{"id":"https://openalex.org/W4283814913","doi":"https://doi.org/10.1145/3476446.3536185","title":"Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs","display_name":"Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4283814913","doi":"https://doi.org/10.1145/3476446.3536185"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3536185","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3476446.3536185","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3476446.3536185","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3476446.3536185","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040814649","display_name":"Sebastian Falkensteiner","orcid":"https://orcid.org/0000-0001-8701-5317"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Sebastian Falkensteiner","raw_affiliation_strings":["Johannes Kepler University, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler University, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040814649"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10005819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"63","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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":0.9993000030517578,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7570577263832092},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6419394016265869},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.574713408946991},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5627819895744324},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5121009349822998},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5010230541229248},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4981405735015869},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.48687711358070374},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.41599082946777344},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3721321225166321},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3687346577644348},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.3601554036140442},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3537002205848694}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7570577263832092},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6419394016265869},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.574713408946991},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5627819895744324},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5121009349822998},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5010230541229248},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4981405735015869},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.48687711358070374},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.41599082946777344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3721321225166321},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3687346577644348},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.3601554036140442},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3537002205848694},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3476446.3536185","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3476446.3536185","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3476446.3536185","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3476446.3536185","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3476446.3536185","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3476446.3536185","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-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/G1419670400","display_name":null,"funder_award_id":"GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1650125035","display_name":null,"funder_award_id":"B-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5805502524","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6589649124","display_name":null,"funder_award_id":"PID2020-","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283814913.pdf","grobid_xml":"https://content.openalex.org/works/W4283814913.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W93303455","https://openalex.org/W196899843","https://openalex.org/W642365271","https://openalex.org/W1541797978","https://openalex.org/W1582148746","https://openalex.org/W1983469327","https://openalex.org/W2003699415","https://openalex.org/W2014684859","https://openalex.org/W2017112157","https://openalex.org/W2027411255","https://openalex.org/W2067705970","https://openalex.org/W2124409237","https://openalex.org/W2139009791","https://openalex.org/W2159699280","https://openalex.org/W2486876072","https://openalex.org/W3037032005","https://openalex.org/W3181346485","https://openalex.org/W3199833776","https://openalex.org/W3201780710","https://openalex.org/W4206293930","https://openalex.org/W4232970652","https://openalex.org/W6959718767"],"related_works":["https://openalex.org/W4288410816","https://openalex.org/W2924426067","https://openalex.org/W586764485","https://openalex.org/W3036967699","https://openalex.org/W2128560657","https://openalex.org/W1480298971","https://openalex.org/W21216597","https://openalex.org/W1580450640","https://openalex.org/W2970232819","https://openalex.org/W2051868556"],"abstract_inverted_index":{"Given":[0],"an":[1,52],"autonomous":[2],"first":[3],"order":[4],"algebraic":[5,46],"ordinary":[6],"differential":[7,54,64],"equation":[8],"$F(y,y')=0$,":[9],"we":[10,29],"provide":[11],"algorithms":[12],"for":[13],"computing":[14],"formal":[15,58],"Puiseux":[16,59],"series":[17,60],"solutions":[18,40,61,73],"of":[19,38,51,62],"$F(y,y')=0$":[20],"with":[21],"real":[22,76],"or":[23],"rational":[24],"coefficients.":[25],"For":[26],"this":[27],"purpose":[28],"give":[30],"necessary":[31],"and":[32,48],"sufficient":[33],"conditions":[34],"on":[35],"the":[36,49,72],"existence":[37],"such":[39,63],"by":[41],"combining":[42],"classical":[43],"methods":[44],"from":[45],"geometry":[47],"study":[50],"associated":[53],"equation.":[55],"Since":[56],"all":[57],"equations":[65],"are":[66],"convergent":[67],"in":[68],"a":[69],"certain":[70],"neighborhood,":[71],"also":[74],"define":[75],"solution":[77],"functions.":[78]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
