{"id":"https://openalex.org/W4251509274","doi":"https://doi.org/10.1007/3-540-48340-3_9","title":"On the Complexity of Recognizing the Hilbert Basis of a Linear Diophantine System","display_name":"On the Complexity of Recognizing the Hilbert Basis of a Linear Diophantine System","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W4251509274","doi":"https://doi.org/10.1007/3-540-48340-3_9"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-48340-3_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-48340-3_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5059509786","display_name":"Arnaud Durand","orcid":"https://orcid.org/0000-0002-7629-2121"},"institutions":[{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I2800365227","display_name":"Paris-Est Sup","ror":"https://ror.org/0268ecp52","country_code":"FR","type":"education","lineage":["https://openalex.org/I2800365227"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Arnaud Durand","raw_affiliation_strings":["LACL, Department of Computer Science, Universit\u00e9 Paris 12, 61, av. gen. de Gaule, 94010, Cr\u00e9teil, France","LACL, Department of Computer Science, Universit\u00e9 Paris 12, Cr\u00e9teil, France"],"affiliations":[{"raw_affiliation_string":"LACL, Department of Computer Science, Universit\u00e9 Paris 12, 61, av. gen. de Gaule, 94010, Cr\u00e9teil, France","institution_ids":["https://openalex.org/I197681013","https://openalex.org/I2800365227"]},{"raw_affiliation_string":"LACL, Department of Computer Science, Universit\u00e9 Paris 12, Cr\u00e9teil, France","institution_ids":["https://openalex.org/I197681013"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074896214","display_name":"Miki Hermann","orcid":"https://orcid.org/0000-0003-2517-2127"},"institutions":[{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210164347","display_name":"Henri Poincar\u00e9 Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210164347"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Miki Hermann","raw_affiliation_strings":["LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, BP 239, 54506, Vandceuvre-l\u00e8s-Nancy, France","LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, Vandceuvre-l\u00e8s-Nancy, France"],"affiliations":[{"raw_affiliation_string":"LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, BP 239, 54506, Vandceuvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, Vandceuvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I4210164347","https://openalex.org/I90183372","https://openalex.org/I1294671590","https://openalex.org/I4210121838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008850227","display_name":"Laurent Juban","orcid":null},"institutions":[{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210164347","display_name":"Henri Poincar\u00e9 Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210164347"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent Juban","raw_affiliation_strings":["LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, BP 239, 54506, Vandceuvre-l\u00e8s-Nancy, France","LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, Vandceuvre-l\u00e8s-Nancy, France"],"affiliations":[{"raw_affiliation_string":"LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, BP 239, 54506, Vandceuvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LORIA (CNRS and Universit\u00e9 Henri Poincar\u00e9 Nancy 1, Vandceuvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I4210164347","https://openalex.org/I90183372","https://openalex.org/I1294671590","https://openalex.org/I4210121838"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059509786"],"corresponding_institution_ids":["https://openalex.org/I197681013","https://openalex.org/I2800365227"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.41633428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"92","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.996999979019165,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9944999814033508,"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/diophantine-equation","display_name":"Diophantine equation","score":0.740972638130188},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7248082756996155},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.5748411417007446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5737649202346802},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.547450602054596},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4646781086921692},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4642335772514343},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4317021071910858},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.339482843875885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3116375505924225},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2599813640117645}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.740972638130188},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7248082756996155},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.5748411417007446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5737649202346802},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.547450602054596},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4646781086921692},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4642335772514343},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4317021071910858},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.339482843875885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3116375505924225},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2599813640117645},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-48340-3_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-48340-3_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W184033727","https://openalex.org/W272982077","https://openalex.org/W276224435","https://openalex.org/W1530895745","https://openalex.org/W1652781893","https://openalex.org/W1977818404","https://openalex.org/W1991466985","https://openalex.org/W2011618311","https://openalex.org/W2016416448","https://openalex.org/W2032980094","https://openalex.org/W2033288425","https://openalex.org/W2062908445","https://openalex.org/W2103658959","https://openalex.org/W3140292214"],"related_works":["https://openalex.org/W2325635326","https://openalex.org/W2061854932","https://openalex.org/W3135745187","https://openalex.org/W2505077532","https://openalex.org/W2053402117","https://openalex.org/W1651871864","https://openalex.org/W1984486938","https://openalex.org/W2245813304","https://openalex.org/W2050191224","https://openalex.org/W2792126174"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
