{"id":"https://openalex.org/W2611625450","doi":"https://doi.org/10.1145/2442829.2442847","title":"Fast computation of common left multiples of linear ordinary differential operators","display_name":"Fast computation of common left multiples of linear ordinary differential operators","publication_year":2012,"publication_date":"2012-07-22","ids":{"openalex":"https://openalex.org/W2611625450","doi":"https://doi.org/10.1145/2442829.2442847","mag":"2611625450"},"language":"en","primary_location":{"id":"doi:10.1145/2442829.2442847","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th 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":null,"display_name":"Alin Bostan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Alin Bostan","raw_affiliation_strings":["Algorithms Project, INRIA (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms Project, INRIA (France)","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Fr\u00e9d\u00e9ric Chyzak","orcid":null},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Chyzak","raw_affiliation_strings":["Algorithms Project, INRIA (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms Project, INRIA (France)","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Bruno Salvy","orcid":null},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Bruno Salvy","raw_affiliation_strings":["Algorithms Project, INRIA (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms Project, INRIA (France)","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ziming Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210125823","display_name":"KLE University","ror":"https://ror.org/03aam9155","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210125823"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ziming Li","raw_affiliation_strings":["KLMM and AMSS (China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KLMM and AMSS (China)","institution_ids":["https://openalex.org/I4210125823"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0838,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.88087936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"99","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987999796867371,"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":0.9987999796867371,"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/T11130","display_name":"Coding theory and cryptography","score":0.9980999827384949,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9810000061988831,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6401000022888184},{"id":"https://openalex.org/keywords/multiple","display_name":"Multiple","score":0.5802000164985657},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5662999749183655},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5084999799728394},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.46549999713897705},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.43309998512268066},{"id":"https://openalex.org/keywords/linear-operators","display_name":"Linear operators","score":0.42160001397132874},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.40630000829696655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.751800000667572},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6401000022888184},{"id":"https://openalex.org/C164680029","wikidata":"https://www.wikidata.org/wiki/Q1055293","display_name":"Multiple","level":2,"score":0.5802000164985657},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5662999749183655},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5084999799728394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4921000003814697},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.46549999713897705},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43059998750686646},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.42160001397132874},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.40630000829696655},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37709999084472656},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2800999879837036},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2442829.2442847","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W60296969","https://openalex.org/W180233073","https://openalex.org/W1585998846","https://openalex.org/W1976677460","https://openalex.org/W1979740015","https://openalex.org/W1980283844","https://openalex.org/W1984950894","https://openalex.org/W1990226699","https://openalex.org/W1995653528","https://openalex.org/W2001894830","https://openalex.org/W2002188635","https://openalex.org/W2003189478","https://openalex.org/W2010830127","https://openalex.org/W2014038993","https://openalex.org/W2019367635","https://openalex.org/W2020079313","https://openalex.org/W2029001542","https://openalex.org/W2040334793","https://openalex.org/W2083368929","https://openalex.org/W2084801848","https://openalex.org/W2093914057","https://openalex.org/W2103078973","https://openalex.org/W2129139293","https://openalex.org/W2320632938","https://openalex.org/W2325126376","https://openalex.org/W2331005958","https://openalex.org/W2483931130","https://openalex.org/W4232551748","https://openalex.org/W6605342772"],"related_works":[],"abstract_inverted_index":{"We":[0,17,35],"study":[1],"tight":[2],"bounds":[3,58,74],"and":[4],"fast":[5],"algorithms":[6,24],"for":[7,25],"LCLMs":[8],"of":[9,22,32,63,70,81,98],"several":[10],"linear":[11,47],"differential":[12],"operators":[13],"with":[14],"polynomial":[15,52],"coefficients.":[16],"analyse":[18],"the":[19,30,42,60,64,72,82,89,95,99],"arithmetic":[20,96],"complexity":[21,80],"existing":[23],"LCLMs,":[26],"as":[27,29],"well":[28],"size":[31,97],"their":[33],"outputs.":[34],"propose":[36],"a":[37,46,51],"new":[38,83],"algorithm":[39,55,84],"that":[40,91],"recasts":[41],"LCLM":[43],"computation":[44],"in":[45,88],"algebra":[48],"problem":[49],"on":[50,59],"matrix.":[53],"This":[54],"yields":[56],"sharp":[57],"coefficient":[61],"degrees":[62],"LCLM,":[65],"improving":[66],"by":[67],"one":[68],"order":[69],"magnitude":[71],"best":[73],"obtained":[75],"using":[76],"previous":[77],"algorithms.":[78],"The":[79],"is":[85],"almost":[86],"optimal,":[87],"sense":[90],"it":[92],"nearly":[93],"matches":[94],"output.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2017-05-12T00:00:00"}