{"id":"https://openalex.org/W2021153515","doi":"https://doi.org/10.1145/1993886.1993903","title":"Computing with semi-algebraic sets represented by triangular decomposition","display_name":"Computing with semi-algebraic sets represented by triangular decomposition","publication_year":2011,"publication_date":"2011-06-08","ids":{"openalex":"https://openalex.org/W2021153515","doi":"https://doi.org/10.1145/1993886.1993903","mag":"2021153515"},"language":"en","primary_location":{"id":"doi:10.1145/1993886.1993903","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993903","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5011795147","display_name":"Changbo Chen","orcid":"https://orcid.org/0000-0002-7412-7667"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Changbo Chen","raw_affiliation_strings":["University of Western Ontario, London, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"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":["University of Bath, Bath, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bath, Bath, United Kingdom","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081832433","display_name":"Marc Moreno Maza","orcid":"https://orcid.org/0000-0003-3011-0756"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Marc Moreno Maza","raw_affiliation_strings":["University of Western Ontario, London, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065639971","display_name":"Bican Xia","orcid":"https://orcid.org/0000-0002-2570-2338"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bican Xia","raw_affiliation_strings":["Peking University, Beijing, China","Peking University, Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"Peking University, Beijing, China#TAB#","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061550044","display_name":"Rong Xiao","orcid":"https://orcid.org/0000-0002-6214-8057"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Rong Xiao","raw_affiliation_strings":["UNIVERSITY OF WESTERN ONTARIO, London, Canada","University of Western Ontario, London, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UNIVERSITY OF WESTERN ONTARIO, London, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"University of Western Ontario, London, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5875,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.92768746,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"75","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9926000237464905,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9905999898910522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.8123251795768738},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.7003835439682007},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6534925699234009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.610511064529419},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4309222400188446},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4226635694503784},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39476478099823},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30647963285446167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09824714064598083}],"concepts":[{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.8123251795768738},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.7003835439682007},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6534925699234009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.610511064529419},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4309222400188446},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4226635694503784},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39476478099823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30647963285446167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09824714064598083},{"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/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":3,"locations":[{"id":"doi:10.1145/1993886.1993903","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993903","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:opus.bath.ac.uk:24950","is_oa":false,"landing_page_url":"http://opus.bath.ac.uk/24950/1/Chen_ISSAC2011_75.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:purehost.bath.ac.uk:publications/eb4f208f-9b96-4ece-aedc-864ace0cafed","is_oa":false,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/eb4f208f-9b96-4ece-aedc-864ace0cafed","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W399280277","https://openalex.org/W1536271794","https://openalex.org/W1558198085","https://openalex.org/W1574151794","https://openalex.org/W1813686459","https://openalex.org/W1903368241","https://openalex.org/W1992483196","https://openalex.org/W2011212572","https://openalex.org/W2012079420","https://openalex.org/W2013742763","https://openalex.org/W2016056788","https://openalex.org/W2021431116","https://openalex.org/W2053029682","https://openalex.org/W2054005723","https://openalex.org/W2128486174","https://openalex.org/W2149652522","https://openalex.org/W2561675875","https://openalex.org/W3217399827","https://openalex.org/W6806048796"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4229560034","https://openalex.org/W4210910892","https://openalex.org/W2206497186","https://openalex.org/W4225691068","https://openalex.org/W2277985843"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2],"a":[3],"continuation":[4],"of":[5,14],"our":[6],"earlier":[7],"work":[8],"[3],":[9],"which":[10,30],"introduced":[11],"triangular":[12],"decompositions":[13],"semi-algebraic":[15],"systems":[16],"and":[17],"algorithms":[18],"for":[19,35],"computing":[20],"them.":[21],"Our":[22],"new":[23],"contributions":[24],"include":[25],"theoretical":[26],"results":[27],"based":[28],"on":[29],"we":[31],"obtain":[32],"practical":[33],"improvements":[34],"these":[36],"decomposition":[37],"algorithms.":[38]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
