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.
Tag
Regulator
Every page in the KEVOS library tagged Regulator. 7 pages.
Engineering↗
Reduction of Indefinite Forms and the Cycle Structure
Reduction of indefinite binary forms, the cycle of reduced forms in each class, and how the cycle encodes the regulator.
Engineering↗
Regulator and Fundamental Unit Recovery
Extracting fundamental units and the regulator from the kernel of the relation matrix, and confirming the unit system is fundamental.
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 Fundamental Unit of a Real Quadratic Field
Computing the fundamental unit of a real quadratic field by continued fractions, its connection to the Pell equation, and its size.
Engineering↗
The Regulator: Definition and Computation
The regulator as the covolume of the unit lattice, its computation, and the precision and verification it demands.
Engineering↗
Real Quadratic Fields and the Infrastructure Method
Regulators and fundamental units of real quadratic fields, the continued fraction algorithm, the exponential cost problem, and Shanks's infrastructure with the distance function.
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