{"id":"https://openalex.org/W4383221770","doi":"https://doi.org/10.1145/3597066.3597107","title":"On Isolating Roots in a Multiple Field Extension","display_name":"On Isolating Roots in a Multiple Field Extension","publication_year":2023,"publication_date":"2023-07-05","ids":{"openalex":"https://openalex.org/W4383221770","doi":"https://doi.org/10.1145/3597066.3597107"},"language":"en","primary_location":{"id":"doi:10.1145/3597066.3597107","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3597066.3597107","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04116621/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036559688","display_name":"Christina Katsamaki","orcid":"https://orcid.org/0000-0002-3177-010X"},"institutions":[{"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":true,"raw_author_name":"Christina Katsamaki","raw_affiliation_strings":["INRIA Paris, Sorbonne Universit\u00e9 and Paris Universit\u00e9, France"],"raw_orcid":"https://orcid.org/0000-0002-3177-010X","affiliations":[{"raw_affiliation_string":"INRIA Paris, Sorbonne Universit\u00e9 and Paris Universit\u00e9, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016765679","display_name":"Fabrice Rouillier","orcid":"https://orcid.org/0009-0004-2972-822X"},"institutions":[{"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":"Fabrice Rouillier","raw_affiliation_strings":["INRIA Paris, Sorbonne Universit\u00e9 and Paris Universit\u00e9, France"],"raw_orcid":"https://orcid.org/0009-0004-2972-822X","affiliations":[{"raw_affiliation_string":"INRIA Paris, Sorbonne Universit\u00e9 and Paris Universit\u00e9, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036559688"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13811073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"363","last_page":"371"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.8692890405654907},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6387019157409668},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6287747621536255},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5688532590866089},{"id":"https://openalex.org/keywords/field-extension","display_name":"Field extension","score":0.5688481330871582},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4990389347076416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4962828755378723},{"id":"https://openalex.org/keywords/isolation","display_name":"Isolation (microbiology)","score":0.487710565328598},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.451994925737381},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3804127275943756},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35913652181625366},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16804033517837524},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08329230546951294},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07884609699249268},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.056877970695495605}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8692890405654907},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6387019157409668},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6287747621536255},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5688532590866089},{"id":"https://openalex.org/C103738662","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Field extension","level":3,"score":0.5688481330871582},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4990389347076416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4962828755378723},{"id":"https://openalex.org/C2775941552","wikidata":"https://www.wikidata.org/wiki/Q25212305","display_name":"Isolation (microbiology)","level":2,"score":0.487710565328598},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.451994925737381},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3804127275943756},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35913652181625366},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16804033517837524},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08329230546951294},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07884609699249268},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.056877970695495605},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C89423630","wikidata":"https://www.wikidata.org/wiki/Q7193","display_name":"Microbiology","level":1,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3597066.3597107","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3597066.3597107","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-04116621v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04116621","pdf_url":"https://hal.science/hal-04116621/document","source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC '23: 2023 International Symposium on Symbolic and Algebraic Computation, Jul 2023, Tromso, Norway. pp.363-371, &#x27E8;10.1145/3597066.3597107&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04116621v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04116621","pdf_url":"https://hal.science/hal-04116621/document","source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC '23: 2023 International Symposium on Symbolic and Algebraic Computation, Jul 2023, Tromso, Norway. pp.363-371, &#x27E8;10.1145/3597066.3597107&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4383221770.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1502087103","https://openalex.org/W1990397880","https://openalex.org/W1992962227","https://openalex.org/W2024331629","https://openalex.org/W2026489546","https://openalex.org/W2048847637","https://openalex.org/W2053029682","https://openalex.org/W2054337539","https://openalex.org/W2059173068","https://openalex.org/W2068201416","https://openalex.org/W2072205301","https://openalex.org/W2134534233","https://openalex.org/W2144619406","https://openalex.org/W2245029098","https://openalex.org/W2344308227","https://openalex.org/W2475226043","https://openalex.org/W2618948979","https://openalex.org/W2626508605","https://openalex.org/W2941649468","https://openalex.org/W2963548828","https://openalex.org/W3036763234","https://openalex.org/W4289420046"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W2911841387","https://openalex.org/W2803255289","https://openalex.org/W1512294453","https://openalex.org/W1993992974","https://openalex.org/W2053002746","https://openalex.org/W4246881104","https://openalex.org/W2347268433"],"abstract_inverted_index":{"We":[0,15,31],"address":[1],"univariate":[2],"root":[3],"isolation":[4],"when":[5],"the":[6,43],"polynomial\u2019s":[7],"coefficients":[8],"are":[9],"in":[10],"a":[11,17,25],"multiple":[12,26],"field":[13],"extension.":[14],"consider":[16],"polynomial":[18],"F":[19,36],"\u2208":[20],"L[Y],":[21],"where":[22],"L":[23],"is":[24],"algebraic":[27],"extension":[28],"of":[29,45],".":[30],"provide":[32],"aggregate":[33],"bounds":[34],"for":[35,42],"and":[37,39],"algorithmic":[38],"bit-complexity":[40],"results":[41],"problem":[44],"isolating":[46],"its":[47],"roots.":[48]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
