Projects per year
Abstract
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both performance and output and summarise what may be done to assist with this choice. We then survey other questions of problem formulation and algorithm optimisation that have become pertinent following advances in CAD theory, including both work that is already published and work that is currently underway.
With implementations now in reach of real world applications and new theory meaning algorithms are far more sensitive to the input, our thesis is that intelligently formulating problems for algorithms, and indeed choosing the correct algorithm variant for a problem, is key to improving the practical use of both quantifier elimination and symbolic real algebraic geometry in general.
With implementations now in reach of real world applications and new theory meaning algorithms are far more sensitive to the input, our thesis is that intelligently formulating problems for algorithms, and indeed choosing the correct algorithm variant for a problem, is key to improving the practical use of both quantifier elimination and symbolic real algebraic geometry in general.
Original language | English |
---|---|
Title of host publication | Proceedings of XIV Encuentro de Álgebra Computacional y Aplicaciones |
Subtitle of host publication | Barcelona, June 18-20 2014 |
Pages | 107-110 |
Publication status | Published - 2014 |
Keywords
- symbolic computation
- computer algebra
- problem formulation
- computational algebraic geometry
- real algebraic geometry
Fingerprint
Dive into the research topics of 'Formulating problems for real algebraic geometry'. Together they form a unique fingerprint.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