{"id":"https://openalex.org/W2793471795","doi":"https://doi.org/10.1142/s0218196718500194","title":"The square-freeness of the offset equation to a rational planar curve, computed via resultants","display_name":"The square-freeness of the offset equation to a rational planar curve, computed via resultants","publication_year":2018,"publication_date":"2018-03-19","ids":{"openalex":"https://openalex.org/W2793471795","doi":"https://doi.org/10.1142/s0218196718500194","mag":"2793471795"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500194","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500194","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5041883278","display_name":"Juan Gerardo Alc\u00e1zar","orcid":"https://orcid.org/0000-0002-1665-9710"},"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":"Juan Gerardo Alc\u00e1zar","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, E-28871 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, E-28871 Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008199804","display_name":"Jorge Caravantes","orcid":"https://orcid.org/0000-0001-9550-2481"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jorge Caravantes","raw_affiliation_strings":["Departamento de \u00c1lgebra, Universidad Complutense de Madrid, E-28040 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de \u00c1lgebra, Universidad Complutense de Madrid, E-28040 Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039054074","display_name":"Gema M. Diaz\u2013Toca","orcid":"https://orcid.org/0000-0001-8652-4312"},"institutions":[{"id":"https://openalex.org/I80180929","display_name":"Universidad de Murcia","ror":"https://ror.org/03p3aeb86","country_code":"ES","type":"education","lineage":["https://openalex.org/I80180929"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gema M. Diaz\u2013Toca","raw_affiliation_strings":["Departamento de Ingenier\u00eda y Tecnolog\u00eda, de Computadores, Universidad de Murcia, E-30100 Murcia, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda y Tecnolog\u00eda, de Computadores, Universidad de Murcia, E-30100 Murcia, Spain","institution_ids":["https://openalex.org/I80180929"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041883278"],"corresponding_institution_ids":["https://openalex.org/I189268942"],"apc_list":null,"apc_paid":null,"fwci":0.2027,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47286013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"03","first_page":"395","last_page":"409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9814000129699707,"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":0.9444000124931335,"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/mathematics","display_name":"Mathematics","score":0.830687940120697},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6391716003417969},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.5769570469856262},{"id":"https://openalex.org/keywords/offset","display_name":"Offset (computer science)","score":0.5761349201202393},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.5223332643508911},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47771358489990234},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.47409045696258545},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.4719333350658417},{"id":"https://openalex.org/keywords/irreducible-component","display_name":"Irreducible component","score":0.43684279918670654},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39019647240638733},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36769235134124756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07791784405708313}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.830687940120697},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6391716003417969},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.5769570469856262},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.5761349201202393},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.5223332643508911},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47771358489990234},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.47409045696258545},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4719333350658417},{"id":"https://openalex.org/C54654531","wikidata":"https://www.wikidata.org/wiki/Q6073574","display_name":"Irreducible component","level":5,"score":0.43684279918670654},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39019647240638733},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36769235134124756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07791784405708313},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"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/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196718500194","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500194","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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":15,"referenced_works":["https://openalex.org/W1532721371","https://openalex.org/W1911628721","https://openalex.org/W1977395304","https://openalex.org/W1988973985","https://openalex.org/W1997387407","https://openalex.org/W2026138521","https://openalex.org/W2030113803","https://openalex.org/W2053958920","https://openalex.org/W2065148335","https://openalex.org/W2066253548","https://openalex.org/W2070076125","https://openalex.org/W2088782186","https://openalex.org/W2486876072","https://openalex.org/W4206293930","https://openalex.org/W4241628619"],"related_works":["https://openalex.org/W2550122689","https://openalex.org/W2051712499","https://openalex.org/W1498993739","https://openalex.org/W1647114756","https://openalex.org/W3197207566","https://openalex.org/W2080290915","https://openalex.org/W1967787874","https://openalex.org/W2072691921","https://openalex.org/W2054981054","https://openalex.org/W2030471012"],"abstract_inverted_index":{"It":[0],"is":[1,53,119,125,165,169,179,185,222],"well":[2,55],"known":[3,56],"[Algebraic":[4,75],"properties":[5],"of":[6,21,37,40,48,66,77,94,102,142,176,205,225],"plane":[7],"offset":[8,23,108,144,204,224],"curves,":[9],"Comput.":[10],"Aided":[11],"Geom.":[12],"Des.":[13],"7":[14],"(1990)":[15],"101\u2013127]":[16],"that":[17,57,99,134],"an":[18],"implicit":[19,59],"equation":[20,60],"the":[22,34,38,46,49,58,63,91,100,103,107,117,123,130,143,149,153,163,173,177,203,223],"to":[24,79,106,138,152,187,198],"a":[25,139,195,206,211,218],"rational":[26,208,220],"planar":[27],"curve":[28,124,209,221],"can":[29,109],"be":[30,110,188],"computed":[31,44,111],"by":[32,62,97,129],"removing":[33],"extraneous":[35],"components":[36],"resultant":[39,68,96,178],"two":[41,72],"certain":[42],"polynomials":[43],"from":[45],"parametrization":[47,118,164],"curve.":[50,227],"Furthermore,":[51],"it":[52],"also":[54,189],"provided":[61],"nonextraneous":[64,174],"component":[65,141],"this":[67,87,95,183,192],"has":[69,145,158,210],"at":[70],"most":[71],"irreducible":[73],"factors":[74,104],"analysis":[76],"offsets":[78],"hypersurfaces,":[80],"Math.":[81],"Z.":[82],"234":[83],"(2000)":[84],"697\u2013719].":[85],"In":[86,114,181],"paper,":[88],"we":[89,132],"complete":[90],"algebraic":[92],"description":[93],"showing":[98],"multiplicity":[101,146,159],"corresponding":[105,137,151],"in":[112,215],"advance.":[113],"particular,":[115],"when":[116,122],"proper,":[120],"i.e.":[121],"just":[126],"traced":[127],"once":[128],"parametrization,":[131],"prove":[133],"any":[135],"factor":[136,150],"simple":[140,196],"1,":[147],"while":[148],"special":[154,171,212],"component,":[155,172,213],"if":[156,162],"any,":[157],"2.":[160],"Hence,":[161],"proper":[166],"and":[167,214],"there":[168],"no":[170],"part":[175],"square-free.":[180],"fact,":[182],"condition":[184],"proven":[186],"sufficient.":[190],"Therefore,":[191],"result":[193],"provides":[194],"test":[197],"check":[199],"whether":[200,217],"or":[201],"not":[202],"given":[207,219],"turn,":[216],"another":[226]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}