{"id":"https://openalex.org/W2904582217","doi":"https://doi.org/10.1007/s10817-018-09504-w","title":"A Verified Implementation of Algebraic Numbers in Isabelle/HOL","display_name":"A Verified Implementation of Algebraic Numbers in Isabelle/HOL","publication_year":2018,"publication_date":"2018-12-09","ids":{"openalex":"https://openalex.org/W2904582217","doi":"https://doi.org/10.1007/s10817-018-09504-w","mag":"2904582217","pmid":"https://pubmed.ncbi.nlm.nih.gov/32226180"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-018-09504-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-018-09504-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-018-09504-w.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10817-018-09504-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006751254","display_name":"Sebastiaan J. C. Joosten","orcid":"https://orcid.org/0000-0002-6590-6220"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sebastiaan J. C. Joosten","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0002-6590-6220","affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078037586","display_name":"Ren\u00e9 Thiemann","orcid":"https://orcid.org/0000-0002-0323-8829"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Ren\u00e9 Thiemann","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0002-0323-8829","affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003947273","display_name":"Akihisa Yamada","orcid":"https://orcid.org/0000-0001-8872-2240"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Akihisa Yamada","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0001-8872-2240","affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078037586"],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.1866,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66264138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"64","issue":"3","first_page":"363","last_page":"389"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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/T10142","display_name":"Formal Methods in Verification","score":0.9865999817848206,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9672999978065491,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/hol","display_name":"HOL","score":0.818246603012085},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5946112871170044},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5754733681678772},{"id":"https://openalex.org/keywords/haskell","display_name":"Haskell","score":0.5334079265594482},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4993877410888672},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4700773060321808},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.427173376083374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42077019810676575},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.41418367624282837},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37292128801345825},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3492411971092224},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.33010268211364746},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2510106563568115},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15267005562782288},{"id":"https://openalex.org/keywords/functional-programming","display_name":"Functional programming","score":0.1271395981311798}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.818246603012085},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5946112871170044},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5754733681678772},{"id":"https://openalex.org/C2780624054","wikidata":"https://www.wikidata.org/wiki/Q34010","display_name":"Haskell","level":3,"score":0.5334079265594482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4993877410888672},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4700773060321808},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.427173376083374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42077019810676575},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.41418367624282837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37292128801345825},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3492411971092224},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.33010268211364746},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2510106563568115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15267005562782288},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.1271395981311798},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10817-018-09504-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-018-09504-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-018-09504-w.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmid:32226180","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32226180","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of automated reasoning","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:7089722","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7089722","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Autom Reason","raw_type":"Text"},{"id":"pmh:ut:oai:ris.utwente.nl:publications/5399b8ea-ea34-40d4-bba8-d3a066f33e2c","is_oa":true,"landing_page_url":"https://research.utwente.nl/experts/en/publications/5399b8ea-ea34-40d4-bba8-d3a066f33e2c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of automated reasoning. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10817-018-09504-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-018-09504-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-018-09504-w.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2904582217.pdf","grobid_xml":"https://content.openalex.org/works/W2904582217.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1713610","https://openalex.org/W101424827","https://openalex.org/W1419314641","https://openalex.org/W1568929477","https://openalex.org/W1966712204","https://openalex.org/W1966726229","https://openalex.org/W1977340462","https://openalex.org/W2008957088","https://openalex.org/W2022441937","https://openalex.org/W2070866504","https://openalex.org/W2090541423","https://openalex.org/W2134124371","https://openalex.org/W2256286306","https://openalex.org/W2269587551","https://openalex.org/W2295544473","https://openalex.org/W2295691230","https://openalex.org/W2400061809","https://openalex.org/W2564206325","https://openalex.org/W2775546494","https://openalex.org/W2798401172","https://openalex.org/W2951586102","https://openalex.org/W3151773185","https://openalex.org/W4210736085","https://openalex.org/W4239648988","https://openalex.org/W4250846042"],"related_works":["https://openalex.org/W2801835562","https://openalex.org/W2585743557","https://openalex.org/W196828063","https://openalex.org/W4247743232","https://openalex.org/W4238447024","https://openalex.org/W1602185604","https://openalex.org/W2911281194","https://openalex.org/W173120711","https://openalex.org/W1488646450","https://openalex.org/W2404299756"],"abstract_inverted_index":{"We":[0,21,52],"formalize":[1],"algebraic":[2,14,42],"numbers":[3],"in":[4],"Isabelle/HOL.":[5],"Our":[6],"development":[7,65],"serves":[8],"as":[9,71],"a":[10],"verified":[11,54],"implementation":[12],"of":[13,34],"operations":[15,59],"on":[16],"real":[17,30],"and":[18,37,47,75,78,90],"complex":[19,32],"numbers.":[20],"moreover":[22],"provide":[23],"algorithms":[24],"that":[25],"can":[26],"identify":[27],"all":[28],"the":[29],"or":[31],"roots":[33],"rational":[35],"polynomials,":[36,85],"two":[38],"implementations":[39],"to":[40],"display":[41],"numbers,":[43],"an":[44,48],"approximative":[45],"version":[46],"injective":[49],"precise":[50],"one.":[51],"obtain":[53],"Haskell":[55],"code":[56,62],"for":[57],"these":[58],"via":[60],"Isabelle's":[61],"generator.":[63],"The":[64],"combines":[66],"various":[67],"existing":[68],"formalizations":[69,82],"such":[70],"matrices,":[72],"Sturm's":[73],"theorem,":[74],"polynomial":[76],"factorization,":[77],"it":[79],"includes":[80],"new":[81],"about":[83],"bivariate":[84],"unique":[86],"factorization":[87],"domains,":[88],"resultants":[89],"subresultants.":[91]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}