{"id":"https://openalex.org/W1997215029","doi":"https://doi.org/10.2478/v10037-011-0010-9","title":"Formalization of Integral Linear Space","display_name":"Formalization of Integral Linear Space","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1997215029","doi":"https://doi.org/10.2478/v10037-011-0010-9","mag":"1997215029"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-011-0010-9","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0010-9","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0010-9","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-011-0010-9","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076839736","display_name":"Yuichi Futa","orcid":null},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]},{"id":"https://openalex.org/I4210162928","display_name":"\u014ctani University","ror":"https://ror.org/05b7rex33","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210162928"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuichi Futa","raw_affiliation_strings":["Shinshu University Nagano, Japan","Yasunari Shidama Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]},{"raw_affiliation_string":"Yasunari Shidama Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476","https://openalex.org/I4210162928"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048322538","display_name":"Hiroyuki Okazaki","orcid":"https://orcid.org/0009-0000-1022-361X"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]},{"id":"https://openalex.org/I4210162928","display_name":"\u014ctani University","ror":"https://ror.org/05b7rex33","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210162928"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Okazaki","raw_affiliation_strings":["Shinshu University Nagano, Japan","Yasunari Shidama Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]},{"raw_affiliation_string":"Yasunari Shidama Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476","https://openalex.org/I4210162928"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055549852","display_name":"Yasunari Shidama","orcid":"https://orcid.org/0000-0001-5634-0838"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yasunari Shidama","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13721987,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13608","display_name":"Advanced Computational Techniques in Science and Engineering","score":0.8313999772071838,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T13608","display_name":"Advanced Computational Techniques in Science and Engineering","score":0.8313999772071838,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T14438","display_name":"Advanced Scientific Research Methods","score":0.804099977016449,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T14470","display_name":"Advanced Data Processing Techniques","score":0.7890999913215637,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.7398947477340698},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5370017886161804},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4233737587928772},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3202540874481201},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28273317217826843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22323566675186157}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7398947477340698},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5370017886161804},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4233737587928772},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3202540874481201},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28273317217826843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22323566675186157},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2478/v10037-011-0010-9","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0010-9","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0010-9","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:86b3afda-d592-4c28-8e64-0afed7479f02/oai:repozytorium.uwb.edu.pl:11320/3597","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401248","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.228.9529","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.228.9529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mizar.org/fm/2011-19/pdf19-1/rlvect_x.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:2717383ee3ad455cbf2179c929ad4a11","is_oa":false,"landing_page_url":"https://doaj.org/article/2717383ee3ad455cbf2179c929ad4a11","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 19, Iss 1, Pp 61-64 (2011)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3597","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/3597","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-011-0010-9","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0010-9","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0010-9","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997215029.pdf","grobid_xml":"https://content.openalex.org/works/W1997215029.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W68895216","https://openalex.org/W1619732349","https://openalex.org/W2098464720","https://openalex.org/W2105559527","https://openalex.org/W2134234040","https://openalex.org/W2143779468","https://openalex.org/W2150348213","https://openalex.org/W2150348943","https://openalex.org/W2159772409","https://openalex.org/W2160628721","https://openalex.org/W2163641194","https://openalex.org/W4234359518"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Formalization":[0],"of":[1],"Integral":[2,20],"Linear":[3],"SpaceIn":[4],"this":[5],"article,":[6],"we":[7],"formalize":[8],"integral":[9],"linear":[10,15,21],"spaces,":[11],"that":[12,33],"is":[13],"a":[14],"space":[16],"with":[17,41],"integer":[18],"coefficients.":[19],"spaces":[22],"are":[23],"necessary":[24],"for":[25],"lattice":[26,36,42],"problems,":[27],"LLL":[28],"(Lenstra-Lenstra-Lov\u00e1sz)":[29],"base":[30,37],"reduction":[31],"algorithm":[32],"outputs":[34],"short":[35],"and":[38],"cryptographic":[39],"systems":[40],"[8].":[43]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}