Adèles and idèles are nowadays frequently used in theoretical algebraic number theory, for example in class field theory. For explicit computations however, people still use the classical ideals....Show moreAdèles and idèles are nowadays frequently used in theoretical algebraic number theory, for example in class field theory. For explicit computations however, people still use the classical ideals. In this thesis we define representations of adèles and idèles, enabling us to perform explicit computations in adèle rings and idèle groups. We also discuss two applications of our representations: computing the profinite Fibonacci graph and computing Hilbert class fields of imaginary quadratic number fields using Shimura’s reciprocity law. We implemented these representations as well as the applications in the computer algebra package SageMath.Show less
