Description
A map is an embedding of a (finite) graph into a (compact) surface. We may imagine a map as a graph G drawn on a surface such that no pair of edges of G intersects. Many questions in science reduced to problems which can be formulated in the language of theory of maps: just to mention, solutions of differential equations in particle physics, shapes of molecules in chemistry and many others. As follows, the maps with symmetries plays the prominent role in all areas and the algorithms to compute symmetries or to generate symmetric maps are mainly of interest.
The most algorithms to attack the problems in the theory of maps are based on two basic algorithms: Schreier-Sims algorithm and Todd-Coxeter procedure. In the talk we will show the basic data structures for representing maps (as subgroups of a permutation groups), and the crucial basic algorithms to solve standard problems. We will also discuss some contemporary systems of computational algebra: their advantages and disadvantages in the field of theory of maps.
Primary author
Dr
Ján Karabáš
(University of Primorska)
