{"id":"https://openalex.org/W1983787096","doi":"https://doi.org/10.1145/2755996.2756678","title":"Improving the Use of Equational Constraints in Cylindrical Algebraic Decomposition","display_name":"Improving the Use of Equational Constraints in Cylindrical Algebraic Decomposition","publication_year":2015,"publication_date":"2015-06-24","ids":{"openalex":"https://openalex.org/W1983787096","doi":"https://doi.org/10.1145/2755996.2756678","mag":"1983787096"},"language":"en","primary_location":{"id":"doi:10.1145/2755996.2756678","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2755996.2756678","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2755996.2756678?download=true","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/2755996.2756678?download=true","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":["Coventry University, Coventry, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Coventry University, Coventry, United Kingdom","institution_ids":["https://openalex.org/I73417466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073640180","display_name":"Russell Bradford","orcid":"https://orcid.org/0009-0003-3251-2051"},"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":"Russell Bradford","raw_affiliation_strings":["University of Bath, Bath, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, United Kingdom","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","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":["University of Bath, Bath, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, United Kingdom","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052550722"],"corresponding_institution_ids":["https://openalex.org/I73417466"],"apc_list":null,"apc_paid":null,"fwci":6.1853,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.96805974,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"165","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9907000064849854,"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":0.9907000064849854,"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":0.9864000082015991,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/lift","display_name":"Lift (data mining)","score":0.7408498525619507},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7271767854690552},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6774744391441345},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6727368235588074},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6108477711677551},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.554222822189331},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.519553005695343},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4907473027706146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4555971622467041},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.4536811411380768},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4300763010978699},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3886604309082031},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3199501931667328},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2496981918811798},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22772818803787231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1721177101135254},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12264370918273926},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10507020354270935},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08453074097633362}],"concepts":[{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.7408498525619507},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7271767854690552},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6774744391441345},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6727368235588074},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6108477711677551},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.554222822189331},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.519553005695343},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4907473027706146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4555971622467041},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.4536811411380768},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4300763010978699},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3886604309082031},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3199501931667328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2496981918811798},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22772818803787231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1721177101135254},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12264370918273926},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10507020354270935},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08453074097633362},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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:10.1145/2755996.2756678","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2755996.2756678","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2755996.2756678?download=true","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1501.04466","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1501.04466","pdf_url":"https://arxiv.org/pdf/1501.04466","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:openaire/9579bee3-0d55-49ce-b58a-4154972afac2","is_oa":true,"landing_page_url":"https://pureportal.coventry.ac.uk/en/publications/9579bee3-0d55-49ce-b58a-4154972afac2","pdf_url":"https://pure.coventry.ac.uk/ws/files/3960952/Symbolic%20and%20algebraic%20computation.pdf","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"England, M, Bradford, R & Davenport, J H 2015, 'Improving the use of equational constraints in cylindrical algebraic decomposition', Paper presented at 40th International Symposium on Symbolic and Algebraic Computation (ISSAC), Bath, United Kingdom, 6/07/15 - 9/07/15 pp. 165-172. https://doi.org/10.1145/2755996.2756678","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:http://curve.coventry.ac.uk/open/p/oai:445a3b52-b73f-4795-8b25-47ce12604e0d/1","is_oa":false,"landing_page_url":"http://curve.coventry.ac.uk/open/items/445a3b52-b73f-4795-8b25-47ce12604e0d/1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401989","display_name":"Coventry University Open Collections (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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference_item,paper - published"},{"id":"pmh:oai:opus.bath.ac.uk:42451","is_oa":false,"landing_page_url":"http://opus.bath.ac.uk/42451/5/EBD15.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401631","display_name":"The University of Bath Online Publications Store (The University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Items"},{"id":"pmh:oai:pure.atira.dk:publications/9579bee3-0d55-49ce-b58a-4154972afac2","is_oa":true,"landing_page_url":"https://pureportal.coventry.ac.uk/en/publications/improving-the-use-of-equational-constraints-in-cylindrical-algebraic-decomposition(9579bee3-0d55-49ce-b58a-4154972afac2).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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"England , M , Bradford , R & Davenport , J H 2015 , ' Improving the use of equational constraints in cylindrical algebraic decomposition ' , Paper presented at 40th International Symposium on Symbolic and Algebraic Computation (ISSAC) , Bath , United Kingdom , 6/07/15 - 9/07/15 pp. 165-172 . https://doi.org/10.1145/2755996.2756678","raw_type":"conferenceObject"}],"best_oa_location":{"id":"doi:10.1145/2755996.2756678","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2755996.2756678","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2755996.2756678?download=true","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.5,"display_name":"Decent work and economic growth"}],"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/W1983787096.pdf","grobid_xml":"https://content.openalex.org/works/W1983787096.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W126540604","https://openalex.org/W979541187","https://openalex.org/W1485955744","https://openalex.org/W1565046294","https://openalex.org/W1565449944","https://openalex.org/W1574151794","https://openalex.org/W1788620677","https://openalex.org/W1797874232","https://openalex.org/W1916563250","https://openalex.org/W1976567870","https://openalex.org/W1982166299","https://openalex.org/W1996657304","https://openalex.org/W2003425586","https://openalex.org/W2013742763","https://openalex.org/W2016056788","https://openalex.org/W2018625447","https://openalex.org/W2026612342","https://openalex.org/W2026774968","https://openalex.org/W2030754929","https://openalex.org/W2031948211","https://openalex.org/W2051595244","https://openalex.org/W2052865204","https://openalex.org/W2057592112","https://openalex.org/W2067705970","https://openalex.org/W2071607852","https://openalex.org/W2075348750","https://openalex.org/W2113881937","https://openalex.org/W2125191920","https://openalex.org/W2126528701","https://openalex.org/W2135122395","https://openalex.org/W2395155819","https://openalex.org/W3098210831","https://openalex.org/W3098430291","https://openalex.org/W3100702068","https://openalex.org/W4241415633","https://openalex.org/W4255213956","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4389397071","https://openalex.org/W2023045191","https://openalex.org/W2952839243","https://openalex.org/W3009154991","https://openalex.org/W2945555514","https://openalex.org/W1967016017","https://openalex.org/W1582343225","https://openalex.org/W2038283895","https://openalex.org/W2506951661","https://openalex.org/W3142989576"],"abstract_inverted_index":{"When":[0],"building":[1],"a":[2,24],"cylindrical":[3],"algebraic":[4],"decomposition":[5],"(CAD)":[6],"savings":[7],"can":[8],"be":[9],"made":[10],"in":[11],"the":[12],"presence":[13],"of":[14],"an":[15,19],"equational":[16],"constraint":[17],"(EC):":[18],"equation":[20],"logically":[21],"implied":[22],"by":[23],"formula.":[25]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2020-11-23T00:00:00"}