Polynomial expressions for non-binomial structures
type: Item
instance of: scholarly article
title: Polynomial expressions for non-binomial structures
zbMATH Open document ID: 1422.13025
author: Rostam Sabeti
published in: Theoretical Computer Science
publication date: 2019-02-28T00:00:00Z
review text: Let \(R=K[x_1,\ldots ,x_n]\) be a polynomial ring over a field \(K\) and \(f,f_1,\ldots ,f_k\in R\). Let us fix a term ordering on \(R\). The classical division algorithm claims that one is able to write \(f\) as an expression like \(g_1f_1+\cdots +g_kf_k+h\) where either \(h=0\) or no term in \(h\) is divisible by the leading terms of the \(f_i\)'s. In this paper, the author presents a framework for performing the division. For this purpose, he describes a process for dividing a polynomial by a single polynomial and then he uses this process for dividing a polynomial by a list of polynomials. In addition, application of the new algorithm on moderately large polynomials is discussed. The paper is concluded by a complexity analysis of some intermediate procedures.
reviewed by: Amir Hashemi
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 7030854
zbMATH Keywords: algebraic expressions
zbMATH Keywords: division algorithms
zbMATH Keywords: cyclic \(n\)-roots
MaRDI profile type: Publication
full work available at URL: j.tcs.2018.10.020
OpenAlex ID: W2896260489
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Wikidata QID: Q129055212
DOI: 10.1016/J.TCS.2018.10.020
description: scientific article; zbMATH DE number 7030854