Tag
Number Fields II
4 resources tagged “Number Fields II” across the knowledge library.
4 items
Guide6 Aug 2026Class Group and Unit Computation in General Number FieldsThe general sub-exponential algorithm for class groups and units: factor base selection, ideal reduction, relation collection, the relation matrix and its kernel, and verification against the analytic class number formula.5 min readRead MoreGuide6 Aug 2026Computing Galois Groups of Number FieldsThe resolvent method for determining Galois groups, the Frobenius cycle-type approach via Dedekind's theorem, transitive group classification by degree, and test polynomials.5 min readRead MoreGuide6 Aug 2026Computing the Maximal Order: the Round 2 AlgorithmThe Pohst-Zassenhaus theorem, the Dedekind criterion, the radical and the ring of multipliers, and the Round 2 algorithm for computing the ring of integers.5 min readRead MoreGuide6 Aug 2026Prime Decomposition: the Buchmann–Lenstra MethodPrime decomposition for primes dividing the index: Newton polygons, splitting separable algebras over F_p, ideal arithmetic modulo p, and the Buchmann-Lenstra algorithm.5 min readRead More