{"id":"https://openalex.org/W2484904073","doi":"https://doi.org/10.1007/978-3-662-53132-7_10","title":"Both Ways Rational Functions","display_name":"Both Ways Rational Functions","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2484904073","doi":"https://doi.org/10.1007/978-3-662-53132-7_10","mag":"2484904073"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-53132-7_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-53132-7_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/A5113563002","display_name":"Christian Choffrut","orcid":"https://orcid.org/0000-0002-9849-3514"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"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":true,"raw_author_name":"Christian Choffrut","raw_affiliation_strings":["IRIF, CNRS and Universit\u00e9 Paris 7 Denis Diderot, Paris, France"],"affiliations":[{"raw_affiliation_string":"IRIF, CNRS and Universit\u00e9 Paris 7 Denis Diderot, Paris, France","institution_ids":["https://openalex.org/I169173203","https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040360969","display_name":"Bruno Guillon","orcid":"https://orcid.org/0000-0003-1630-3404"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"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"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Guillon","raw_affiliation_strings":["IRIF, CNRS and Universit\u00e9 Paris 7 Denis Diderot, Paris, France"],"affiliations":[{"raw_affiliation_string":"IRIF, CNRS and Universit\u00e9 Paris 7 Denis Diderot, Paris, France","institution_ids":["https://openalex.org/I169173203","https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113563002"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I169173203","https://openalex.org/I204730241"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09261603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"114","last_page":"124"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9976000189781189,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.996399998664856,"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/intersection","display_name":"Intersection (aeronautics)","score":0.8425260782241821},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7407333254814148},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6763278841972351},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5527693629264832},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.5356252789497375},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4634734094142914},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43652939796447754},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.4314882755279541},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.379177451133728},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32244807481765747},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30537155270576477},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26666921377182007},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24210989475250244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23359927535057068},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.05521276593208313},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.05006018280982971}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.8425260782241821},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7407333254814148},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6763278841972351},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5527693629264832},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.5356252789497375},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4634734094142914},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43652939796447754},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.4314882755279541},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.379177451133728},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32244807481765747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30537155270576477},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26666921377182007},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24210989475250244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23359927535057068},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.05521276593208313},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.05006018280982971},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-662-53132-7_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-53132-7_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":[{"id":"https://metadata.un.org/sdg/10","score":0.6800000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1505482284","https://openalex.org/W1584451387","https://openalex.org/W1965306495","https://openalex.org/W1981523035","https://openalex.org/W1990283467","https://openalex.org/W2034243894","https://openalex.org/W2054801208","https://openalex.org/W2068490784","https://openalex.org/W2106181999","https://openalex.org/W2107847539","https://openalex.org/W2167954650","https://openalex.org/W2406753696","https://openalex.org/W4206635485"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2954004777","https://openalex.org/W2949638731","https://openalex.org/W2951102138","https://openalex.org/W3098481198"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}