Volume 7, Issue 3 (Vol.7, No.3, 2021)                   mmr 2021, 7(3): 513-526 | Back to browse issues page


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harfsheno H, basiri A, rahmany S. Generalization of Buchberger’s Algorithm with Respect to Several Orderings on Difference Modules. mmr 2021; 7 (3) :513-526
URL: http://mmr.khu.ac.ir/article-1-2951-en.html
1- Damghan university
2- Damghan university , basiri@du.ac.ir
Abstract:   (675 Views)

Grobner basis with respect to several orderings is a powerful tool to compute multivariate difference dimension polynomials. In this paper, an algorithm for computing a Grobner basis of a difference module over a ground difference field with respect to several term orderings is presented. In this direction, a representation of an element of a difference module with respect to several term orderings is introduced. Based on such representation, we generalize the Buchberger theorem to the case of free modules over difference rings with several term orderings associated with a partition of the set of variables. Furthermore, the necessary and sufficient condition is given for the existence of a Grobner basis with respect to several term orderings. In the sequel, we present our implementation of the algorithm on Maple.

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Type of Study: Research Paper | Subject: alg
Received: 2019/05/25 | Revised: 2022/05/7 | Accepted: 2019/11/23 | Published: 2021/12/1 | ePublished: 2021/12/1

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