{"id":"https://openalex.org/W4400648518","doi":"https://doi.org/10.1145/3666000.3669707","title":"Liouvillian Solutions of Third Order Differential Equations","display_name":"Liouvillian Solutions of Third Order Differential Equations","publication_year":2024,"publication_date":"2024-07-15","ids":{"openalex":"https://openalex.org/W4400648518","doi":"https://doi.org/10.1145/3666000.3669707"},"language":"en","primary_location":{"id":"doi:10.1145/3666000.3669707","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669707","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2024 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/A5034609451","display_name":"Thierry Combot","orcid":"https://orcid.org/0000-0003-3488-1291"},"institutions":[{"id":"https://openalex.org/I177064439","display_name":"Universit\u00e9 de Bourgogne","ror":"https://ror.org/03k1bsr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I177064439"]},{"id":"https://openalex.org/I4210112333","display_name":"Institut de Math\u00e9matiques de Bourgogne","ror":"https://ror.org/021f0sa24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210112333","https://openalex.org/I4405253280"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Thierry Combot","raw_affiliation_strings":["Institut Math\u00e9matique de Bourgogne, Universit\u00e9 de Bourgogne, France"],"raw_orcid":"https://orcid.org/0000-0003-3488-1291","affiliations":[{"raw_affiliation_string":"Institut Math\u00e9matique de Bourgogne, Universit\u00e9 de Bourgogne, France","institution_ids":["https://openalex.org/I4210112333","https://openalex.org/I177064439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043563784","display_name":"Camilo Sanabria","orcid":"https://orcid.org/0000-0002-4870-3827"},"institutions":[{"id":"https://openalex.org/I162096671","display_name":"Universidad de Los Andes","ror":"https://ror.org/02mhbdp94","country_code":"CO","type":"education","lineage":["https://openalex.org/I162096671"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Camilo Sanabria","raw_affiliation_strings":["Universidad de los Andes, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-4870-3827","affiliations":[{"raw_affiliation_string":"Universidad de los Andes, Colombia","institution_ids":["https://openalex.org/I162096671"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034609451"],"corresponding_institution_ids":["https://openalex.org/I177064439","https://openalex.org/I4210112333"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10114651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"342","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9973999857902527,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9954000115394592,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9926999807357788,"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/mathematics","display_name":"Mathematics","score":0.763209342956543},{"id":"https://openalex.org/keywords/differential-galois-theory","display_name":"Differential Galois theory","score":0.6827067732810974},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5886988639831543},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.5698638558387756},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5505207777023315},{"id":"https://openalex.org/keywords/hypergeometric-distribution","display_name":"Hypergeometric distribution","score":0.522342324256897},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47505733370780945},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.46828505396842957},{"id":"https://openalex.org/keywords/differential-algebra","display_name":"Differential algebra","score":0.4467087388038635},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.420606791973114},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4141896963119507},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.33874523639678955},{"id":"https://openalex.org/keywords/galois-extension","display_name":"Galois extension","score":0.2653477191925049},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.24402859807014465},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.19098308682441711},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17226862907409668},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1012328565120697}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.763209342956543},{"id":"https://openalex.org/C197968787","wikidata":"https://www.wikidata.org/wiki/Q2383624","display_name":"Differential Galois theory","level":4,"score":0.6827067732810974},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5886988639831543},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.5698638558387756},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5505207777023315},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.522342324256897},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47505733370780945},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.46828505396842957},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.4467087388038635},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.420606791973114},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4141896963119507},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.33874523639678955},{"id":"https://openalex.org/C26204071","wikidata":"https://www.wikidata.org/wiki/Q2020004","display_name":"Galois extension","level":3,"score":0.2653477191925049},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.24402859807014465},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.19098308682441711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17226862907409668},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1012328565120697},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3666000.3669707","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669707","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-04829148v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04829148","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://dl.acm.org/doi/10.1145/3666000.3669707","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1549074832","https://openalex.org/W1560726565","https://openalex.org/W1966728617","https://openalex.org/W1977364449","https://openalex.org/W1987322017","https://openalex.org/W1993485537","https://openalex.org/W2000081048","https://openalex.org/W2006334502","https://openalex.org/W2041376609","https://openalex.org/W2058369414","https://openalex.org/W2067358142","https://openalex.org/W2086624608","https://openalex.org/W2157748663","https://openalex.org/W2321545942","https://openalex.org/W3159408585"],"related_works":["https://openalex.org/W3106514099","https://openalex.org/W1999806526","https://openalex.org/W2950187810","https://openalex.org/W1511103833","https://openalex.org/W2751818697","https://openalex.org/W4393213885","https://openalex.org/W1582080390","https://openalex.org/W2131699399","https://openalex.org/W1494321688","https://openalex.org/W2478362166"],"abstract_inverted_index":{"Consider":[0],"a":[1],"third":[2],"order":[3,42],"linear":[4],"differential":[5,52,58],"equation":[6],"L(f)":[7,29],"=":[8,30],"0,":[9],"where":[10],"<Formula":[11],"format=\"inline\"><TexMath><?TeX":[12],"$L\\in":[13],"\\mathbb":[14],"{Q}(z)[\\partial":[15],"_z]$?></TexMath><AltText>Math":[16],"1</AltText><File":[17],"name=\"issac24-37-inline1\"":[18],"type=\"svg\"/></Formula>.":[19],"We":[20],"design":[21],"an":[22],"algorithm":[23],"computing":[24],"the":[25,37,46,73],"Liouvillian":[26],"solutions":[27,74],"of":[28,40,66,82],"0.":[31],"The":[32,57,88],"reducible":[33],"cases":[34],"devolve":[35],"to":[36],"classical":[38],"case":[39],"second":[41],"operators,":[43],"and":[44,68,70,79],"in":[45],"irreducible":[47],"cases,":[48],"only":[49],"finitely":[50],"many":[51],"Galois":[53,59],"groups":[54],"are":[55,75],"possible.":[56],"group":[60],"is":[61,91],"obtained":[62],"through":[63],"optimized":[64],"computations":[65],"invariants":[67],"semi-invariants,":[69],"if":[71],"solvable,":[72],"returned":[76],"as":[77],"pullbacks":[78],"gauge":[80],"transformations":[81],"algebraic":[83],"generalized":[84],"hypergeometric":[85],"function":[86],"3F2.":[87],"computation":[89],"time":[90],"practical":[92],"for":[93],"reasonable":[94],"size":[95],"operators.":[96]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2024-07-16T00:00:00"}