Engineering↗
Discriminants and Integral Bases
The discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.
Tag
Integral Basis
Every page in the KEVOS library tagged Integral Basis. 7 pages.
Engineering↗
Module Representation by Hermite Normal Form
Representing ideals and modules as Hermite normal form matrices relative to an integral basis, with a common denominator.
Engineering↗
Quadratic Field Discriminants and Integral Bases
Discriminants and integral bases of quadratic fields, given by closed formulas with no computation required.
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↗
The Standard Representation of Algebraic Numbers
Representing field elements as coefficient vectors relative to a power basis or integral basis, with a common denominator.
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.
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