Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0747-7171(03)00085-3 | J. Symb. Comput. |
Keywords | Field | DocType |
line disjoint,finite number,real projective space,orientable real algebraic surface,constructive algorithm,non-singular orientable real algebraic,entire procedure,quartic surface,projective surface,decidable problem,basic tool morse theory,connected component,morse theory | Projective line,Line at infinity,Algebraic curve,Quartic surface,Real projective plane,Discrete mathematics,Topology,Combinatorics,Algorithm,Complex projective space,Real projective line,Mathematics,Projective space | Journal |
Volume | Issue | ISSN |
36 | 3-4 | Journal of Symbolic Computation |
Citations | PageRank | References |
13 | 1.40 | 13 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| E. Fortuna | 1 | 37 | 6.33 |
| P. Gianni | 2 | 48 | 7.08 |
| P. Parenti | 3 | 19 | 2.95 |
| C. Traverso | 4 | 48 | 9.26 |