The study of integrals of univariate algebraic functions (1-periods) provided the impetus to develop much of algebraic geometry and transcendental number theory. This old saga is now at a point of resolution. In 2022, Huber and Wüstholz gave a "qualitative description" of all linear relations with algebraic coefficients between 1-periods. New techniques for determining symmetries of complex tori allow us to develop algorithms to explicate these qualitative relations and decide the transcendence of 1-periods. This is a work-in-progress with Joël Ouaknine (MPI SWS) and James Worrell (Oxford).