{"id":"https://openalex.org/W2070693439","doi":"https://doi.org/10.1145/1145768.1145818","title":"A note on implicitization and normal parametrization of rational curves","display_name":"A note on implicitization and normal parametrization of rational curves","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W2070693439","doi":"https://doi.org/10.1145/1145768.1145818","mag":"2070693439"},"language":"en","primary_location":{"id":"doi:10.1145/1145768.1145818","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 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/A5062690475","display_name":"Rosario Rubio","orcid":"https://orcid.org/0000-0002-1525-3436"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rosario Rubio","raw_affiliation_strings":["Industrial Universidad Antonio, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Industrial Universidad Antonio, Madrid, Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022604635","display_name":"Jos\u00e9 Miguel Serradilla-Merinero","orcid":"https://orcid.org/0000-0002-8140-1169"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Miguel Serradilla","raw_affiliation_strings":["Industrial Universidad Antonio, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Industrial Universidad Antonio, Madrid, Spain","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010034022","display_name":"M. Pilar V\u00e9lez","orcid":"https://orcid.org/0000-0002-5724-4300"},"institutions":[{"id":"https://openalex.org/I4210134847","display_name":"Centro Tecnol\u00f3gico de Investigaci\u00f3n, Desarrollo e Innovaci\u00f3n en tecnolog\u00edas de la Informaci\u00f3n y las Comunicaciones (TIC)","ror":"https://ror.org/02s69db58","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I4210134847"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Pilar V\u00e9lez","raw_affiliation_strings":["Inform\u00e1tica Universidad, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Inform\u00e1tica Universidad, Madrid, Spain","institution_ids":["https://openalex.org/I4210134847"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062690475"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4116,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.65751388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"296","issue":null,"first_page":"306","last_page":"309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9973999857902527,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9894000291824341,"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/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.891840934753418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5956708192825317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5280227065086365},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3687714636325836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3554455637931824},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33544671535491943},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32276904582977295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11277168989181519}],"concepts":[{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.891840934753418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5956708192825317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5280227065086365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3687714636325836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3554455637931824},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33544671535491943},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32276904582977295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11277168989181519},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1145768.1145818","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 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":18,"referenced_works":["https://openalex.org/W23879940","https://openalex.org/W1486147404","https://openalex.org/W1939915063","https://openalex.org/W1971343670","https://openalex.org/W1984258784","https://openalex.org/W2022637219","https://openalex.org/W2064044318","https://openalex.org/W2079392836","https://openalex.org/W2082714069","https://openalex.org/W2086855586","https://openalex.org/W2114788602","https://openalex.org/W2139009791","https://openalex.org/W2232657515","https://openalex.org/W2406129278","https://openalex.org/W2490484610","https://openalex.org/W2500071694","https://openalex.org/W2612686320","https://openalex.org/W4234682643"],"related_works":["https://openalex.org/W2153421756","https://openalex.org/W4239315977","https://openalex.org/W2054489697","https://openalex.org/W2077818434","https://openalex.org/W2361081803","https://openalex.org/W2036241269","https://openalex.org/W2109057766","https://openalex.org/W4250375811","https://openalex.org/W2078644396","https://openalex.org/W2026930022"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper":[2],"we":[3,41,53,67],"present":[4],"a":[5,12,55,60,69],"method":[6,26,34],"to":[7,57],"compute":[8,68],"an":[9,17,21],"implicitization":[10],"of":[11,31,49],"rational":[13],"parametrized":[14],"curve":[15],"in":[16],"affine":[18],"space":[19],"over":[20],"algebraically":[22],"closed":[23],"field.":[24],"This":[25],"is":[27,62],"the":[28,32,47,50],"natural":[29],"generalization":[30],"resultant":[33],"for":[35],"planar":[36],"curves.":[37],"For":[38],"purpose":[40],"need":[42],"some":[43],"normality":[44],"assumptions":[45],"on":[46],"parametrization":[48,61],"curve.":[51],"Furthermore,":[52],"provide":[54],"test":[56],"decide":[58],"whether":[59],"normal":[63,70],"and":[64],"if":[65],"not,":[66],"parametrization.":[71]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2025-10-10T00:00:00"}