{"id":"https://openalex.org/W2054337539","doi":"https://doi.org/10.1145/2442829.2442878","title":"Univariate real root isolation in multiple extension fields","display_name":"Univariate real root isolation in multiple extension fields","publication_year":2012,"publication_date":"2012-07-22","ids":{"openalex":"https://openalex.org/W2054337539","doi":"https://doi.org/10.1145/2442829.2442878","mag":"2054337539"},"language":"en","primary_location":{"id":"doi:10.1145/2442829.2442878","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442878","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-00776074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011129468","display_name":"Adam Strzebo\u0144ski","orcid":"https://orcid.org/0000-0003-1282-4640"},"institutions":[{"id":"https://openalex.org/I65760639","display_name":"Wolfram Research (United States)","ror":"https://ror.org/03k118f17","country_code":"US","type":"company","lineage":["https://openalex.org/I65760639"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adam Strzebo\u0144ski","raw_affiliation_strings":["Wolfram Research Inc., Champaign, IL","Wolfram Research Inc., Champaign, IL#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wolfram Research Inc., Champaign, IL","institution_ids":["https://openalex.org/I65760639"]},{"raw_affiliation_string":"Wolfram Research Inc., Champaign, IL#TAB#","institution_ids":["https://openalex.org/I65760639"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002548887","display_name":"Elias Tsigaridas","orcid":"https://orcid.org/0009-0003-5015-3988"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"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":"Elias P. Tsigaridas","raw_affiliation_strings":["UPMC, Univ Paris, France","UPMC, Univ Paris, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UPMC, Univ Paris, France","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"UPMC, Univ Paris, France#TAB#","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5744,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89484127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"343","last_page":"350"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9807000160217285,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9715999960899353,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/univariate","display_name":"Univariate","score":0.9586248397827148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6137518882751465},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6072478890419006},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5594108700752258},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48496031761169434},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4538910388946533},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4521031081676483},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42433372139930725},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4178589880466461},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33740222454071045},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32430437207221985},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3240160346031189},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32147330045700073},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27148666977882385},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.256229966878891},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13835272192955017},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11557790637016296}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.9586248397827148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6137518882751465},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6072478890419006},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5594108700752258},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48496031761169434},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4538910388946533},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4521031081676483},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42433372139930725},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4178589880466461},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33740222454071045},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32430437207221985},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3240160346031189},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32147330045700073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27148666977882385},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.256229966878891},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13835272192955017},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11557790637016296},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2442829.2442878","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442878","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.5479","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.5479","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/77/60/74/PDF/st-rsmef.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00776074v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00776074","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"ISSAC 2012 - 37th ACM International Symposium on Symbolic and Algebraic Computation, Jul 2012, Grenoble, France. pp.343-350, ⟨10.1145/2442829.2442878⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00776074v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00776074","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"ISSAC 2012 - 37th ACM International Symposium on Symbolic and Algebraic Computation, Jul 2012, Grenoble, France. pp.343-350, ⟨10.1145/2442829.2442878⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2621858412","display_name":null,"funder_award_id":"60911130369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G354915875","display_name":null,"funder_award_id":"NSFC 60911130369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4215019062","display_name":"Calcul exact ou certifi\u00e9 avec des syst\u00e8mes alg\u00e9briques","funder_award_id":"ANR-09-BLAN-0371","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5380210879","display_name":null,"funder_award_id":"61061130540","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309928","display_name":"Aarhus Universitet","ror":"https://ror.org/01aj84f44"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320320943","display_name":"Danmarks Grundforskningsfond","ror":"https://ror.org/00znyv691"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334770","display_name":"Danish Agency for Science and Higher Education","ror":"https://ror.org/03ge1nb22"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W74955198","https://openalex.org/W278227866","https://openalex.org/W1502087103","https://openalex.org/W1506764403","https://openalex.org/W1511166374","https://openalex.org/W1516027685","https://openalex.org/W1539205156","https://openalex.org/W1552350973","https://openalex.org/W1577339277","https://openalex.org/W1664198596","https://openalex.org/W1761037128","https://openalex.org/W1964839258","https://openalex.org/W1973494154","https://openalex.org/W1990397880","https://openalex.org/W1990564835","https://openalex.org/W1997509004","https://openalex.org/W2020812938","https://openalex.org/W2025561788","https://openalex.org/W2026489546","https://openalex.org/W2032316414","https://openalex.org/W2053029682","https://openalex.org/W2067705970","https://openalex.org/W2068201416","https://openalex.org/W2073601981","https://openalex.org/W2077569399","https://openalex.org/W2077961479","https://openalex.org/W2095715976","https://openalex.org/W2099287615","https://openalex.org/W2108888104","https://openalex.org/W2128486174","https://openalex.org/W2130952444","https://openalex.org/W2134277629","https://openalex.org/W2144619406","https://openalex.org/W2151319732","https://openalex.org/W2949482817","https://openalex.org/W4212780959","https://openalex.org/W4212788863","https://openalex.org/W4285719527","https://openalex.org/W6602933805","https://openalex.org/W6629894968","https://openalex.org/W6630178116","https://openalex.org/W6632188598","https://openalex.org/W6632910055","https://openalex.org/W6637280297"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W1993992974","https://openalex.org/W1512294453","https://openalex.org/W2738234280","https://openalex.org/W2550734047","https://openalex.org/W2911841387","https://openalex.org/W2982781090","https://openalex.org/W2091797280"],"abstract_inverted_index":{"We":[0,56,128,158,167],"present":[1,129],"algorithmic,":[2],"complexity":[3,88,162],"and":[4,43,102,140,181],"implementation":[5],"results":[6],"for":[7,50],"the":[8,12,33,45,51,75,81,97,100,103,107,117,122,137,169,176],"problem":[9,123],"of":[10,15,32,78,84,89,99,106,143,156,163,175,179],"isolating":[11],"real":[13,76,82],"roots":[14,77,83],"a":[16,68,125,160],"univariate":[17,69,126,138],"polynomial":[18,70,118],"in":[19,41,48,171],"B\u03b1":[20],"\u2208":[21],"L[y],":[22],"where":[23,94],"L":[24],"=":[25,54],"Q(\u03b11,...,":[26],"\u03b1\u2113)":[27],"is":[28,92,96],"an":[29,130],"algebraic":[30],"extension":[31],"rational":[34],"numbers.":[35],"Our":[36],"bounds":[37],"are":[38,80,148],"single":[39],"exponential":[40],"\u2113":[42,53],"match":[44],"ones":[46],"presented":[47],"[34]":[49],"case":[52],"1.":[55],"consider":[57],"two":[58],"approaches.":[59],"The":[60,86,110],"first,":[61],"indirect":[62],"approach,":[63,113],"using":[64],"multivariate":[65],"resultants,":[66],"computes":[67],"with":[71],"integer":[72],"coefficients,":[73],"among":[74],"which":[79],"B\u03b1.":[85],"Boolean":[87,161],"this":[90],"approach":[91],"OB(N4\u2113+4),":[93],"N":[95],"maximum":[98],"degrees":[101],"coefficient":[104],"bitsize":[105],"involved":[108],"polynomials.":[109],"second,":[111],"direct":[112],"tries":[114],"to":[115,124],"solve":[116],"directly,":[119],"without":[120],"reducing":[121],"one.":[127],"algorithm":[131,135],"that":[132,147],"generalizes":[133],"Sturm":[134],"from":[136],"case,":[139],"modified":[141],"versions":[142],"well":[144],"known":[145],"solvers":[146],"either":[149],"numerical":[150],"or":[151],"based":[152],"on":[153],"Descartes'":[154],"rule":[155],"sign.":[157],"achieve":[159],"OB":[164],"[equation],":[165],"respectively.":[166],"implemented":[168],"algorithms":[170],"C":[172],"as":[173],"part":[174],"core":[177],"library":[178],"Mathematica":[180],"we":[182],"illustrate":[183],"their":[184],"efficiency":[185],"over":[186],"various":[187],"data":[188],"sets.":[189]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}