{"id":"https://openalex.org/W2124409237","doi":"https://doi.org/10.1145/1005285.1005309","title":"Rational general solutions of algebraic ordinary differential equations","display_name":"Rational general solutions of algebraic ordinary differential equations","publication_year":2004,"publication_date":"2004-07-04","ids":{"openalex":"https://openalex.org/W2124409237","doi":"https://doi.org/10.1145/1005285.1005309","mag":"2124409237"},"language":"en","primary_location":{"id":"doi:10.1145/1005285.1005309","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 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/A5050890628","display_name":"Ruyong Feng","orcid":"https://orcid.org/0000-0001-6508-8486"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruyong Feng","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization Institute of Systems Science, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization Institute of Systems Science, Beijing, China","institution_ids":["https://openalex.org/I4210129227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017479931","display_name":"Xiao-Shan Gao","orcid":"https://orcid.org/0000-0003-2021-9395"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-shan Gao","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization Institute of Systems Science, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization Institute of Systems Science, Beijing, China","institution_ids":["https://openalex.org/I4210129227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050890628"],"corresponding_institution_ids":["https://openalex.org/I4210129227"],"apc_list":null,"apc_paid":null,"fwci":2.0742,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.87133621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"155","last_page":"162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.6552674770355225},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.6368635892868042},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6115575432777405},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5008485317230225},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.48459064960479736},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4597052037715912},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.39936596155166626},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39526182413101196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3313335180282593},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29731136560440063},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22534534335136414}],"concepts":[{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.6552674770355225},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.6368635892868042},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6115575432777405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5008485317230225},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.48459064960479736},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4597052037715912},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.39936596155166626},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39526182413101196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3313335180282593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29731136560440063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22534534335136414}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1005285.1005309","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.580.6948","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.580.6948","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mmrc.iss.ac.cn/~xgao/paper/p42-feng.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.838.3150","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.838.3150","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mmrc.iss.ac.cn/%7Eweili/papers/p155-feng.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1524305136","https://openalex.org/W1560726565","https://openalex.org/W1966102258","https://openalex.org/W1966728617","https://openalex.org/W1975426154","https://openalex.org/W1977359769","https://openalex.org/W1980662086","https://openalex.org/W1983317518","https://openalex.org/W1983529122","https://openalex.org/W1991137059","https://openalex.org/W1997290261","https://openalex.org/W2006334502","https://openalex.org/W2015612966","https://openalex.org/W2017794685","https://openalex.org/W2036241965","https://openalex.org/W2041942111","https://openalex.org/W2052387938","https://openalex.org/W2067358142","https://openalex.org/W2070444228","https://openalex.org/W2071113133","https://openalex.org/W2081381163","https://openalex.org/W2082714069","https://openalex.org/W2083947292","https://openalex.org/W2098971625","https://openalex.org/W2102976686","https://openalex.org/W2140443967","https://openalex.org/W2143569865","https://openalex.org/W2143650198","https://openalex.org/W2162465934","https://openalex.org/W2370045957","https://openalex.org/W2626734060"],"related_works":["https://openalex.org/W2502480061","https://openalex.org/W21216597","https://openalex.org/W4288410816","https://openalex.org/W2924426067","https://openalex.org/W2517966731","https://openalex.org/W1992952893","https://openalex.org/W2490075509","https://openalex.org/W4234783915","https://openalex.org/W4298202720","https://openalex.org/W2047656848"],"abstract_inverted_index":{"We":[0],"give":[1,25],"a":[2,13,30],"necessary":[3],"and":[4,52,66],"sufficient":[5],"condition":[6],"for":[7],"an":[8,19,26],"algebraic":[9,58],"ODE":[10,51,65],"to":[11,28],"have":[12],"rational":[14,31,45,53],"type":[15],"general":[16,32],"solution.":[17],"For":[18],"autonomous":[20],"first":[21,49,63],"order":[22,50,64],"ODE,":[23],"we":[24],"algorithm":[27,38],"compute":[29],"solution":[33],"if":[34],"it":[35],"exists.":[36],"The":[37],"is":[39],"based":[40],"on":[41],"the":[42,48,56,62],"relation":[43],"between":[44],"solutions":[46],"of":[47,55],"parametrizations":[54],"plane":[57],"curve":[59],"defined":[60],"by":[61],"Pad\u00e9":[67],"approximants.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}