Mat. Univ. Complut. Madrid 10, 283290. (Special Issue, suppl.). Recio, T., Sendra, J.R., Tabera, L.F., Villarino, C., 2007. Generalizing circles over algebraic extensions. arXiv:0704.1384v1<http:// arxiv.org/abs/0704.1384v1>[math.AG]. Recio, T., Sendra, J.R., Villarino, C., 2004. From hypercircles to units. In: Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation. ACM, New York, pp. 258265. Schicho, J., 1998a. Inversion of birational maps with Gröbner bases. In: Gröbner Bases and Applications (Linz, 1998). In: London Math. Soc. Lect. Note Ser., vol. 251. Cambridge Univ. Press, Cambridge, pp. 495503. Schicho, J., 1998b. Rational parameterization of real surfaces. In: Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock). ACM, New York, pp. 302308 (electronic). Schicho, J., 2002. Simplification of surface parametrizations. In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation. ACM, New York, pp. 229237 (electronic). Sederberg, T.W., 1986. Improperly parametrized rational curves. Comput. Aided Geom. Design 3, 6775. Sendra, J.R., Winkler, F., 2001. Tracing index of rational curve parametrizations. Comput. Aided Geom. Design 18 (8), 771795. Shafarevich, I.R., 1994. Basic Algebraic Geometry, 2nd ed. vol I, II. Springer-Verlag, Berlin. Weil, A., 1995. Adèles et groupes algébriques. In: Séminaire Bourbaki. In: Soc. Math. France, Paris, vol. 5. pp. 249257. Exp. No. 186. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a74c23fe-4059-4e73-806b-71967e14ab67 | |
| relation.isAuthorOfPublication.latestForDiscovery | a74c23fe-4059-4e73-806b-71967e14ab67 |
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