Computation of the unit group

Abstract

Let R be any order of our given algebraic number field F. In the sequel we assume that a ℤ-basis ω₁,…, ω_n of R is known and that computations can be carried out in terms of that basis along the lines of chapter IV. The units of R, i.e. those elements of R which have a multiplicative inverse, form a group whose structure is well known since about 150 years.