On the topology of real algebraic plane curves
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Publication:626980
DOI10.1007/s11786-010-0044-3zbMath1205.14038OpenAlexW2027411255MaRDI QIDQ626980
Fabrice Rouillier, Marc Pouget, Sylvain Lazard, Luis Mariano Peñaranda, Jin-San Cheng~
Publication date: 19 February 2011
Published in: Mathematics in Computer Science (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/inria-00517175/file/Revision_MCS.pdf
Real algebraic sets (14P05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Plane and space curves (14H50) Homotopy theory and fundamental groups in algebraic geometry (14F35)
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Uses Software
Cites Work
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- Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets
- Topology and arrangement computation of semi-algebraic planar curves
- Singular points of algebraic curves
- A polynomial-time algorithm for the topological type of real algebraic curve
- Constructing roadmaps of semi-algebraic sets. I: Completeness
- Solving zero-dimensional systems through the rational univariate representation
- A new efficient algorithm for computing Gröbner bases \((F_4)\)
- Efficient isolation of polynomial's real roots.
- An efficient method for analyzing the topology of plane real algebraic curves.
- Local box adjacency algorithms for cylindrical algebraic decompositions
- Recent progress in exact geometric computation
- Efficient topology determination of implicitly defined algebraic plane curves.
- An improved upper complexity bound for the topology computation of a real algebraic plane curve
- Cylindrical algebraic decomposition using validated numerics
- Almost tight recursion tree bounds for the Descartes method
- The topological configuration of a real algebraic curve
- Braids, Links, and Mapping Class Groups. (AM-82)
- Using Algebraic Geometry
- The computational geometry algorithms library CGAL
- Cylindrical Algebraic Decomposition I: The Basic Algorithm
- A List of Challenges for Real Algebraic Plane Curve Visualization Software
- Generalized normal forms and polynomial system solving
- Real Algebraic Numbers: Complexity Analysis and Experimentation
- On the exact computation of the topology of real algebraic curves
- On the topology of planar algebraic curves
- Computer Algebra in Scientific Computing
- Algorithms in real algebraic geometry
- Sylvester-Habicht sequences and fast Cauchy index computation
- A Gröbner free alternative for polynomial system solving
- Improved projection for cylindrical algebraic decomposition
