{"id":"https://openalex.org/W2077320196","doi":"https://doi.org/10.1016/s0747-7171(88)80010-5","title":"An improved projection operation for cylindrical algebraic decomposition of three-dimensional space","display_name":"An improved projection operation for cylindrical algebraic decomposition of three-dimensional space","publication_year":1988,"publication_date":"1988-02-01","ids":{"openalex":"https://openalex.org/W2077320196","doi":"https://doi.org/10.1016/s0747-7171(88)80010-5","mag":"2077320196"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(88)80010-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(88)80010-5","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"},"type":"article","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/A5061480464","display_name":"Scott McCallum","orcid":"https://orcid.org/0000-0002-5682-7993"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Scott McCallum","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4","Dept. of Computer Science, University of Toronto, Toronto, Canada, M5S 1A4#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Dept. of Computer Science, University of Toronto, Toronto, Canada, M5S 1A4#TAB#","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061480464"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":2770,"currency":"USD","value_usd":2770},"apc_paid":null,"fwci":3.1304,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.91614518,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"5","issue":"1-2","first_page":"141","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9739999771118164,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9739999771118164,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9631999731063843,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9232000112533569,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8361772298812866},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7974843978881836},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47247669100761414},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43419772386550903},{"id":"https://openalex.org/keywords/planar-projection","display_name":"Planar projection","score":0.41735684871673584},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4167134165763855},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.41299617290496826},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.41299039125442505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21376129984855652},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.21133971214294434},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19759076833724976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09124019742012024}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8361772298812866},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7974843978881836},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47247669100761414},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43419772386550903},{"id":"https://openalex.org/C105513272","wikidata":"https://www.wikidata.org/wiki/Q7200962","display_name":"Planar projection","level":3,"score":0.41735684871673584},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4167134165763855},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.41299617290496826},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.41299039125442505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21376129984855652},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.21133971214294434},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19759076833724976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09124019742012024},{"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":1,"locations":[{"id":"doi:10.1016/s0747-7171(88)80010-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(88)80010-5","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W158349087","https://openalex.org/W161930422","https://openalex.org/W569467521","https://openalex.org/W1551705509","https://openalex.org/W1553142094","https://openalex.org/W1557452007","https://openalex.org/W1558198085","https://openalex.org/W1565449944","https://openalex.org/W1815267262","https://openalex.org/W2000754328","https://openalex.org/W2008957088","https://openalex.org/W2016390696","https://openalex.org/W2036346865","https://openalex.org/W2054581185","https://openalex.org/W2067705970","https://openalex.org/W2329334599","https://openalex.org/W2798442789","https://openalex.org/W3217399827","https://openalex.org/W4231471038","https://openalex.org/W4256365759","https://openalex.org/W4298290503","https://openalex.org/W6633361761","https://openalex.org/W6633998609","https://openalex.org/W6638588722","https://openalex.org/W6650760358","https://openalex.org/W6659480769","https://openalex.org/W6663959707"],"related_works":["https://openalex.org/W2351452215","https://openalex.org/W2526789875","https://openalex.org/W2506410001","https://openalex.org/W2387516019","https://openalex.org/W1515849601","https://openalex.org/W2365072210","https://openalex.org/W2393270639","https://openalex.org/W2011889107","https://openalex.org/W2077320196","https://openalex.org/W4313054720"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}