论文信息 - The Proper Parametrization of a Special Class of Rational Parametric Equations

The Proper Parametrization of a Special Class of Rational Parametric Equations

We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equations belongs to this class, and if it does, we reparametrize it such that the new parametric equations are proper.

Xiao-Shan Gao | Jia Li

[1] A. Schinzel. Polynomials with Special Regard to Reducibility: Polynomials over a number field , 2000 .

[2] Xiao-Shan Gao,et al. Implicitization of Rational Parametric Equations , 1992, J. Symb. Comput..

[3] A. Schinzel,et al. Polynomials with Special Regard to Reducibility: Index of terms , 2000 .

[4] Wenjun Wu,et al. Basic principles of mechanical theorem proving in elementary geometries , 1986, Journal of Automated Reasoning.

[5] W. Mccrea. Analytical Geometry of Three Dimensions , 1943, Nature.

[6] Ron Goldman,et al. Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants , 1992, Comput. Aided Geom. Des..

[7] Thomas W. Sederberg,et al. Improperly parametrized rational curves , 1986, Comput. Aided Geom. Des..

[8] C. Hoffmann. Algebraic curves , 1988 .

[9] Xiao-Shan Gao,et al. Computations with parametric equations , 1991, ISSAC '91.