A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Computer Aided Geometric Design
Algorithms for intersecting parametric and algebraic curves I: simple intersections
ACM Transactions on Graphics (TOG)
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Algorithms for intersecting parametric and algebraic curves II: multiple intersections
Graphical Models and Image Processing
An improved upper complexity bound for the topology computation of a real algebraic plane curve
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
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
Implicitization of parametric curves and surfaces by using multidimensional Newton formulae
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Applied numerical linear algebra
Applied numerical linear algebra
Concrete Math
Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
SIAM Journal on Matrix Analysis and Applications
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
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
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
New algorithms for matrices, polynomials and matrix polynomials
New algorithms for matrices, polynomials and matrix polynomials
Resultant-based methods for plane curves intersection problems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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We present a collection of methods and tools for computing the topology of real algebraic plane curves de .ned by bivariate polynomial equations that are known at certain values or easy to evaluate, but whose explicit description is not available.The principal techniques used are the reduction of the computation of the real roots of the discriminant to a sparse generalized eigenvalue problem,the use of the structure of the nullspace of the classical Bezoutian, and its description in terms of the Lagrange Basis.