The complexity of robot motion planning
The complexity of robot motion planning
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
Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Algorithms for the Shape of Semialgebraic Sets. A New Approach
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Computation of the topology of real algebraic space curves
Journal of Symbolic Computation
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Cell decomposition of almost smooth real algebraic surfaces
Numerical Algorithms
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We present constructive algorithms to determine the topological type of a non-singular real algebraic projective surface S in the real projective space; we address this question when there exists a line in RP3 not intersecting the surface. Starting from a polynomial equation with rational coefficients for S, our algorithm computes the homology of the various connected components of the surface. We reconstruct the homology in a finite number of steps, using as a basic tool Morse theory. The entire procedure has been implemented in Axiom.