Tag
LLL
10 resources tagged “LLL” across the knowledge library.
10 items
Article7 Aug 2026Detecting Algebraic and Linear Dependence with LLLRecovering exact integer relations from numerical approximations using LLL, and the precision requirements that make the method reliable.2 min readRead MoreArticle7 Aug 2026Factoring Polynomials over the IntegersThe modular-lift-recombine pipeline, the exponential recombination problem, and the LLL-based algorithm that makes factorisation polynomial time.2 min readRead MoreArticle7 Aug 2026Ideal Reduction in Number FieldsFinding a small ideal in a given ideal class by lattice reduction, and why reduction is the enabling step for relation collection.2 min readRead MoreArticle7 Aug 2026Integer Kernel and Image via LLLComputing a reduced basis of the integer kernel and image of a matrix, and why this is not the same as clearing denominators from a rational kernel.2 min readRead MoreArticle7 Aug 2026LLL for Linearly Dependent Generating SetsExtending LLL to generating sets that are not independent, and using the resulting zero vectors to extract relations.2 min readRead MoreArticle7 Aug 2026LLL-Based Hermite Normal Form ComputationUsing lattice reduction to control entry growth during Hermite normal form computation, and when this beats the modular approach.2 min readRead MoreArticle7 Aug 2026The LLL Lattice Basis Reduction AlgorithmThe LLL algorithm: size reduction interleaved with swaps under the Lovasz condition, and the guarantees it provides in polynomial time.3 min readRead MoreArticle7 Aug 2026The LLL Lattice Basis Reduction AlgorithmThe LLL algorithm: size reduction interleaved with swaps under the Lovasz condition, and the guarantees it provides in polynomial time.3 min readRead MoreArticle7 Aug 2026The Polynomial Reduction AlgorithmFinding a small defining polynomial for a number field using lattice reduction on the maximal order, and why this pays for itself.2 min readRead MoreArticle7 Aug 2026The Subfield ProblemFinding the subfields of a number field, by lattice methods and by linear algebra over the complex numbers.2 min readRead More