{"id":"https://openalex.org/W2799015977","doi":"https://doi.org/10.1007/s11786-019-00394-8","title":"Using Machine Learning to Improve Cylindrical Algebraic Decomposition","display_name":"Using Machine Learning to Improve Cylindrical Algebraic Decomposition","publication_year":2019,"publication_date":"2019-04-03","ids":{"openalex":"https://openalex.org/W2799015977","doi":"https://doi.org/10.1007/s11786-019-00394-8","mag":"2799015977"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-019-00394-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-019-00394-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-019-00394-8.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11786-019-00394-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089028965","display_name":"Zongyan Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Zongyan Huang","raw_affiliation_strings":["Computer Laboratory, University of Cambridge, Cambridge, CB3 0FD, UK"],"affiliations":[{"raw_affiliation_string":"Computer Laboratory, University of Cambridge, Cambridge, CB3 0FD, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","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":["Faculty of Engineering, Environment and Computing, Coventry University, Coventry, CV1 2JH, UK"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Environment and Computing, Coventry University, Coventry, CV1 2JH, UK","institution_ids":["https://openalex.org/I73417466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052009668","display_name":"David J. D. Wilson","orcid":"https://orcid.org/0000-0002-0007-4486"},"institutions":[{"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":false,"raw_author_name":"David J. Wilson","raw_affiliation_strings":["Department of Computer Science, University of Bath, Bath, BA2 7AY, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108373792","display_name":"James Bridge","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Bridge","raw_affiliation_strings":["Computer Laboratory, University of Cambridge, Cambridge, CB3 0FD, UK"],"affiliations":[{"raw_affiliation_string":"Computer Laboratory, University of Cambridge, Cambridge, CB3 0FD, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043054372","display_name":"James H. Davenport","orcid":"https://orcid.org/0000-0002-3982-7545"},"institutions":[{"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":false,"raw_author_name":"James H. Davenport","raw_affiliation_strings":["Department of Computer Science, University of Bath, Bath, BA2 7AY, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086565312","display_name":"Lawrence C. Paulson","orcid":"https://orcid.org/0000-0003-0288-4279"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lawrence C. Paulson","raw_affiliation_strings":["Computer Laboratory, University of Cambridge, Cambridge, CB3 0FD, UK"],"affiliations":[{"raw_affiliation_string":"Computer Laboratory, University of Cambridge, Cambridge, CB3 0FD, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5052550722"],"corresponding_institution_ids":["https://openalex.org/I73417466"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.7172,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.89896173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"461","last_page":"488"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9977999925613403,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9965000152587891,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.8269233703613281},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.6310018301010132},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6079896092414856},{"id":"https://openalex.org/keywords/cad","display_name":"CAD","score":0.4937797486782074},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47027331590652466},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4689326584339142},{"id":"https://openalex.org/keywords/imperfect","display_name":"Imperfect","score":0.468350350856781},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.43581289052963257},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4198412299156189},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.41958385705947876},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4176397919654846},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4066857099533081},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38376355171203613},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.38181793689727783},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3670695424079895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2787907123565674},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0961744487285614},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.08089619874954224}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.8269233703613281},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.6310018301010132},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6079896092414856},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.4937797486782074},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47027331590652466},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4689326584339142},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.468350350856781},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.43581289052963257},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4198412299156189},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.41958385705947876},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4176397919654846},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4066857099533081},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38376355171203613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38181793689727783},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3670695424079895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2787907123565674},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0961744487285614},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.08089619874954224},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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":6,"locations":[{"id":"doi:10.1007/s11786-019-00394-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-019-00394-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-019-00394-8.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/52c17e8f-df15-4a29-a75a-4436336c927b","is_oa":true,"landing_page_url":"https://pureportal.coventry.ac.uk/en/publications/52c17e8f-df15-4a29-a75a-4436336c927b","pdf_url":null,"source":{"id":"https://openalex.org/S4306402411","display_name":"Pure (Coventry University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I73417466","host_organization_name":"Coventry University","host_organization_lineage":["https://openalex.org/I73417466"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Huang, Z, England, M, Wilson, D, Bridge, J, Davenport, J H & Paulson, L C 2019, 'Using Machine Learning to Improve Cylindrical Algebraic Decomposition', Mathematics in Computer Science, vol. 13, no. 4, pp. 461-488. https://doi.org/10.1007/s11786-019-00394-8","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1804.10520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.10520","pdf_url":"https://arxiv.org/pdf/1804.10520","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":null,"raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/52c17e8f-df15-4a29-a75a-4436336c927b","is_oa":true,"landing_page_url":"https://pureportal.coventry.ac.uk/en/publications/using-machine-learning-to-improve-cylindrical-algebraic-decomposition(52c17e8f-df15-4a29-a75a-4436336c927b).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402411","display_name":"Pure (Coventry University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I73417466","host_organization_name":"Coventry University","host_organization_lineage":["https://openalex.org/I73417466"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/291189","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/291189","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.17863/cam.38369","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.38369","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s11786-019-00394-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-019-00394-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-019-00394-8.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","display_name":"No poverty","score":0.4399999976158142}],"awards":[{"id":"https://openalex.org/G1093520412","display_name":null,"funder_award_id":"Scholarship","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1598339071","display_name":null,"funder_award_id":"EP/I011005/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2300736770","display_name":null,"funder_award_id":"(CSC)","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G4467992213","display_name":"Real Geometry and Connectedness via Triangular Description","funder_award_id":"EP/J003247/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4810374866","display_name":null,"funder_award_id":"China Scholarship Council","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5548776230","display_name":"SC-square - Satisfiability Checking and Symbolic Computation: uniting two communities to solve real problems","funder_award_id":"712689","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5633611288","display_name":null,"funder_award_id":"EP/R019622/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5769379255","display_name":null,"funder_award_id":"EP/J003247/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8589651859","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2799015977.pdf","grobid_xml":"https://content.openalex.org/works/W2799015977.grobid-xml"},"referenced_works_count":110,"referenced_works":["https://openalex.org/W8060374","https://openalex.org/W126540604","https://openalex.org/W171313677","https://openalex.org/W578769015","https://openalex.org/W979541187","https://openalex.org/W1482222746","https://openalex.org/W1485955744","https://openalex.org/W1493060511","https://openalex.org/W1510073064","https://openalex.org/W1514032333","https://openalex.org/W1526146785","https://openalex.org/W1526453320","https://openalex.org/W1535116423","https://openalex.org/W1542652324","https://openalex.org/W1553142094","https://openalex.org/W1560107318","https://openalex.org/W1560494575","https://openalex.org/W1565449944","https://openalex.org/W1565786776","https://openalex.org/W1570787829","https://openalex.org/W1574151794","https://openalex.org/W1574862351","https://openalex.org/W1585743408","https://openalex.org/W1708197474","https://openalex.org/W1797874232","https://openalex.org/W1859938857","https://openalex.org/W1916563250","https://openalex.org/W1949239131","https://openalex.org/W1976567870","https://openalex.org/W1983621455","https://openalex.org/W1983787096","https://openalex.org/W1984067593","https://openalex.org/W1987281309","https://openalex.org/W1988004808","https://openalex.org/W1995341919","https://openalex.org/W1995875735","https://openalex.org/W2004746351","https://openalex.org/W2007074311","https://openalex.org/W2010429995","https://openalex.org/W2013504313","https://openalex.org/W2016056788","https://openalex.org/W2020386454","https://openalex.org/W2021431116","https://openalex.org/W2026612342","https://openalex.org/W2026774968","https://openalex.org/W2030754929","https://openalex.org/W2031948211","https://openalex.org/W2034519924","https://openalex.org/W2038345254","https://openalex.org/W2040870580","https://openalex.org/W2041404167","https://openalex.org/W2051595244","https://openalex.org/W2052865204","https://openalex.org/W2057592112","https://openalex.org/W2063938083","https://openalex.org/W2065776042","https://openalex.org/W2067705970","https://openalex.org/W2067974800","https://openalex.org/W2070771761","https://openalex.org/W2075348750","https://openalex.org/W2087347434","https://openalex.org/W2093850840","https://openalex.org/W2106974669","https://openalex.org/W2107432340","https://openalex.org/W2109553965","https://openalex.org/W2109676405","https://openalex.org/W2109943925","https://openalex.org/W2113881937","https://openalex.org/W2118020653","https://openalex.org/W2119821739","https://openalex.org/W2133990480","https://openalex.org/W2135122395","https://openalex.org/W2137983211","https://openalex.org/W2147492008","https://openalex.org/W2149706766","https://openalex.org/W2163171771","https://openalex.org/W2194192157","https://openalex.org/W2370198512","https://openalex.org/W2378550892","https://openalex.org/W2403668100","https://openalex.org/W2482086987","https://openalex.org/W2482690948","https://openalex.org/W2486519520","https://openalex.org/W2510395247","https://openalex.org/W2567628972","https://openalex.org/W2611332476","https://openalex.org/W2724130349","https://openalex.org/W2726594508","https://openalex.org/W2750178884","https://openalex.org/W2751060233","https://openalex.org/W2751318774","https://openalex.org/W2810716043","https://openalex.org/W2952776748","https://openalex.org/W2978725006","https://openalex.org/W3098210831","https://openalex.org/W3098379678","https://openalex.org/W3098430291","https://openalex.org/W3099931346","https://openalex.org/W3100702068","https://openalex.org/W3101527056","https://openalex.org/W3103265545","https://openalex.org/W3103381322","https://openalex.org/W3105428479","https://openalex.org/W3146803896","https://openalex.org/W3168122661","https://openalex.org/W3217399827","https://openalex.org/W4229917934","https://openalex.org/W4255213956","https://openalex.org/W4285719527","https://openalex.org/W4312960235"],"related_works":["https://openalex.org/W3095068681","https://openalex.org/W2035631589","https://openalex.org/W1813686459","https://openalex.org/W2039279140","https://openalex.org/W1617297050","https://openalex.org/W1995150618","https://openalex.org/W2904925137","https://openalex.org/W3217399827","https://openalex.org/W2049666462","https://openalex.org/W2589479599"],"abstract_inverted_index":{"Cylindrical":[0],"Algebraic":[1],"Decomposition":[2],"(CAD)":[3],"is":[4,40,124],"a":[5,15,27,53,129,133,161,170],"key":[6],"tool":[7],"in":[8,33,43,55,65,149,196],"computational":[9],"algebraic":[10],"geometry,":[11],"best":[12],"known":[13],"as":[14],"procedure":[16],"to":[17,73,82,117,132,155,167,182,191],"enable":[18],"Quantifier":[19],"Elimination":[20],"over":[21],"real-closed":[22],"fields.":[23],"However,":[24],"it":[25,148],"has":[26,46],"worst":[28],"case":[29,151],"complexity":[30],"doubly":[31],"exponential":[32],"the":[34,37,88,92,108,125,153,165,184,200],"size":[35],"of":[36,77,91,110,127,188],"input,":[38],"which":[39],"often":[41],"encountered":[42],"practice.":[44],"It":[45],"been":[47,80],"observed":[48],"that":[49,199],"for":[50,159],"many":[51],"problems":[52],"change":[54],"algorithm":[56],"settings":[57],"or":[58],"problem":[59,69,172],"formulation":[60],"can":[61,101],"cause":[62],"huge":[63],"differences":[64],"runtime":[66],"costs,":[67],"changing":[68],"instances":[70],"from":[71,140,176],"intractable":[72],"easy.":[74],"A":[75],"number":[76],"heuristics":[78,158],"have":[79],"developed":[81,206],"help":[83],"with":[84],"such":[85,119,186],"choices,":[86],"but":[87],"complicated":[89],"nature":[90],"geometric":[93],"relationships":[94],"involved":[95],"means":[96],"these":[97],"are":[98],"imperfect":[99],"and":[100],"sometimes":[102],"make":[103,118],"poor":[104],"choices.":[105],"We":[106,194],"investigate":[107],"use":[109],"machine":[111,189,201],"learning":[112,123,190],"(specifically":[113],"support":[114],"vector":[115],"machines)":[116],"choices":[120],"instead.":[121],"Machine":[122],"process":[126],"fitting":[128],"computer":[130],"model":[131],"complex":[134],"function":[135],"based":[136],"on":[137],"properties":[138],"learned":[139,202],"measured":[141],"data.":[142],"In":[143],"this":[144],"paper":[145],"we":[146],"apply":[147],"two":[150],"studies:":[152],"first":[154,185],"select":[156],"between":[157],"choosing":[160],"CAD":[162,171],"variable":[163],"ordering;":[164],"second":[166],"identify":[168],"when":[169],"instance":[173],"would":[174],"benefit":[175],"Gr\u00f6bner":[177],"Basis":[178],"preconditioning.":[179],"These":[180],"appear":[181],"be":[183],"applications":[187],"Symbolic":[192],"Computation.":[193],"demonstrate":[195],"both":[197],"cases":[198],"choice":[203],"outperforms":[204],"human":[205],"heuristics.":[207]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2020-11-23T00:00:00"}
