A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bezout identities

TL;DR

This paper introduces an efficient algorithm for identifying minimal hyperplane unit cells and solving N-dimensional Bezout identities, facilitating computations in higher-dimensional lattice problems.

Contribution

It presents a novel fast algorithm to find reduced hyperplane unit cells and solve associated N-dimensional Bezout identities, improving computational efficiency.

Findings

Algorithm efficiently computes minimal hyperplane unit cells.

Method provides all solutions to N-dimensional Bezout identities.

Enhances computational tools for lattice and number theory problems.

Abstract

The paper explains the method to determine a short unit cell attached to any hyperplane given by its integer vector $\mathbf{p}$. Equivalently, it gives all the solutions of the $N$-dimensional Bezout identity associated with the coordinates of $\mathbf{p}$.