{"id":"https://openalex.org/W1535723389","doi":"https://doi.org/10.1007/10930755_10","title":"Embedding of Systems of Affine Recurrence Equations in Coq","display_name":"Embedding of Systems of Affine Recurrence Equations in Coq","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1535723389","doi":"https://doi.org/10.1007/10930755_10","mag":"1535723389"},"language":"en","primary_location":{"id":"doi:10.1007/10930755_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/10930755_10","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/A5026717554","display_name":"David Cachera","orcid":null},"institutions":[{"id":"https://openalex.org/I11559806","display_name":"\u00c9cole Normale Sup\u00e9rieure Paris-Saclay","ror":"https://ror.org/00hx6zz33","country_code":"FR","type":"education","lineage":["https://openalex.org/I11559806","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"David Cachera","raw_affiliation_strings":["IRISA / ENS Cachan (Bretagne), IRISA, Campus de Beaulieu, F-35042, France, Rennes"],"affiliations":[{"raw_affiliation_string":"IRISA / ENS Cachan (Bretagne), IRISA, Campus de Beaulieu, F-35042, France, Rennes","institution_ids":["https://openalex.org/I11559806","https://openalex.org/I2802519937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046752375","display_name":"David Pichardie","orcid":"https://orcid.org/0000-0002-2504-1760"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I11559806","display_name":"\u00c9cole Normale Sup\u00e9rieure Paris-Saclay","ror":"https://ror.org/00hx6zz33","country_code":"FR","type":"education","lineage":["https://openalex.org/I11559806","https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"David Pichardie","raw_affiliation_strings":["IRISA / ENS Cachan (Bretagne), IRISA, Campus de Beaulieu, F-35042, France, Rennes"],"affiliations":[{"raw_affiliation_string":"IRISA / ENS Cachan (Bretagne), IRISA, Campus de Beaulieu, F-35042, France, Rennes","institution_ids":["https://openalex.org/I11559806","https://openalex.org/I2802519937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026717554"],"corresponding_institution_ids":["https://openalex.org/I11559806","https://openalex.org/I2802519937"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5524,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64602437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"155","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9965999722480774,"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":0.9965999722480774,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9772999882698059,"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/embedding","display_name":"Embedding","score":0.7289625406265259},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7237211465835571},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.5825573801994324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5396644473075867},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.4970896542072296},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.46345752477645874},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4548512101173401},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.44547346234321594},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43124523758888245},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4148053228855133},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40537726879119873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3889373540878296},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.33067721128463745},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3292720913887024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19213774800300598},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.15342700481414795},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12742772698402405}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7289625406265259},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7237211465835571},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.5825573801994324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5396644473075867},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.4970896542072296},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.46345752477645874},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4548512101173401},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.44547346234321594},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43124523758888245},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4148053228855133},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40537726879119873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3889373540878296},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.33067721128463745},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3292720913887024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19213774800300598},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.15342700481414795},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12742772698402405},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/10930755_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/10930755_10","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1489250027","https://openalex.org/W1529227536","https://openalex.org/W1586367033","https://openalex.org/W1779991881","https://openalex.org/W2002252837","https://openalex.org/W2021592352","https://openalex.org/W2056859537","https://openalex.org/W2074367725","https://openalex.org/W2122523586","https://openalex.org/W2123984632","https://openalex.org/W2140447295","https://openalex.org/W2202520356","https://openalex.org/W2742127623"],"related_works":["https://openalex.org/W2120447654","https://openalex.org/W2977179488","https://openalex.org/W2144453115","https://openalex.org/W2128223750","https://openalex.org/W4238532390","https://openalex.org/W2188872161","https://openalex.org/W2002978035","https://openalex.org/W2961779879","https://openalex.org/W797688974","https://openalex.org/W2209382646"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
