{"id":"https://openalex.org/W3046029616","doi":"https://doi.org/10.1145/3373207.3403981","title":"Real quantifier elimination by cylindrical algebraic decomposition, and improvements by machine learning","display_name":"Real quantifier elimination by cylindrical algebraic decomposition, and improvements by machine learning","publication_year":2020,"publication_date":"2020-07-20","ids":{"openalex":"https://openalex.org/W3046029616","doi":"https://doi.org/10.1145/3373207.3403981","mag":"3046029616"},"language":"en","primary_location":{"id":"doi:10.1145/3373207.3403981","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3403981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-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/A5052550722","display_name":"Matthew England","orcid":"https://orcid.org/0000-0001-5729-3420"},"institutions":[{"id":"https://openalex.org/I73417466","display_name":"Coventry University","ror":"https://ror.org/01tgmhj36","country_code":"GB","type":"education","lineage":["https://openalex.org/I73417466"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Matthew England","raw_affiliation_strings":["Coventry University, Coventry, UK"],"affiliations":[{"raw_affiliation_string":"Coventry University, Coventry, UK","institution_ids":["https://openalex.org/I73417466"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052550722"],"corresponding_institution_ids":["https://openalex.org/I73417466"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12236548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"13","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9782000184059143,"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":0.9782000184059143,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9377999901771545,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.9363561272621155},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.786618173122406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5939927101135254},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.5888106226921082},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5114861726760864},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49409225583076477},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4757392406463623},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4409593939781189},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42222124338150024},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.42187580466270447},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3909589648246765},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38997095823287964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3194640278816223},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25350096821784973},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1521349549293518},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14065581560134888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11515715718269348}],"concepts":[{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.9363561272621155},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.786618173122406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5939927101135254},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.5888106226921082},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5114861726760864},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49409225583076477},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4757392406463623},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4409593939781189},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42222124338150024},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.42187580466270447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3909589648246765},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38997095823287964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3194640278816223},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25350096821784973},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1521349549293518},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14065581560134888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11515715718269348},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3373207.3403981","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3403981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1570787829","https://openalex.org/W2799015977","https://openalex.org/W2941893175","https://openalex.org/W2993256971","https://openalex.org/W3100617857","https://openalex.org/W3101511967","https://openalex.org/W4229917934"],"related_works":["https://openalex.org/W3095068681","https://openalex.org/W2035631589","https://openalex.org/W2911817544","https://openalex.org/W141438329","https://openalex.org/W4286970214","https://openalex.org/W3200656118","https://openalex.org/W4289097017","https://openalex.org/W2906702131","https://openalex.org/W2358241947","https://openalex.org/W4313326369"],"abstract_inverted_index":{"Given":[0],"a":[1,21,49],"quantified":[2,32],"logical":[3],"formula":[4,24],"whose":[5],"atoms":[6],"are":[7],"polynomial":[8],"constraints":[9],"with":[10],"real":[11,50],"valued":[12],"variables,":[13],"Real":[14,40,78],"Quantifier":[15],"Elimination":[16],"(QE)":[17],"means":[18],"to":[19,53,64],"derive":[20],"logically":[22],"equivalent":[23,66],"which":[25],"does":[26],"not":[27],"involve":[28],"quantifiers":[29],"or":[30],"the":[31,35,44,54,65,69],"variables":[33],"from":[34],"original":[36],"statement.":[37],"For":[38],"example,":[39],"QE":[41,79],"would":[42],"reduce":[43],"statement":[45],"that":[46],"there":[47],"exists":[48],"solution":[51],"x":[52],"quadratic":[55],"equation":[56],"x2":[57],"+":[58,60],"bx":[59],"c":[61],"=":[62],"0":[63],"condition":[67],"on":[68],"discriminant:":[70],"b2":[71],"-":[72],"4c":[73],"\u2265":[74],"0.":[75],"Tarski":[76],"proved":[77],"is":[80],"always":[81],"possible":[82],"(with":[83],"sufficient":[84],"resources)":[85],"[7].":[86]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
