Tag
Prime Decomposition
8 resources tagged “Prime Decomposition” across the knowledge library.
8 items
Article7 Aug 2026Essential Discriminant DivisorsPrimes that divide the index for every choice of defining polynomial, why they exist, and what they force computationally.2 min readRead MoreArticle7 Aug 2026Newton Polygon Methods for Prime DecompositionUsing Newton polygons to decompose primes locally, handling the cases where factoring modulo p is insufficient.2 min readRead MoreArticle7 Aug 2026Prime Decomposition in Quadratic FieldsHow rational primes split, remain inert or ramify in a quadratic field, decided entirely by the Kronecker symbol.2 min readRead MoreArticle7 Aug 2026Prime Decomposition when p Does Not Divide the IndexDecomposing a prime that does not divide the index, by factoring the defining polynomial modulo that prime.2 min readRead MoreArticle7 Aug 2026Prime Decomposition: Theory and RamificationHow rational primes factor in the maximal order, ramification indices and residue degrees, and the degree relation that constrains them.2 min readRead MoreArticle7 Aug 2026The Buchmann-Lenstra Prime Decomposition MethodDecomposing any prime, including those dividing the index, by splitting the algebra of the order modulo that prime.2 min readRead MoreArticle7 Aug 2026The Four Core Computational Tasks of Number FieldsThe four fundamental computational problems for a number field, their dependencies, and what counts as a complete answer to each.4 min readRead MoreGuide6 Aug 2026Decomposition of Prime Numbers in Number FieldsRamification indices and residue degrees, the fundamental identity, Dedekind's theorem relating prime decomposition to polynomial factorisation modulo p, and computing valuations.5 min readRead More