{"id":"https://openalex.org/W2066187694","doi":"https://doi.org/10.1112/s1461157000000073","title":"Reduction of Binary Cubic and Quartic Forms","display_name":"Reduction of Binary Cubic and Quartic Forms","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2066187694","doi":"https://doi.org/10.1112/s1461157000000073","mag":"2066187694"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000000073","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000073","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42450F8E40C047314EA654FBD2536CA1/S1461157000000073a.pdf/div-class-title-reduction-of-binary-cubic-and-quartic-forms-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42450F8E40C047314EA654FBD2536CA1/S1461157000000073a.pdf/div-class-title-reduction-of-binary-cubic-and-quartic-forms-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084924590","display_name":"J. E. Cremona","orcid":"https://orcid.org/0000-0002-7212-0162"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"J. E. Cremona","raw_affiliation_strings":["School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD","School of Mathematical Sciences University of Nottingham University Park Nottingham NG7 2RD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD","institution_ids":["https://openalex.org/I142263535"]},{"raw_affiliation_string":"School of Mathematical Sciences University of Nottingham University Park Nottingham NG7 2RD","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084924590"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":null,"apc_paid":null,"fwci":2.833,"has_fulltext":true,"cited_by_count":82,"citation_normalized_percentile":{"value":0.90568414,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":null,"first_page":"62","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9948999881744385,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8920943737030029},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.8318001627922058},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.6595858931541443},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6201596260070801},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6117290258407593},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5760433673858643},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5627020001411438},{"id":"https://openalex.org/keywords/cubic-form","display_name":"Cubic form","score":0.5495331883430481},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.4992492198944092},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.474420964717865},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.461064875125885},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44886764883995056},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.44357994198799133},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.4230692386627197},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4203079640865326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36088597774505615},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34781593084335327},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3255869150161743},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23860859870910645},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1317180097103119},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0795089602470398}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8920943737030029},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.8318001627922058},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.6595858931541443},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6201596260070801},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6117290258407593},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5760433673858643},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5627020001411438},{"id":"https://openalex.org/C91429207","wikidata":"https://www.wikidata.org/wiki/Q5192245","display_name":"Cubic form","level":2,"score":0.5495331883430481},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.4992492198944092},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.474420964717865},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.461064875125885},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44886764883995056},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.44357994198799133},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.4230692386627197},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4203079640865326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36088597774505615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34781593084335327},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3255869150161743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23860859870910645},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1317180097103119},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0795089602470398},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/s1461157000000073","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000073","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42450F8E40C047314EA654FBD2536CA1/S1461157000000073a.pdf/div-class-title-reduction-of-binary-cubic-and-quartic-forms-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.2193","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.2193","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"http://www.maths.nott.ac.uk/personal/jec/papers/r34jcm.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.1910","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.1910","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.nott.ac.uk/personal/jec/papers/r34.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1112/s1461157000000073","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000073","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42450F8E40C047314EA654FBD2536CA1/S1461157000000073a.pdf/div-class-title-reduction-of-binary-cubic-and-quartic-forms-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.7400000095367432,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2066187694.pdf","grobid_xml":"https://content.openalex.org/works/W2066187694.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1507575253","https://openalex.org/W1529471319","https://openalex.org/W1557027117","https://openalex.org/W1569977378","https://openalex.org/W1856096826","https://openalex.org/W1976120821","https://openalex.org/W2037752680","https://openalex.org/W2075469879","https://openalex.org/W2084626845","https://openalex.org/W2118942434","https://openalex.org/W2143027996","https://openalex.org/W2145344196","https://openalex.org/W2501812802","https://openalex.org/W4241352183","https://openalex.org/W4247310437","https://openalex.org/W6644520302"],"related_works":["https://openalex.org/W2980799738","https://openalex.org/W4288092579","https://openalex.org/W2544050567","https://openalex.org/W2287431136","https://openalex.org/W2570358410","https://openalex.org/W2355296867","https://openalex.org/W2391489321","https://openalex.org/W2015868478","https://openalex.org/W4300374303","https://openalex.org/W2127260120"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"reduction":[2],"theory":[3],"is":[4],"developed":[5],"for":[6],"binary":[7],"forms":[8,68],"(homogeneous":[9],"polynomials)":[10],"of":[11,35,42,55,64],"degrees":[12],"three":[13],"and":[14,24,46],"four":[15],"with":[16],"integer":[17],"coefficients.":[18],"The":[19],"resulting":[20],"coefficient":[21],"bounds":[22],"simplify":[23],"improve":[25],"on":[26,48],"those":[27],"in":[28,32],"the":[29,33,53,62],"literature,":[30],"particularly":[31],"case":[34],"negative":[36],"discriminant.":[37],"Applications":[38],"include":[39],"systematic":[40],"enumeration":[41],"cubic":[43],"number":[44,71],"fields,":[45],"2-descent":[47],"elliptic":[49],"curves":[50],"defined":[51,69],"over":[52,70],"set":[54],"rational":[56],"numbers.":[57],"Remarks":[58],"are":[59],"given":[60],"concerning":[61],"extension":[63],"these":[65],"results":[66],"to":[67],"fields.":[72]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}