arXiv subjects

Wessel P. J. van Woerden

Publications and source records attributed to Wessel P. J. van Woerden.

2 recordsLinked to original sources

arXiv2020

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 is exponential in the dimension $n$, but it is practical and more efficient than canonical forms based on Minkowski reduction.

math.NT↗

arXiv2020

An upper bound on the number of perfect quadratic forms

In a recent preprint on arXiv Roland Bacher showed that the number $p_d$ of non-similar perfect $d$-dimensional quadratic forms satisfies $e^{Ω(d)} < p_d < e^{O(d^3\log(d))}$. We improve the upper bound to $e^{O(d^2\log(d))}$ by a volumetric argument based on Voronoi's first reduction theory.

math.NT↗