A Canonical Form for Positive Definite Matrices

2020/04/29 by Sikirić, Mathieu Dutour, Haensch, Anna, Voight, John +1 · 2 citations
#05C60 #05E18 #11H55 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.14022

Abstract

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension n, but it is practical and more efficient than canonical forms based on Minkowski reduction.

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• The lattice packing problem in dimension 9 by Voronoi's algorithm
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