{"id":"https://openalex.org/W2914710059","doi":"https://doi.org/10.1007/s11424-019-8348-0","title":"The Algebro-Geometric Method for Solving Algebraic Differential Equations \u2014 A Survey","display_name":"The Algebro-Geometric Method for Solving Algebraic Differential Equations \u2014 A Survey","publication_year":2019,"publication_date":"2019-02-01","ids":{"openalex":"https://openalex.org/W2914710059","doi":"https://doi.org/10.1007/s11424-019-8348-0","mag":"2914710059"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-019-8348-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-019-8348-0","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/A5076705512","display_name":"Franz Winkler","orcid":null},"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":"Franz Winkler","raw_affiliation_strings":["Research Institute for Symbolic Computation, J. Kepler University, A-4040, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Research Institute for Symbolic Computation, J. Kepler University, A-4040, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076705512"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.2992,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87374806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"1","first_page":"256","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9973000288009644,"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":0.9969000220298767,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9926999807357788,"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":0.7695950865745544},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.7103040218353271},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.6805359721183777},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5891086459159851},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.5398465991020203},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.508777916431427},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.48478907346725464},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.4829972982406616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46545082330703735},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.4426094591617584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43314746022224426},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43000873923301697},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4176065921783447},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38787350058555603},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.36661165952682495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08873531222343445}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7695950865745544},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.7103040218353271},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.6805359721183777},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5891086459159851},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.5398465991020203},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.508777916431427},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.48478907346725464},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.4829972982406616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46545082330703735},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.4426094591617584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43314746022224426},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43000873923301697},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4176065921783447},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38787350058555603},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.36661165952682495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08873531222343445},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-019-8348-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-019-8348-0","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W80392993","https://openalex.org/W150583336","https://openalex.org/W196899843","https://openalex.org/W417189238","https://openalex.org/W622632975","https://openalex.org/W1550148117","https://openalex.org/W1553893196","https://openalex.org/W1560726565","https://openalex.org/W1603468845","https://openalex.org/W1695547469","https://openalex.org/W1966102258","https://openalex.org/W1977359769","https://openalex.org/W1980426588","https://openalex.org/W1980662086","https://openalex.org/W1981889146","https://openalex.org/W1983456333","https://openalex.org/W2006125674","https://openalex.org/W2012638934","https://openalex.org/W2014684859","https://openalex.org/W2021540843","https://openalex.org/W2025287430","https://openalex.org/W2041942111","https://openalex.org/W2046919642","https://openalex.org/W2064034118","https://openalex.org/W2067358142","https://openalex.org/W2077290427","https://openalex.org/W2078894485","https://openalex.org/W2079392836","https://openalex.org/W2124409237","https://openalex.org/W2159699280","https://openalex.org/W2161469702","https://openalex.org/W2220846421","https://openalex.org/W2226737729","https://openalex.org/W2285279104","https://openalex.org/W2370045957","https://openalex.org/W2486876072","https://openalex.org/W2492830809","https://openalex.org/W2728218654","https://openalex.org/W2738808405","https://openalex.org/W2761161999","https://openalex.org/W2792012667","https://openalex.org/W2970232819","https://openalex.org/W4206293930","https://openalex.org/W4236238707","https://openalex.org/W4251463789","https://openalex.org/W4252870413","https://openalex.org/W4256665550"],"related_works":["https://openalex.org/W4288410816","https://openalex.org/W2924426067","https://openalex.org/W586764485","https://openalex.org/W2128560657","https://openalex.org/W1480298971","https://openalex.org/W21216597","https://openalex.org/W196899843","https://openalex.org/W2364665719","https://openalex.org/W1519099790","https://openalex.org/W3027747609"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
