{"id":"https://openalex.org/W2040802412","doi":"https://doi.org/10.1142/s0218196712500439","title":"PARALLEL COMPUTATION OF RESOLVENTS BY MULTIMODULAR TECHNIQUES AND DECOMPOSITION FORMULA","display_name":"PARALLEL COMPUTATION OF RESOLVENTS BY MULTIMODULAR TECHNIQUES AND DECOMPOSITION FORMULA","publication_year":2012,"publication_date":"2012-04-18","ids":{"openalex":"https://openalex.org/W2040802412","doi":"https://doi.org/10.1142/s0218196712500439","mag":"2040802412"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196712500439","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500439","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-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/A5050155106","display_name":"Philippe Aubry","orcid":"https://orcid.org/0000-0002-0964-1942"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"PHILIPPE AUBRY","raw_affiliation_strings":["LIP6, Universit\u00e9 Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex 05, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP6, Universit\u00e9 Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex 05, France","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072064238","display_name":"Annick Valibouze","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"ANNICK VALIBOUZE","raw_affiliation_strings":["LIP6, LSTA, Universit\u00e9 Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex 05, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP6, LSTA, Universit\u00e9 Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex 05, France","institution_ids":["https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050155106"],"corresponding_institution_ids":["https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11507567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"05","first_page":"1250043","last_page":"1250043"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9825000166893005,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9817000031471252,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.7471134066581726},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7459680438041687},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6478984951972961},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.504700779914856},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.4818752706050873},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32383018732070923},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31710320711135864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28737568855285645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22720953822135925},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08812141418457031}],"concepts":[{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.7471134066581726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459680438041687},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6478984951972961},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.504700779914856},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4818752706050873},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32383018732070923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31710320711135864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28737568855285645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22720953822135925},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08812141418457031}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196712500439","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500439","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00694906v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00694906","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":"International Journal of Algebra and Computation, 2012, 22 (5), pp.1-21. &#x27E8;10.1142/S0218196712500439&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1579945670","https://openalex.org/W1964681364","https://openalex.org/W1986626290","https://openalex.org/W1997236224","https://openalex.org/W2012218416","https://openalex.org/W2016345856","https://openalex.org/W2033472558","https://openalex.org/W2071299862"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2350866827","https://openalex.org/W2200939905","https://openalex.org/W2963600173","https://openalex.org/W2951761543","https://openalex.org/W4327812601","https://openalex.org/W2795788140","https://openalex.org/W4298288727","https://openalex.org/W4289241582","https://openalex.org/W4251748586"],"abstract_inverted_index":{"In":[0,67],"this":[1],"paper":[2],"we":[3,69],"significantly":[4],"extend":[5],"the":[6,32,41,49,62],"limits":[7],"of":[8,28,34,43,64,83],"existing":[9],"algebraic":[10],"algorithms":[11,17],"for":[12],"computing":[13],"Lagrange":[14],"resolvents.":[15],"Such":[16],"are":[18,27],"fundamental":[19],"in":[20,51],"effective":[21],"Galois":[22],"theory.":[23],"However,":[24],"they":[25],"usually":[26],"high":[29],"complexity.":[30],"For":[31],"case":[33],"absolute":[35],"resolvents,":[36],"N.":[37],"Rennert":[38],"has":[39],"shown":[40],"value":[42],"a":[44,71],"multimodular":[45],"approach":[46],"to":[47,61,77,94],"reduce":[48],"complexity":[50],"space":[52],"and":[53,57,90],"time.":[54],"We":[55],"improve":[56],"generalize":[58],"his":[59],"work":[60],"computation":[63],"any":[65],"resolvent.":[66],"addition,":[68],"introduce":[70],"decomposition":[72],"formula":[73],"which":[74],"allows":[75],"us":[76],"split":[78],"modular":[79],"resolvents":[80,82],"into":[81],"smaller":[84],"degrees,":[85],"thus":[86],"both":[87],"speeding":[88],"computations":[89],"making":[91],"it":[92],"possible":[93],"efficiently":[95],"parallelize":[96],"them.":[97]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
