{"id":"https://openalex.org/W2058865345","doi":"https://doi.org/10.1145/1837934.1837944","title":"A new incremental algorithm for computing Groebner bases","display_name":"A new incremental algorithm for computing Groebner bases","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W2058865345","doi":"https://doi.org/10.1145/1837934.1837944","mag":"2058865345"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837944","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837944","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 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/A5008978009","display_name":"Shuhong Gao","orcid":"https://orcid.org/0000-0002-0937-1727"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuhong Gao","raw_affiliation_strings":["Clemson University, Clemson, SC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clemson University, Clemson, SC","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037241972","display_name":"Yinhua Guan","orcid":null},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yinhua Guan","raw_affiliation_strings":["Clemson University, Clemson, SC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clemson University, Clemson, SC","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072902951","display_name":"Frank Volny","orcid":null},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frank Volny","raw_affiliation_strings":["Clemson University, Clemson, SC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clemson University, Clemson, SC","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.9627,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.98598632,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"13","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9940999746322632,"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":0.9918000102043152,"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/ideal","display_name":"Ideal (ethics)","score":0.7461299300193787},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.7226776480674744},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6862725019454956},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6084252595901489},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.586324155330658},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.577756404876709},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5095422863960266},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46833324432373047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43278008699417114}],"concepts":[{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.7461299300193787},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.7226776480674744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6862725019454956},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6084252595901489},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.586324155330658},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.577756404876709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5095422863960266},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46833324432373047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43278008699417114},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1837934.1837944","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837944","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3882996133","display_name":null,"funder_award_id":"DMS-0302549CCF-0830481","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G483551510","display_name":null,"funder_award_id":"H98230-08-1-0030","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1480291365","https://openalex.org/W1480389758","https://openalex.org/W1481997196","https://openalex.org/W1483218536","https://openalex.org/W1512302998","https://openalex.org/W1524190946","https://openalex.org/W1583871653","https://openalex.org/W1977574397","https://openalex.org/W1993995116","https://openalex.org/W2038345254","https://openalex.org/W2062777165","https://openalex.org/W2077725083","https://openalex.org/W2116004197","https://openalex.org/W2128687423","https://openalex.org/W4238858352","https://openalex.org/W4292096448","https://openalex.org/W6601133693","https://openalex.org/W6628651355"],"related_works":["https://openalex.org/W4364360507","https://openalex.org/W627423529","https://openalex.org/W4389670741","https://openalex.org/W2055878129","https://openalex.org/W2949221213","https://openalex.org/W605041788","https://openalex.org/W3149342578","https://openalex.org/W2117849070","https://openalex.org/W2952826522","https://openalex.org/W1984961932"],"abstract_inverted_index":{"In":[0,88,110],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5,25,31,49],"new":[6,54],"algorithm":[7,13,77,140],"for":[8,35,52,81],"computing":[9],"Gr\u00f6bner":[10,32,50,79],"bases.":[11],"Our":[12,76],"is":[14,29,45,141],"incremental":[15],"in":[16,98,119,125],"the":[17,53,68,128],"same":[18],"fashion":[19],"as":[20,106,108],"F5":[21,100,151],"and":[22,39,43,84,122,152],"F5C.":[23,153],"At":[24],"typical":[26],"step,":[27],"one":[28],"given":[30],"basis":[33,51],"G":[34],"an":[36],"ideal":[37,55,70],"I":[38,60,72],"any":[40],"polynomial":[41],"g,":[42],"it":[44],"desired":[46],"to":[47,94,102,146],"compute":[48],"<I,":[56,82],"g>,":[57],"obtained":[58],"from":[59],"by":[61,74],"joining":[62],"g.":[63,75],"Let":[64],"(I:":[65,85,120],"g)":[66,86,121],"denote":[67],"colon":[69],"of":[71],"divided":[73],"computes":[78],"bases":[80],"g>":[83],"simultaneously.":[87],"previous":[89],"algorithms,":[90],"S-polynomials":[91,116],"that":[92,138],"reduce":[93],"zero":[95],"are":[96,123],"useless,":[97],"fact,":[99],"tries":[101],"avoid":[103],"such":[104],"reductions":[105],"much":[107,142],"possible.":[109],"our":[111,139],"algorithm,":[112],"however,":[113],"these":[114],"\"useless\"":[115],"give":[117],"elements":[118],"useful":[124],"speeding":[126],"up":[127],"subsequent":[129],"computations.":[130],"Computer":[131],"experiments":[132],"on":[133],"some":[134],"benchmark":[135],"examples":[136],"indicate":[137],"more":[143],"efficient":[144],"(two":[145],"ten":[147],"times":[148],"faster)":[149],"than":[150]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}