Generalization of Buchberger’s Algorithm with Respect to Several Orderings on Difference Modules
| Autor: | hamzeh harfsheno, abdolali basiri, sajjad rahmany |
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| Jazyk: | perština |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | پژوهشهای ریاضی, Vol 7, Iss 3, Pp 513-526 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2588-2546 2588-2554 |
| Popis: | 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. ./files/site1/files/%D8%AD%D8%B1%D9%81_%D8%B4%D9%86%D9%88%D8%A8%D8%B5%DB%8C%D8%B1%DB%8C(1).pdf p { margin-bottom: 0.1in; direction: ltr; line-height: 115%; text-align: left; } |
| Databáze: | Directory of Open Access Journals |
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