{"id":"https://openalex.org/W2103185909","doi":"https://doi.org/10.1145/1837934.1837946","title":"A new algorithm for computing comprehensive Gr\u00f6bner systems","display_name":"A new algorithm for computing comprehensive Gr\u00f6bner systems","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W2103185909","doi":"https://doi.org/10.1145/1837934.1837946","mag":"2103185909"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837946","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837946","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":"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/A5003856856","display_name":"Deepak Kapur","orcid":"https://orcid.org/0000-0003-2464-2895"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deepak Kapur","raw_affiliation_strings":["University of New Mexico, Albuquerque, NM","University of New Mexico, albuquerque, NM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, NM","institution_ids":["https://openalex.org/I169521973"]},{"raw_affiliation_string":"University of New Mexico, albuquerque, NM","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101536898","display_name":"Yao Sun","orcid":"https://orcid.org/0000-0002-1163-9630"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao Sun","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science, CAS, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science, CAS, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101585436","display_name":"Dingkang Wang","orcid":"https://orcid.org/0000-0002-5844-1277"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dingkang Wang","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science, CAS, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science, CAS, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"29","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9929999709129333,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9889000058174133,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6956223845481873},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5839491486549377},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5729946494102478},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.5724111795425415},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.524825394153595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49720457196235657},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4563515782356262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4200923442840576},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.2722522020339966}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6956223845481873},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5839491486549377},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5729946494102478},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.5724111795425415},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.524825394153595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49720457196235657},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4563515782356262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4200923442840576},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2722522020339966},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1837934.1837946","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837946","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.362.3303","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.362.3303","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.unm.edu/~kapur/mypapers/ISSAC2010.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2093698350","display_name":null,"funder_award_id":"109712171077120660821002/F02","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6301138391","display_name":null,"funder_award_id":"CCF-0729097","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W1483218536","https://openalex.org/W1543638401","https://openalex.org/W1990119084","https://openalex.org/W2045154989","https://openalex.org/W2057105460","https://openalex.org/W2070075204","https://openalex.org/W2078863580","https://openalex.org/W2095764258","https://openalex.org/W2097649661","https://openalex.org/W2104693850","https://openalex.org/W2157458292","https://openalex.org/W2159289729","https://openalex.org/W2168553897","https://openalex.org/W2501430986","https://openalex.org/W2949560367","https://openalex.org/W3086943959","https://openalex.org/W3102191769","https://openalex.org/W4292096448"],"related_works":["https://openalex.org/W3162124064","https://openalex.org/W2953857700","https://openalex.org/W2590472383","https://openalex.org/W3091355467","https://openalex.org/W2383873009","https://openalex.org/W2393580911","https://openalex.org/W2212184297","https://openalex.org/W3156456913","https://openalex.org/W2055878129","https://openalex.org/W2379877967"],"abstract_inverted_index":{"A":[0],"new":[1,74,218],"algorithm":[2,19,29,43,75,78,122,226,259,265],"for":[3,147,181,193],"computing":[4,89],"a":[5,10,40,80,91,131,135,184,188,208,217,235,245],"comprehensive":[6,48,136],"Gr\u00f6bner":[7,49,92,116,137],"system":[8],"of":[9,51,64,72,94,115,118,161,197,200,237,248],"parametric":[11,52,105,186,201],"polynomial":[12,53,146],"ideal":[13,96,199],"over":[14,97],"k[U][X]":[15],"is":[16,44,76,140,165,177,191,204],"presented.":[17],"This":[18,203],"generates":[20],"fewer":[21],"branches":[22,102,169,249],"(segments)":[23],"compared":[24,255],"to":[25,46,134,143,171,207,270],"Suzuki":[26,84],"and":[27,85,113,232,250,260],"Sato's":[28],"as":[30,32,220],"well":[31,66],"Nabeshima's":[33,222,261],"algorithm,":[34],"resulting":[35],"in":[36,130,153,205,221,230],"considerable":[37],"efficiency.":[38],"As":[39],"result,":[41],"the":[42,62,73,120,124,156,159,172,257,272],"able":[45],"compute":[47],"systems":[50],"ideals":[54],"arising":[55],"from":[56,239,276],"applications":[57],"which":[58],"have":[59],"been":[60,228,254,267],"beyond":[61],"reach":[63],"other":[65,168],"known":[67],"algorithms.":[68],"The":[69,224,264],"starting":[70],"point":[71],"Weispfenning's":[77],"with":[79,155,183,234,256],"key":[81],"insight":[82],"by":[83],"Sato":[86],"who":[87],"proposed":[88,121,225],"first":[90],"basis":[93,117],"an":[95,198],"k[U,X]":[98],"before":[99],"performing":[100],"any":[101,128],"based":[103,212],"on":[104,108,213],"constraints.":[106,202],"Based":[107],"Kalkbrener's":[109],"results":[110],"about":[111],"stability":[112],"specialization":[114],"ideals,":[119],"exploits":[123],"result":[125],"that":[126,158],"along":[127],"branch":[129],"tree":[132],"corresponding":[133],"system,":[138],"it":[139],"only":[141],"necessary":[142],"consider":[144],"one":[145],"each":[148],"nondivisible":[149],"leading":[150,163],"power":[151],"product":[152,160,176],"k(U)[X]":[154],"condition":[157],"their":[162],"coefficients":[164],"not":[166],"0;":[167],"correspond":[170],"cases":[173],"where":[174],"this":[175],"0.":[178],"In":[179],"addition,":[180],"dealing":[182],"disequality":[185],"constraint,":[187],"probabilistic":[189],"check":[190,211],"employed":[192],"radical":[194],"membership":[195],"test":[196],"contrast":[206],"general":[209],"expensive":[210],"Rabinovitch's":[214],"trick":[215],"using":[216],"variable":[219],"algorithm.":[223,263],"has":[227,253,266],"implemented":[229],"Magma":[231],"experimented":[233],"number":[236,247],"examples":[238],"different":[240],"applications.":[241],"Its":[242],"performance":[243],"(vis":[244],"vie":[246],"execution":[251],"timings)":[252],"Suzuki-Sato's":[258],"speed-up":[262],"successfully":[268],"used":[269],"solve":[271],"famous":[273],"P3P":[274],"problem":[275],"computer":[277],"vision.":[278]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
