Dr. Matthew England

Position

Matthew is a Lecturer in Computer Science at Coventry University.

Qualifications

Ph.D. Mathematics, Heriot Watt University

M.Sc. Applied Mathematical Sciences, Heriot Watt University

B.Sc. Mathematics with Economics, Royal Holloway University of London

Postgraduate Certificate in Academic Practice, University of Glasgow

Fellow of the Higher Education Academy

Research

Matthew’s research centres around Symbolic Computation (also known as Computer Algebra). This encompasses the study and development of algorithms and software for manipulating mathematical expressions and object. It is distinct from the more ubiquitous numerical computation which uses floating point arithmetic to give approximate results. Some of the areas include (but are not limited to):

- Computational algebraic geometry;

- Polynomial algebra;

- Quantifier elimination;

- Algebraic simplification;

- Programming over complex space;

- Machine learning to improve algorithms;

- Problem formulation for computer algebra;

- Integration of symbolic computation with theorem provers;

- Use of computer algebra in mathematics education;

- Parallel algorithms for symbolic computation;

- User interface for computer algebra;

- Applications of symbolic computation.

Selected Outputs

J.C. Eilbeck, M. England, Y. Ônishi. Some new addition formulae for Weierstrass elliptic functions.
Proceedings of the Royal Society A, 470:2171, p. 20140051, 2014.

D. Wilson, M. England, R. Bradford and J.H. Davenport. Using the distribution of cells by dimension in a cylindrical algebraic decomposition. Proceedings of the 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC '14), pp. 53--60. IEEE, 2014.

R. Bradford, C. Chen, J.H. Davenport, M. England, M. Moreno Maza and D. Wilson. Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains. In: V.P. Gerdt W. Koepf, W.M. Seiler and E.V. Vorozhtsov, eds. Computer Algebra in Scientific Computing, pp. 44-58. (Lecture Notes in Computer Science, 8660). Springer International, 2014.

M. England, R. Bradford, C. Chen, J.H. Davenport, M. Moreno Maza and D. Wilson. Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. In: S.M. Watt, J.H. Davenport, A.P. Sexton, P. Sojka and J. Urban, eds. Intelligent Computer Mathematics, pp. 45-60. (Lecture Notes in Artificial Intelligence, 8543). Springer Berlin Heidelberg, 2014.

Z. Huang, M. England, D. Wilson, J.H. Davenport, L.C. Paulson and J. Bridge. Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. In: S.M. Watt, J.H. Davenport, A.P. Sexton, P. Sojka and J. Urban, eds. Intelligent Computer Mathematics, pp. 92-107. (Lecture Notes in Artificial Intelligence, 8543). Springer Berlin Heidelberg, 2014.

M. England, E. Cheb-Terrab, R. Bradford, J.H. Davenport and D. Wilson. Branch cuts in Maple 17. ACM Communications in Computer Algebra 48:1 (issue 187), pp. 24-27, ACM, 2014.

D. Wilson, R. Bradford, J.H. Davenport and M. England. Cylindrical algebraic sub-decompositions. Mathematics in Computer Science (Special Issue on Computational Algebraic Geometry) 8:2, pp. 263-288, Springer, 2014.