{"id":"https://openalex.org/W1977406733","doi":"https://doi.org/10.1145/1145768.1145804","title":"Rank reduction of a class of pfaffian systems in two variables","display_name":"Rank reduction of a class of pfaffian systems in two variables","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W1977406733","doi":"https://doi.org/10.1145/1145768.1145804","mag":"1977406733"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145804","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"proceedings-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/A5113226554","display_name":"Nicolas Le Roux","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":"Nicolas Le Roux","raw_affiliation_strings":["Facult\u00e9 des Sciences et Techniques, Limoges, France"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 des Sciences et Techniques, Limoges, France","institution_ids":["https://openalex.org/I65806277"]}]},{"author_position":"last","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 Barkatou","raw_affiliation_strings":["Facult\u00e9 des Sciences et Techniques, Limoges, France"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 des Sciences et Techniques, Limoges, France","institution_ids":["https://openalex.org/I65806277"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":6,"citation_normalized_percentile":{"value":0.876059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":78,"max":79},"biblio":{"volume":null,"issue":null,"first_page":"204","last_page":"211"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Bifurcations in Planar Polynomial Systems","score":0.9992,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Bifurcations in Planar Polynomial Systems","score":0.9992,"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/T11435","display_name":"Symbolic Computing in Algebraic Geometry and Cryptography","score":0.9966,"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 Moduli Theory","score":0.9939,"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/pfaffian","display_name":"Pfaffian","score":0.9556337},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6015028},{"id":"https://openalex.org/keywords/polynomial-systems","display_name":"Polynomial Systems","score":0.485236}],"concepts":[{"id":"https://openalex.org/C2775956649","wikidata":"https://www.wikidata.org/wiki/Q1189744","display_name":"Pfaffian","level":2,"score":0.9556337},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6833396},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6015028},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.53636247},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47163153},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.4515901},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41906348},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41394258},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19070989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06642702},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145804","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.science/hal-00110541","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":true,"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":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00110541","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":true,"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":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":13,"referenced_works":["https://openalex.org/W1564350692","https://openalex.org/W1575803131","https://openalex.org/W1594931873","https://openalex.org/W1970323071","https://openalex.org/W1984719724","https://openalex.org/W2042217408","https://openalex.org/W2046973290","https://openalex.org/W2054688955","https://openalex.org/W2120078368","https://openalex.org/W2322535491","https://openalex.org/W323935674","https://openalex.org/W4291439952","https://openalex.org/W581559033"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4390755055","https://openalex.org/W4376311966","https://openalex.org/W3205583637","https://openalex.org/W3037479919","https://openalex.org/W2490147476","https://openalex.org/W2247174527","https://openalex.org/W2044523622","https://openalex.org/W2000615432","https://openalex.org/W1978623376"],"abstract_inverted_index":{"Several":[0],"algorithms":[1],"exist":[2],"to":[3,18,45,103,156],"reduce":[4],"the":[5,22,37,104,114,117,125,136,168],"rank":[6,24],"of":[7,39,42,139,142,147],"an":[8],"ordinary":[9],"linear":[10],"differential":[11],"system":[12,89],"at":[13,113,152],"a":[14,85,108,132,148,162],"point,":[15],"say":[16],"0,":[17,116,161],"its":[19],"minimal":[20],"value,":[21],"Poincar\u00e9":[23,29],"(also,":[25],"sometimes":[26],"called":[27],"true":[28],"rank).":[30],"We":[31],"extend":[32],"Levelt":[33],"algorithm,":[34],"based":[35],"on":[36],"existence":[38],"stationary":[40],"sequences":[41],"free":[43],"lattices,":[44],"completely":[46,86],"integrable":[47,87],"Pfaffian":[48,88],"systems":[49],"with":[50,70,90],"normal":[51,91],"crossings":[52,92],"in":[53,72],"two":[54],"variables":[55],"dY":[56],"=":[57,94,158,160],"(1/xp+1":[58,95],"A(x,":[59,96],"y)dx":[60,97],"+":[61,98],"1/yq+1B(x,":[62],"y)dy)Y":[63],"where":[64],"A,":[65],"B":[66],"are":[67,78],"m\u00d7m":[68],"matrices":[69],"entries":[71],"C[[x,":[73],"y]]":[74],"and":[75,123],"p,":[76,119],"q":[77,120,159],"non":[79],"negative":[80],"integers.":[81],"The":[82],"algorithm":[83],"returns":[84],"dZ":[93],"1/yq+1":[99],"B(x,":[100],"y)dy)Z":[101],"equivalent":[102,155],"initial":[105],"one":[106],"through":[107],"formal":[109,140],"meromorphic":[110],"gauge":[111],"transformation":[112],"origin":[115],"integers":[118],"being":[121],"simultaneously":[122],"individually":[124],"smallest":[126],"possible.":[127],"We,":[128],"thus,":[129],"set":[130],"up":[131],"first":[133],"step":[134],"towards":[135],"explicit":[137],"calculation":[138],"solutions":[141],"such":[143],"systems.The":[144],"particular":[145],"case":[146],"regular":[149],"singular":[150],"point":[151],"0":[153],"is":[154],"p":[157],"condition":[163],"easily":[164],"checked":[165],"by":[166],"applying":[167],"algorithm.":[169]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1977406733","counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2024-12-02T14:59:27.528657","created_date":"2016-06-24"}