{"id":"https://openalex.org/W2081006967","doi":"https://doi.org/10.1090/s0025-5718-00-01295-3","title":"Classification of quintic eutactic forms","display_name":"Classification of quintic eutactic forms","publication_year":2000,"publication_date":"2000-07-21","ids":{"openalex":"https://openalex.org/W2081006967","doi":"https://doi.org/10.1090/s0025-5718-00-01295-3","mag":"2081006967"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01295-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01295-3","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01295-3/S0025-5718-00-01295-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01295-3/S0025-5718-00-01295-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066506660","display_name":"Christian Batut","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Christian Batut","raw_affiliation_strings":["A2X, Math\u00c3\u00a9matiques, Universit\u00c3\u00a9 Bordeaux I, 351, cours de la Lib\u00c3\u00a9ration, 33405 Talence cedex, France","A2X, Math\u00e9matiques, Universit\u00e9 Bordeaux I, 351, cours de la Lib\u00e9ration, 33405 Talence cedex, France"],"affiliations":[{"raw_affiliation_string":"A2X, Math\u00c3\u00a9matiques, Universit\u00c3\u00a9 Bordeaux I, 351, cours de la Lib\u00c3\u00a9ration, 33405 Talence cedex, France","institution_ids":[]},{"raw_affiliation_string":"A2X, Math\u00e9matiques, Universit\u00e9 Bordeaux I, 351, cours de la Lib\u00e9ration, 33405 Talence cedex, France","institution_ids":["https://openalex.org/I15057530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066506660"],"corresponding_institution_ids":["https://openalex.org/I15057530"],"apc_list":null,"apc_paid":null,"fwci":1.0112,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.73960139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"70","issue":"233","first_page":"395","last_page":"417"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9157134294509888},{"id":"https://openalex.org/keywords/quintic-function","display_name":"Quintic function","score":0.85565185546875},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.799117922782898},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.6678541898727417},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5673662424087524},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.5537607669830322},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49912095069885254},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3550805449485779},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35186028480529785},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3451826572418213},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34257346391677856},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3275824189186096},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10868656635284424},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07791301608085632},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05581149458885193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9157134294509888},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.85565185546875},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.799117922782898},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.6678541898727417},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5673662424087524},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.5537607669830322},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49912095069885254},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3550805449485779},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35186028480529785},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3451826572418213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34257346391677856},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3275824189186096},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10868656635284424},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07791301608085632},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05581149458885193},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-00-01295-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01295-3","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01295-3/S0025-5718-00-01295-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01295-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01295-3","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01295-3/S0025-5718-00-01295-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2081006967.pdf","grobid_xml":"https://content.openalex.org/works/W2081006967.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W21857574","https://openalex.org/W1603671530","https://openalex.org/W1993093767","https://openalex.org/W1995990042","https://openalex.org/W1996668224","https://openalex.org/W2020577201","https://openalex.org/W2052896737","https://openalex.org/W2170524054","https://openalex.org/W2322563986","https://openalex.org/W2334812593","https://openalex.org/W4293259454"],"related_works":["https://openalex.org/W3020555194","https://openalex.org/W4254786939","https://openalex.org/W2793256277","https://openalex.org/W2348235448","https://openalex.org/W4360958759","https://openalex.org/W2116218375","https://openalex.org/W2389906634","https://openalex.org/W288156810","https://openalex.org/W2092846166","https://openalex.org/W4283827273"],"abstract_inverted_index":{"From":[0],"the":[1,34,41,44,52,60],"classical":[2],"Voronoi":[3],"algorithm,":[4],"we":[5,19,39,50,58],"derive":[6],"an":[7],"algorithm":[8,35],"to":[9,36],"classify":[10],"quadratic":[11],"positive":[12],"definite":[13],"forms":[14],"by":[15],"their":[16],"minimal":[17],"vectors;":[18],"define":[20],"some":[21],"new":[22],"invariants":[23],"for":[24,27],"a":[25],"class,":[26],"which":[28],"several":[29],"conjectures":[30],"are":[31],"proposed.":[32],"Applying":[33],"dimension":[37],"5":[38],"obtain":[40],"table":[42],"of":[43],"136":[45],"classes":[46],"in":[47],"this":[48],"dimension,":[49],"enumerate":[51],"118":[53],"eutactic":[54],"quintic":[55],"forms,":[56],"and":[57],"verify":[59],"Ash":[61],"formula.":[62]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}