Tag
Integral Basis
7 resources tagged “Integral Basis” across the knowledge library.
7 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 2026Module Representation by Hermite Normal FormRepresenting ideals and modules as Hermite normal form matrices relative to an integral basis, with a common denominator.2 min readRead MoreArticle7 Aug 2026Quadratic Field Discriminants and Integral BasesDiscriminants and integral bases of quadratic fields, given by closed formulas with no computation required.2 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 MoreArticle7 Aug 2026The Standard Representation of Algebraic NumbersRepresenting field elements as coefficient vectors relative to a power basis or integral basis, with a common denominator.2 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 More