On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5)
The generalized and ordinary Hilbert series for Sibirsky graded algebras of comitants and invariants of autonomous polynomial differential systems are of particular importance for some problems of qualitative theory of differential systems. In the \linebreak Republic of Moldova the computation of th...
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"Ion Creanga" State Pedagogical University
2025-01-01
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| Series: | Acta et Commentationes: Ştiinţe Exacte şi ale Naturii |
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| Online Access: | https://revistaust.upsc.md/index.php/acta_exacte/article/view/1087 |
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| author | Lidia Mușinschi Victor Pricop |
| author_facet | Lidia Mușinschi Victor Pricop |
| author_sort | Lidia Mușinschi |
| collection | DOAJ |
| description | The generalized and ordinary Hilbert series for Sibirsky graded algebras of comitants and invariants of autonomous polynomial differential systems are of particular importance for some problems of qualitative theory of differential systems. In the \linebreak Republic of Moldova the computation of these series have their beginnings in the works of Professor M. N. Popa and his disciples. But the construction of these series for some complicated differential systems encounters insurmountable computational difficulties, especially, for the generalized Hilbert series, from which the ordinary Hilbert series can be easily obtained. In this paper, it is shown how the adaptation of Molien's formula address to the mentioned problem to overcome the enormous calculations, an ordinary Hilbert series were obtained for Sibirsky graded algebras of comitants and invariants for the differential system $s(3,5)$.
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| format | Article |
| id | doaj-art-0b5b84fd14424632b9ec03e75b685002 |
| institution | Kabale University |
| issn | 2537-6284 2587-3644 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | "Ion Creanga" State Pedagogical University |
| record_format | Article |
| series | Acta et Commentationes: Ştiinţe Exacte şi ale Naturii |
| spelling | doaj-art-0b5b84fd14424632b9ec03e75b6850022025-02-11T21:03:57Zeng"Ion Creanga" State Pedagogical UniversityActa et Commentationes: Ştiinţe Exacte şi ale Naturii2537-62842587-36442025-01-0118210.36120/2587-3644.v18i2.70-77On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5)Lidia Mușinschi0Victor Pricop1Vladimir Andrunachievici Institute of Mathematics and Computer Science, Moldova State University, 5 Academiei St., Chisinau, Republic of MoldovaTechnical University of Moldova, 9/8 Studentilor St., Chisinau; Vladimir Andrunachievici Institute of Mathematics and Computer Science, Moldova State University, 5 Academiei St., Chisinau, Republic of MoldovaThe generalized and ordinary Hilbert series for Sibirsky graded algebras of comitants and invariants of autonomous polynomial differential systems are of particular importance for some problems of qualitative theory of differential systems. In the \linebreak Republic of Moldova the computation of these series have their beginnings in the works of Professor M. N. Popa and his disciples. But the construction of these series for some complicated differential systems encounters insurmountable computational difficulties, especially, for the generalized Hilbert series, from which the ordinary Hilbert series can be easily obtained. In this paper, it is shown how the adaptation of Molien's formula address to the mentioned problem to overcome the enormous calculations, an ordinary Hilbert series were obtained for Sibirsky graded algebras of comitants and invariants for the differential system $s(3,5)$. https://revistaust.upsc.md/index.php/acta_exacte/article/view/1087differential systemsSibirsky graded algebrasHilbert seriesKrull dimension |
| spellingShingle | Lidia Mușinschi Victor Pricop On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5) Acta et Commentationes: Ştiinţe Exacte şi ale Naturii differential systems Sibirsky graded algebras Hilbert series Krull dimension |
| title | On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5) |
| title_full | On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5) |
| title_fullStr | On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5) |
| title_full_unstemmed | On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5) |
| title_short | On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3,5) |
| title_sort | on computation of the ordinary hilbert series for sibirsky graded algebras of differential system s 3 5 |
| topic | differential systems Sibirsky graded algebras Hilbert series Krull dimension |
| url | https://revistaust.upsc.md/index.php/acta_exacte/article/view/1087 |
| work_keys_str_mv | AT lidiamusinschi oncomputationoftheordinaryhilbertseriesforsibirskygradedalgebrasofdifferentialsystems35 AT victorpricop oncomputationoftheordinaryhilbertseriesforsibirskygradedalgebrasofdifferentialsystems35 |