{"id":"https://openalex.org/W4382927847","doi":"https://doi.org/10.1007/s10472-023-09856-z","title":"Design and implementation of symbolic algorithms for the computation of generalized asymptotes","display_name":"Design and implementation of symbolic algorithms for the computation of generalized asymptotes","publication_year":2023,"publication_date":"2023-07-03","ids":{"openalex":"https://openalex.org/W4382927847","doi":"https://doi.org/10.1007/s10472-023-09856-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10472-023-09856-z","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10472-023-09856-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10472-023-09856-z.pdf","source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10472-023-09856-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080554574","display_name":"Mari\u00e1n Fern\u00e1ndez de Sevilla","orcid":"https://orcid.org/0000-0002-0630-1141"},"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":"Mari\u00e1n Fern\u00e1ndez de Sevilla","raw_affiliation_strings":["University of Alcal\u00e1, Department of Computer Science, Ctra. Madrid-Barcelona, km.33,6, Alcal\u00e1 de Henares, 28871, Madrid, Spain","University of Alcal\u00e1, Department of Computer Science, Alcal\u00e1 de Henares, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0630-1141","affiliations":[{"raw_affiliation_string":"University of Alcal\u00e1, Department of Computer Science, Ctra. Madrid-Barcelona, km.33,6, Alcal\u00e1 de Henares, 28871, Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]},{"raw_affiliation_string":"University of Alcal\u00e1, Department of Computer Science, Alcal\u00e1 de Henares, Spain","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013174077","display_name":"Rafael Magdalena\u2010Benedito","orcid":"https://orcid.org/0000-0003-3752-8231"},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael Magdalena Benedicto","raw_affiliation_strings":["Department of Electronic Engineering, University of Valencia, Av. Universidades s/n, Burjassot, 46100, Valencia, Spain","Department of Electronic Engineering, University of Valencia, Burjassot, Spain"],"raw_orcid":"https://orcid.org/0000-0003-3752-8231","affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, University of Valencia, Av. Universidades s/n, Burjassot, 46100, Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Department of Electronic Engineering, University of Valencia, Burjassot, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031696800","display_name":"Sonia P\u00e9rez-D\u0131\u0301az","orcid":"https://orcid.org/0000-0002-0174-5325"},"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":"Sonia P\u00e9rez-D\u00edaz","raw_affiliation_strings":["University of Alcal\u00e1, Department of Physics and Mathematics, Ctra. Madrid-Barcelona, km.33,6, Alcal\u00e1 de Henares, 28871, Madrid, Spain","University of Alcal\u00e1, Department of Physics and Mathematics, Alcal\u00e1 de Henares, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0174-5325","affiliations":[{"raw_affiliation_string":"University of Alcal\u00e1, Department of Physics and Mathematics, Ctra. Madrid-Barcelona, km.33,6, Alcal\u00e1 de Henares, 28871, Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]},{"raw_affiliation_string":"University of Alcal\u00e1, Department of Physics and Mathematics, Alcal\u00e1 de Henares, Spain","institution_ids":["https://openalex.org/I189268942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031696800"],"corresponding_institution_ids":["https://openalex.org/I189268942"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.2071,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45300432,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"91","issue":"4","first_page":"537","last_page":"561"},"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":0.9980000257492065,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9724000096321106,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/asymptote","display_name":"Asymptote","score":0.8987460732460022},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6777894496917725},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36691778898239136},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3606675863265991},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3345091938972473},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2595124840736389}],"concepts":[{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.8987460732460022},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6777894496917725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36691778898239136},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3606675863265991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3345091938972473},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2595124840736389}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10472-023-09856-z","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10472-023-09856-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10472-023-09856-z.pdf","source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:ebuah.uah.es:10017/57923","is_oa":true,"landing_page_url":"http://hdl.handle.net/10017/57923","pdf_url":"https://ebuah.uah.es/dspace/bitstream/10017/57923/2/Design_Fernandez_Ann_Math_Artif_Intell_2023.pdf","source":{"id":"https://openalex.org/S7407055200","display_name":"e_Buah","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s10472-023-09856-z","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10472-023-09856-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10472-023-09856-z.pdf","source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1287161024","display_name":null,"funder_award_id":"PID2020-113192GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G394450247","display_name":null,"funder_award_id":"PID2020-113192GB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G4668947194","display_name":null,"funder_award_id":"PID2021-127946OB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5135626188","display_name":null,"funder_award_id":"PID2021-127946OB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6731524417","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G7840447800","display_name":null,"funder_award_id":"CCEE2011/R34","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8552110872","display_name":null,"funder_award_id":"101100728","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4382927847.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1969941084","https://openalex.org/W1995985203","https://openalex.org/W2002016471","https://openalex.org/W2007876024","https://openalex.org/W2019307524","https://openalex.org/W2024239067","https://openalex.org/W2042712358","https://openalex.org/W2486876072","https://openalex.org/W2919115771","https://openalex.org/W2963643668","https://openalex.org/W3106448918","https://openalex.org/W4221084075","https://openalex.org/W4367180606"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2352240723","https://openalex.org/W2587369532","https://openalex.org/W3110746766","https://openalex.org/W4230779047","https://openalex.org/W2268640537","https://openalex.org/W2051260552","https://openalex.org/W139824870","https://openalex.org/W2052734696","https://openalex.org/W83911077"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,151,195,203],"paper":[3,196],"we":[4,153],"present":[5],"two":[6],"algorithms":[7,141,164,185,241],"for":[8],"computing":[9],"the":[10,44,80,90,116,147,155,163,173,181,184,220,223,226,243],"g-asymptotes":[11,132],"or":[12,29,133,207,239],"generalized":[13,134],"asymptotes":[14,33,135],",":[15,27],"of":[16,34,46,66,118,139,162,172,183,222],"a":[17,35,67,76,100,198,212,231],"plane":[18],"algebraic":[19],"curve,":[20],"$$\\mathscr":[21,37,47,69,83,102,119],"{C}$$":[22,38,48,70,84,103,120],"<mml:math":[23,39,49,71,85,104,121],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[24,40,50,72,86,105,122],"<mml:mi>C</mml:mi>":[25,41,51,73,87,106,123],"</mml:math>":[26,42,52,74,88,107,124],"implicitly":[28],"parametrically":[30],"defined.":[31],"The":[32,137,191],"curve":[36,68,101],"reflect":[43],"status":[45,117],"at":[53,125],"points":[54],"with":[55],"sufficiently":[56],"large":[57],"coordinates.":[58],"It":[59],"is":[60,75,165],"well":[61,145,216],"known":[62,130],"that":[63,79],"an":[64],"asymptote":[65],"line":[77,91],"such":[78],"distance":[81],"between":[82],"and":[89,176,186,233],"approaches":[92],"zero":[93],"as":[94,131,144,146,215,217],"they":[95],"tend":[96],"to":[97,179,187,201,205,208,218],"infinity.":[98,126],"However,":[99],"may":[108],"have":[109],"more":[110],"general":[111],"curves":[112,128,175,209],"than":[113],"lines":[114],"describing":[115],"These":[127],"are":[129,142,197],".":[136,158],"pseudocodes":[138],"these":[140],"presented,":[143],"corresponding":[148],"implementations.":[149],"For":[150],"purpose,":[152],"use":[154],"algebra":[156],"software":[157],"A":[159],"comparative":[160,189],"analysis":[161],"carried":[166],"out,":[167],"based":[168],"on":[169],"some":[170],"properties":[171],"input":[174],"their":[177],"results":[178,192],"analyze":[180],"efficiency":[182,221],"establish":[188],"criteria.":[190],"presented":[193],"in":[194,236,242],"starting":[199],"point":[200],"generalize":[202],"study":[204],"surfaces":[206],"defined":[210],"by":[211],"non-rational":[213],"parametrization,":[214],"improve":[219],"algorithms.":[224],"Additionally,":[225],"methods":[227],"developed":[228],"can":[229],"provide":[230],"new":[232],"different":[234],"approach":[235],"prediction":[237],"(regression)":[238],"classification":[240],"machine":[244],"learning":[245],"field.":[246]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}
