Algorithms to compute the topology of orientable real algebraic surfaces

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 RP 3 not inte...

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Bibliographic Details
Published in:Journal of symbolic computation 2003-09, Vol.36 (3), p.343-364
Main Authors: Fortuna, E., Gianni, P., Parenti, P., Traverso, C.
Format: Article
Language:English
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Summary: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 RP 3 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.
ISSN:0747-7171
1095-855X
DOI:10.1016/S0747-7171(03)00085-3