Some improvements for the algorithm of Gröbner bases over dual valuation domain Article Swipe
Licui Zheng
,
Dongmei Li
,
Jinwang Liu
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3934/era.2023203
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3934/era.2023203
As a special ring with zero divisors, the dual noetherian valuation domain has attracted much attention from scholars. This article aims at to improve the Buchberger's algorithm over the dual noetherian valuation domain. We present some criterions that can be applied in the algorithm for computing Gröbner bases, and the criterions may drastically reduce the number of S-polynomials in the course of the algorithm. In addition, we clearly demonstrate the improvement with an example.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3934/era.2023203
- OA Status
- gold
- Cited By
- 1
- References
- 14
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4377294196
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4377294196Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3934/era.2023203Digital Object Identifier
- Title
-
Some improvements for the algorithm of Gröbner bases over dual valuation domainWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-01-01Full publication date if available
- Authors
-
Licui Zheng, Dongmei Li, Jinwang LiuList of authors in order
- Landing page
-
https://doi.org/10.3934/era.2023203Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.3934/era.2023203Direct OA link when available
- Concepts
-
Valuation (finance), Noetherian, Dual (grammatical number), Algorithm, Mathematics, Domain (mathematical analysis), Computer science, Algebra over a field, Pure mathematics, Accounting, Linguistics, Business, Mathematical analysis, PhilosophyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 1Per-year citation counts (last 5 years)
- References (count)
-
14Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4377294196 |
|---|---|
| doi | https://doi.org/10.3934/era.2023203 |
| ids.doi | https://doi.org/10.3934/era.2023203 |
| ids.openalex | https://openalex.org/W4377294196 |
| fwci | 0.3089612 |
| type | article |
| title | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| biblio.issue | 7 |
| biblio.volume | 31 |
| biblio.last_page | 4010 |
| biblio.first_page | 3999 |
| topics[0].id | https://openalex.org/T11435 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9997000098228455 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1703 |
| topics[0].subfield.display_name | Computational Theory and Mathematics |
| topics[0].display_name | Polynomial and algebraic computation |
| topics[1].id | https://openalex.org/T11693 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9968000054359436 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1710 |
| topics[1].subfield.display_name | Information Systems |
| topics[1].display_name | Cryptography and Residue Arithmetic |
| topics[2].id | https://openalex.org/T11245 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9962000250816345 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2206 |
| topics[2].subfield.display_name | Computational Mechanics |
| topics[2].display_name | Advanced Numerical Analysis Techniques |
| is_xpac | False |
| apc_list.value | 1000 |
| apc_list.currency | USD |
| apc_list.value_usd | 1000 |
| apc_paid.value | 1000 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 1000 |
| concepts[0].id | https://openalex.org/C186027771 |
| concepts[0].level | 2 |
| concepts[0].score | 0.8400167226791382 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q4008379 |
| concepts[0].display_name | Valuation (finance) |
| concepts[1].id | https://openalex.org/C2779057376 |
| concepts[1].level | 3 |
| concepts[1].score | 0.7886966466903687 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q3342676 |
| concepts[1].display_name | Noetherian |
| concepts[2].id | https://openalex.org/C2780980858 |
| concepts[2].level | 2 |
| concepts[2].score | 0.555789589881897 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q110022 |
| concepts[2].display_name | Dual (grammatical number) |
| concepts[3].id | https://openalex.org/C11413529 |
| concepts[3].level | 1 |
| concepts[3].score | 0.5263879299163818 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[3].display_name | Algorithm |
| concepts[4].id | https://openalex.org/C33923547 |
| concepts[4].level | 0 |
| concepts[4].score | 0.5247761607170105 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[4].display_name | Mathematics |
| concepts[5].id | https://openalex.org/C36503486 |
| concepts[5].level | 2 |
| concepts[5].score | 0.4326939582824707 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q11235244 |
| concepts[5].display_name | Domain (mathematical analysis) |
| concepts[6].id | https://openalex.org/C41008148 |
| concepts[6].level | 0 |
| concepts[6].score | 0.4020546078681946 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[6].display_name | Computer science |
| concepts[7].id | https://openalex.org/C136119220 |
| concepts[7].level | 2 |
| concepts[7].score | 0.28929877281188965 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1000660 |
| concepts[7].display_name | Algebra over a field |
| concepts[8].id | https://openalex.org/C202444582 |
| concepts[8].level | 1 |
| concepts[8].score | 0.2610045075416565 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[8].display_name | Pure mathematics |
| concepts[9].id | https://openalex.org/C121955636 |
| concepts[9].level | 1 |
| concepts[9].score | 0.12375983595848083 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q4116214 |
| concepts[9].display_name | Accounting |
| concepts[10].id | https://openalex.org/C41895202 |
| concepts[10].level | 1 |
| concepts[10].score | 0.06637367606163025 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q8162 |
| concepts[10].display_name | Linguistics |
| concepts[11].id | https://openalex.org/C144133560 |
| concepts[11].level | 0 |
| concepts[11].score | 0.059703052043914795 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q4830453 |
| concepts[11].display_name | Business |
| concepts[12].id | https://openalex.org/C134306372 |
| concepts[12].level | 1 |
| concepts[12].score | 0.04058006405830383 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[12].display_name | Mathematical analysis |
| concepts[13].id | https://openalex.org/C138885662 |
| concepts[13].level | 0 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q5891 |
| concepts[13].display_name | Philosophy |
| keywords[0].id | https://openalex.org/keywords/valuation |
| keywords[0].score | 0.8400167226791382 |
| keywords[0].display_name | Valuation (finance) |
| keywords[1].id | https://openalex.org/keywords/noetherian |
| keywords[1].score | 0.7886966466903687 |
| keywords[1].display_name | Noetherian |
| keywords[2].id | https://openalex.org/keywords/dual |
| keywords[2].score | 0.555789589881897 |
| keywords[2].display_name | Dual (grammatical number) |
| keywords[3].id | https://openalex.org/keywords/algorithm |
| keywords[3].score | 0.5263879299163818 |
| keywords[3].display_name | Algorithm |
| keywords[4].id | https://openalex.org/keywords/mathematics |
| keywords[4].score | 0.5247761607170105 |
| keywords[4].display_name | Mathematics |
| keywords[5].id | https://openalex.org/keywords/domain |
| keywords[5].score | 0.4326939582824707 |
| keywords[5].display_name | Domain (mathematical analysis) |
| keywords[6].id | https://openalex.org/keywords/computer-science |
| keywords[6].score | 0.4020546078681946 |
| keywords[6].display_name | Computer science |
| keywords[7].id | https://openalex.org/keywords/algebra-over-a-field |
| keywords[7].score | 0.28929877281188965 |
| keywords[7].display_name | Algebra over a field |
| keywords[8].id | https://openalex.org/keywords/pure-mathematics |
| keywords[8].score | 0.2610045075416565 |
| keywords[8].display_name | Pure mathematics |
| keywords[9].id | https://openalex.org/keywords/accounting |
| keywords[9].score | 0.12375983595848083 |
| keywords[9].display_name | Accounting |
| keywords[10].id | https://openalex.org/keywords/linguistics |
| keywords[10].score | 0.06637367606163025 |
| keywords[10].display_name | Linguistics |
| keywords[11].id | https://openalex.org/keywords/business |
| keywords[11].score | 0.059703052043914795 |
| keywords[11].display_name | Business |
| keywords[12].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[12].score | 0.04058006405830383 |
| keywords[12].display_name | Mathematical analysis |
| language | en |
| locations[0].id | doi:10.3934/era.2023203 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210240239 |
| locations[0].source.issn | 2688-1594 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2688-1594 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | Electronic Research Archive |
| locations[0].source.host_organization | https://openalex.org/P4310315844 |
| locations[0].source.host_organization_name | American Institute of Mathematical Sciences |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310315844 |
| locations[0].source.host_organization_lineage_names | American Institute of Mathematical Sciences |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Electronic Research Archive |
| locations[0].landing_page_url | https://doi.org/10.3934/era.2023203 |
| locations[1].id | pmh:oai:doaj.org/article:33ded9fafb894caabe13b168cd0b7338 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | Electronic Research Archive, Vol 31, Iss 7, Pp 3999-4010 (2023) |
| locations[1].landing_page_url | https://doaj.org/article/33ded9fafb894caabe13b168cd0b7338 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5005298522 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Licui Zheng |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Licui Zheng |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5100417612 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-3444-8861 |
| authorships[1].author.display_name | Dongmei Li |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Dongmei Li |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5103228907 |
| authorships[2].author.orcid | |
| authorships[2].author.display_name | Jinwang Liu |
| authorships[2].countries | CN |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I121296143 |
| authorships[2].affiliations[0].raw_affiliation_string | Department of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China |
| authorships[2].institutions[0].id | https://openalex.org/I121296143 |
| authorships[2].institutions[0].ror | https://ror.org/02m9vrb24 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I121296143 |
| authorships[2].institutions[0].country_code | CN |
| authorships[2].institutions[0].display_name | Hunan University of Science and Technology |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Jinwang Liu |
| authorships[2].is_corresponding | True |
| authorships[2].raw_affiliation_strings | Department of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.3934/era.2023203 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11435 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9997000098228455 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1703 |
| primary_topic.subfield.display_name | Computational Theory and Mathematics |
| primary_topic.display_name | Polynomial and algebraic computation |
| related_works | https://openalex.org/W2051487156, https://openalex.org/W2073681303, https://openalex.org/W2060681561, https://openalex.org/W2963791579, https://openalex.org/W2544423928, https://openalex.org/W2949541930, https://openalex.org/W2053286651, https://openalex.org/W2897764602, https://openalex.org/W4289401232, https://openalex.org/W2023718222 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2024 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 2 |
| best_oa_location.id | doi:10.3934/era.2023203 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210240239 |
| best_oa_location.source.issn | 2688-1594 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2688-1594 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | Electronic Research Archive |
| best_oa_location.source.host_organization | https://openalex.org/P4310315844 |
| best_oa_location.source.host_organization_name | American Institute of Mathematical Sciences |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310315844 |
| best_oa_location.source.host_organization_lineage_names | American Institute of Mathematical Sciences |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Electronic Research Archive |
| best_oa_location.landing_page_url | https://doi.org/10.3934/era.2023203 |
| primary_location.id | doi:10.3934/era.2023203 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210240239 |
| primary_location.source.issn | 2688-1594 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2688-1594 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | Electronic Research Archive |
| primary_location.source.host_organization | https://openalex.org/P4310315844 |
| primary_location.source.host_organization_name | American Institute of Mathematical Sciences |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310315844 |
| primary_location.source.host_organization_lineage_names | American Institute of Mathematical Sciences |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Electronic Research Archive |
| primary_location.landing_page_url | https://doi.org/10.3934/era.2023203 |
| publication_date | 2023-01-01 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W4238858352, https://openalex.org/W1481997196, https://openalex.org/W3210795898, https://openalex.org/W1971329974, https://openalex.org/W2608996626, https://openalex.org/W1994964419, https://openalex.org/W3128245956, https://openalex.org/W2123108892, https://openalex.org/W1998748237, https://openalex.org/W2081582540, https://openalex.org/W1986386765, https://openalex.org/W3120303595, https://openalex.org/W2604801819, https://openalex.org/W2269221822 |
| referenced_works_count | 14 |
| abstract_inverted_index.a | 1 |
| abstract_inverted_index.In | 64 |
| abstract_inverted_index.We | 33 |
| abstract_inverted_index.an | 72 |
| abstract_inverted_index.at | 21 |
| abstract_inverted_index.be | 39 |
| abstract_inverted_index.in | 41, 58 |
| abstract_inverted_index.of | 56, 61 |
| abstract_inverted_index.to | 22 |
| abstract_inverted_index.we | 66 |
| abstract_inverted_index.and | 48 |
| abstract_inverted_index.can | 38 |
| abstract_inverted_index.for | 44 |
| abstract_inverted_index.has | 12 |
| abstract_inverted_index.may | 51 |
| abstract_inverted_index.the | 7, 24, 28, 42, 49, 54, 59, 62, 69 |
| abstract_inverted_index.This | 18 |
| abstract_inverted_index.aims | 20 |
| abstract_inverted_index.dual | 8, 29 |
| abstract_inverted_index.from | 16 |
| abstract_inverted_index.much | 14 |
| abstract_inverted_index.over | 27 |
| abstract_inverted_index.ring | 3 |
| abstract_inverted_index.some | 35 |
| abstract_inverted_index.that | 37 |
| abstract_inverted_index.with | 4, 71 |
| abstract_inverted_index.zero | 5 |
| abstract_inverted_index.bases, | 47 |
| abstract_inverted_index.course | 60 |
| abstract_inverted_index.domain | 11 |
| abstract_inverted_index.number | 55 |
| abstract_inverted_index.reduce | 53 |
| abstract_inverted_index.applied | 40 |
| abstract_inverted_index.article | 19 |
| abstract_inverted_index.clearly | 67 |
| abstract_inverted_index.domain. | 32 |
| abstract_inverted_index.improve | 23 |
| abstract_inverted_index.present | 34 |
| abstract_inverted_index.special | 2 |
| abstract_inverted_index.Gröbner | 46 |
| abstract_inverted_index.addition, | 65 |
| abstract_inverted_index.algorithm | 26, 43 |
| abstract_inverted_index.attention | 15 |
| abstract_inverted_index.attracted | 13 |
| abstract_inverted_index.computing | 45 |
| abstract_inverted_index.divisors, | 6 |
| abstract_inverted_index.scholars. | 17 |
| abstract_inverted_index.valuation | 10, 31 |
| abstract_inverted_index.algorithm. | 63 |
| abstract_inverted_index.criterions | 36, 50 |
| abstract_inverted_index.noetherian | 9, 30 |
| abstract_inverted_index.demonstrate | 68 |
| abstract_inverted_index.drastically | 52 |
| abstract_inverted_index.improvement | 70 |
| abstract_inverted_index.Buchberger's | 25 |
| abstract_inverted_index.S-polynomials | 57 |
| abstract_inverted_index.<abstract><p>As | 0 |
| abstract_inverted_index.example.</p></abstract> | 73 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 90 |
| corresponding_author_ids | https://openalex.org/A5103228907 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I121296143 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/9 |
| sustainable_development_goals[0].score | 0.5199999809265137 |
| sustainable_development_goals[0].display_name | Industry, innovation and infrastructure |
| citation_normalized_percentile.value | 0.54574014 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |