{"id":"https://openalex.org/W1538583102","doi":"https://doi.org/10.1007/11832225_9","title":"An Efficient Implementation for Computing Gr\u00f6bner Bases over Algebraic Number Fields","display_name":"An Efficient Implementation for Computing Gr\u00f6bner Bases over Algebraic Number Fields","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1538583102","doi":"https://doi.org/10.1007/11832225_9","mag":"1538583102"},"language":"en","primary_location":{"id":"doi:10.1007/11832225_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11832225_9","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":"conference-paper","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/A5024995691","display_name":"Masayuki Noro","orcid":"https://orcid.org/0009-0003-4953-8258"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masayuki Noro","raw_affiliation_strings":["Kobe University, Rokko, Kobe, 657-8501, Japan","Kobe University, Rokko, Kobe, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kobe University, Rokko, Kobe, 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]},{"raw_affiliation_string":"Kobe University, Rokko, Kobe, Japan","institution_ids":["https://openalex.org/I65837984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024995691"],"corresponding_institution_ids":["https://openalex.org/I65837984"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.0554919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"99","last_page":"109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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/T11435","display_name":"Polynomial and algebraic computation","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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.7507457137107849},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6969572901725769},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6665377020835876},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6580411791801453},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.6080211997032166},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6037611961364746},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.597034215927124},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5778192281723022},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5754030346870422},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4254446029663086},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31857460737228394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2850682735443115},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2537745237350464},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12724918127059937}],"concepts":[{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.7507457137107849},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6969572901725769},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6665377020835876},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6580411791801453},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.6080211997032166},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6037611961364746},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.597034215927124},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5778192281723022},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5754030346870422},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4254446029663086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31857460737228394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2850682735443115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2537745237350464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12724918127059937},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11832225_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11832225_9","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W174479171","https://openalex.org/W611235695","https://openalex.org/W1496095451","https://openalex.org/W1604184456","https://openalex.org/W1969466615","https://openalex.org/W1980349404","https://openalex.org/W2085980606","https://openalex.org/W2128687423","https://openalex.org/W2187227451","https://openalex.org/W2495327222"],"related_works":["https://openalex.org/W4251748586","https://openalex.org/W2138135391","https://openalex.org/W3009369759","https://openalex.org/W1982652078","https://openalex.org/W4287829090","https://openalex.org/W2324501057","https://openalex.org/W2032816783","https://openalex.org/W2045665062","https://openalex.org/W225384710","https://openalex.org/W2057238117"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}