An Algorithm to Compute the H-Bases for Ideals of Subalgebras
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. Simil...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/2400073 |
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| author | Rabia Muhammad Ahsan Binyamin Nazia Jabeen Adnan Aslam Kraidi Anoh Yannick |
| author_facet | Rabia Muhammad Ahsan Binyamin Nazia Jabeen Adnan Aslam Kraidi Anoh Yannick |
| author_sort | Rabia |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d8faf4a6f8ff4e5fb4b79a200504f4dc |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d8faf4a6f8ff4e5fb4b79a200504f4dc2025-02-03T05:45:21ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/24000732400073An Algorithm to Compute the H-Bases for Ideals of SubalgebrasRabia0Muhammad Ahsan Binyamin1Nazia Jabeen2Adnan Aslam3Kraidi Anoh Yannick4Department of Mathematics, GC University, Faisalabad, PakistanDepartment of Mathematics, GC University, Faisalabad, PakistanDepartment of Mathematical Sciences, Institute of Business Administration, Karachi, PakistanDepartment of Natural Sciences, University of Engineering and Technology (RCET), Lahore, PakistanUFR of Mathematics and Informatics, University Félix Houphouët Boigny, Abidjan, Côte d’IvoireThe 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.http://dx.doi.org/10.1155/2021/2400073 |
| spellingShingle | Rabia Muhammad Ahsan Binyamin Nazia Jabeen Adnan Aslam Kraidi Anoh Yannick An Algorithm to Compute the H-Bases for Ideals of Subalgebras Discrete Dynamics in Nature and Society |
| title | An Algorithm to Compute the H-Bases for Ideals of Subalgebras |
| title_full | An Algorithm to Compute the H-Bases for Ideals of Subalgebras |
| title_fullStr | An Algorithm to Compute the H-Bases for Ideals of Subalgebras |
| title_full_unstemmed | An Algorithm to Compute the H-Bases for Ideals of Subalgebras |
| title_short | An Algorithm to Compute the H-Bases for Ideals of Subalgebras |
| title_sort | algorithm to compute the h bases for ideals of subalgebras |
| url | http://dx.doi.org/10.1155/2021/2400073 |
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