{"id":"https://openalex.org/W4283819752","doi":"https://doi.org/10.1145/3476446.3535496","title":"Rational Univariate Representation of Zero-Dimensional Ideals with Parameters","display_name":"Rational Univariate Representation of Zero-Dimensional Ideals with Parameters","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4283819752","doi":"https://doi.org/10.1145/3476446.3535496"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3535496","doi":"https://doi.org/10.1145/3476446.3535496","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3535496","pdf_url":null,"source":{"id":"https://openalex.org/S4306420219","display_name":"International Symposium on Symbolic and Algebraic Computation","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"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","observed_orcids":["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":["KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000191189","display_name":"Jingjing Wei","orcid":"https://orcid.org/0009-0006-3943-1993","observed_orcids":["https://orcid.org/0009-0006-3943-1993"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jingjing Wei","raw_affiliation_strings":["Beijing ETown Academy, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing ETown Academy, Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045096504","display_name":"Fanghui Xiao","orcid":"https://orcid.org/0000-0001-7833-3727","observed_orcids":["https://orcid.org/0000-0001-7833-3727"]},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanghui Xiao","raw_affiliation_strings":["Hunan Normal University, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053853859","display_name":"Xiaopeng Zheng","orcid":"https://orcid.org/0000-0002-5484-7552","observed_orcids":["https://orcid.org/0000-0002-5484-7552"]},"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":"Xiaopeng Zheng","raw_affiliation_strings":["KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06201708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"217","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":1.0,"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":1.0,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/zero-dimensional-ideals","display_name":"zero-dimensional ideals","score":0.9549999833106995},{"id":"https://openalex.org/keywords/parametric-polynomial-systems","display_name":"parametric polynomial systems","score":0.8130000233650208},{"id":"https://openalex.org/keywords/parameter-space-partitioning","display_name":"parameter space partitioning","score":0.9010000228881836},{"id":"https://openalex.org/keywords/number-of-zeros","display_name":"number of zeros","score":0.5180000066757202}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.8397203683853149},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6328345537185669},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6134507060050964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4612829089164734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4244702458381653},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27225351333618164},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.17751604318618774},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.09096771478652954},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07000425457954407},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3476446.3535496","doi":"https://doi.org/10.1145/3476446.3535496","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3535496","pdf_url":null,"source":{"id":"https://openalex.org/S4306420219","display_name":"International Symposium on Symbolic and Algebraic Computation","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G140934820","display_name":null,"funder_award_id":"12171469","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3804672359","display_name":null,"funder_award_id":"2020 YFA0712300","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W1481556851","https://openalex.org/W1968235836","https://openalex.org/W1990119084","https://openalex.org/W1998550351","https://openalex.org/W2011693299","https://openalex.org/W2019127701","https://openalex.org/W2037381995","https://openalex.org/W2054253602","https://openalex.org/W2057105460","https://openalex.org/W2095764258","https://openalex.org/W2113205422","https://openalex.org/W2379645207","https://openalex.org/W2530332639","https://openalex.org/W2737200916","https://openalex.org/W2737431615","https://openalex.org/W2772425481","https://openalex.org/W2915009128","https://openalex.org/W3101467985","https://openalex.org/W4243098353","https://openalex.org/W4292096448","https://openalex.org/W7214765424"],"related_works":["https://openalex.org/W4393213373","https://openalex.org/W1968235836","https://openalex.org/W1998550351","https://openalex.org/W7128410034","https://openalex.org/W2007024563","https://openalex.org/W3150522271","https://openalex.org/W7167720295","https://openalex.org/W2724529143","https://openalex.org/W2011693299","https://openalex.org/W63386126"],"abstract_inverted_index":{"An":[0],"algorithm":[1],"for":[2,97],"computing":[3,55],"the":[4,16,20,29,49,52,56,67,72,82,85,93,100,110,118,130],"rational":[5,21,57,131],"univariate":[6,22,58,132],"representation":[7,23,133],"of":[8,24,31,33,88,113,120,129,134],"zero-dimensional":[9,25,34,135],"ideals":[10,26,35,136],"with":[11,36,109,117,137],"parameters":[12,37,138],"is":[13,41,60,107],"presented":[14],"in":[15],"paper.":[17],"Different":[18],"from":[19],"without":[27],"parameters,":[28],"number":[30,87],"zeros":[32],"under":[38,79],"various":[39],"specializations":[40],"different,":[42],"which":[43],"leads":[44],"to":[45,54,64,104],"choosing":[46],"and":[47],"checking":[48],"separating":[50,68,101],"element,":[51,69],"key":[53],"representation,":[59],"difficult.":[61],"In":[62],"order":[63],"pick":[65],"out":[66],"by":[70],"partitioning":[71],"parameter":[73,114],"space":[74],"we":[75],"can":[76,139],"ensure":[77],"that":[78],"each":[80,105],"branch":[81,106],"ideal":[83],"has":[84],"same":[86],"zeros.":[89],"Subsequently":[90],"based":[91],"on":[92],"extended":[94],"subresultant":[95],"theorem":[96],"parametric":[98,121],"cases,":[99],"element":[102],"corresponding":[103],"chosen":[108],"further":[111],"partition":[112],"space.":[115],"Finally,":[116],"help":[119],"greatest":[122],"common":[123],"divisor":[124],"theory":[125],"a":[126],"finite":[127],"set":[128],"be":[140],"obtained.":[141]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-07-06T00:00:00"}