{"id":"https://openalex.org/W1967644849","doi":"https://doi.org/10.1016/s0747-7171(89)80053-7","title":"The computation of polynomial greatest common divisors over an algebraic number field","display_name":"The computation of polynomial greatest common divisors over an algebraic number field","publication_year":1989,"publication_date":"1989-11-01","ids":{"openalex":"https://openalex.org/W1967644849","doi":"https://doi.org/10.1016/s0747-7171(89)80053-7","mag":"1967644849"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(89)80053-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(89)80053-7","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/A5022694274","display_name":"Lars Langemyr","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Lars Langemyr","raw_affiliation_strings":["Numerical Analysis and Computing Science Royal Institute of Technology S-100 44 Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Analysis and Computing Science Royal Institute of Technology S-100 44 Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061480464","display_name":"Scott McCallum","orcid":"https://orcid.org/0000-0002-5682-7993"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Scott McCallum","raw_affiliation_strings":["Institut f\u00fcr Mathematik Johannes Kepler Universit\u00e4t A-4040 Linz, Austria","Institut f\u00fcr Mathematik Johannes Kepler Universit\u00e4t A-4040 Linz, Austria#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik Johannes Kepler Universit\u00e4t A-4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik Johannes Kepler Universit\u00e4t A-4040 Linz, Austria#TAB#","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3160,"currency":"USD","value_usd":3160},"apc_paid":null,"fwci":2.4676,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.91392801,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"5","first_page":"429","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9610999822616577,"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/mathematics","display_name":"Mathematics","score":0.8639586567878723},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.7726150751113892},{"id":"https://openalex.org/keywords/divisor","display_name":"Divisor (algebraic geometry)","score":0.5940150022506714},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5379109978675842},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.5113405585289001},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5019872188568115},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.49595460295677185},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4547147750854492},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4466700851917267},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.4391537010669708},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.4384395480155945},{"id":"https://openalex.org/keywords/factorization-of-polynomials","display_name":"Factorization of polynomials","score":0.43142300844192505},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.4252453148365021},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41713839769363403},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41442596912384033},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3953297734260559},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.24143120646476746},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21271124482154846},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17963632941246033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09453490376472473}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8639586567878723},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.7726150751113892},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.5940150022506714},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5379109978675842},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.5113405585289001},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5019872188568115},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.49595460295677185},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4547147750854492},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4466700851917267},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.4391537010669708},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.4384395480155945},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.43142300844192505},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4252453148365021},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41713839769363403},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41442596912384033},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3953297734260559},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.24143120646476746},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21271124482154846},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17963632941246033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09453490376472473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0747-7171(89)80053-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(89)80053-7","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W45802723","https://openalex.org/W180799239","https://openalex.org/W1480319329","https://openalex.org/W1527913126","https://openalex.org/W1558198085","https://openalex.org/W1565449944","https://openalex.org/W1580549372","https://openalex.org/W1594459799","https://openalex.org/W1815267262","https://openalex.org/W1966711586","https://openalex.org/W2003536029","https://openalex.org/W2008957088","https://openalex.org/W2029317328","https://openalex.org/W2040355635","https://openalex.org/W2054581185","https://openalex.org/W2067705970","https://openalex.org/W3217399827","https://openalex.org/W6601851074","https://openalex.org/W6631715684","https://openalex.org/W6633998609","https://openalex.org/W6634835210","https://openalex.org/W6635447470","https://openalex.org/W6638414094","https://openalex.org/W6638588722"],"related_works":["https://openalex.org/W1985839497","https://openalex.org/W4245225834","https://openalex.org/W2091873297","https://openalex.org/W2950634696","https://openalex.org/W2049824936","https://openalex.org/W2963486187","https://openalex.org/W2917630846","https://openalex.org/W4296215569","https://openalex.org/W2073501925","https://openalex.org/W2407588445"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}