2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164772We introduce the notion of magic functions of a general domain in d-dimensional complex space and show that the set of magic functions of a given domain is an intrinsic complex-geometric object. We determine the set of magic functions of the symmetrised bidisc G, and thereby find all automorphisms of G and a formula for the Caratheodory distance on G.17 pages. This version contains an additional proposition (2.11) and some minor corrections, notably to Propositions 3.6 and 3.7Complex VariablesFunctional Analysis32M05, 32F45, 32F32, 46A55text