{"id":"https://openalex.org/W2082053683","doi":"https://doi.org/10.1145/2608628.2608670","title":"On the computation of the topology of plane curves","display_name":"On the computation of the topology of plane curves","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W2082053683","doi":"https://doi.org/10.1145/2608628.2608670","mag":"2082053683"},"language":"en","primary_location":{"id":"doi:10.1145/2608628.2608670","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608670","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00935728","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060833363","display_name":"Daouda Niang Diatta","orcid":null},"institutions":[{"id":"https://openalex.org/I3133343326","display_name":"Ziguinchor University","ror":"https://ror.org/01xprs690","country_code":"SN","type":"education","lineage":["https://openalex.org/I3133343326"]}],"countries":["SN"],"is_corresponding":false,"raw_author_name":"Daouda Niang Diatta","raw_affiliation_strings":["Universit\u00e9 Assane Seck de Ziguinchor, Senegal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Assane Seck de Ziguinchor, Senegal","institution_ids":["https://openalex.org/I3133343326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016765679","display_name":"Fabrice Rouillier","orcid":"https://orcid.org/0009-0004-2972-822X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabrice Rouillier","raw_affiliation_strings":["Paris Rocquencourt, IMJ-Universit\u00e9 Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Paris Rocquencourt, IMJ-Universit\u00e9 Paris, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032403197","display_name":"Marie-Fran\u00e7oise Roy","orcid":"https://orcid.org/0000-0002-6955-6491"},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marie-Fran\u00e7oise Roy","raw_affiliation_strings":["IRMAR, Universit\u00e9 Rennes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRMAR, Universit\u00e9 Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I4210161663"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6441,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70774038,"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":"130","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9988999962806702,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/topology","display_name":"Topology (electrical circuits)","score":0.6552149057388306},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6493488550186157},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5217588543891907},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5038182139396667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49051207304000854},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.4237907826900482},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.4117621183395386},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4104045629501343},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3719356060028076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3495821952819824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3326385021209717},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31613314151763916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11883664131164551}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6552149057388306},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6493488550186157},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5217588543891907},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5038182139396667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49051207304000854},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.4237907826900482},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.4117621183395386},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4104045629501343},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3719356060028076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3495821952819824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3326385021209717},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31613314151763916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11883664131164551}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2608628.2608670","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608670","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-00935728v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00935728","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, Kobe University, Jul 2014, Kobe, Japan. pp.130-137, &#x27E8;10.1145/2608628.2608670&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00935728v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00935728","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, Kobe University, Jul 2014, Kobe, Japan. pp.130-137, &#x27E8;10.1145/2608628.2608670&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1515683204","https://openalex.org/W1562183207","https://openalex.org/W1574151794","https://openalex.org/W1966047467","https://openalex.org/W1986084578","https://openalex.org/W2005187819","https://openalex.org/W2007053866","https://openalex.org/W2025941018","https://openalex.org/W2047906192","https://openalex.org/W2054337539","https://openalex.org/W2059173068","https://openalex.org/W2061179469","https://openalex.org/W2069507832","https://openalex.org/W2075500668","https://openalex.org/W2077569399","https://openalex.org/W2080645379","https://openalex.org/W2130344412","https://openalex.org/W2130952444","https://openalex.org/W2134534233","https://openalex.org/W2139169093","https://openalex.org/W2144619406","https://openalex.org/W2151319732","https://openalex.org/W2164300104","https://openalex.org/W2165741765","https://openalex.org/W2167849855","https://openalex.org/W2397130712","https://openalex.org/W4255213956"],"related_works":["https://openalex.org/W4248744973","https://openalex.org/W4383700488","https://openalex.org/W3037015124","https://openalex.org/W3021699323","https://openalex.org/W4287780535","https://openalex.org/W1969064169","https://openalex.org/W2129100545","https://openalex.org/W2313835838","https://openalex.org/W1556007363","https://openalex.org/W4390784559"],"abstract_inverted_index":{"Let":[0],"P":[1],"\u2208":[2,13],"Z[X,":[3],"Y]":[4],"be":[5,19],"a":[6,41,84,91,96,108],"square-free":[7],"polynomial":[8],"and":[9,49,72,94],"C(P):=":[10],"{(\u03b1,":[11],"\u03b2)":[12,16],"R2,":[14],"P(\u03b1,":[15],"=":[17],"0}":[18],"the":[20,34,37,46,53,56,78,100,103],"real":[21],"algebraic":[22],"curve":[23],"defined":[24],"by":[25],"P.":[26],"Our":[27],"main":[28],"result":[29,89],"is":[30],"an":[31],"algorithm":[32,98],"for":[33,82,99],"computation":[35,101],"of":[36,43,45,52,77,102,105],"local":[38],"topology":[39,104],"in":[40,58,70,115],"neighbourhood":[42],"each":[44],"singular":[47],"points":[48,51],"critical":[50],"projection":[54],"wrt":[55],"X-axis":[57],"\u00d5(d6\u03c4+d7)":[59],"bit":[60,119],"operations":[61],"where":[62],"\u00d5":[63],"means":[64],"that":[65],"we":[66],"ignore":[67],"logarithmic":[68],"factors":[69],"d":[71],"\u03c4.":[73],"Compared":[74],"to":[75,113],"state":[76],"art":[79],"sub-algorithms":[80],"used":[81],"computing":[83],"Cylindrical":[85],"Algebraic":[86],"Decomposition,":[87],"this":[88],"avoids":[90],"generic":[92],"shear":[93],"gives":[95],"deterministic":[97],"C(P)":[106,114],"i.e":[107],"straight-line":[109],"planar":[110],"graph":[111],"isotopic":[112],"\u00d5(d6\u03c4":[116],"+":[117],"d7)":[118],"operations.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
