{"id":"https://openalex.org/W1998762286","doi":"https://doi.org/10.1090/s0025-5718-2012-02591-9","title":"Tabulation of cubic function fields via polynomial binary cubic forms","display_name":"Tabulation of cubic function fields via polynomial binary cubic forms","publication_year":2012,"publication_date":"2012-03-14","ids":{"openalex":"https://openalex.org/W1998762286","doi":"https://doi.org/10.1090/s0025-5718-2012-02591-9","mag":"1998762286"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02591-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02591-9","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02591-9/S0025-5718-2012-02591-9.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02591-9/S0025-5718-2012-02591-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004135941","display_name":"Pieter Rozenhart","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pieter Rozenhart","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102825975","display_name":"Michael J. Jacobson","orcid":"https://orcid.org/0000-0002-4906-0544"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael Jacobson Jr.","raw_affiliation_strings":["Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066623074","display_name":"Renate Scheidler","orcid":"https://orcid.org/0000-0001-7164-8769"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Renate Scheidler","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3269,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.8319509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"81","issue":"280","first_page":"2335","last_page":"2359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6496078968048096},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43404942750930786},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.432253897190094},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4113122224807739},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38836994767189026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36261096596717834},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07195383310317993}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6496078968048096},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43404942750930786},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.432253897190094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4113122224807739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38836994767189026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36261096596717834},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07195383310317993},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02591-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02591-9","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02591-9/S0025-5718-2012-02591-9.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:inria-00477111v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00477111","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2012, 81 (280), pp.2335-2359. &#x27E8;10.1090/S0025-5718-2012-02591-9&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/190147","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/190147","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02591-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02591-9","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02591-9/S0025-5718-2012-02591-9.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1998762286.pdf","grobid_xml":"https://content.openalex.org/works/W1998762286.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W749598","https://openalex.org/W72697576","https://openalex.org/W165937803","https://openalex.org/W622152705","https://openalex.org/W1499271983","https://openalex.org/W1501170577","https://openalex.org/W1507575253","https://openalex.org/W1509364989","https://openalex.org/W1557415002","https://openalex.org/W1561228940","https://openalex.org/W1569612250","https://openalex.org/W1606822455","https://openalex.org/W1648977533","https://openalex.org/W1997590243","https://openalex.org/W2005936791","https://openalex.org/W2029177216","https://openalex.org/W2045882129","https://openalex.org/W2057642197","https://openalex.org/W2062753988","https://openalex.org/W2066187694","https://openalex.org/W2075469879","https://openalex.org/W2084626845","https://openalex.org/W2124113125","https://openalex.org/W2124624829","https://openalex.org/W2144314931","https://openalex.org/W2150309870","https://openalex.org/W2158480122","https://openalex.org/W2478014714","https://openalex.org/W2487302930","https://openalex.org/W2488363997","https://openalex.org/W2489377303","https://openalex.org/W2497267164","https://openalex.org/W4252543992"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2625833328"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,95,133,183,198,201,213],"method":[3,179,187],"for":[4,188,216,314],"tabulating":[5,189],"all":[6],"cubic":[7,190,208,218,231],"function":[8,209],"fields":[9],"over":[10],"<inline-formula":[11,48,73,98,136,150,236,279,315],"content-type=\"math/mathml\">":[12,49,74,99,137,151,237,280,316],"<mml:math":[13,50,75,100,138,152,238,281,317],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,51,76,101,139,153,239,282,318],"alttext=\"double-struck":[15,102],"upper":[16,79,103,156,243,250],"F":[17,104],"Subscript":[18,105],"q":[19,106,248],"Baseline":[20,247,252],"left-parenthesis":[21,155,242],"t":[22],"right-parenthesis\">":[23,158,253],"<mml:semantics>":[24,54,81,109,142,159,254,288,328],"<mml:mrow>":[25,82,160,255,289,329],"<mml:msub>":[26],"<mml:mrow":[27,111,116],"class=\"MJX-TeXAtom-ORD\">":[28,112,117],"<mml:mi":[29,113,295],"mathvariant=\"double-struck\">F</mml:mi>":[30,114],"</mml:mrow>":[31,39,88,115,119,170,269,299,339],"<mml:mi>q</mml:mi>":[32,118,264,330],"</mml:msub>":[33],"<mml:mo":[34,37,165,168,257,267,291],"stretchy=\"false\">(</mml:mo>":[35,166,258],"<mml:mi>t</mml:mi>":[36],"stretchy=\"false\">)</mml:mo>":[38,169,268],"<mml:annotation":[40,56,89,124,144,171,270,300,340],"encoding=\"application/x-tex\">\\mathbb":[41,125],"{F}_q(t)</mml:annotation>":[42],"</mml:semantics>":[43,58,91,127,146,174,273,304,342],"</mml:math>":[44,59,92,128,147,175,274,305,343],"</inline-formula>":[45,60,93,129,148,176,275,306,344],"whose":[46],"discriminant":[47],"alttext=\"upper":[52,140,240,283],"D\">":[53,80],"<mml:mi>D</mml:mi>":[55,87,167],"encoding=\"application/x-tex\">D</mml:annotation>":[57],"has":[61],"either":[62],"odd":[63],"degree":[64,67],"or":[65],"even":[66],"and":[68,205,311],"the":[69],"leading":[70],"coefficient":[71],"of":[72,185,200,203,229],"alttext=\"minus":[77],"3":[78],"<mml:mo>":[83,120,162],"\u2212":[84],"</mml:mo>":[85,122,164,294],"<mml:mn>3</mml:mn>":[86],"encoding=\"application/x-tex\">-3D</mml:annotation>":[90],"is":[94,180,197],"non-square":[96],"in":[97],"Superscript":[107,245,249],"asterisk\">":[108],"<mml:msubsup>":[110],"\u2217":[121],"</mml:msubsup>":[123],"{F}_{q}^*</mml:annotation>":[126],",":[130],"up":[131],"to":[132,207,225],"given":[134],"bound":[135],"B\">":[141],"<mml:mi>B</mml:mi>":[143,260,265,290],"encoding=\"application/x-tex\">B</mml:annotation>":[145],"on":[149,182],"alttext=\"degree":[154],"D":[157],"<mml:mi>deg</mml:mi>":[161],"\u2061":[163],"encoding=\"application/x-tex\">\\deg":[172],"(D)</mml:annotation>":[173],".":[177,307],"Our":[178],"based":[181],"generalization":[184,199],"Belabas\u2019":[186],"number":[191],"fields.":[192],"The":[193,233,308],"main":[194],"theoretical":[195],"ingredient":[196],"theorem":[202],"Davenport":[204],"Heilbronn":[206],"fields,":[210],"along":[211],"with":[212],"reduction":[214],"theory":[215],"binary":[217,230],"forms":[219],"that":[220],"provides":[221],"an":[222],"efficient":[223],"way":[224],"compute":[226],"equivalence":[227],"classes":[228],"forms.":[232],"algorithm":[234],"requires":[235],"O":[241],"B":[244,251,284],"4":[246],"<mml:mi>O</mml:mi>":[256],"<mml:msup>":[259,263],"<mml:mn>4</mml:mn>":[261],"</mml:msup>":[262,266],"encoding=\"application/x-tex\">O(B^4":[271],"q^B)</mml:annotation>":[272],"field":[276],"operations":[277],"as":[278],"right-arrow":[285],"normal":[286],"infinity\">":[287],"stretchy=\"false\">":[292],"\u2192":[293],"mathvariant=\"normal\">":[296],"\u221e":[297],"</mml:mi>":[298],"encoding=\"application/x-tex\">B":[301],"\\rightarrow":[302],"\\infty</mml:annotation>":[303],"algorithm,":[309],"examples":[310],"numerical":[312],"data":[313],"alttext=\"q":[319],"equals":[320],"5":[321],"comma":[322,324,326],"7":[323],"11":[325],"13\">":[327],"<mml:mo>=</mml:mo>":[331],"<mml:mn>5</mml:mn>":[332],"<mml:mo>,</mml:mo>":[333,335,337],"<mml:mn>7</mml:mn>":[334],"<mml:mn>11</mml:mn>":[336],"<mml:mn>13</mml:mn>":[338],"encoding=\"application/x-tex\">q=5,7,11,13</mml:annotation>":[341],"are":[345],"included.":[346]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}