{"id":"https://openalex.org/W2071390560","doi":"https://doi.org/10.1016/s0167-8396(01)00033-4","title":"Using polynomial interpolation for implicitizing algebraic curves","display_name":"Using polynomial interpolation for implicitizing algebraic curves","publication_year":2001,"publication_date":"2001-05-01","ids":{"openalex":"https://openalex.org/W2071390560","doi":"https://doi.org/10.1016/s0167-8396(01)00033-4","mag":"2071390560"},"language":"en","primary_location":{"id":"doi:10.1016/s0167-8396(01)00033-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-8396(01)00033-4","pdf_url":null,"source":{"id":"https://openalex.org/S135221619","display_name":"Computer Aided Geometric Design","issn_l":"0167-8396","issn":["0167-8396","1879-2332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Aided Geometric Design","raw_type":"journal-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/A5080907582","display_name":"Ana Marco","orcid":"https://orcid.org/0000-0003-4662-6327"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Marco","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares, Madrid, Spain","Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares (Madrid), Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares, Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares (Madrid), Spain#TAB#","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052327276","display_name":"Jos\u00e9\u2010Javier Mart\u00ednez","orcid":"https://orcid.org/0000-0002-8322-0361"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J.J. Mart\u0131\u0301nez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares, Madrid, Spain","Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares (Madrid), Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares, Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Alcal\u00e1, Campus Universitario, 28871-Alcal\u00e1 de Henares (Madrid), Spain#TAB#","institution_ids":["https://openalex.org/I189268942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052327276"],"corresponding_institution_ids":["https://openalex.org/I189268942"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.8184,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.85048124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"18","issue":"4","first_page":"309","last_page":"319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9965999722480774,"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":0.9965999722480774,"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":0.9961000084877014,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9599999785423279,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.804155707359314},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.626103401184082},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6246904730796814},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.5598670244216919},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5514397621154785},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.5414156913757324},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5292862057685852},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4800587594509125},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4661952555179596},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4646470248699188},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.4304271936416626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.325980544090271},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.2867647707462311},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23791125416755676},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2379070520401001},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22871911525726318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0979354977607727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.804155707359314},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.626103401184082},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6246904730796814},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.5598670244216919},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5514397621154785},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.5414156913757324},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5292862057685852},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4800587594509125},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4661952555179596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4646470248699188},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4304271936416626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.325980544090271},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.2867647707462311},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23791125416755676},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2379070520401001},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22871911525726318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0979354977607727},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0167-8396(01)00033-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-8396(01)00033-4","pdf_url":null,"source":{"id":"https://openalex.org/S135221619","display_name":"Computer Aided Geometric Design","issn_l":"0167-8396","issn":["0167-8396","1879-2332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Aided Geometric Design","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W145541016","https://openalex.org/W1483218536","https://openalex.org/W1488435683","https://openalex.org/W1551207461","https://openalex.org/W1964673636","https://openalex.org/W1968699543","https://openalex.org/W1971343670","https://openalex.org/W2007778702","https://openalex.org/W2020298878","https://openalex.org/W2026722217","https://openalex.org/W2049773063","https://openalex.org/W2055481061","https://openalex.org/W2057531663","https://openalex.org/W2079392836","https://openalex.org/W2316418224","https://openalex.org/W2530332639","https://openalex.org/W2798909945","https://openalex.org/W2923935037","https://openalex.org/W4205491081","https://openalex.org/W4206360718","https://openalex.org/W4234741915","https://openalex.org/W4244681853","https://openalex.org/W6642542717"],"related_works":["https://openalex.org/W2030471012","https://openalex.org/W2051712499","https://openalex.org/W2550122689","https://openalex.org/W1498993739","https://openalex.org/W1647114756","https://openalex.org/W1967787874","https://openalex.org/W1525419764","https://openalex.org/W4245708675","https://openalex.org/W285356538","https://openalex.org/W2031947084"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
