Edge reduction for weakly non-negative quadratic forms
type: Item
instance of: scholarly article
title: Edge reduction for weakly non-negative quadratic forms
zbMATH Open document ID: 0912.15034
author: Hans-Joachim von Höhne
author: José A. de la Peña
published in: Archiv der Mathematik
publication date: 1999-05-05T00:00:00Z
review text: Let \(q: {\mathcal Z}^n \to{\mathcal Z}\) be an integral quadratic form in \(n\) variables. Here \(q\) is a semi-unit form if each coefficient on the square of a single variable is \(\leq 1\), and \(q\) is weakly nonnegative provided \(q(x) \geq 0\) for every nonzero vector \(x\) with nonnegative coordinates. The authors study a process (called edge reduction) of replacing \(q\) with an integral quadratic form \(q'\) in \(n+1\) variables that is a weakly nonnegative semi-unit form if and only if \(q\) is. (There is also a close relationship between the isotropic vectors of \(q\) and those of \(q'\).) This is developed into an algorithm to decide whether or not a given semi-unit form is weakly nonnegative. A computer implementation of the algorithm is working.
reviewed by: Stanley E. Payne
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15-04
zbMATH DE Number: 1185639
zbMATH Keywords: integral quadratic form
zbMATH Keywords: edge reduction
zbMATH Keywords: weakly nonnegative semi-unit form
MaRDI profile type: Publication
full work available at URL: s000130050195
OpenAlex ID: W131155666
DOI: 10.1007/S000130050195
description: scientific article; zbMATH DE number 1185639