Engineering↗
Baby-Step Giant-Step and Class Group Structure
The baby-step giant-step method for discrete logarithms and group order, its application to class groups when an approximation to the order is available, and determination of gr…
Tag
Quadratic Fields
Every page in the KEVOS library tagged Quadratic Fields. 5 pages.
Engineering↗
Class Numbers of Imaginary Quadratic Fields
Computing class numbers of imaginary quadratic fields by enumeration of reduced forms, by analytic class number formulas, and by modular form methods, with the Gauss class numbe…
Engineering↗
Quadratic Fields and Binary Quadratic Forms
Quadratic fields, their discriminants and integral bases, prime decomposition by the Kronecker symbol, binary quadratic forms, reduction, and the correspondence between form cla…
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.
Engineering↗
The Cohen–Lenstra Heuristics
The Cohen-Lenstra heuristics for class groups of quadratic fields, the weighting principle, predicted divisibility frequencies, and their role in validating computations.
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