Projects per year
Abstract
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truthtable invariance, making the CAD invariant with respect to the truth of logical formulae rather than the signs of polynomials; and CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint. We here consider how best to formulate problems for input to this algorithm. We focus on a choice (not relevant for other CAD algorithms) about the order in which constraints are presented. We develop new heuristics to help make this choice and thus allow the best use of the algorithm in practice. We also consider other choices of problem formulation for CAD, as discussed in CICM 2013, revisiting these in the context of the new algorithm.
Original language  English 

Title of host publication  Intelligent Computer Mathematics 
Editors  S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka, J. Urban 
Publisher  Springer 
Pages  4560 
Number of pages  15 
ISBN (Electronic)  9783319084343 
ISBN (Print)  9783319084336 
DOIs  
Publication status  Published  2014 
Publication series
Name  Lecture Notes in Artificial Intelligence 

Publisher  Springer 
Volume  8543 
Keywords
 cylindrical algebraic decomposition
 truth table invariance
 regular chains
 triangular decomposition
 problem formulation
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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