{"id":"https://openalex.org/W2045154989","doi":"https://doi.org/10.1145/1145768.1145821","title":"A simple algorithm to compute comprehensive Gr\u00f6bner bases using Gr\u00f6bner bases","display_name":"A simple algorithm to compute comprehensive Gr\u00f6bner bases using Gr\u00f6bner bases","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W2045154989","doi":"https://doi.org/10.1145/1145768.1145821","mag":"2045154989"},"language":"en","primary_location":{"id":"doi:10.1145/1145768.1145821","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5006300612","display_name":"Akira Suzuki","orcid":"https://orcid.org/0000-0002-5950-8808"},"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":"Akira Suzuki","raw_affiliation_strings":["Kobe University, Kobe, Japan","[Kobe University, Kobe, JAPAN]"],"affiliations":[{"raw_affiliation_string":"Kobe University, Kobe, Japan","institution_ids":["https://openalex.org/I65837984"]},{"raw_affiliation_string":"[Kobe University, Kobe, JAPAN]","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050208307","display_name":"Yosuke Sato","orcid":"https://orcid.org/0000-0002-2772-2332"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yosuke Sato","raw_affiliation_strings":["Tokyo University of Science, Tokyo, Japan","Tokyo Univ. of Science, Tokyo, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Tokyo University of Science, Tokyo, Japan","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"Tokyo Univ. of Science, Tokyo, Japan#TAB#","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006300612"],"corresponding_institution_ids":["https://openalex.org/I65837984"],"apc_list":null,"apc_paid":null,"fwci":8.789,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.98305842,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"326","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9937999844551086,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.7912561297416687},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6807923913002014},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5940966606140137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5819911360740662},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.5735967755317688},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49941110610961914},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.49764397740364075},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47427019476890564},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3143273591995239},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09337058663368225},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08419856429100037}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7912561297416687},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6807923913002014},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5940966606140137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5819911360740662},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.5735967755317688},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49941110610961914},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.49764397740364075},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47427019476890564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3143273591995239},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09337058663368225},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08419856429100037},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1145768.1145821","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W1543638401","https://openalex.org/W1976913643","https://openalex.org/W1986264093","https://openalex.org/W2051458738","https://openalex.org/W2057105460","https://openalex.org/W2078863580","https://openalex.org/W2095764258","https://openalex.org/W2168553897","https://openalex.org/W3007626758","https://openalex.org/W3086943959","https://openalex.org/W4243098353"],"related_works":["https://openalex.org/W2120447654","https://openalex.org/W2977179488","https://openalex.org/W2144453115","https://openalex.org/W2128223750","https://openalex.org/W4238532390","https://openalex.org/W2188872161","https://openalex.org/W2363922099","https://openalex.org/W908473976","https://openalex.org/W4251421746","https://openalex.org/W2384965142"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,41],"simple":[3,27],"algorithm":[4],"to":[5,43],"compute":[6,44],"comprehensive":[7],"Gr\u00f6bner":[8,16,46],"bases.":[9,47],"It":[10,24],"requires":[11],"only":[12],"computations":[13],"of":[14],"reduced":[15,45],"bases":[17],"in":[18],"polynomial":[19],"rings":[20],"over":[21],"ground":[22],"fields.":[23],"is":[25,58],"so":[26],"that":[28,39,56],"we":[29],"can":[30],"easily":[31],"implement":[32],"it":[33,57],"on":[34,50],"any":[35],"computer":[36,52],"algebra":[37,53],"system":[38],"has":[40],"routine":[42],"Our":[48],"implementations":[49],"several":[51],"systems":[54],"show":[55],"also":[59],"sufficiently":[60],"fast":[61],"comparing":[62],"with":[63],"other":[64],"existing":[65],"algorithms.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2026-03-12T06:13:28.667946","created_date":"2025-10-10T00:00:00"}