Algorithmic \(P\)- distributions and applications
type: Item
instance of: scholarly article
title: Algorithmic \(P\)- distributions and applications
zbMATH Open document ID: 0768.14022
author: Thoralf Land
author: J. Stückrad
published in: Beiträge zur Algebra und Geometrie
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/138495
review text: Goal of this paper is to represent a given (projective) algebraic variety in \(\mathbb{P}^ n\) as set theoretical complete intersection of hypersurfaces of minimal number and to realize this representation on computers. Given an ideal \(I\subset R=K[X_ 1,\dots,X_ n]\), \(K\) a field, one has to find an algorithm which gives homogeneous polynomials \(f_ 1,\dots,f_ r\) of minimal number such that rad\((f_ 1,\dots,f_ r)R=\text{rad} I\). As solution of this problem the authors find the so called algorithmic \(P\)-decomposition and they show by examples possibilities of its application to computers. Algorithmic \(P\)- decompositions are special \(P\)-decompositions with the following definition: Let \(R\) be a commutative ring with unit, let \(P\subset R\) be finite and \(P_ i\subset P\) subsets, \(i=0,\dots,r\). \(\{P_ 0,\dots,P_ r\}\) is named `\(P\)-decomposition', if the following holds: (1) \(\bigcup^ r_{i=0}P_ i=P\); (2) \(P_ 0\) consists of one element; (3) For \(p,p''\in P_ i\), \(0<i\leq r\), \(p\neq p'\), one can find \(j\), \(0\leq j<i\), and \(p'\in P_ i\), such that \(p\cdot p''\in p'R\).
Mathematics Subject Classification ID: 14Q99
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 13P99
zbMATH DE Number: 95951
zbMATH Keywords: algorithmic \(P\)-decomposition
zbMATH Keywords: complete intersection
zbMATH Keywords: application to computers
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 95951