CIRCA

The Centre for Interdisciplinary Research in Computational Algebra (CIRCA) was established in 2000 to foster new and existing collaborative research between members of the Schools of Computer Science and of Mathematics and Statistics in the area of computational abstract algebra.

The Centre undertakes mathematical research with computer assistance, develops new techniques for computation in abstract algebra and develops and distributes software implementing these techniques. This work is supported by research grants from EPSRC, the Leverhulme Trust, the Royal Society, the British Council, the European Commission and the Royal Society of Edinburgh.

The Centre also organises conferences, seminars and training courses and plays a significant role in the international efforts to develop maintain and promote the GAP (groups, algorithms and programming) software package, a leading integrated system for computational discrete mathematics and algebra.

News and Events

CIRCA seminar March 28th


There will be a CIRCA lunchtime seminar on 28th March at 1pm in Theatre D of Maths.

David Stewart (University of Manchester) will speak.

Title: You need 27 tickets to guarantee a win on the UK National Lottery (Jt with David Cushing)

Abstract: The authors came across the problem of finding minimal lottery design numbers j=L(n,k,p,t); that is, a set B_1, …, B_j subsets of {1,..,n} each of size k, such that for any subset D of {1,..,n} of size p, one finds an intersection D\cap B_i with at least t elements. In the context of a lottery, n represents the. number of balls, k the number of choices of balls on a ticket, p the size of a draw.
For the UK national lottery, n=59, k=p=6 and one gets a (rather meagre) prize as long as t is at least 2.
Using the constraint solving library in Prolog, we calculated j for k=p=6, t=2 and n all the way up to 70. For example L(59,6,6,2)=27. This is the second paper where we have aimed to show the value of Prolog and constraint programming in pure mathematics.
I’ll give an overview of constraint programming, logic programming in Prolog, and describe how we used these tools to solve the problem described in the title.


CIRCA seminar March 14th


There will be a CIRCA lunchtime seminar on 14th March at 1pm in Theatre D of Maths.

Peiran Wu and Yayi Zhu will speak.

Peiran’s Title: Irredundant bases for classical groups

Peiran’s Abstract: Given a classical group G(V) over a finite field, a subgroup of G(V) is in Aschbacher class C_1 if it stabilises a subspace of V. I will talk about my ongoing search for bounds on irredundant bases of classical groups acting primitively with point stabilisers in C_1.

Yayi’s Title: Presentations for ideals in T_n
Yayi’s Abstract: The Green’s D relation on the full transformation semigroup T_n partitions T_n into n subsets, each containing all transformations of a certain rank. Any ideal I of T_n is a union of D-classes, and consists of all maps of rank 1, 2,…, m for some m no bigger than n. We investigate the presentations of the ideals. For some of them, we determine how large portion of their Cayley table is needed to define a ‘nice’ presentation.