{"id":"https://openalex.org/W2809228707","doi":"https://doi.org/10.1145/3208976.3209023","title":"Real Root Finding for Equivariant Semi-algebraic Systems","display_name":"Real Root Finding for Equivariant Semi-algebraic Systems","publication_year":2018,"publication_date":"2018-07-11","ids":{"openalex":"https://openalex.org/W2809228707","doi":"https://doi.org/10.1145/3208976.3209023","mag":"2809228707"},"language":"en","primary_location":{"id":"doi:10.1145/3208976.3209023","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3208976.3209023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 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":"green","oa_url":"https://arxiv.org/pdf/1806.08121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043861722","display_name":"Cordian Riener","orcid":"https://orcid.org/0000-0002-1192-3500"},"institutions":[{"id":"https://openalex.org/I78037679","display_name":"UiT The Arctic University of Norway","ror":"https://ror.org/00wge5k78","country_code":"NO","type":"education","lineage":["https://openalex.org/I78037679"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Cordian Riener","raw_affiliation_strings":["UiT The Arctic University of Norway, Troms\u00f8, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UiT The Arctic University of Norway, Troms\u00f8, Norway","institution_ids":["https://openalex.org/I78037679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048254079","display_name":"Mohab Safey El Din","orcid":"https://orcid.org/0000-0001-9463-1257"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mohab Safey el Din","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, INRIA, LIP6, \u00c9quipe PolSys, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, INRIA, LIP6, \u00c9quipe PolSys, Paris, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8579,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76180829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"335","last_page":"342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9943000078201294,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9602000117301941,"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/mathematics","display_name":"Mathematics","score":0.717904806137085},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.6686535477638245},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6006749868392944},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.5838161110877991},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.5625684261322021},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5511646866798401},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4754216969013214},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.46842801570892334},{"id":"https://openalex.org/keywords/zero-set","display_name":"Zero set","score":0.45608043670654297},{"id":"https://openalex.org/keywords/algebraic-extension","display_name":"Algebraic extension","score":0.42083877325057983},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3578440546989441},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3007816970348358},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14540117979049683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.717904806137085},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6686535477638245},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6006749868392944},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.5838161110877991},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.5625684261322021},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5511646866798401},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4754216969013214},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.46842801570892334},{"id":"https://openalex.org/C17183583","wikidata":"https://www.wikidata.org/wiki/Q214604","display_name":"Zero set","level":2,"score":0.45608043670654297},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.42083877325057983},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3578440546989441},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3007816970348358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14540117979049683},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3208976.3209023","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3208976.3209023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1806.08121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.08121","pdf_url":"https://arxiv.org/pdf/1806.08121","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":"","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.08121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.08121","pdf_url":"https://arxiv.org/pdf/1806.08121","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1558722870","display_name":"Games through the lens of ALgebra and geometry of OPtimization","funder_award_id":"ANR-17-CE40-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W136633354","https://openalex.org/W230585924","https://openalex.org/W428349526","https://openalex.org/W822690258","https://openalex.org/W1516027685","https://openalex.org/W1520462245","https://openalex.org/W1539838732","https://openalex.org/W1550331971","https://openalex.org/W1559197676","https://openalex.org/W1559760555","https://openalex.org/W1599833186","https://openalex.org/W1796954330","https://openalex.org/W1888404329","https://openalex.org/W1967686635","https://openalex.org/W1973993014","https://openalex.org/W1993402990","https://openalex.org/W1996754055","https://openalex.org/W1996871887","https://openalex.org/W2001255903","https://openalex.org/W2001393258","https://openalex.org/W2007438578","https://openalex.org/W2008160486","https://openalex.org/W2011695558","https://openalex.org/W2016056788","https://openalex.org/W2029109623","https://openalex.org/W2033158463","https://openalex.org/W2041840902","https://openalex.org/W2046787108","https://openalex.org/W2055993677","https://openalex.org/W2063194632","https://openalex.org/W2065337200","https://openalex.org/W2067754486","https://openalex.org/W2068856273","https://openalex.org/W2072992931","https://openalex.org/W2075348750","https://openalex.org/W2077870553","https://openalex.org/W2082387287","https://openalex.org/W2086785654","https://openalex.org/W2089478560","https://openalex.org/W2093850840","https://openalex.org/W2104223485","https://openalex.org/W2106264424","https://openalex.org/W2119014037","https://openalex.org/W2134386365","https://openalex.org/W2139517149","https://openalex.org/W2141144514","https://openalex.org/W2143920029","https://openalex.org/W2151549243","https://openalex.org/W2166375258","https://openalex.org/W2172207126","https://openalex.org/W2187638739","https://openalex.org/W2192231489","https://openalex.org/W2279788372","https://openalex.org/W2318268489","https://openalex.org/W2342402779","https://openalex.org/W2732096052","https://openalex.org/W2755087097","https://openalex.org/W2962904734","https://openalex.org/W2963147061","https://openalex.org/W3100496417","https://openalex.org/W3105468562","https://openalex.org/W4293207255","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W1502419693","https://openalex.org/W2170846659","https://openalex.org/W415152954","https://openalex.org/W2019519844","https://openalex.org/W4387637555","https://openalex.org/W1992024209","https://openalex.org/W635989923","https://openalex.org/W2066092589","https://openalex.org/W2089339786","https://openalex.org/W2809228707"],"abstract_inverted_index":{"Let":[0],"R":[1],"be":[2,148],"a":[3,38,54,62],"real":[4,78],"closed":[5],"field.":[6],"We":[7,50],"consider":[8],"basic":[9,93],"semi-algebraic":[10,39,94],"sets":[11,95],"defined":[12,96],"by":[13,33,43,97],"n":[14,114],"-variate":[15],"equations/inequalities":[16],"of":[17,25,28,30,46,92,100,127],"s":[18,98],"symmetric":[19,48],"polynomials":[20,99],"and":[21,124],"an":[22],"equivariant":[23],"family":[24],"polynomials,":[26],"all":[27],"them":[29],"degree":[31,101],"bounded":[32],"2d":[34],"<":[35],"n.":[36],"Such":[37],"set":[40,55],"is":[41,56,111],"invariant":[42],"the":[44,47,83,90,108,117,125,128,141],"action":[45],"group.":[49],"show":[51],"that":[52,140],"such":[53],"either":[57],"empty":[58],"or":[59],"it":[60],"contains":[61],"point":[63,85],"with":[64,74],"at":[65],"most":[66],"2d-1":[67],"distinct":[68],"coordinates.":[69],"Combining":[70],"this":[71],"geometric":[72],"result":[73],"efficient":[75],"algorithms":[76],"for":[77],"root":[79],"finding":[80],"(based":[81],"on":[82,132],"critical":[84],"method),":[86],"one":[87,137],"can":[88,147],"decide":[89],"emptiness":[91],"d":[102],"in":[103,113,150],"time":[104,151],"(sn)O(d).":[105],"This":[106],"improves":[107],"state-of-the-art":[109],"which":[110],"exponential":[112],".":[115],"When":[116],"variables":[118],"x1,":[119],"\u0142dots,":[120,135],"xn":[121],"are":[122],"quantified":[123],"coefficients":[126],"input":[129],"system":[130],"depend":[131],"parameters":[133],"y1,":[134],"yt,":[136],"also":[138],"demonstrates":[139],"corresponding":[142],"one-block":[143],"quantifier":[144],"elimination":[145],"problem":[146],"solved":[149],"(sn)O(dt).":[152]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}