We now distinguish between root systems, defined over real vector spaces, and root data, defined over integer lattices. The former are designed for the study of reflection groups and Coxeter groups; the later are designed for Lie algebras and groups of Lie type. A small number of commands that worked previously will no longer work: for example RootDatum("H3") must be changed to RootSystem("H3") since the root system of type H3 cannot be defined in an integer lattice.