{"id":"https://openalex.org/W1991813962","doi":"https://doi.org/10.1016/s0747-7171(10)80003-3","title":"On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals","display_name":"On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals","publication_year":1992,"publication_date":"1992-03-01","ids":{"openalex":"https://openalex.org/W1991813962","doi":"https://doi.org/10.1016/s0747-7171(10)80003-3","mag":"1991813962"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(10)80003-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(10)80003-3","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","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/A5015511691","display_name":"James Renegar","orcid":"https://orcid.org/0000-0002-6171-204X"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James Renegar","raw_affiliation_strings":["School of Operations Research and Industrial Engineering, College of Engineering, Cornell University, Ithaca, New York 14853-7501, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Operations Research and Industrial Engineering, College of Engineering, Cornell University, Ithaca, New York 14853-7501, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015511691"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":{"value":2770,"currency":"USD","value_usd":2770},"apc_paid":null,"fwci":23.0494,"has_fulltext":false,"cited_by_count":622,"citation_normalized_percentile":{"value":0.99796456,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"13","issue":"3","first_page":"255","last_page":"299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987000226974487,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987000226974487,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9980999827384949,"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/T11435","display_name":"Polynomial and algebraic computation","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7913997173309326},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.7157915830612183},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7109885811805725},{"id":"https://openalex.org/keywords/model-of-computation","display_name":"Model of computation","score":0.5258881449699402},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.49545013904571533},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.46935921907424927},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.448871910572052},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.437522828578949},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35618066787719727},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31189557909965515},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17730119824409485}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7913997173309326},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.7157915830612183},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7109885811805725},{"id":"https://openalex.org/C184596265","wikidata":"https://www.wikidata.org/wiki/Q2651576","display_name":"Model of computation","level":3,"score":0.5258881449699402},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.49545013904571533},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.46935921907424927},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.448871910572052},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.437522828578949},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35618066787719727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31189557909965515},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17730119824409485},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0747-7171(10)80003-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(10)80003-3","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W60917887","https://openalex.org/W136633354","https://openalex.org/W143396627","https://openalex.org/W1497846389","https://openalex.org/W1577570451","https://openalex.org/W1590407118","https://openalex.org/W1973117121","https://openalex.org/W1976392590","https://openalex.org/W1979600155","https://openalex.org/W1991581432","https://openalex.org/W1995150618","https://openalex.org/W2006918089","https://openalex.org/W2033040247","https://openalex.org/W2035153735","https://openalex.org/W2044850435","https://openalex.org/W2059985428","https://openalex.org/W2067754486","https://openalex.org/W2071846104","https://openalex.org/W2078730239","https://openalex.org/W2082387287","https://openalex.org/W2102074804","https://openalex.org/W2103985627","https://openalex.org/W2104882047","https://openalex.org/W2113097540","https://openalex.org/W2139480317","https://openalex.org/W2158795180","https://openalex.org/W2318268489","https://openalex.org/W2611147814","https://openalex.org/W4229917934","https://openalex.org/W4252229975","https://openalex.org/W4298290503","https://openalex.org/W6602514562","https://openalex.org/W6605815167","https://openalex.org/W6629769661","https://openalex.org/W6634467275","https://openalex.org/W6665422471","https://openalex.org/W6667373794"],"related_works":["https://openalex.org/W124095581","https://openalex.org/W1496964288","https://openalex.org/W2001255903","https://openalex.org/W2024271250","https://openalex.org/W87467805","https://openalex.org/W4221140179","https://openalex.org/W814988660","https://openalex.org/W2762130752","https://openalex.org/W1967093019","https://openalex.org/W2498409332"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":24},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":24},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":14}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
