{"id":"https://openalex.org/W2065776042","doi":"https://doi.org/10.1007/s11786-014-0191-z","title":"Cylindrical Algebraic Sub-Decompositions","display_name":"Cylindrical Algebraic Sub-Decompositions","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2065776042","doi":"https://doi.org/10.1007/s11786-014-0191-z","mag":"2065776042"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-014-0191-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-014-0191-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11786-014-0191-z.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"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs11786-014-0191-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"D. J. Wilson","orcid":null},"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":"D. J. Wilson","raw_affiliation_strings":["Department of Computer Science, University of Bath, Bath, BA2 7AY, UK"],"raw_orcid":null,"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":null,"display_name":"R. J. Bradford","orcid":null},"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":"R. J. Bradford","raw_affiliation_strings":["Department of Computer Science, University of Bath, Bath, BA2 7AY, UK"],"raw_orcid":null,"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":null,"display_name":"J. H. Davenport","orcid":null},"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":"J. H. Davenport","raw_affiliation_strings":["Department of Computer Science, University of Bath, Bath, BA2 7AY, UK"],"raw_orcid":null,"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":null,"display_name":"M. England","orcid":null},"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":true,"raw_author_name":"M. England","raw_affiliation_strings":["Department of Computer Science, University of Bath, Bath, BA2 7AY, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I51601045"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2200,"currency":"EUR","value_usd":2372},"fwci":2.4434,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.89085222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"8","issue":"2","first_page":"263","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9124000072479248,"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":0.9124000072479248,"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/T10142","display_name":"Formal Methods in Verification","score":0.017799999564886093,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.009100000374019146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6643000245094299},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5792999863624573},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.5756999850273132},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5282999873161316},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.526199996471405},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.5062999725341797},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4918999969959259},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.4867999851703644},{"id":"https://openalex.org/keywords/algebraic-variety","display_name":"Algebraic variety","score":0.44830000400543213}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6643000245094299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6241999864578247},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5792999863624573},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.5756999850273132},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.526199996471405},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.5062999725341797},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4918999969959259},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.4867999851703644},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.44830000400543213},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.4138999879360199},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C554573382","wikidata":"https://www.wikidata.org/wiki/Q4723988","display_name":"Algebraic analysis","level":5,"score":0.3910999894142151},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.3831999897956848},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.36250001192092896},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33959999680519104},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3249000012874603},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.3093999922275543},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.3019999861717224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3010999858379364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29319998621940613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27970001101493835},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11786-014-0191-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-014-0191-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11786-014-0191-z.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:arXiv.org:1401.0647","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.0647","pdf_url":"https://arxiv.org/pdf/1401.0647","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"doi:10.1007/s11786-014-0191-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-014-0191-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11786-014-0191-z.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":[],"awards":[{"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/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"}],"funders":[{"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/W2065776042.pdf","grobid_xml":"https://content.openalex.org/works/W2065776042.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W979541187","https://openalex.org/W1530330307","https://openalex.org/W1565449944","https://openalex.org/W1969379715","https://openalex.org/W1976567870","https://openalex.org/W1982166299","https://openalex.org/W1984527805","https://openalex.org/W1996657304","https://openalex.org/W2003425586","https://openalex.org/W2007074311","https://openalex.org/W2016056788","https://openalex.org/W2021431116","https://openalex.org/W2022125816","https://openalex.org/W2026612342","https://openalex.org/W2026774968","https://openalex.org/W2031948211","https://openalex.org/W2033013465","https://openalex.org/W2035781448","https://openalex.org/W2051595244","https://openalex.org/W2052865204","https://openalex.org/W2052869011","https://openalex.org/W2057592112","https://openalex.org/W2067705970","https://openalex.org/W2075348750","https://openalex.org/W2093850840","https://openalex.org/W2098365657","https://openalex.org/W2113881937","https://openalex.org/W2126528701","https://openalex.org/W2135122395","https://openalex.org/W2149652522","https://openalex.org/W4229917934"],"related_works":[],"abstract_inverted_index":{"Cylindrical":[0],"algebraic":[1,10,30],"decompositions":[2],"(CADs)":[3],"are":[4,34,61],"a":[5,45,48,65,69,84,115],"key":[6],"tool":[7],"in":[8,64,135],"real":[9],"geometry,":[11],"used":[12],"primarily":[13],"for":[14,47],"eliminating":[15],"quantifiers":[16],"over":[17],"the":[18,40,96,106],"reals":[19],"and":[20,72,93,105],"studying":[21],"semi-algebraic":[22],"sets.":[23],"In":[24],"this":[25],"paper":[26],"we":[27],"introduce":[28],"cylindrical":[29],"sub-decompositions":[31],"(sub-CADs),":[32],"which":[33,60,75,127],"subsets":[35],"of":[36,56,80,109],"CADs":[37],"containing":[38],"all":[39],"information":[41],"needed":[42],"to":[43,90],"specify":[44],"solution":[46],"given":[49],"problem.":[50],"We":[51,87,113],"define":[52],"two":[53,97],"new":[54],"types":[55],"sub-CAD:":[57],"variety":[58],"sub-CADs":[59,74],"those":[62,78],"cells":[63,79],"CAD":[66],"lying":[67],"on":[68],"designated":[70],"variety;":[71],"layered":[73],"have":[76],"only":[77],"dimension":[81],"higher":[82],"than":[83],"specified":[85],"value.":[86],"present":[88],"algorithms":[89],"produce":[91],"these":[92,120],"describe":[94],"how":[95],"approaches":[98],"may":[99],"be":[100],"combined":[101],"with":[102],"each":[103],"other":[104],"recent":[107],"theory":[108],"truth-table":[110],"invariant":[111],"CAD.":[112],"give":[114],"complexity":[116],"analysis":[117],"showing":[118],"that":[119],"techniques":[121],"can":[122],"offer":[123],"substantial":[124],"theoretical":[125],"savings,":[126],"is":[128],"supported":[129],"by":[130],"experimentation":[131],"using":[132],"an":[133],"implementation":[134],"Maple":[136],".":[137]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}
