Projects per year
Abstract
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truthinvariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heuristics to help with the choice for this algorithm, suggest improvements and then derive a new heuristic more closely aligned with the mechanics of the new algorithm.
Original language  English 

Title of host publication  Mathematical Software – ICMS 2014 
Subtitle of host publication  4th International Congress, Seoul, South Korea, August 59, 2014. Proceedings 
Publisher  Springer 
Pages  450457 
Number of pages  8 
Volume  8592 
ISBN (Print)  9783662441985 
DOIs  
Publication status  Published  2014 
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Projects
 1 Finished

Real Geometry and Connectedness via Triangular Description
Davenport, J., Bradford, R., England, M. & Wilson, D.
Engineering and Physical Sciences Research Council
1/10/11 → 31/12/15
Project: Research council