{"id":"https://openalex.org/W2006948763","doi":"https://doi.org/10.1007/s00211-014-0635-z","title":"Computing the common zeros of two bivariate functions via B\u00e9zout resultants","display_name":"Computing the common zeros of two bivariate functions via B\u00e9zout resultants","publication_year":2014,"publication_date":"2014-05-08","ids":{"openalex":"https://openalex.org/W2006948763","doi":"https://doi.org/10.1007/s00211-014-0635-z","mag":"2006948763"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-014-0635-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-014-0635-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008129578","display_name":"Yuji Nakatsukasa","orcid":"https://orcid.org/0000-0001-7911-1501"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuji Nakatsukasa","raw_affiliation_strings":["Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan","Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan 113-8656#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan 113-8656#TAB#","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064797994","display_name":"Vanni Noferini","orcid":"https://orcid.org/0000-0002-1775-041X"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Vanni Noferini","raw_affiliation_strings":["School of Mathematics, University of Manchester, Manchester, M13 9PL, UK","School of Mathematics, University of Manchester, Manchester, UK M13 9PL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Manchester, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"School of Mathematics, University of Manchester, Manchester, UK M13 9PL","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003110773","display_name":"Alex Townsend","orcid":"https://orcid.org/0000-0002-8183-7077"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alex Townsend","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","Mathematical Institute, University of Oxford, Oxford, UK OX2 6GG#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, UK OX2 6GG#TAB#","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064797994"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.2417,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.96737044,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"129","issue":"1","first_page":"181","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8385845422744751},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6404125094413757},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5938544869422913},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.51996910572052},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4509921371936798},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.44761592149734497},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.411246657371521},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3995082378387451},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3880014419555664},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3539919853210449},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29764556884765625},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.2845917344093323},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21745160222053528}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8385845422744751},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6404125094413757},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5938544869422913},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.51996910572052},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4509921371936798},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.44761592149734497},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.411246657371521},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3995082378387451},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3880014419555664},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3539919853210449},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29764556884765625},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2845917344093323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21745160222053528},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-014-0635-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-014-0635-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:uuid:5b6f5fad-c3e6-4485-866b-ec13c2960353","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/","raw_type":"Technical Report"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:5b6f5fad-c3e6-4485-866b-ec13c2960353","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:5b6f5fad-c3e6-4485-866b-ec13c2960353","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/","raw_type":"Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2449384599","display_name":null,"funder_award_id":"EP/I005293/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W253307310","https://openalex.org/W389472000","https://openalex.org/W647818151","https://openalex.org/W1480381100","https://openalex.org/W1518341038","https://openalex.org/W1522512418","https://openalex.org/W1523185471","https://openalex.org/W1570420806","https://openalex.org/W1576168588","https://openalex.org/W1581306515","https://openalex.org/W1823734658","https://openalex.org/W1963627383","https://openalex.org/W1963833004","https://openalex.org/W1966749257","https://openalex.org/W1968297701","https://openalex.org/W1974176001","https://openalex.org/W1978833296","https://openalex.org/W1979057868","https://openalex.org/W1984435191","https://openalex.org/W1999834714","https://openalex.org/W2006141568","https://openalex.org/W2007088323","https://openalex.org/W2008739241","https://openalex.org/W2020804487","https://openalex.org/W2025485823","https://openalex.org/W2034357416","https://openalex.org/W2040006659","https://openalex.org/W2045717636","https://openalex.org/W2048590331","https://openalex.org/W2051754724","https://openalex.org/W2057761680","https://openalex.org/W2059154724","https://openalex.org/W2059586807","https://openalex.org/W2064109025","https://openalex.org/W2064384667","https://openalex.org/W2066012338","https://openalex.org/W2070179402","https://openalex.org/W2091039488","https://openalex.org/W2101827296","https://openalex.org/W2106114934","https://openalex.org/W2107005172","https://openalex.org/W2115308285","https://openalex.org/W2121050416","https://openalex.org/W2159229958","https://openalex.org/W2163336887","https://openalex.org/W2251586653","https://openalex.org/W2315098614","https://openalex.org/W2319466955","https://openalex.org/W2756708080","https://openalex.org/W2798573187","https://openalex.org/W2798909945","https://openalex.org/W4230094279","https://openalex.org/W4236419838","https://openalex.org/W4237587600"],"related_works":["https://openalex.org/W2054607094","https://openalex.org/W591910118","https://openalex.org/W1997963656","https://openalex.org/W4390947848","https://openalex.org/W2149734642","https://openalex.org/W3216258873","https://openalex.org/W2056024401","https://openalex.org/W2185931218","https://openalex.org/W2897473460","https://openalex.org/W2003232594"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
