Engineering↗
Discriminants and Integral Bases
The discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.
Tag
Maximal Order
Every page in the KEVOS library tagged Maximal Order. 8 pages.
Engineering↗
Orders in Number Fields
Orders as subrings that are full-rank lattices, the equation order, the maximal order, and the index that separates them.
Engineering↗
The Four Core Computational Tasks of Number Fields
The four fundamental computational problems for a number field, their dependencies, and what counts as a complete answer to each.
Engineering↗
The Maximal Order Problem
The maximal order problem, its reduction to a prime-by-prime question, and the factoring obstruction that limits it.
Engineering↗
The Round 2 Maximal Order Algorithm
The Round 2 algorithm: computing the maximal order prime by prime via radicals and rings of multipliers.
Engineering↗
Computing the Maximal Order: the Round 2 Algorithm
The Pohst-Zassenhaus theorem, the Dedekind criterion, the radical and the ring of multipliers, and the Round 2 algorithm for computing the ring of integers.
Engineering↗
Discriminants and Integral Bases
The field discriminant, integral bases, the index of an equation order, and why computing the maximal order reduces to factoring the polynomial discriminant.
Engineering↗
Orders and Ideals in Number Fields
Orders, 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 repr…
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