{"id":"https://openalex.org/W1986524226","doi":"https://doi.org/10.1145/1073884.1073896","title":"Picard--Vessiot extensions for linear functional systems","display_name":"Picard--Vessiot extensions for linear functional systems","publication_year":2005,"publication_date":"2005-07-24","ids":{"openalex":"https://openalex.org/W1986524226","doi":"https://doi.org/10.1145/1073884.1073896","mag":"1986524226"},"language":"en","primary_location":{"id":"doi:10.1145/1073884.1073896","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1073884.1073896","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 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/A5053428066","display_name":"Manuel Bronstein","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Manuel Bronstein","raw_affiliation_strings":["INRIA -- Caf\u00c9, Sophia Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA -- Caf\u00c9, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040935769","display_name":"Ziming Li","orcid":"https://orcid.org/0000-0003-0964-6724"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziming Li","raw_affiliation_strings":["Acad. of Math. and Syst. Sci., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Acad. of Math. and Syst. Sci., Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101860728","display_name":"Min Wu","orcid":"https://orcid.org/0009-0007-8206-3855"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Min Wu","raw_affiliation_strings":["INRIA -- Caf\u00c9, Sophia Antipolis, France, Acad. of Math. and Syst. Sci., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA -- Caf\u00c9, Sophia Antipolis, France, Acad. of Math. and Syst. Sci., Beijing, China","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3733,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92315456,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"68","last_page":"75"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11752","display_name":"Cancer Treatment and Pharmacology","score":0.9560999870300293,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.70116126537323},{"id":"https://openalex.org/keywords/differential-galois-theory","display_name":"Differential Galois theory","score":0.6218082904815674},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5688717365264893},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5564104318618774},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4836515188217163},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.419209748506546},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39842337369918823},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36834293603897095},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.35571300983428955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34770452976226807},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2797781527042389},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15266862511634827},{"id":"https://openalex.org/keywords/galois-extension","display_name":"Galois extension","score":0.1492028832435608},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14086127281188965}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.70116126537323},{"id":"https://openalex.org/C197968787","wikidata":"https://www.wikidata.org/wiki/Q2383624","display_name":"Differential Galois theory","level":4,"score":0.6218082904815674},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5688717365264893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5564104318618774},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4836515188217163},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.419209748506546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39842337369918823},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36834293603897095},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.35571300983428955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34770452976226807},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2797781527042389},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15266862511634827},{"id":"https://openalex.org/C26204071","wikidata":"https://www.wikidata.org/wiki/Q2020004","display_name":"Galois extension","level":3,"score":0.1492028832435608},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14086127281188965}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1073884.1073896","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1073884.1073896","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.9078","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.9078","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sop.inria.fr/cafe/Manuel.Bronstein/publications/issac2005.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.482.9768","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.482.9768","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sop.inria.fr/cafe/Min.Wu/Publications/blwissac.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W602391989","https://openalex.org/W1486594615","https://openalex.org/W1526781295","https://openalex.org/W1560726565","https://openalex.org/W1628154048","https://openalex.org/W1975356036","https://openalex.org/W1977049875","https://openalex.org/W1980662086","https://openalex.org/W2014788014","https://openalex.org/W2151085185","https://openalex.org/W2162009465","https://openalex.org/W2185851898","https://openalex.org/W2325892776"],"related_works":["https://openalex.org/W1966164177","https://openalex.org/W2897880338","https://openalex.org/W2963711648","https://openalex.org/W4214969844","https://openalex.org/W1673188045","https://openalex.org/W4213407414","https://openalex.org/W2730690530","https://openalex.org/W1758039898","https://openalex.org/W1603971190","https://openalex.org/W2170956753"],"abstract_inverted_index":{"Picard-Vessiot":[0,29],"extensions":[1,30,46],"for":[2,31],"ordinary":[3],"differential":[4],"and":[5,11,28],"difference":[6],"equations":[7,37],"are":[8,12],"well":[9],"known":[10],"at":[13],"the":[14,17,51,66],"core":[15],"of":[16,33,53,56,65],"associated":[18],"Galois":[19],"theories.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24],"construct":[25],"fundamental":[26],"matrices":[27],"systems":[32],"linear":[34,40],"partial":[35],"functional":[36],"having":[38],"finite":[39],"dimension.":[41],"We":[42],"then":[43],"use":[44],"those":[45],"to":[47,63],"show":[48],"that":[49],"all":[50],"solutions":[52,64],"a":[54,58],"factor":[55],"such":[57],"system":[59],"can":[60],"be":[61],"completed":[62],"original":[67],"system.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
