A delineability-based method for computing critical sets of algebraic surfaces

Autores: Juan Gerardo Alcázar Arribas , Josef Schicho , Juan Rafael Sendra Pons
Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 42, Nº 6, 2007, págs. 678-691
Idioma: inglés
DOI: 10.1016/j.jsc.2007.02.001
Texto completo no disponible (Saber más ...)
Resumen
- In this paper, we address the problem of determining a real finite set of z-values where the topology type of the level curves of a (maybe singular) algebraic surface may change. We use as a fundamental and crucial tool McCallum¿s theorem on analytic delineability of polynomials (see [McCallum, S., 1998. An improved projection operation for cylindrical algebraic decomposition. In: Caviness, B.F., Johnson, J.R. (Eds.), Quantifier Elimination and Cylindrical Algebraic Decomposition. Springer Verlag, pp. 242¿268]). Our results allow to algorithmically compute this finite set by analyzing the real roots of a univariate polynomial; namely, the double discriminant of the implicit equation of the surface. As a consequence, an application to offsets is shown