On some exotic cylindrical algebraic decompositions and cells
Abstract
Abstract Cylindrical algebraic decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and the algorithmic study of the topology of semi‐algebraic sets. In this paper, we construct explicit examples of CADs and CAD cells that refute several conjectures and open questions of J. H. Davenport, A. Locatelli, and G. K. Sankaran concerning these topological assumptions.
Fields of Study & Subjects
Polynomial and algebraic computation
Advanced Combinatorial Mathematics
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 10
- Publication date
- 1 October 2026
- Language
- EN