{"id":"https://openalex.org/W2068937275","doi":"https://doi.org/10.1006/jsco.1998.0235","title":"A Fast and Numerically Stable Euclidean-like Algorithm for Detecting Relatively Prime Numerical Polynomials","display_name":"A Fast and Numerically Stable Euclidean-like Algorithm for Detecting Relatively Prime Numerical Polynomials","publication_year":1998,"publication_date":"1998-12-01","ids":{"openalex":"https://openalex.org/W2068937275","doi":"https://doi.org/10.1006/jsco.1998.0235","mag":"2068937275"},"language":"en","primary_location":{"id":"doi:10.1006/jsco.1998.0235","is_oa":false,"landing_page_url":"https://doi.org/10.1006/jsco.1998.0235","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"},"type":"article","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/A5108751370","display_name":"Bernhard Beckermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Beckermann","raw_affiliation_strings":["Laboratoire d'Analyse Num\u00e9rique et d'Optimisation, Universit\u00e9 des Sciences et Technologies de Lille, Villeneuve d'Ascq Cedex, 59655, France","Laboratoire d'Analyse Num\u00e9rique et d'Optimisation, Universit\u00e9 des Sciences et Technologies de Lille, Villeneuve d'Ascq Cedex, 59655, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse Num\u00e9rique et d'Optimisation, Universit\u00e9 des Sciences et Technologies de Lille, Villeneuve d'Ascq Cedex, 59655, France","institution_ids":[]},{"raw_affiliation_string":"Laboratoire d'Analyse Num\u00e9rique et d'Optimisation, Universit\u00e9 des Sciences et Technologies de Lille, Villeneuve d'Ascq Cedex, 59655, France#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001656489","display_name":"George Labahn","orcid":"https://orcid.org/0009-0005-8977-4890"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"G. Labahn","raw_affiliation_strings":["Department of Computing Science, University of Waterloo, Waterloo, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3160,"currency":"USD","value_usd":3160},"apc_paid":null,"fwci":1.5046,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.82813849,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"6","first_page":"691","last_page":"714"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9955000281333923,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9955000281333923,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9934999942779541,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8427705764770508},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7418338060379028},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5752080082893372},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5161774754524231},{"id":"https://openalex.org/keywords/euclidean-algorithm","display_name":"Euclidean algorithm","score":0.48223528265953064},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.47567787766456604},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47555750608444214},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4495653808116913},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.4107821583747864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35895413160324097},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21780750155448914},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15600955486297607},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12983524799346924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09595745801925659},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09086108207702637}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8427705764770508},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7418338060379028},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5752080082893372},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5161774754524231},{"id":"https://openalex.org/C98371066","wikidata":"https://www.wikidata.org/wiki/Q230848","display_name":"Euclidean algorithm","level":2,"score":0.48223528265953064},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.47567787766456604},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47555750608444214},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4495653808116913},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.4107821583747864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35895413160324097},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21780750155448914},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15600955486297607},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12983524799346924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09595745801925659},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09086108207702637},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1006/jsco.1998.0235","is_oa":false,"landing_page_url":"https://doi.org/10.1006/jsco.1998.0235","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.20.8765","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.8765","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ano.univ-lille1.fr/pub/1998/ano382.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.22.4287","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.4287","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.scg.uwaterloo.ca/~glabahn/stable.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W208025404","https://openalex.org/W1572189095","https://openalex.org/W1628745019","https://openalex.org/W1976910007","https://openalex.org/W1990436029","https://openalex.org/W2017333591","https://openalex.org/W2021148028","https://openalex.org/W2034679035","https://openalex.org/W2038336192","https://openalex.org/W2045680067","https://openalex.org/W2046250296","https://openalex.org/W2055716315","https://openalex.org/W2061311874","https://openalex.org/W2089240964","https://openalex.org/W2150277007","https://openalex.org/W3104215207"],"related_works":["https://openalex.org/W283968525","https://openalex.org/W2182540961","https://openalex.org/W4250443881","https://openalex.org/W2299429778","https://openalex.org/W2953831318","https://openalex.org/W2102789413","https://openalex.org/W2610477248","https://openalex.org/W1691154265","https://openalex.org/W150316276","https://openalex.org/W2096467061"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
