On the computation of units and class numbers by a generalization of Lagrange's algorithm
The author describes an algorithm which allows one to compute a fundamental system of units, a cycle of reduced ideals and the class number of any order \({\mathfrak O}\) of an arbitrary algebraic number field F. His algorithm is a number geometric generalization of Lagrange's continued fraction algorithm and leads to a fundamental system of units of F in \(O(RD^{\epsilon})\) binary operations, for any \(\epsilon >0\); here R is the regulator of F, D is the absolute value of the discriminant of F, and the big O-constant depends only on the degree n of F over \({\mathbb{Q}}\). Examples involving 20 totally real quartic fields are given.
scientific article; zbMATH DE number 3995815
scientific article