{"id":"https://openalex.org/W1981987468","doi":"https://doi.org/10.1145/1993886.1993896","title":"Formal first integrals along solutions of differential systems I","display_name":"Formal first integrals along solutions of differential systems I","publication_year":2011,"publication_date":"2011-06-08","ids":{"openalex":"https://openalex.org/W1981987468","doi":"https://doi.org/10.1145/1993886.1993896","mag":"1981987468"},"language":"en","primary_location":{"id":"doi:10.1145/1993886.1993896","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993896","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},"type":"preprint","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/A5049014255","display_name":"Ainhoa Aparicio-Monforte","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":false,"raw_author_name":"Ainhoa Aparicio-Monforte","raw_affiliation_strings":["Johannes Kepler University, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johannes Kepler University, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105411881","display_name":"Moulay A. Barkatou","orcid":"https://orcid.org/0000-0001-9892-9448"},"institutions":[{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Moulay A. Barkatou","raw_affiliation_strings":["Universit\u00e9 de Limoges, Limoges, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges, Limoges, France","institution_ids":["https://openalex.org/I65806277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034865801","display_name":"Sergi Sim\u00f3n","orcid":"https://orcid.org/0000-0002-1603-3312"},"institutions":[{"id":"https://openalex.org/I63072094","display_name":"University of Portsmouth","ror":"https://ror.org/03ykbk197","country_code":"GB","type":"education","lineage":["https://openalex.org/I63072094"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sergi Simon","raw_affiliation_strings":["University of Portsmouth, Portsmouth, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Portsmouth, Portsmouth, United Kingdom","institution_ids":["https://openalex.org/I63072094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108684467","display_name":"Jacques-Arthur Weil","orcid":null},"institutions":[{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jacques-Arthur Weil","raw_affiliation_strings":["Universit\u00e9 de Limoges, Limoges, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges, Limoges, France","institution_ids":["https://openalex.org/I65806277"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6523,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68391183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"19","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9976999759674072,"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":0.9887999892234802,"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/taylor-series","display_name":"Taylor series","score":0.5709290504455566},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5558499097824097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5320965051651001},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5260719656944275},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5015585422515869},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.43163636326789856},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.42371857166290283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35847872495651245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2814441919326782},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1741809844970703},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1271478235721588}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5709290504455566},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5558499097824097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5320965051651001},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5260719656944275},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5015585422515869},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43163636326789856},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.42371857166290283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35847872495651245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2814441919326782},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1741809844970703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1271478235721588},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1993886.1993896","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993896","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-00602143v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00602143","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":"ISSAC 2011, 36th International Symposium on Symbolic and Algebraic Computation, Jun 2011, San Jos\u00e9, Californie, United States. pp.19-26, &#x27E8;10.1145/1993886.1993896&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W153920099","https://openalex.org/W1575475998","https://openalex.org/W1988098065","https://openalex.org/W1999118470","https://openalex.org/W1999546194","https://openalex.org/W2006334502","https://openalex.org/W2034882117","https://openalex.org/W2058369414","https://openalex.org/W2067639492","https://openalex.org/W2107008183","https://openalex.org/W2120078368","https://openalex.org/W2120250226","https://openalex.org/W2317218640","https://openalex.org/W2601803591","https://openalex.org/W2780238195","https://openalex.org/W3039948875","https://openalex.org/W4214972453"],"related_works":["https://openalex.org/W2395105737","https://openalex.org/W2369507325","https://openalex.org/W3208270790","https://openalex.org/W3135719690","https://openalex.org/W2368550193","https://openalex.org/W1985023705","https://openalex.org/W2061027733","https://openalex.org/W2387252559","https://openalex.org/W1984106009","https://openalex.org/W1815130818"],"abstract_inverted_index":{"We":[0,22,59],"consider":[1],"an":[2],"analytic":[3,19],"vector":[4],"field":[5],"x":[6],"=":[7],"X(x\\right)":[8],"and":[9,29,85],"study,":[10],"via":[11],"a":[12],"variational":[13,34,57],"approach,":[14],"whether":[15],"it":[16],"may":[17],"possess":[18],"first":[20,47,96],"integrals.":[21],"assume":[23],"one":[24],"solution":[25],"\u0393":[26],"is":[27],"known":[28],"we":[30,70],"study":[31],"the":[32,54,72,95],"successive":[33],"equations":[35],"along":[36],"\u0393.":[37],"Constructions":[38],"in":[39],"[MRRS07]":[40],"show":[41,60],"that":[42,61],"Taylor":[43],"expansion":[44],"coefficients":[45],"of":[46,53,90],"integrals":[48],"appear":[49],"as":[50],"rational":[51],"solutions":[52],"dual":[55],"linearized":[56],"equations.":[58],"they":[62],"also":[63],"satisfy":[64],"linear":[65],"\"filter\"":[66],"conditions.":[67],"Using":[68],"this,":[69],"adapt":[71],"algorithms":[73],"from":[74,94],"[Bar99,":[75],"vHW97]":[76],"to":[77,82],"design":[78],"new":[79],"ones":[80],"optimized":[81],"this":[83,91],"effect":[84],"demonstrate":[86],"their":[87],"use.":[88],"Part":[89],"work":[92],"stems":[93],"author's":[97],"Ph.D.":[98],"thesis1":[99],"[AM10].":[100]},"counts_by_year":[{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
