Tag
Maximal Order
8 resources tagged “Maximal Order” across the knowledge library.
8 items
Article7 Aug 2026Discriminants and Integral BasesThe discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.2 min readRead MoreArticle7 Aug 2026Orders in Number FieldsOrders as subrings that are full-rank lattices, the equation order, the maximal order, and the index that separates them.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 MoreArticle7 Aug 2026The Maximal Order ProblemThe maximal order problem, its reduction to a prime-by-prime question, and the factoring obstruction that limits it.2 min readRead MoreArticle7 Aug 2026The Round 2 Maximal Order AlgorithmThe Round 2 algorithm: computing the maximal order prime by prime via radicals and rings of multipliers.2 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 2026Discriminants and Integral BasesThe field discriminant, integral bases, the index of an equation order, and why computing the maximal order reduces to factoring the polynomial discriminant.5 min readRead MoreGuide6 Aug 2026Orders and Ideals in Number FieldsOrders, the maximal order, fractional and integral ideals, unique factorisation of ideals in a Dedekind domain, ideal arithmetic by Hermite normal form, and the two-element representation.4 min readRead More