Hermite and Smith normal form algorithms over Dedekind domains

DOI10.1090/S0025-5718-96-00766-1zbMath0853.11100MaRDI QIDQ4718416

Henri Cohen

Publication date: 3 December 1996

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Dedekind domainfractional idealsHermite normal formSmith normal formrelative extensions of number fields

Mathematics Subject Classification ID

Computational aspects and applications of commutative rings (13P99) Algebraic number theory computations (11Y40) Algebraic number theory: global fields (11R99) Algebraic numbers; rings of algebraic integers (11R04) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (14)

Computing the multiplicative group of residue class rings ⋮ CANONICAL FORMS FOR 2-DIMENSIONAL LINEAR SYSTEMS OVER COMMUTAT IVE RINGS ⋮ On realization of isometries for higher rank quadratic lattices over number fields ⋮ Two-sided Galois duals of multi-twisted codes ⋮ On module unique-SVP and NTRU ⋮ Genuine Bianchi modular forms of higher level at varying weight and discriminant ⋮ On the computation of the HNF of a module over the ring of integers of a number field ⋮ Computing ray class groups, conductors and discriminants ⋮ Short Bases of Lattices over Number Fields ⋮ Two efficient algorithms for the computation of ideal sums in quadratic orders ⋮ A survey of computational class field theory ⋮ Explicit realization of elements of the Tate-Shafarevich group constructed from Kolyvagin classes ⋮ Computing local Artin maps, and solvability of norm equations ⋮ Computing in quotients of rings of integers

Cites Work

• Hermite Normal Form Computation Using Modulo Determinant Arithmetic
• Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
• Asymptotically Fast Triangularization of Matrices over Rings
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