Eliminations in Weyl algebras and identities.
type: Item
instance of: scholarly article
title: Eliminations in Weyl algebras and identities.
zbMATH Open document ID: 1102.16019
author: Weiping Wang
author: Yuxia Xu
author: Tianming Wang
published in: Advances in Applied Mathematics
publication date: 2006-03-08T00:00:00Z
review text: Consider two operators \(N,K\) on the algebra of polynomials in two variables \(n,k\), namely \[ N(f(n,k))=f(n+1,k),\quad K(f(n,k))=f(n,k+1). \] Denote by \(C\langle N,K,n,k\rangle\) the algebra of operators on polynomials generated by \(N,K,n,k\), where \(n,k\) are identified with operators of multiplication. Given \(P,Q\in C\langle N,K,n,k\rangle\) there exist nontrivial elements \(u,v,r,s\in C\langle N,K,n,k\rangle\) such that \(uP=vQ + R\), \(rP=sQ\) and \(\deg_kR<\deg_kQ\). This result is applied to elimination in Weyl algebras, for verification of termination of some hypergeometric identities, of identities in two variables, and so on.
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 33F10
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 16Z05
zbMATH DE Number: 5009828
zbMATH Keywords: generalized Weyl algebras
zbMATH Keywords: Zeilberger algorithm
zbMATH Keywords: Wu method
zbMATH Keywords: computer proofs
zbMATH Keywords: eliminations
zbMATH Keywords: combinatorial identities
reviewed by: Vyacheslav A. Artamonov
describes a project that uses: DEtools
MaRDI profile type: Publication
full work available at URL: j.aam.2005.03.003
OpenAlex ID: W2027587685
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DOI: 10.1016/J.AAM.2005.03.003
description: scientific article; zbMATH DE number 5009828