{"id":"https://openalex.org/W1563257127","doi":"https://doi.org/10.1090/mcom/2969","title":"A new framework for computing Gr\u00f6bner bases","display_name":"A new framework for computing Gr\u00f6bner bases","publication_year":2015,"publication_date":"2015-05-20","ids":{"openalex":"https://openalex.org/W1563257127","doi":"https://doi.org/10.1090/mcom/2969","mag":"1563257127"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/2969","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/2969","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of 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/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":["Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","institution_ids":["https://openalex.org/I8078737"]},{"raw_affiliation_string":"Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"middle","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":["Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","institution_ids":["https://openalex.org/I8078737"]},{"raw_affiliation_string":"Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108047865","display_name":"Ming\u2010Sheng Wang","orcid":"https://orcid.org/0000-0002-2400-719X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingsheng Wang","raw_affiliation_strings":["Information Security Lab, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100190, People\u00e2\u0080\u0099s Republic of China","Information Security Lab, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100190, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Security Lab, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100190, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Information Security Lab, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100190, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0879,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.9555102,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"85","issue":"297","first_page":"449","last_page":"465"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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":0.9993000030517578,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9797999858856201,"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/hilberts-syzygy-theorem","display_name":"Hilbert's syzygy theorem","score":0.991586446762085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7243212461471558},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.7099616527557373},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.570105791091919},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5601344704627991},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5509131550788879},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5371181964874268},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.46924474835395813},{"id":"https://openalex.org/keywords/commutative-algebra","display_name":"Commutative algebra","score":0.45771661400794983},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.43801623582839966},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3824644088745117},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36866313219070435},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3081969618797302}],"concepts":[{"id":"https://openalex.org/C55101346","wikidata":"https://www.wikidata.org/wiki/Q85776755","display_name":"Hilbert's syzygy theorem","level":2,"score":0.991586446762085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7243212461471558},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7099616527557373},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.570105791091919},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5601344704627991},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5509131550788879},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5371181964874268},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.46924474835395813},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.45771661400794983},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.43801623582839966},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3824644088745117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36866313219070435},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3081969618797302},{"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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/2969","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/2969","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8225308827","display_name":null,"funder_award_id":"DMS-1005369","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1481997196","https://openalex.org/W1513904472","https://openalex.org/W1524190946","https://openalex.org/W1540142749","https://openalex.org/W1576188537","https://openalex.org/W1583871653","https://openalex.org/W1974339543","https://openalex.org/W1979128220","https://openalex.org/W1979661810","https://openalex.org/W1989653154","https://openalex.org/W1993995116","https://openalex.org/W2020179897","https://openalex.org/W2035842864","https://openalex.org/W2038345254","https://openalex.org/W2054143903","https://openalex.org/W2058865345","https://openalex.org/W2079751279","https://openalex.org/W2098942149","https://openalex.org/W2099172492","https://openalex.org/W2128687423","https://openalex.org/W2755856747","https://openalex.org/W2995200218","https://openalex.org/W4238858352"],"related_works":["https://openalex.org/W2352831285","https://openalex.org/W2351561193","https://openalex.org/W2023845786","https://openalex.org/W1991925681","https://openalex.org/W3187960866","https://openalex.org/W4287592125","https://openalex.org/W3107024117","https://openalex.org/W1753062909","https://openalex.org/W2070901745","https://openalex.org/W4226434942"],"abstract_inverted_index":{"This":[0,69,155],"paper":[1,183],"presents":[2],"a":[3,21,62,169],"new":[4],"framework":[5],"for":[6,10,44,50,103,116,128,158,166,173,187],"computing":[7,163,188],"Gr\u00f6bner":[8,42,48,67],"bases":[9,49,165],"ideals":[11],"and":[12,28,54,92,106],"syzygy":[13,31,56,130],"modules.":[14],"It":[15,82,132],"is":[16,61,133,156,168],"proposed":[17],"to":[18],"work":[19],"in":[20,90,96,176,191],"module":[22,32,46],"that":[23,141],"accommodates":[24],"any":[25,113],"given":[26,35,102],"ideal":[27,53],"the":[29,34,38,52,55,86,93,97,104,110,125,129,179],"corresponding":[30],"(for":[33],"generators":[36],"of":[37,65,109,181],"ideal).":[39],"A":[40],"strong":[41,66],"basis":[43],"this":[45,182],"contains":[47],"both":[51],"module.":[57],"The":[58],"main":[59,170],"result":[60],"simple":[63],"characterization":[64,70],"bases.":[68],"can":[71],"detect":[72],"useless":[73],"S-polynomials":[74],"without":[75],"reductions,":[76],"thus":[77],"yields":[78],"an":[79,117],"efficient":[80],"algorithm.":[81,111],"also":[83],"explains":[84],"all":[85],"rewritten":[87],"rules":[88],"used":[89],"F5":[91],"recent":[94],"papers":[95],"literature.":[98],"Rigorous":[99],"proofs":[100],"are":[101,148],"correctness":[105],"finite":[107],"termination":[108],"For":[112],"term":[114,126],"order":[115],"ideal,":[118],"one":[119],"may":[120],"vary":[121],"signature":[122,142,153],"orders":[123,127,143],"(i.e.":[124],"module).":[131],"shown":[134],"by":[135],"computer":[136],"experiments":[137],"on":[138,145],"benchmark":[139],"examples":[140],"based":[144],"weighted":[146],"terms":[147],"much":[149],"better":[150],"than":[151],"other":[152],"orders.":[154],"useful":[157,186],"practical":[159],"computation.":[160],"Also,":[161],"since":[162],"G\u00f6bner":[164],"syzygies":[167],"computational":[171],"task":[172],"free":[174,189],"resolutions":[175,190],"commutative":[177],"algebra,":[178],"algorithm":[180],"should":[184],"be":[185],"practice.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}