Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree \((1,1)\): algorithms and complexity
type: Item
instance of: scholarly article
title: Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree \((1,1)\): algorithms and complexity
zbMATH Open document ID: 1226.13017
author: Jean-Charles Faugère
author: Mohab Safey El Din
author: Pierre-Jean Spaenlehauer
published in: Journal of Symbolic Computation
publication date: 2011-03-09T00:00:00Z
review text: The authors analyze the structure of ideals generated by generic bilinear equations. They describe very explicitly the syzygy module of these ideals. They propose a powerful extension of the well-known \(\mathbb{F}_5\) criterion in the case of bilinear systems. Furthermore, using the combinatorics of the syzygy module they derive an explicit, but complicated formula for the Hilbert bi-series. This helps them to understand the complexity analysis of a multihomogeneous variant of the \(F_5\) Algorithm. Finally, they analyze the complexity of computation of Gröbner bases of affine bilinear systems. They prove that the generic bilinear systems are regular, and they give an upper bound for the degree of regularity of these systems.
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 5862849
zbMATH Keywords: Gröbner basis
zbMATH Keywords: bihomogeneous ideal
zbMATH Keywords: algorithms
zbMATH Keywords: complexity
describes a project that uses: FGb
MaRDI profile type: Publication
full work available at URL: j.jsc.2010.10.014
OpenAlex ID: W2010865943
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DOI: 10.1016/J.JSC.2010.10.014
description: scientific article; zbMATH DE number 5862849