A Canonical Form for Positive Definite Matrices

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 i...

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Bibliographic Details
Main Authors Sikirić, Mathieu Dutour, Haensch, Anna, Voight, John, van Woerden, Wessel P. J
Format Journal Article
LanguageEnglish
Published 29.04.2020
Subjects
Mathematics - Group Theory
Mathematics - Number Theory
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Summary: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.
DOI:10.48550/arxiv.2004.14022