The theory of Gröbner bases
type: Item
instance of: scholarly article
title: The theory of Gröbner bases
zbMATH Open document ID: 0702.13019
author: F. Pauer
author: Marlene Pfeifhofer
published in: L'Enseignement Mathématique. 2e Série
publication date: 1988-01-01T00:00:00Z
review text: The aim of this paper is the study of Gröbner bases which are finite ideal bases, such that the initial terms of them generate the ideal generated by all initial terms of polynomials of the given ideal. Such bases are characterized based on a generalization of a usual division algorithm of univariate polynomials (see also Bayer, Buchberger 1985). A construction of a Gröbner basis from a given finite ideal basis is explained (see also Kandry-Rody and Kapru 1984) and the method of Gröbner basis is applied to a geometric problem: to obtain the Zariski- closure in the projective n-space of an algebraic subset of affine n- space. The work contains the ``algebraic'' results about Gröbner bases but no results about complexity of corresponding algorithms.
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 4150360
zbMATH Keywords: Gröbner bases
zbMATH Keywords: Zariski-closure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4150360