We present constructive algorithms to determine the topological type of a non-singular orientable real algebraic projective surface S in the real projective space, starting from a polynomial equation with rational coefficients for S. We address this question when there exists a line in RP3 not intersecting the surface, which is a decidable problem; in the case of quartic surfaces, when this condition is always fulfilled, we give a procedure to find a line disjoint from the surface. Our algorithm computes the homology of the various connected components of the surface in a finite number of steps, using as a basic tool Morse theory. The entire procedure has been implemented in Axiom.
|Autori:||FORTUNA E; GIANNI P; PARENTI P; TRAVERSO C|
|Titolo:||Algorithms to compute the topology of orientable real algebraic surfaces|
|Anno del prodotto:||2003|
|Digital Object Identifier (DOI):||10.1016/S0747-7171(03)00085-3|
|Appare nelle tipologie:||1.1 Articolo in rivista|