An Algorithm to Compute the H-Bases for Ideals of Subalgebras. (7th July 2021)

• Record Type: Journal Article
• Authors: Rabia, ; Binyamin, Muhammad Ahsan; Jabeen, Nazia; Aslam, Adnan; Anoh Yannick, Kraidi
• Other Names: Din Qamar Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2021(2021)
• Publication Date: 2021-07-07
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2021/2400073
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : The concept of H-bases, introduced long ago by Macauly, has become an important ingredient for the treatment of various problems in computational algebra. The concept of H-bases is for ideals in polynomial rings, which allows an investigation of multivariate polynomial spaces degree by degree. Similarly, we have the analogue of H-bases for subalgebras, termed as SH-bases. In this paper, we present an analogue of H-bases for finitely generated ideals in a given subalgebra of a polynomial ring, and we call them "HSG-bases." We present their connection to the SAGBI-Gröbner basis concept, characterize HSG-basis, and show how to construct them.