{"id":"https://openalex.org/W3045647318","doi":"https://doi.org/10.1145/3373207.3404019","title":"An extended GCD algorithm for parametric univariate polynomials and application to parametric smith normal form","display_name":"An extended GCD algorithm for parametric univariate polynomials and application to parametric smith normal form","publication_year":2020,"publication_date":"2020-07-20","ids":{"openalex":"https://openalex.org/W3045647318","doi":"https://doi.org/10.1145/3373207.3404019","mag":"3045647318"},"language":"en","primary_location":{"id":"doi:10.1145/3373207.3404019","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404019","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th 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/A5101585436","display_name":"Dingkang Wang","orcid":"https://orcid.org/0000-0002-5844-1277"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dingkang Wang","raw_affiliation_strings":["University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101805499","display_name":"Hesong Wang","orcid":"https://orcid.org/0000-0003-4072-5973"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hesong Wang","raw_affiliation_strings":["University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045096504","display_name":"Fanghui Xiao","orcid":"https://orcid.org/0000-0001-7833-3727"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanghui Xiao","raw_affiliation_strings":["University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101585436"],"corresponding_institution_ids":["https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.12487469,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"442","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998999834060669,"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":0.9998999834060669,"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":0.998199999332428,"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/T11130","display_name":"Coding theory and cryptography","score":0.9958999752998352,"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/univariate","display_name":"Univariate","score":0.7768787741661072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7466814517974854},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.6611667275428772},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6247237920761108},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4574337601661682},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45057326555252075},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.4335097074508667},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3878723680973053},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3844704031944275},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33939045667648315},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32039257884025574},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2077733278274536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09078755974769592},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0718812644481659}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7768787741661072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7466814517974854},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.6611667275428772},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6247237920761108},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4574337601661682},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45057326555252075},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.4335097074508667},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3878723680973053},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3844704031944275},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33939045667648315},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32039257884025574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2077733278274536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09078755974769592},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0718812644481659},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3373207.3404019","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404019","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th 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":31,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W45707961","https://openalex.org/W634201324","https://openalex.org/W1599026900","https://openalex.org/W1628745019","https://openalex.org/W1964126554","https://openalex.org/W1966711586","https://openalex.org/W1989675557","https://openalex.org/W1990119084","https://openalex.org/W1994234357","https://openalex.org/W2005536816","https://openalex.org/W2026253506","https://openalex.org/W2053029682","https://openalex.org/W2057105460","https://openalex.org/W2059860265","https://openalex.org/W2065304692","https://openalex.org/W2065989671","https://openalex.org/W2070075204","https://openalex.org/W2085849252","https://openalex.org/W2086405591","https://openalex.org/W2095764258","https://openalex.org/W2113205422","https://openalex.org/W2117535139","https://openalex.org/W2128978199","https://openalex.org/W2737200916","https://openalex.org/W2740152569","https://openalex.org/W2913046577","https://openalex.org/W3007626758","https://openalex.org/W4241969257","https://openalex.org/W4252341881","https://openalex.org/W4292096448"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W2911841387","https://openalex.org/W2737200916","https://openalex.org/W2053002746","https://openalex.org/W2055878129","https://openalex.org/W2379877967","https://openalex.org/W1998550351","https://openalex.org/W2469926590"],"abstract_inverted_index":{"An":[0],"extended":[1,158,171],"greatest":[2],"common":[3],"divisor":[4],"(GCD)":[5],"algorithm":[6,17,57,160,173,185],"for":[7,39,60,150,161,186],"parametric":[8,24,49,142,162],"univariate":[9,25,50,70,163,189],"polynomials":[10,26,71,101],"is":[11,58],"presented":[12],"in":[13,27],"this":[14],"paper.":[15],"This":[16,134],"computes":[18],"not":[19],"only":[20],"the":[21,33,40,63,77,82,92,96,110,116,121,132,141,146,169,175,183],"GCD":[22,41,64,122,159,172],"of":[23,47,55,65,69,81,90,95,131,145,177],"each":[28],"constructible":[29],"set":[30],"but":[31],"also":[32],"corresponding":[34],"representation":[35,117,124],"coefficients":[36,125],"(or":[37],"multipliers)":[38],"expressed":[42],"as":[43],"a":[44,105,128,153,188],"linear":[45],"combination":[46],"these":[48],"polynomials.":[51,87,164],"The":[52],"key":[53],"idea":[54],"our":[56],"that":[59],"non-parametric":[61],"case":[62,143],"arbitrary":[66],"finite":[67],"number":[68],"can":[72,114,136],"be":[73,137],"obtained":[74],"by":[75,85,99,108,126],"computing":[76,91,127],"minimal":[78],"Gr\u00f6bner":[79,93,129,148],"basis":[80,94,130],"ideal":[83,97],"generated":[84,98],"those":[86,100],"But":[88],"instead":[89],"directly,":[102],"we":[103,155,167],"construct":[104],"special":[106],"module":[107],"adding":[109],"unit":[111],"vectors":[112],"which":[113],"record":[115],"coefficients,":[118],"then":[119],"obtain":[120,156],"and":[123,181],"module.":[133],"method":[135],"naturally":[138],"generalized":[139],"to":[140,174,194],"because":[144],"comprehensive":[147],"systems":[149],"modules.":[151],"As":[152],"consequence,":[154],"an":[157],"More":[165],"importantly,":[166],"apply":[168],"proposed":[170],"computation":[176],"Smith":[178,196],"normal":[179,197],"form,":[180],"give":[182],"first":[184],"reducing":[187],"polynomial":[190],"matrix":[191],"with":[192],"parameters":[193],"its":[195],"form.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
