{"id":"https://openalex.org/W2026317867","doi":"https://doi.org/10.1145/1277548.1277550","title":"Computing super-irreducible forms of systems of linear differential equations via moser-reduction","display_name":"Computing super-irreducible forms of systems of linear differential equations via moser-reduction","publication_year":2007,"publication_date":"2007-07-29","ids":{"openalex":"https://openalex.org/W2026317867","doi":"https://doi.org/10.1145/1277548.1277550","mag":"2026317867"},"language":"en","primary_location":{"id":"doi:10.1145/1277548.1277550","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 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/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":true,"raw_author_name":"Moulay A. Barkatou","raw_affiliation_strings":["Universit\u00e9 de Limoges, Limoges, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges, Limoges, France","institution_ids":["https://openalex.org/I65806277"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111917045","display_name":"Eckhard Pfl\u00fcgel","orcid":null},"institutions":[{"id":"https://openalex.org/I205051169","display_name":"Kingston University","ror":"https://ror.org/05bbqza97","country_code":"GB","type":"education","lineage":["https://openalex.org/I205051169"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Eckhard Pfl\u00fcgel","raw_affiliation_strings":["Kingston University, Kingston upon Thames, Surrey, United Kingdom","Kingston University, Kingston-upon-Thames, Surrey, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Kingston University, Kingston upon Thames, Surrey, United Kingdom","institution_ids":["https://openalex.org/I205051169"]},{"raw_affiliation_string":"Kingston University, Kingston-upon-Thames, Surrey, United Kingdom","institution_ids":["https://openalex.org/I205051169"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5105411881"],"corresponding_institution_ids":["https://openalex.org/I65806277"],"apc_list":null,"apc_paid":null,"fwci":2.3467,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.89521891,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6070986986160278},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5666626691818237},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5398731231689453},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.525033712387085},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5080580711364746},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4381784498691559},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42233920097351074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4149268567562103},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3370228409767151},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3219255208969116},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27996861934661865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1597593128681183},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08290743827819824}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6070986986160278},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5666626691818237},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5398731231689453},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.525033712387085},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5080580711364746},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4381784498691559},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42233920097351074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4149268567562103},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3370228409767151},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3219255208969116},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27996861934661865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1597593128681183},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08290743827819824},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1277548.1277550","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W153920099","https://openalex.org/W1511632607","https://openalex.org/W1970323071","https://openalex.org/W1973099752","https://openalex.org/W1988098065","https://openalex.org/W1991092316","https://openalex.org/W1993448820","https://openalex.org/W2000814183","https://openalex.org/W2002986350","https://openalex.org/W2036718210","https://openalex.org/W2078168416","https://openalex.org/W2082188408","https://openalex.org/W2120078368","https://openalex.org/W2133527753","https://openalex.org/W2172255526","https://openalex.org/W2315704228","https://openalex.org/W2601803591","https://openalex.org/W6651066057"],"related_works":["https://openalex.org/W2112835755","https://openalex.org/W4291951920","https://openalex.org/W2349674371","https://openalex.org/W2097495471","https://openalex.org/W1696545756","https://openalex.org/W2952827811","https://openalex.org/W2056202066","https://openalex.org/W2963262648","https://openalex.org/W4301867002","https://openalex.org/W2532234348"],"abstract_inverted_index":{"The":[0],"notion":[1],"of":[2,5,7,35,39,41,93,98],"irreducible":[3],"forms":[4,22],"systems":[6,40],"linear":[8,42,60],"differential":[9,43,61],"equations":[10,44],"as":[11,68],"defined":[12],"by":[13,24],"Moser":[14],"[14":[15],"]":[16,28],"and":[17,109],"its":[18],"generalisation,":[19],"the":[20,33,36,81,99,105],"super-irreducible":[21],"introduced":[23],"Hilali/Wazner":[25],"in":[26,32,80,95,107],"[9":[27],"are":[29],"important":[30],"concepts":[31],"context":[34],"symbolic":[37],"resolution":[38],"[3,15,16":[45],"].":[46],"In":[47],"this":[48],"paper,":[49],"we":[50],"give":[51],"a":[52,90],"new":[53],"algorithm":[54,77],"for":[55],"computing,":[56],"given":[57],"an":[58,70],"arbitrary":[59],"system":[62,72],"with":[63],"formal":[64],"power":[65],"series":[66],"coefficients":[67],"input,":[69],"equivalent":[71],"which":[73,88],"is":[74,78],"super-irreducible.":[75],"Our":[76],"optimal":[79],"sense":[82],"that":[83],"it":[84,103],"computes":[85],"transformation":[86],"matrices":[87],"obtain":[89],"maximal":[91],"reduction":[92],"rank":[94],"each":[96],"step":[97],"algorithm.":[100],"This":[101],"distinguishes":[102],"from":[104],"algorithms":[106],"[9,14,2]":[108],"generalises":[110],"[7].":[111]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}