Journal of Symbolic Computation
Algebraic decomposition of regular curves
Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Computer Aided Geometric Design
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
A new approach to the surface intersection problem
Computer Aided Geometric Design
Asymptotically fast computation of subresultants
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Computer Aided Geometric Design
Local box adjacency algorithms for cylindrical algebraic decompositions
Journal of Symbolic Computation
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Modern Computer Algebra
Algorithms to compute the topology of orientable real algebraic surfaces
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
A delineability-based method for computing critical sets of algebraic surfaces
Journal of Symbolic Computation
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Topology of real algebraic space curves
Journal of Symbolic Computation
On the computation of the topology of a non-reduced implicit space curve
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Computation of the topology of real algebraic space curves
Journal of Symbolic Computation
Algorithmical determination of the topology of a real algebraic surface
Journal of Symbolic Computation
Journal of Symbolic Computation
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We present a new and complete algorithm for computing the topology of an algebraic surface S given by a square free polynomial in Q[X,Y,Z]. Our algorithm involves only subresultant computations and entirely relies on rational manipulation, which makes it direct to implement. We extend the work in Diatta et al. (2008), on the topology of non-reduced algebraic space curves, and apply it to the polar curve or apparent contour of the surface S. We exploit a simple algebraic criterion to certify the pseudo-genericity and genericity position of the surface. This gives us rational parametrizations of the components of the polar curve, which are used to lift the topology of the projection of the polar curve. We deduce the connection of the two-dimensional components above the cell defined by the projection of the polar curve. A complexity analysis of the algorithm is provided leading to a bound in O@?"B(d^2^1@t) for the complexity of the computation of the topology of an implicit algebraic surface defined by integer coefficient polynomial of degree d and coefficient size @t. Examples illustrate the implementation in Mathemagix of this first complete code for certified topology of algebraic surfaces.