Complutense University Library

On the simplification of the coefficients of a parametrization

Andradas Heranz, Carlos and Recio, Tomas and Tabera, Luis F. and Sendra, J. Rafael (2009) On the simplification of the coefficients of a parametrization. Journal of Symbolic Computation, 44 (2). pp. 192-210. ISSN 0747-7171

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:

View download statistics for this eprint

==>>> Export to other formats


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.

Item Type:Article
Uncontrolled Keywords:Parametric varieties; Field of definition; Simplification of parametrizations
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14730

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),


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://>[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.


Deposited On:17 Apr 2012 10:59
Last Modified:06 Feb 2014 10:07

Repository Staff Only: item control page