Closed subsets of root systems and regular subalgebras

We describe an algorithm for classifying the closed subsets of a root system, up to conjugation by associated Weyl group. Our is implemented in language computer algebra system GAP 4. discuss implementation and give runtimes on some sample inputs. The classification irreducible closely related regular subalgebras, inner automorphism, corresponding simple Lie algebra. show how obtain subalgebras given set systems rank 3. version this paper arxiv has tables describing that were obtained.