{"id":"https://openalex.org/W2809606640","doi":"https://doi.org/10.1145/3208976.3209004","title":"On Continuity of the Roots of a Parametric Zero Dimensional Multivariate Polynomial Ideal","display_name":"On Continuity of the Roots of a Parametric Zero Dimensional Multivariate Polynomial Ideal","publication_year":2018,"publication_date":"2018-07-11","ids":{"openalex":"https://openalex.org/W2809606640","doi":"https://doi.org/10.1145/3208976.3209004","mag":"2809606640"},"language":"en","primary_location":{"id":"doi:10.1145/3208976.3209004","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3208976.3209004","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":"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/A5050208307","display_name":"Yosuke Sato","orcid":"https://orcid.org/0000-0002-2772-2332"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yosuke Sato","raw_affiliation_strings":["Tokyo University of Science, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo University of Science, Tokyo, Japan","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046742707","display_name":"Ryoya Fukasaku","orcid":null},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryoya Fukasaku","raw_affiliation_strings":["Tokyo University of Science, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo University of Science, Tokyo, Japan","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021311433","display_name":"Hiroshi Sekigawa","orcid":"https://orcid.org/0009-0003-1770-0994"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Sekigawa","raw_affiliation_strings":["Tokyo University of Science, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo University of Science, Tokyo, Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050208307"],"corresponding_institution_ids":["https://openalex.org/I161296585"],"apc_list":null,"apc_paid":null,"fwci":0.6058,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69762075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8592","issue":null,"first_page":"359","last_page":"365"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9958000183105469,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/zero","display_name":"Zero (linguistics)","score":0.7616511583328247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.697145402431488},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.669695258140564},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6257702708244324},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5890867710113525},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5409444570541382},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.41501322388648987},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32125163078308105},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.3095654547214508},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.2586440443992615},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2388904094696045}],"concepts":[{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.7616511583328247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.697145402431488},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.669695258140564},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6257702708244324},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5890867710113525},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5409444570541382},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.41501322388648987},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32125163078308105},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3095654547214508},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.2586440443992615},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2388904094696045},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3208976.3209004","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3208976.3209004","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W3002826","https://openalex.org/W105797038","https://openalex.org/W1570787829","https://openalex.org/W1988004808","https://openalex.org/W1990119084","https://openalex.org/W2028158012","https://openalex.org/W2045154989","https://openalex.org/W2103185909","https://openalex.org/W2187852886","https://openalex.org/W2897961174","https://openalex.org/W3007626758","https://openalex.org/W4292096448"],"related_works":["https://openalex.org/W2044942888","https://openalex.org/W2018038902","https://openalex.org/W2010647489","https://openalex.org/W2078605119","https://openalex.org/W2361047409","https://openalex.org/W2002780414","https://openalex.org/W1481263923","https://openalex.org/W1997153034","https://openalex.org/W2052795968","https://openalex.org/W2018314172"],"abstract_inverted_index":{"Let":[0,54],"F=":[1],"f1(A,":[2],"X),...,fl(A,":[3],"X)":[4,52,88],"be":[5,59],"a":[6,30,34,60,73,77,95,105],"finite":[7],"set":[8],"of":[9,23,31,36,44,64,76,111,137,145],"polynomials":[10],"in":[11],"Q[A,":[12],"X]":[13],"with":[14],"variables":[15],"A=A1,...,Am":[16],"and":[17,108],"X=X1,...,Xn.":[18],"We":[19],"study":[20],"the":[21,24,42,45,82,109,135,146],"continuity":[22],"map":[25],"\u03b8":[26,126],"from":[27],"an":[28,138],"element":[29],"Cm":[32],"to":[33],"subset":[35],"Cn":[37],"defined":[38],"by":[39],"\u03b8(a)=":[40],"\"":[41],"zeros":[43],"polynomial":[46],"ideal":[47,83],"<":[48,65,84],"f1(a,":[49,85],"X),...,":[50,86],"fl(a,":[51,87],">\".":[53],"G=(G1,":[55],"S1),...,":[56],"(Gk,":[57],"Sk)":[58],"comprehensive":[61,78],"Gr\u00f6bner":[62,79],"system":[63],"F":[66],">":[67,89],"regarding":[68],"A":[69],"as":[70],"parameters.":[71],"By":[72],"basic":[74],"property":[75],"system,":[80],"when":[81],"is":[90,99,113,127],"zero":[91,101],"dimensional":[92,102],"for":[93,103,140],"some":[94],"\u0131n":[96,106],"Si,":[97],"it":[98],"also":[100,128],"any":[104],"Si":[107,116],"cardinality":[110],"\u03b8(a)":[112],"identical":[114],"on":[115,130],"counting":[117],"their":[118],"multiplicities.":[119],"In":[120],"this":[121],"paper,":[122],"we":[123],"prove":[124],"that":[125],"continuous":[129],"Si.":[131],"Our":[132],"result":[133],"ensures":[134],"correctness":[136],"algorithm":[139],"real":[141],"quantifier":[142],"elimination":[143],"one":[144],"authors":[147],"has":[148],"recently":[149],"developed.":[150]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
