Engineering↗
Buchmann's Sub-exponential Algorithm: Overview
Buchmann's algorithm for class groups and units of arbitrary number fields, its structure, and where its cost concentrates.
Tag
Class Group
Every page in the KEVOS library tagged Class Group. 10 pages.
Engineering↗
Class Group and Unit Computation: the Computational Problem
Why class group and unit computation are a single problem, what the combined algorithm produces, and how the results are verified.
Engineering↗
Computational Algebraic Number Theory: Field Overview
What computational algebraic number theory actually computes, why the problems are hard, and how the subject's algorithms fit together.
Engineering↗
Shanks's Class Group Factoring Method
Shanks's method factoring an integer by finding an ambiguous form in the class group of the corresponding discriminant.
Engineering↗
Sub-exponential Class Group Computation for Quadratic Fields
Sub-exponential class group and regulator computation for quadratic fields by relation collection over a factor base.
Engineering↗
The Four Core Computational Tasks of Number Fields
The four fundamental computational problems for a number field, their dependencies, and what counts as a complete answer to each.
Engineering↗
The Ideal Class Group
The class group as the obstruction to unique factorisation, its finiteness, and what a complete computation must produce.
Engineering↗
The Schnorr-Lenstra Class Group Factoring Method
Factoring via class groups of quadratic orders, and its place as the conceptual bridge to the elliptic curve method.
Engineering↗
The Sub-exponential Algorithm in Practice
Practical considerations in running class group computations: parameter tuning, parallelism, precision management and diagnostics.
Engineering↗
Class Groups, Units and the Regulator
The ideal class group, Dirichlet's unit theorem, the regulator, Minkowski's bound, and the analytic class number formula used to verify computed values.
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