A Canonical Form for Positive Definite Matrices
Number Theory
2020-11-17 v3 Group Theory
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 , but it is practical and more efficient than canonical forms based on Minkowski reduction.
Cite
@article{arxiv.2004.14022,
title = {A Canonical Form for Positive Definite Matrices},
author = {Mathieu Dutour Sikirić and Anna Haensch and John Voight and Wessel P. J. van Woerden},
journal= {arXiv preprint arXiv:2004.14022},
year = {2020}
}