Fast computation of Hermite normal forms of random integer matrices

DOI10.1016/j.jnt.2010.01.017zbMath1206.15027OpenAlexW2130870229MaRDI QIDQ984852

J. Martínez

Publication date: 20 July 2010

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.01.017

zbMATH Keywords

Hermite normal formexact linear algebra

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Random matrices (algebraic aspects) (15B52)

Related Items

On random nonsingular Hermite normal form ⋮ Zero-Knowledge Interactive Proof Systems for New Lattice Problems ⋮ Natural density distribution of Hermite normal forms of integer matrices ⋮ Storage efficient algorithm for Hermite normal form using LLL ⋮ Verification protocols with sub-linear communication for polynomial matrix operations ⋮ Enhancing Goldreich, Goldwasser and Halevi's scheme with intersecting lattices ⋮ Bijectivity Certification of 3D Digitized Rotations

Uses Software

• GAP
• LinBox
• NTL
• SageMath

Cites Work

• Exact solution of linear equations using p-adic expansions
• Computing Hermite and Smith normal forms of triangular integer matrices
• The shifted number system for fast linear algebra on integer matrices
• A linear space algorithm for computing the hermite normal form
• Hermite Normal Form Computation Using Modulo Determinant Arithmetic
• Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
• A BLAS based C library for exact linear algebra on integer matrices
• Sage: creating a viable free open source alternative to Magma, Maple, Mathematica, and MATLAB
• Hermite normal forms for integer matrices
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