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Quadratic Fields

5 resources tagged “Quadratic Fields” across the knowledge library.

5 items

Guide6 Aug 2026Baby-Step Giant-Step and Class Group StructureThe 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 group structure.4 min readRead More Guide6 Aug 2026Class Numbers of Imaginary Quadratic FieldsComputing 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 number problem.4 min readRead More Guide6 Aug 2026Quadratic Fields and Binary Quadratic FormsQuadratic fields, their discriminants and integral bases, prime decomposition by the Kronecker symbol, binary quadratic forms, reduction, and the correspondence between form classes and ideal classes.5 min readRead More Guide6 Aug 2026Real Quadratic Fields and the Infrastructure MethodRegulators and fundamental units of real quadratic fields, the continued fraction algorithm, the exponential cost problem, and Shanks's infrastructure with the distance function.5 min readRead More Guide6 Aug 2026The Cohen–Lenstra HeuristicsThe Cohen-Lenstra heuristics for class groups of quadratic fields, the weighting principle, predicted divisibility frequencies, and their role in validating computations.4 min readRead More