{"id":"https://openalex.org/W2126528701","doi":"https://doi.org/10.1007/978-3-642-39320-4_2","title":"Optimising Problem Formulation for Cylindrical Algebraic Decomposition","display_name":"Optimising Problem Formulation for Cylindrical Algebraic Decomposition","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2126528701","doi":"https://doi.org/10.1007/978-3-642-39320-4_2","mag":"2126528701"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-39320-4_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39320-4_2","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.7222","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Russell 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":true,"raw_author_name":"Russell Bradford","raw_affiliation_strings":["University of Bath, Bath, BA2 7AY, U.K"],"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, BA2 7AY, U.K","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":null,"display_name":"James 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":"James H. Davenport","raw_affiliation_strings":["University of Bath, Bath, BA2 7AY, U.K"],"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, BA2 7AY, U.K","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Matthew 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":false,"raw_author_name":"Matthew England","raw_affiliation_strings":["University of Bath, Bath, BA2 7AY, U.K"],"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, BA2 7AY, U.K","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":null,"display_name":"David 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":"David Wilson","raw_affiliation_strings":["University of Bath, Bath, BA2 7AY, U.K"],"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, BA2 7AY, U.K","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I51601045"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":7.3525,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.97806324,"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":"19","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9779000282287598,"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":0.9779000282287598,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.004900000058114529,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.002899999963119626,"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/heuristics","display_name":"Heuristics","score":0.6086000204086304},{"id":"https://openalex.org/keywords/precondition","display_name":"Precondition","score":0.582099974155426},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5472999811172485},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5067999958992004},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.48539999127388},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44620001316070557},{"id":"https://openalex.org/keywords/cad","display_name":"CAD","score":0.4390000104904175},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4203999936580658},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.41839998960494995}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6086000204086304},{"id":"https://openalex.org/C192465680","wikidata":"https://www.wikidata.org/wiki/Q1413450","display_name":"Precondition","level":2,"score":0.582099974155426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5644000172615051},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5472999811172485},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5067999958992004},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.48539999127388},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.41690000891685486},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3894999921321869},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3855000138282776},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31360000371932983},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.3122999966144562},{"id":"https://openalex.org/C119823426","wikidata":"https://www.wikidata.org/wiki/Q184793","display_name":"Computer Aided Design","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2777999937534332},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2660999894142151},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.26330000162124634}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-642-39320-4_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39320-4_2","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"},{"id":"pmh:oai:arXiv.org:1304.7222","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.7222","pdf_url":"https://arxiv.org/pdf/1304.7222","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:purehost.bath.ac.uk:publications/6a98aa34-c714-45d9-98a7-b759f220cd2d","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=84880711618&partnerID=8YFLogxK","pdf_url":"https://purehost.bath.ac.uk/ws/files/11544318/Formulations.pdf","source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bradford, R, Davenport, J H, England, M & Wilson, D 2013, Optimising problem formulation for cylindrical algebraic decomposition. in J Carette, D Aspinall, C Lange, P Sojka & W Windsteiger (eds), Intelligent Computer Mathematics : MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings. Lecture Notes in Computer Science, vol. 7961, Springer, Berlin, pp. 19-34, Conferences on Intelligent Computer Mathematics: CICM 2013, Bath, UK United Kingdom, 7/07/13. https://doi.org/10.1007/978-3-642-39320-4_2","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:purehost.bath.ac.uk:openaire/6a98aa34-c714-45d9-98a7-b759f220cd2d","is_oa":true,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/6a98aa34-c714-45d9-98a7-b759f220cd2d","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bradford, R, Davenport, J H, England, M & Wilson, D 2013, Optimising problem formulation for cylindrical algebraic decomposition. in J Carette, D Aspinall, C Lange, P Sojka & W Windsteiger (eds), Intelligent Computer Mathematics : MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings. Lecture Notes in Computer Science, vol. 7961, Springer, Berlin, pp. 19-34, Conferences on Intelligent Computer Mathematics: CICM 2013, Bath, UK United Kingdom, 7/07/13. https://doi.org/10.1007/978-3-642-39320-4_2","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1304.7222","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.7222","pdf_url":"https://arxiv.org/pdf/1304.7222","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"},"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1492057809","https://openalex.org/W1565046294","https://openalex.org/W1565449944","https://openalex.org/W1927398404","https://openalex.org/W1930661832","https://openalex.org/W1976567870","https://openalex.org/W2003425586","https://openalex.org/W2007074311","https://openalex.org/W2008288068","https://openalex.org/W2019882358","https://openalex.org/W2026612342","https://openalex.org/W2026774968","https://openalex.org/W2033013465","https://openalex.org/W2040139795","https://openalex.org/W2051595244","https://openalex.org/W2052865204","https://openalex.org/W2077320196","https://openalex.org/W2093850840","https://openalex.org/W2113881937","https://openalex.org/W2164887032","https://openalex.org/W4229917934"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2016-06-24T00:00:00"}