{"id":"https://openalex.org/W2065658438","doi":"https://doi.org/10.1007/s10208-014-9207-y","title":"Overdetermined Systems of Sparse Polynomial Equations","display_name":"Overdetermined Systems of Sparse Polynomial Equations","publication_year":2014,"publication_date":"2014-06-10","ids":{"openalex":"https://openalex.org/W2065658438","doi":"https://doi.org/10.1007/s10208-014-9207-y","mag":"2065658438"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-014-9207-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-014-9207-y","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1307.5788","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071970376","display_name":"Francesco Amoroso","orcid":"https://orcid.org/0000-0002-8436-9168"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4387155825","display_name":"Laboratoire de Math\u00e9matiques Nicolas Oresme","ror":"https://ror.org/03jm2hc44","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210105918","https://openalex.org/I4387155825","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Francesco Amoroso","raw_affiliation_strings":["Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, BP 5186, 14032\u00a0, Caen Cedex, France","Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, Caen Cedex, France 14032#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, BP 5186, 14032\u00a0, Caen Cedex, France","institution_ids":["https://openalex.org/I98702875","https://openalex.org/I4210155549","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, Caen Cedex, France 14032#TAB#","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I1294671590","https://openalex.org/I4387155825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010545225","display_name":"Louis Patrick Leroux","orcid":"https://orcid.org/0000-0003-3691-5811"},"institutions":[{"id":"https://openalex.org/I4387155825","display_name":"Laboratoire de Math\u00e9matiques Nicolas Oresme","ror":"https://ror.org/03jm2hc44","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210105918","https://openalex.org/I4387155825","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Louis Leroux","raw_affiliation_strings":["Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, BP 5186, 14032\u00a0, Caen Cedex, France","Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, Caen Cedex, France 14032#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, BP 5186, 14032\u00a0, Caen Cedex, France","institution_ids":["https://openalex.org/I98702875","https://openalex.org/I4210155549","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire de math\u00e9matiques Nicolas Oresme, CNRS UMR 6139, Universit\u00e9 de Caen, Caen Cedex, France 14032#TAB#","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I1294671590","https://openalex.org/I4387155825"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027538609","display_name":"Mart\u0131\u0301n Sombra","orcid":"https://orcid.org/0000-0002-3400-4240"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]},{"id":"https://openalex.org/I11932220","display_name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats","ror":"https://ror.org/0371hy230","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I11932220"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mart\u00edn Sombra","raw_affiliation_strings":["ICREA & Departament d\u2019\u00c0lgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007\u00a0, Barcelona, Spain","ICREA & Departament d'\u00c0lgebra i Geometria, Universitat de Barcelona, Barcelona, Spain 08007#TAB#"],"affiliations":[{"raw_affiliation_string":"ICREA & Departament d\u2019\u00c0lgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007\u00a0, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"ICREA & Departament d'\u00c0lgebra i Geometria, Universitat de Barcelona, Barcelona, Spain 08007#TAB#","institution_ids":["https://openalex.org/I71999127","https://openalex.org/I11932220"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071970376"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210155549","https://openalex.org/I4387155825","https://openalex.org/I98702875"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.735,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73146172,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"1","first_page":"53","last_page":"87"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9991000294685364,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/overdetermined-system","display_name":"Overdetermined system","score":0.903380274772644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8987617492675781},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6898469924926758},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6178826093673706},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6000658869743347},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.529249370098114},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5193718075752258},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.4555169641971588},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.44918522238731384},{"id":"https://openalex.org/keywords/system-of-polynomial-equations","display_name":"System of polynomial equations","score":0.44888392090797424},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4431774914264679},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.4349954128265381},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4319990277290344},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41415566205978394},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39132484793663025},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34811171889305115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33657485246658325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18697777390480042},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.15849536657333374}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.903380274772644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8987617492675781},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6898469924926758},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6178826093673706},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6000658869743347},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.529249370098114},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5193718075752258},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.4555169641971588},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.44918522238731384},{"id":"https://openalex.org/C105335568","wikidata":"https://www.wikidata.org/wiki/Q7663735","display_name":"System of polynomial equations","level":3,"score":0.44888392090797424},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4431774914264679},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.4349954128265381},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4319990277290344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41415566205978394},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39132484793663025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34811171889305115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33657485246658325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18697777390480042},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.15849536657333374},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-014-9207-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-014-9207-y","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1307.5788","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.5788","pdf_url":"https://arxiv.org/pdf/1307.5788","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1307.5788","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.5788","pdf_url":"https://arxiv.org/pdf/1307.5788","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320323428","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W600381672","https://openalex.org/W640426850","https://openalex.org/W1489178803","https://openalex.org/W1495060254","https://openalex.org/W1496801598","https://openalex.org/W1559103132","https://openalex.org/W1562183207","https://openalex.org/W1579005859","https://openalex.org/W1588985647","https://openalex.org/W1629557808","https://openalex.org/W1976382086","https://openalex.org/W1977022731","https://openalex.org/W2005567558","https://openalex.org/W2018338763","https://openalex.org/W2048346597","https://openalex.org/W2056622035","https://openalex.org/W2113672208","https://openalex.org/W2114225435","https://openalex.org/W2324465849","https://openalex.org/W2488464333","https://openalex.org/W2750957391","https://openalex.org/W2989788546","https://openalex.org/W4241884799","https://openalex.org/W4285719527","https://openalex.org/W4401384828"],"related_works":["https://openalex.org/W4382516418","https://openalex.org/W2990591761","https://openalex.org/W4386576538","https://openalex.org/W2019363796","https://openalex.org/W3041626282","https://openalex.org/W1973100193","https://openalex.org/W4309260173","https://openalex.org/W4287998014","https://openalex.org/W2970640972","https://openalex.org/W3089295049"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}