An LLL algorithm with symmetries

2024/08/13 by Beth Romano, Jack A. Thorne, Romano, Beth +1
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.07012

openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a generalisation of the Lenstra-Lenstra-Lovász (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group G. This can be regarded as `lattice reduction with symmetries'. We make this algorithm explicit for the classical groups G = Sp_2g, SO_2g, and for the exceptional group G = G₂.

Related

• Algorithm for Lang's Theorem
• Symmetries of matrix multiplication algorithms. I
• A Las Vegas Rewriting Algorithm for the Symmetric Square Representation of Classical Groups
• Symmetries in Linear and Integer Programs
• An L2-quotient algorithm for finitely presented groups on arbitrarily many generators