{"id":"https://openalex.org/W2071102429","doi":"https://doi.org/10.1007/s10208-012-9137-5","title":"A New Computational Approach to Ideal Theory in Number Fields","display_name":"A New Computational Approach to Ideal Theory in Number Fields","publication_year":2012,"publication_date":"2012-10-03","ids":{"openalex":"https://openalex.org/W2071102429","doi":"https://doi.org/10.1007/s10208-012-9137-5","mag":"2071102429"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-012-9137-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-012-9137-5","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/2117/28201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048913025","display_name":"Jordi Gu\u00e0rdia","orcid":"https://orcid.org/0000-0003-3287-9358"},"institutions":[{"id":"https://openalex.org/I4210133992","display_name":"Cidete (Spain)","ror":"https://ror.org/03v79p997","country_code":"ES","type":"company","lineage":["https://openalex.org/I4210133992"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jordi Gu\u00e0rdia","raw_affiliation_strings":["Departament de Matem\u00e0tica Aplicada IV, Escola Polit\u00e8cnica Superior d\u2019Enginyera de Vilanova i la Geltr\u00fa, Av. V\u00edctor Balaguer s/n., 08800, Vilanova i la Geltr\u00fa, Catalonia, Spain","Departament de Matem\u00e0tica Aplicada IV, Escola Polit\u00e8cnica Superior d\u2019Enginyera de Vilanova i la Geltr\u00fa, Vilanova i la Geltr\u00fa, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada IV, Escola Polit\u00e8cnica Superior d\u2019Enginyera de Vilanova i la Geltr\u00fa, Av. V\u00edctor Balaguer s/n., 08800, Vilanova i la Geltr\u00fa, Catalonia, Spain","institution_ids":["https://openalex.org/I4210133992"]},{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada IV, Escola Polit\u00e8cnica Superior d\u2019Enginyera de Vilanova i la Geltr\u00fa, Vilanova i la Geltr\u00fa, Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067393096","display_name":"Jes\u00fas Sanz Montes","orcid":"https://orcid.org/0000-0002-2059-0648"},"institutions":[{"id":"https://openalex.org/I2801339427","display_name":"Universitat Abat Oliba CEU","ror":"https://ror.org/00vkhbp60","country_code":"ES","type":"education","lineage":["https://openalex.org/I2801318690","https://openalex.org/I2801339427"]},{"id":"https://openalex.org/I42134832","display_name":"Barcelona School of Economics","ror":"https://ror.org/02k09n368","country_code":"ES","type":"education","lineage":["https://openalex.org/I42134832"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jes\u00fas Montes","raw_affiliation_strings":["Departament de Ci\u00e8ncies Econ\u00f2miques i Empresarials, Facultat de Ci\u00e8ncies Socials, Universitat Abat Oliba CEU, Bellesguard 30, 08022, Barcelona, Catalonia, Spain","Departament de Matem\u00e0tica Econ\u00f2mica, Financera i Actuarial, Facultat d\u2019Economia i Empresa, Univ. de Barcelona, Av. Diagonal 690, 08034, Barcelona, Catalonia, Spain","Departament de Ci\u00e8ncies Econ\u00f2miques i Empresarials, Facultat de Ci\u00e8ncies Socials, Universitat Abat Oliba CEU, Barcelona, Spain","Departament de Matem\u00e0tica Econ\u00f2mica, Financera i Actuarial, Facultat d\u2019Economia i Empresa, Univ. de Barcelona, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Ci\u00e8ncies Econ\u00f2miques i Empresarials, Facultat de Ci\u00e8ncies Socials, Universitat Abat Oliba CEU, Bellesguard 30, 08022, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I2801339427"]},{"raw_affiliation_string":"Departament de Matem\u00e0tica Econ\u00f2mica, Financera i Actuarial, Facultat d\u2019Economia i Empresa, Univ. de Barcelona, Av. Diagonal 690, 08034, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I42134832"]},{"raw_affiliation_string":"Departament de Ci\u00e8ncies Econ\u00f2miques i Empresarials, Facultat de Ci\u00e8ncies Socials, Universitat Abat Oliba CEU, Barcelona, Spain","institution_ids":["https://openalex.org/I2801339427"]},{"raw_affiliation_string":"Departament de Matem\u00e0tica Econ\u00f2mica, Financera i Actuarial, Facultat d\u2019Economia i Empresa, Univ. de Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I42134832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085265108","display_name":"Enric Nart","orcid":"https://orcid.org/0000-0003-1122-3587"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Enric Nart","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Catalonia, Spain","Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085265108"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.1907,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.93910806,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"5","first_page":"729","last_page":"762"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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":0.9995999932289124,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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":0.8674699068069458},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6838988065719604},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.6789791584014893},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.6301243305206299},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5890881419181824},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5850397944450378},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5189570784568787},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5080165863037109},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.47544193267822266},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4721809923648834},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4655948579311371},{"id":"https://openalex.org/keywords/ideal-class-group","display_name":"Ideal class group","score":0.4611395299434662},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4554223418235779},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.44375696778297424},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4383186101913452},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42945975065231323},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3705534338951111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35371333360671997},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3319825232028961},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13514652848243713},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.11631789803504944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09477189183235168}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8674699068069458},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6838988065719604},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.6789791584014893},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.6301243305206299},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5890881419181824},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5850397944450378},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5189570784568787},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5080165863037109},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.47544193267822266},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4721809923648834},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4655948579311371},{"id":"https://openalex.org/C8367249","wikidata":"https://www.wikidata.org/wiki/Q912083","display_name":"Ideal class group","level":3,"score":0.4611395299434662},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4554223418235779},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.44375696778297424},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4383186101913452},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42945975065231323},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3705534338951111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35371333360671997},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3319825232028961},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13514652848243713},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.11631789803504944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09477189183235168},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10208-012-9137-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-012-9137-5","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dnet:upcommonspor::98d5845edfd75c12131408a44a5e9986","is_oa":false,"landing_page_url":"http://hdl.handle.net/2117/28201","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/submittedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/28201","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/28201","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/28201","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/28201","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6899999976158142}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W101645569","https://openalex.org/W1507575253","https://openalex.org/W1517477680","https://openalex.org/W1559749967","https://openalex.org/W1600941563","https://openalex.org/W1618719422","https://openalex.org/W1983786246","https://openalex.org/W1989603733","https://openalex.org/W1992593698","https://openalex.org/W1994311642","https://openalex.org/W1996569649","https://openalex.org/W1996919471","https://openalex.org/W2082859462","https://openalex.org/W2105684831","https://openalex.org/W2136801509","https://openalex.org/W2139607673","https://openalex.org/W2152151784","https://openalex.org/W2319760605","https://openalex.org/W2963254673","https://openalex.org/W2963903984","https://openalex.org/W4239519337","https://openalex.org/W4249032716"],"related_works":["https://openalex.org/W4283079877","https://openalex.org/W1985839497","https://openalex.org/W4389775193","https://openalex.org/W1997795239","https://openalex.org/W2917630846","https://openalex.org/W2972191904","https://openalex.org/W90516001","https://openalex.org/W4200059635","https://openalex.org/W1544197109","https://openalex.org/W3171434944"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}