{"id":"https://openalex.org/W2055878129","doi":"https://doi.org/10.1145/1993886.1993918","title":"Computing comprehensive Gr\u00f6bner systems and comprehensive Gr\u00f6bner bases simultaneously","display_name":"Computing comprehensive Gr\u00f6bner systems and comprehensive Gr\u00f6bner bases simultaneously","publication_year":2011,"publication_date":"2011-06-08","ids":{"openalex":"https://openalex.org/W2055878129","doi":"https://doi.org/10.1145/1993886.1993918","mag":"2055878129"},"language":"en","primary_location":{"id":"doi:10.1145/1993886.1993918","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th 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, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, NM, USA","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/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/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":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy Of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy Of Sciences, 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/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/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":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy Of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy Of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"193","last_page":"200"},"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/T10142","display_name":"Formal Methods in Verification","score":0.9842000007629395,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.9109957814216614},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8435367345809937},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.7216650247573853},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6769298911094666},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5855194330215454},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4927377998828888},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.48232147097587585},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4739525318145752},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.4203642010688782},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3327246308326721},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3305714428424835},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.277376651763916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06923374533653259}],"concepts":[{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.9109957814216614},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8435367345809937},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.7216650247573853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6769298911094666},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5855194330215454},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4927377998828888},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.48232147097587585},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4739525318145752},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.4203642010688782},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3327246308326721},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3305714428424835},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.277376651763916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06923374533653259},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1993886.1993918","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th 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":18,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W26772505","https://openalex.org/W1483218536","https://openalex.org/W1536271794","https://openalex.org/W1990119084","https://openalex.org/W1992805538","https://openalex.org/W2045154989","https://openalex.org/W2048154069","https://openalex.org/W2095764258","https://openalex.org/W2097649661","https://openalex.org/W2103185909","https://openalex.org/W2104693850","https://openalex.org/W2157458292","https://openalex.org/W2159289729","https://openalex.org/W2163740240","https://openalex.org/W2168553897","https://openalex.org/W3086943959","https://openalex.org/W3102191769"],"related_works":["https://openalex.org/W2055878129","https://openalex.org/W2149734642","https://openalex.org/W4298079332","https://openalex.org/W4311251537","https://openalex.org/W1523746755","https://openalex.org/W3216258873","https://openalex.org/W4320917455","https://openalex.org/W3114480276","https://openalex.org/W1984887342","https://openalex.org/W4205471980"],"abstract_inverted_index":{"In":[0],"Kapur":[1],"et":[2],"al":[3],"(ISSAC,":[4,279],"2010),":[5],"a":[6,11,16,36,43,48,60,105,110,115,136,174,177,200,211,235,244,251,257,274,283,290],"new":[7,37,54,297],"method":[8,271],"for":[9,41,96,109,134,233,272,281,299],"computing":[10,42,129,234,273,282,300],"comprehensive":[12,44,106,178,202,212,236,245,253,275,284,301],"Grobner":[13,45,107,157,170,179,203,213,237,246,254,276,285,302],"system":[14,19,180,238,247,260,277],"of":[15,47,65,75,104,117,122,163,188,219,256,292],"parameterized":[17,49,222,258],"polynomial":[18,50,61,88,137,209,223,259],"was":[20,29],"proposed":[21,40,270],"and":[22,93,185,196],"its":[23,66],"efficiency":[24],"over":[25],"other":[26,141,231,308],"known":[27],"methods":[28],"effectively":[30],"demonstrated.":[31],"Based":[32],"on":[33,146,160,173,289],"those":[34],"insights,":[35],"approach":[38,263],"is":[39,56,83,181,199,264],"basis":[46,158,171,214,255],"system.":[51,224],"The":[52,262,287],"key":[53],"idea":[55],"not":[57],"to":[58,114,140,205,216,230],"simplify":[59],"under":[62,99],"various":[63],"specialization":[64,98,116],"parameters,":[67],"but":[68,143],"rather":[69],"keep":[70],"track":[71],"in":[72,210,278],"the":[73,76,87,97,102,123,126,144,147,189,197,217,220,268],"polynomial,":[74],"power":[77],"products":[78],"whose":[79],"coefficients":[80],"vanish;":[81],"this":[82,296],"achieved":[84],"by":[85,266],"partitioning":[86],"into":[89],"two":[90],"parts-nonzero":[91],"part":[92,95],"zero":[94,152,186],"consideration.":[100],"During":[101],"computation":[103],"system,":[108],"particular":[111],"branch":[112,195],"corresponding":[113],"parameter":[118],"values,":[119],"nonzero":[120,184],"parts":[121,187],"polynomials":[124,149,164,190],"dictate":[125],"computation,":[127],"i.e.,":[128],"S-polynomials":[130],"as":[131,133,169,239,248,250],"well":[132,249],"simplifying":[135],"with":[138],"respect":[139],"polynomials;":[142],"manipulations":[145],"whole":[148],"(including":[150],"their":[151],"parts)":[153],"are":[154,191],"also":[155,166],"performed.":[156],"computations":[159,172],"such":[161],"pairs":[162],"can":[165],"be":[167,228],"viewed":[168],"module.":[175],"Once":[176],"generated,":[182],"both":[183,243],"collected":[192],"from":[193],"every":[194,208],"result":[198],"faithful":[201,252],"basis,":[204],"mean":[206],"that":[207,295],"belongs":[215],"ideal":[218],"original":[221],"This":[225],"technique":[226],"should":[227],"applicable":[229],"algorithms":[232],"well,":[240],"thus":[241],"producing":[242],"simultaneously.":[261],"exhibited":[265],"adapting":[267],"recently":[269],"2010)":[280],"basis.":[286],"timings":[288],"collection":[291],"examples":[293],"demonstrate":[294],"algorithm":[298],"bases":[303],"has":[304],"better":[305],"performance":[306],"than":[307],"existing":[309],"algorithms.":[310]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
