{"id":"https://openalex.org/W2073509058","doi":"https://doi.org/10.1145/1993886.1993897","title":"Virtual roots of a real polynomial and fractional derivatives","display_name":"Virtual roots of a real polynomial and fractional derivatives","publication_year":2011,"publication_date":"2011-06-08","ids":{"openalex":"https://openalex.org/W2073509058","doi":"https://doi.org/10.1145/1993886.1993897","mag":"2073509058"},"language":"en","primary_location":{"id":"doi:10.1145/1993886.1993897","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993897","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":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00559950","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086171905","display_name":"Daniel Bemb\u00e9","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Bemb\u00e9","raw_affiliation_strings":["der Universitat Munchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"der Universitat Munchen, Munich, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111902088","display_name":"Andr\u00e9 Galligo","orcid":null},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Galligo","raw_affiliation_strings":["Universite de Nice-Sophia Antipolis, NiceMunic, France","Geometry, algebra, algorithms"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universite de Nice-Sophia Antipolis, NiceMunic, France","institution_ids":["https://openalex.org/I201841394"]},{"raw_affiliation_string":"Geometry, algebra, algorithms","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8621,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.89939638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"27","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/maple","display_name":"Maple","score":0.6653120517730713},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6026251316070557},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6020359992980957},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5643552541732788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5150639414787292},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.4327374994754791},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3688061237335205},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34615784883499146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2833741307258606},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.15807506442070007},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15760576725006104},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08586233854293823},{"id":"https://openalex.org/keywords/botany","display_name":"Botany","score":0.06685560941696167},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.06429335474967957}],"concepts":[{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.6653120517730713},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6026251316070557},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6020359992980957},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5643552541732788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5150639414787292},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.4327374994754791},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3688061237335205},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34615784883499146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2833741307258606},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.15807506442070007},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15760576725006104},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08586233854293823},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.06685560941696167},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.06429335474967957},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1993886.1993897","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993897","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:HAL:hal-00559950v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00559950","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":"International Symposium on Symbolic and Algebraic Computation (ISSAC), Jun 2011, San Jose, United States. pp.27-34, ⟨10.1145/1993886.1993897⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00559950v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00559950","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":"International Symposium on Symbolic and Algebraic Computation (ISSAC), Jun 2011, San Jose, United States. pp.27-34, ⟨10.1145/1993886.1993897⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1539838732","https://openalex.org/W1571014766","https://openalex.org/W2013542024","https://openalex.org/W2020175124","https://openalex.org/W2027460976","https://openalex.org/W2034972350","https://openalex.org/W2144292545","https://openalex.org/W2593708767","https://openalex.org/W2970144644","https://openalex.org/W3135774276"],"related_works":["https://openalex.org/W2030498341","https://openalex.org/W2348840575","https://openalex.org/W3122841410","https://openalex.org/W2046205453","https://openalex.org/W2770017172","https://openalex.org/W89977309","https://openalex.org/W2183901182","https://openalex.org/W2030930882","https://openalex.org/W2204614510","https://openalex.org/W3005618458"],"abstract_inverted_index":{"After":[0],"the":[1,17,41,55,64,70,76,95],"works":[2],"of":[3,9,20,43,50,59,73,82],"Gonzales-Vega,":[4],"Lombardi,":[5,12],"Mahe":[6],"[11],":[7],"and":[8,57,79,91],"Coste,":[10],"Lajous,":[11],"Roy":[13],"[6],":[14],"we":[15,31,53],"consider":[16],"virtual":[18,71],"roots":[19,72],"a":[21,35],"univariate":[22],"polynomial":[23,37],"f":[24,34,74],"with":[25,89,94],"real":[26],"coefficients.":[27],"Using":[28],"fractional":[29],"derivatives,":[30],"associate":[32],"to":[33,68],"bivariate":[36],"P(x,t)":[38],"depending":[39],"on":[40,75,80],"choice":[42],"an":[44],"origin":[45],"a,":[46],"then":[47],"two":[48],"type":[49],"plan":[51],"curves":[52],"call":[54],"FDcurve":[56],"stem":[58],"f.":[60],"We":[61],"show,":[62],"in":[63],"generic":[65],"case,":[66],"how":[67],"locate":[69],"Budan":[77],"table":[78],"each":[81],"these":[83],"curves.":[84],"The":[85],"paper":[86],"is":[87],"illustrated":[88],"examples":[90],"pictures":[92],"computed":[93],"computer":[96],"algebra":[97],"system":[98],"Maple.":[99]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}