Advanced Topics in Computational Number Theory

The book focuses on the computation of invariants in algebraic number fields, such as integral bases and ideal class groups, highlighting its significance in solving Diophantine equations. It discusses the advancements made in computational number theory over the past decade, particularly through specialized Computer Algebra Systems like Magma and Pari/GP. While building on previous work, it emphasizes the generalization of algorithms to relative extensions of number fields, maintaining a focus solely on number fields rather than function fields.