Algorithmical determination of the topology of a real algebraic surface

Authors:
E. Fortuna;P. Gianni;D. Luminati
Affiliations:
Dipartimento di Matematica, Universití di Pisa, via Buonarroti 2, I-56127 Pisa, Italy;Dipartimento di Matematica, Universití di Pisa, via Buonarroti 2, I-56127 Pisa, Italy;Dipartimento di Matematica, Universití di Trento, v. Sommarive n. 14 - loc. Povo, I-38050 Trento, Italy
Venue:
Journal of Symbolic Computation
Year:
2004

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Abstract

We present an algorithm to compute the topology of a non-singular real algebraic surface S in RP^3, that is the number of its connected components and a topological model for each of them. Our strategy consists in computing the Euler characteristic of each connected component by means of a Morse-type investigation of S or of a suitably constructed compact affine surface. This procedure can be used to determine the topological type of an arbitrary non-singular surface; in particular it extends an existing algorithm applicable only to surfaces disjoint from a line.