Anne Heyworth

Research Interests

My research project is called Kan: A Categorical Approach to Computer Algebra. It will combine categorical objects with techniques of computer algebra to produce some nicely structured software, Kan, which will be applied to solving various combinatorial problems in a number of different areas.

My particular interests are in: Gröbner basis theory, rewriting, computational category theory, presentations (groups, monoids etc) and Petri nets.

I am a member of the Computational Category Theory Group.

Teaching Interests

My previous position, for one year, was that of a Demonstrator in Computer Science in the Department of Mathematics and Computer Science at the University of Leicester. I helped with the computer labs for MC198/9 Information Management/Systems, MC206 Software Engineering, MC117 Operating Sysyems and and Networks, MC205 Object Oriented Programming using C++ and MC214 Logic Programming. I updated and extended the CORAL project for a (locally) online course in Windows 2000, Word 2000 and Excel 2000 which is used in MC198/9.

Prior to that, I taught undergraduate courses in Linear Algebra and Gröbner Basis Theory (Computer Algebra) to some very nice students at the University of Wales, Bangor. I've also done some voluntary tutoring at Coleg Menai, Bangor and private tutoring for various GCSE, A level and degree students.

Computer Stuff

I mainly like to program in GAP and recommend it highly to anyone wanting to do some computer algebra.

Papers Etc

[1] A. Heyworth.

Rewriting and Noncommutative Gröbner bases with Applications to Kan Extensions and Identities Among Relations, UWB Math Preprint 98.23 (1998).

[2] R. Brown and A. Heyworth.

Using Rewrite Systems to Compute Kan Extensions of Actions of Categories. Journal of Symbolic Computation 29 (2000), 5-31. with: Kan Extension Program (in GAP3)

[3] A. Heyworth.

Rewriting as a special case of Gröbner basis theory. In M. Atkinson, N. Gilbert, J. Howie, S. Linton and E. Robertson (editors), Computational and Geometric Aspects of Modern Algebra, London Math. Soc. Lecture Note Series 275 (2000), 101-105.

[4] A. Chandler and A. Heyworth.

Gröbner Bases as a Tool for Petri Net Analysis (2001). Proceedings of the 5th World Multi-conference on Systematics, Cybernetics and Informatics (SCI2001), Orlando, Florida, July 2001.

[5] A. Heyworth and C. D. Wensley.

Logged Rewriting with Applications to Identities Among Relators, UWB Math Preprint 99.07 (1999). ``Groups - St Andrews 2001''

[6] A. Heyworth and B. Reinert.

Reduction in ZG-modules with Applications to Identities Among Relations, UWB Math Preprint 99.09 (1999). in preparation

[7] A. Heyworth.

One-sided Noncommutative Gröbner Bases with Applications to Green's Relations . Journal of Algebra 242 (2001), 401-415. (please email me if you want a copy)

[8] A. Heyworth.

Using Automata to obtain Regular Expressions for Induced Actions , UWB Math Preprint 99.19 (1999). submitted IJAC

[9] A. Heyworth and J. Snellman.

Gröbner Basis Theory for Modules.

[10] A. Heyworth.

Rewriting procedures generalise to Kan extensions of actions of categories, UWB Math Preprint 99.39. Proceedings of the Federated Logic Conference 1999 Workshop on Groebner Bases and Rewriting Techniques.

[11] A. Heyworth and M. Johnson.

Logged Rewriting for Monoid Presentations (2001). in preparation

[12] R. Brown and A. Heyworth.

Logged Rewriting and Identities Among Relations for Groupoids (2001). in preparation

[13] A. Chandler, A. Heyworth, L. Blair and D. Seward.

Testing Petri Nets for Mobile Robots Using Groebner Bases. In M. Pezze and S. M. Shatz (editors), Proceedings of the 21st International Conference in Application and Theory of Petri nets, Software Engineering and Petri nets Workshop, Aarhus, Denmark June 26-30 2000 , 21-34.

[14] A. Heyworth.

Gröbner Basis Techniques for Computing Actions of K-Categories, UWB Math Preprint 00.01. Proceedings of Category Theory 2000 16-22 July, Como, Italy, 105-113. submitted to TAC

[15] N. Ghani and A. Heyworth.

Computing over K-modules . Proceedings of Computing: The Australasian Theory Symposium: CATS 2002, . Elsevier, Electronic Notes in Theoretical Computer Science (to appear).

[16] A. J. Berrick, N. Ghani and A. Heyworth.

Rewriting for Knot Quandles . (in preparation)

[17] R. Brown, N. Ghani, A. Heyworth and C. D. Wensley.

Double Coset Rewriting Systems . (in preparation)

[18] N. Ghani and A. Heyworth.

A Rewriting Alternative to Reidemeister-Schreier . RTA 2003

Maths Links

School of Mathematics, University of Wales, Bangor

GAP Manual

Group Pub Forum Home Page

Category Theory - Online Book

Petri-nets