Tag
Class Group
10 resources tagged “Class Group” across the knowledge library.
10 items
Article7 Aug 2026Buchmann's Sub-exponential Algorithm: OverviewBuchmann's algorithm for class groups and units of arbitrary number fields, its structure, and where its cost concentrates.2 min readRead MoreArticle7 Aug 2026Class Group and Unit Computation: the Computational ProblemWhy class group and unit computation are a single problem, what the combined algorithm produces, and how the results are verified.2 min readRead MoreArticle7 Aug 2026Computational Algebraic Number Theory: Field OverviewWhat computational algebraic number theory actually computes, why the problems are hard, and how the subject's algorithms fit together.4 min readRead MoreArticle7 Aug 2026Shanks's Class Group Factoring MethodShanks's method factoring an integer by finding an ambiguous form in the class group of the corresponding discriminant.2 min readRead MoreArticle7 Aug 2026Sub-exponential Class Group Computation for Quadratic FieldsSub-exponential class group and regulator computation for quadratic fields by relation collection over a factor base.2 min readRead MoreArticle7 Aug 2026The Four Core Computational Tasks of Number FieldsThe four fundamental computational problems for a number field, their dependencies, and what counts as a complete answer to each.4 min readRead MoreArticle7 Aug 2026The Ideal Class GroupThe class group as the obstruction to unique factorisation, its finiteness, and what a complete computation must produce.2 min readRead MoreArticle7 Aug 2026The Schnorr-Lenstra Class Group Factoring MethodFactoring via class groups of quadratic orders, and its place as the conceptual bridge to the elliptic curve method.2 min readRead MoreArticle7 Aug 2026The Sub-exponential Algorithm in PracticePractical considerations in running class group computations: parameter tuning, parallelism, precision management and diagnostics.2 min readRead MoreGuide6 Aug 2026Class Groups, Units and the RegulatorThe ideal class group, Dirichlet's unit theorem, the regulator, Minkowski's bound, and the analytic class number formula used to verify computed values.4 min readRead More