{"id":"https://openalex.org/W2071607852","doi":"https://doi.org/10.1145/2608628.2608633","title":"Cylindrical algebraic decomposition using local projections","display_name":"Cylindrical algebraic decomposition using local projections","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W2071607852","doi":"https://doi.org/10.1145/2608628.2608633","mag":"2071607852"},"language":"en","primary_location":{"id":"doi:10.1145/2608628.2608633","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608633","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","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/A5011129468","display_name":"Adam Strzebo\u0144ski","orcid":"https://orcid.org/0000-0003-1282-4640"},"institutions":[{"id":"https://openalex.org/I65760639","display_name":"Wolfram Research (United States)","ror":"https://ror.org/03k118f17","country_code":"US","type":"company","lineage":["https://openalex.org/I65760639"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Adam Strzebo\u0144ski","raw_affiliation_strings":["Wolfram Research Inc., Champaign, IL","Wolfram Research Inc., Champaign, IL#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wolfram Research Inc., Champaign, IL","institution_ids":["https://openalex.org/I65760639"]},{"raw_affiliation_string":"Wolfram Research Inc., Champaign, IL#TAB#","institution_ids":["https://openalex.org/I65760639"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011129468"],"corresponding_institution_ids":["https://openalex.org/I65760639"],"apc_list":null,"apc_paid":null,"fwci":3.3827,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.93610619,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"389","last_page":"396"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9925000071525574,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/projection","display_name":"Projection (relational algebra)","score":0.7567000985145569},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6912708878517151},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6695218086242676},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5809894800186157},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5163568258285522},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5135291218757629},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4888843894004822},{"id":"https://openalex.org/keywords/cad","display_name":"CAD","score":0.429662823677063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.394543319940567},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3296639323234558},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10200709104537964},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09031575918197632},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06641662120819092},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.0531192421913147}],"concepts":[{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7567000985145569},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6912708878517151},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6695218086242676},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5809894800186157},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5163568258285522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5135291218757629},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4888843894004822},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.429662823677063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.394543319940567},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3296639323234558},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10200709104537964},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09031575918197632},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06641662120819092},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.0531192421913147},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2608628.2608633","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608633","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.750.708","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.750.708","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1405.4925.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W615276906","https://openalex.org/W1491532135","https://openalex.org/W1493060511","https://openalex.org/W1553142094","https://openalex.org/W1558198085","https://openalex.org/W1565449944","https://openalex.org/W1570787829","https://openalex.org/W1922023418","https://openalex.org/W1982166299","https://openalex.org/W1991813962","https://openalex.org/W2001255903","https://openalex.org/W2007074311","https://openalex.org/W2013702670","https://openalex.org/W2021431116","https://openalex.org/W2026612342","https://openalex.org/W2026774968","https://openalex.org/W2031948211","https://openalex.org/W2035781448","https://openalex.org/W2037114932","https://openalex.org/W2040951317","https://openalex.org/W2071607852","https://openalex.org/W2072992931","https://openalex.org/W2075348750","https://openalex.org/W2077320196","https://openalex.org/W2082387287","https://openalex.org/W2098365657","https://openalex.org/W2124749403","https://openalex.org/W2149652522","https://openalex.org/W2504658842","https://openalex.org/W4249823113"],"related_works":["https://openalex.org/W637098845","https://openalex.org/W2410116073","https://openalex.org/W3044972437","https://openalex.org/W2275866607","https://openalex.org/W2315696258","https://openalex.org/W1908932129","https://openalex.org/W2332669313","https://openalex.org/W2587289131","https://openalex.org/W2951540481","https://openalex.org/W2506951661"],"abstract_inverted_index":{"We":[0,57],"present":[1],"an":[2,59],"algorithm":[3,53,64],"which":[4],"computes":[5],"a":[6,11],"cylindrical":[7],"algebraic":[8],"decomposition":[9],"of":[10,50,62],"semialgebraic":[12],"set":[13,34],"using":[14],"projection":[15,24,33],"sets":[16,25],"computed":[17],"for":[18],"each":[19],"cell":[20],"separately.":[21],"Such":[22],"local":[23],"can":[26],"be":[27],"significantly":[28],"smaller":[29],"than":[30],"the":[31,37,48,52,66],"global":[32],"used":[35],"by":[36],"Cylindrical":[38],"Algebraic":[39],"Decomposition":[40],"(CAD)":[41],"algorithm.":[42,69],"This":[43],"leads":[44],"to":[45,55],"reduction":[46],"in":[47],"number":[49],"cells":[51],"needs":[54],"construct.":[56],"give":[58],"empirical":[60],"comparison":[61],"our":[63],"and":[65],"classical":[67],"CAD":[68]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
