Researcher

Research Summary

I have spent three years researching into Cylindrical Algebraic Decomposition (CAD) for my PhD at the University of Bath. I was supervised by Prof. James Davenport and Dr Russell Bradford, as part of the Real Geometry and Connectedness via Triangular Description resarch group. I submitted by thesis in July 2014 (available: PDF) and successfully defended in November 2014 (with Prof. C K Yap and Prof N Vorobjov as my examiners). I was awarded my PhD in January 2015, and graduated in July 2015.

This page describes my academic work and publications.

The following is a short video explaining the ideas behind my research, submitted for the finals of the EPSRC UK ICT Pioneers competition:

Publications

The following is a list of my peer-reviewed publications, in preprint form, hosted on the arXiv. They are all freely-available on the University of Bath Opus Repository, along with various non-peer reviewed technical reports and peer-reviewed pedagogical articles.

Advances in Cylindrical Algebraic Decomposition David J Wilson (University of Bath)
PhD Thesis | 2014.
Mirrors: University of Bath Opus

Using the distribution of cells by dimension in a cylindrical algebraic decomposition David J. Wilson, Matthew England, Russell J. Bradford, and James H. Davenport (SYNASC 2014)
Proceedings of the 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing ( p.53-60 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Truth table invariant cylindrical algebraic decomposition by regular chains Russell Bradford, Changbo Chen, James H. Davenport, Matthew England,Marc Moreno Maza, and David J. Wilson (CASC 2014)
Lecture Notes in Computer Science ( 8660 : p.44-58 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Choosing a Variable Ordering for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition Matthew England, Russell Bradford, James H. Davenport, and David Wilson. (ICMS 2014)
Lecture Notes in Computer Scienc ( 8592 : p.450-457 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Using the Regular Chains Library to Build Cylindrical Algebraic Decompositions by Projecting and Lifting Matthew England, David J. Wilson, Russell Bradford, and James H. Davenport (ICMS 2014)
Lecture Notes in Computer Scienc ( 8592 : p.458-465 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

A Comparison of Three Heuristics to Choose the Variable Ordering for Cylindrical Algebraic Decomposition Zongyan Huang, Matthew England, David J. Wilson, James H. Davenport, and Lawrence C. Paulson
ACM Communications in Computer Algebra ( 48(3/4) : p.121-123 ) | 2015.
Mirrors: the arXiv and University of Bath Opus

Applying Machine Learning to the Problem of Choosing a Heuristic to Select the Variable Ordering for Cylindrical Algebraic Decomposition Zongyan Huang, Matthew England, David J. Wilson, James H. Davenport, Lawrence C. Paulson, and James Bridge (CICM 2014 (Calculemus))
Lecture Notes in Computer Science (Intelligent Computer Mathematics) ( 8543 : p.92-107 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition Matthew England, Russell J. Bradford, Changbo Chen, James H. Davenport, Marc Moreno Maza, and David J. Wilson (CICM 2014 (Calculemus))
Lecture Notes in Computer Science (Intelligent Computer Mathematics) ( 8543 : p.45-60 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Cylindrical Algebraic Sub-Decompositions David J. Wilson, Russell J. Bradford, James H. Davenport, and Matthew England
Mathematics in Computer Science ( 8(2) : p.263-288 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Branch Cuts in Maple 17 Matthew England, Edgardo Cheb-Terrab, Russell J. Bradford, James H. Davenport, and David J. Wilson
ACM Communications in Computer Algebra ( 48(1/2) : p.24-27 ) | 2014.
Mirrors: the arXiv and University of Bath Opus

Understanding Branch Cuts of Expressions Matthew England, Russell J. Bradford, James H. Davenport, and David J. Wilson (CICM 2013 (MKM))
Lecture Notes in Computer Science (Intelligent Computer Mathematics) ( 7961 : p.136-151 ) | 2013.
Mirrors: the arXiv and University of Bath Opus

Optimising Problem Formulation for Cylindrical Algebraic Decomposition Russell J. Bradford, James H. Davenport, Matthew England, and David J. Wilson (CICM 2013 (Calculemus))
Lecture Notes in Computer Science (Intelligent Computer Mathematics) ( 7961 : p.19-34 ) | 2013.
Mirrors: the arXiv and University of Bath Opus

A “Piano Movers” Problem Reformulated David J. Wilson, James H. Davenport, Matthew England, and Russell J. Bradford (SYNASC 2013)
Proceedings of the 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing ( p.53-60 ) | 2013.
Mirrors: the arXiv and University of Bath Opus

Cylindrical Algebraic Decompositions for Boolean Combinations Russell J. Bradford, James H. Davenport, Matthew England, Scott McCallum, and David J. Wilson (ISSAC 2013)
Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation ( p.125-132 ) | 2013.
Mirrors: the arXiv and University of Bath Opus

A Repository for CAD Examples David J. Wilson, Russell J. Bradford, and James H. Davenport
ACM Communications in Computer Algebra ( 46(3/4) : p.67-69 ) | 2013.
Mirrors: University of Bath Opus

Program Verification in the Presence of Complex Numbers, Functions with Branch Cuts etc. James H. Davenport, Russell J. Bradford, Matthew England, and David J. Wilson (SYNASC 2012)
Proceedings of the 2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing ( p.83-88 ) | 2012.
Mirrors: the arXiv and University of Bath Opus

Speeding Up Cylindrical Algebraic Decomposition by Gröbner Bases David J. Wilson, Russell J. Bradford, and James H. Davenport (CICM 2012 (Calculemus))
Intelligent Computer Mathematics ( 7362 : p.280-294 ) | 2012.
Mirrors: the arXiv and University of Bath Opus

Contact

If you are interested in contacting me regarding academic research: Contact