{"id":"https://openalex.org/W2754485517","doi":"https://doi.org/10.2168/lmcs-8(1:25)2012","title":"Formal Theories for Linear Algebra","display_name":"Formal Theories for Linear Algebra","publication_year":2012,"publication_date":"2012-03-16","ids":{"openalex":"https://openalex.org/W2754485517","doi":"https://doi.org/10.2168/lmcs-8(1:25)2012","mag":"2754485517"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-8(1:25)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:25)2012","pdf_url":"https://lmcs.episciences.org/716/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/716/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034555443","display_name":"Stephen Cook","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Stephen A Cook","raw_affiliation_strings":["University of Toronto Department of Computer Science Sandford Fleming Building 10 King's College Road Toronto, Ontario M5S 3G4 Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto Department of Computer Science Sandford Fleming Building 10 King's College Road Toronto, Ontario M5S 3G4 Canada","institution_ids":["https://openalex.org/I185261750","https://openalex.org/I106938459"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065388772","display_name":"Lila Fontes","orcid":"https://orcid.org/0009-0002-6863-1709"},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lila A Fontes","raw_affiliation_strings":["University of Toronto Department of Computer Science Sandford Fleming Building 10 King's College Road Toronto, Ontario M5S 3G4 Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto Department of Computer Science Sandford Fleming Building 10 King's College Road Toronto, Ontario M5S 3G4 Canada","institution_ids":["https://openalex.org/I185261750","https://openalex.org/I106938459"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034555443"],"corresponding_institution_ids":["https://openalex.org/I106938459","https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.32461223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"Volume 8, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9973999857902527,"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":0.9973999857902527,"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/T11567","display_name":"semigroups and automata theory","score":0.995199978351593,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/algebra-over-a-field","display_name":"Algebra over a field","score":0.6699331402778625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5862732529640198},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5203697085380554},{"id":"https://openalex.org/keywords/universal-algebra","display_name":"Universal algebra","score":0.4760156273841858},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32794949412345886},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3277866244316101}],"concepts":[{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6699331402778625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5862732529640198},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5203697085380554},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.4760156273841858},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32794949412345886},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3277866244316101},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-8(1:25)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:25)2012","pdf_url":"https://lmcs.episciences.org/716/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1101.1449","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1101.1449","pdf_url":"https://arxiv.org/pdf/1101.1449","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:2cd5b3d221e645c68c550f1696f4a38a","is_oa":true,"landing_page_url":"https://doaj.org/article/2cd5b3d221e645c68c550f1696f4a38a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 8, Issue 1 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-8(1:25)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:25)2012","pdf_url":"https://lmcs.episciences.org/716/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2754485517.pdf","grobid_xml":"https://content.openalex.org/works/W2754485517.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W117725373","https://openalex.org/W1537230380","https://openalex.org/W1554948556","https://openalex.org/W1556453281","https://openalex.org/W1876112628","https://openalex.org/W1967948656","https://openalex.org/W1977227483","https://openalex.org/W2017205387","https://openalex.org/W2021238854","https://openalex.org/W2082002555","https://openalex.org/W2105859078","https://openalex.org/W2132876155","https://openalex.org/W2159341052","https://openalex.org/W2165390183","https://openalex.org/W2169150716","https://openalex.org/W2185541742","https://openalex.org/W4236835455"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4285303061","https://openalex.org/W2525488343","https://openalex.org/W622366405","https://openalex.org/W2477677129","https://openalex.org/W2378563121","https://openalex.org/W2383666998","https://openalex.org/W2358786979","https://openalex.org/W2388645548","https://openalex.org/W616292901"],"abstract_inverted_index":{"We":[0,26],"introduce":[1],"two-sorted":[2],"theories":[3],"in":[4,63],"the":[5,10,64,70,75],"style":[6],"of":[7,30,42,50,53,73],"[CN10]":[8],"for":[9],"complexity":[11],"classes":[12],"\\oplusL":[13],"and":[14,23,58],"DET,":[15],"whose":[16],"complete":[17],"problems":[18],"include":[19],"determinants":[20],"over":[21,36,56],"Z2":[22,57],"Z,":[24],"respectively.":[25],"then":[27],"describe":[28],"interpretations":[29],"Soltys'":[31],"linear":[32,54],"algebra":[33,55],"theory":[34],"LAp":[35],"arbitrary":[37],"integral":[38],"domains,":[39],"into":[40],"each":[41],"our":[43],"new":[44],"theories.":[45],"The":[46],"result":[47],"shows":[48],"equivalences":[49],"standard":[51],"theorems":[52,76],"Z":[59],"can":[60,78],"be":[61,79],"proved":[62],"corresponding":[65],"theory,":[66],"but":[67],"leaves":[68],"open":[69],"interesting":[71],"question":[72],"whether":[74],"themselves":[77],"proved.":[80]},"counts_by_year":[{"year":2019,"cited_by_count":27},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}