{"id":"https://openalex.org/W1546485346","doi":"https://doi.org/10.1007/978-3-540-45220-1_45","title":"Effective Quantifier Elimination over Real Closed Fields","display_name":"Effective Quantifier Elimination over Real Closed Fields","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1546485346","doi":"https://doi.org/10.1007/978-3-540-45220-1_45","mag":"1546485346"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-45220-1_45","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-45220-1_45","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5019911905","display_name":"Nicolai Vorobjov","orcid":null},"institutions":[{"id":"https://openalex.org/I91047523","display_name":"Bath Spa University","ror":"https://ror.org/0038jbq24","country_code":"GB","type":"education","lineage":["https://openalex.org/I91047523"]},{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Nicolai Vorobjov","raw_affiliation_strings":["Dept. of Computer Science, University of Bath, \u00a0","#N#\u00a7#N#University of Bath#N#"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, University of Bath, \u00a0","institution_ids":["https://openalex.org/I51601045","https://openalex.org/I91047523"]},{"raw_affiliation_string":"#N#\u00a7#N#University of Bath#N#","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019911905"],"corresponding_institution_ids":["https://openalex.org/I51601045","https://openalex.org/I91047523"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14259029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"545","last_page":"545"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.991100013256073,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9702000021934509,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.9325330257415771},{"id":"https://openalex.org/keywords/elementary-function","display_name":"Elementary function","score":0.6109414100646973},{"id":"https://openalex.org/keywords/elementary-algebra","display_name":"Elementary algebra","score":0.5971683859825134},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5625379681587219},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5531529188156128},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4913405478000641},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.48349931836128235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47007256746292114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4210345149040222},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38312503695487976},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32820597290992737},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3146600127220154},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2567879855632782}],"concepts":[{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.9325330257415771},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.6109414100646973},{"id":"https://openalex.org/C92087941","wikidata":"https://www.wikidata.org/wiki/Q211294","display_name":"Elementary algebra","level":3,"score":0.5971683859825134},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5625379681587219},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5531529188156128},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4913405478000641},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.48349931836128235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47007256746292114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4210345149040222},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38312503695487976},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32820597290992737},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3146600127220154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2567879855632782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-45220-1_45","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-45220-1_45","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1574151794"],"related_works":["https://openalex.org/W1770904122","https://openalex.org/W4312108796","https://openalex.org/W2494123147","https://openalex.org/W1562429120","https://openalex.org/W1981255379","https://openalex.org/W1546485346","https://openalex.org/W2479383195","https://openalex.org/W2796943335","https://openalex.org/W1993439210","https://openalex.org/W4233843817"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}