{"id":"https://openalex.org/W4417067853","doi":"https://doi.org/10.1145/3747199.3747572","title":"Computing Polynomial Representation in Subrings of Multivariate Polynomial Rings","display_name":"Computing Polynomial Representation in Subrings of Multivariate Polynomial Rings","publication_year":2025,"publication_date":"2025-07-28","ids":{"openalex":"https://openalex.org/W4417067853","doi":"https://doi.org/10.1145/3747199.3747572"},"language":"en","primary_location":{"id":"doi:10.1145/3747199.3747572","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747572","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3747199.3747572","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090583072","display_name":"Thi Xuan Vu","orcid":"https://orcid.org/0000-0002-2285-7801"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Thi Xuan Vu","raw_affiliation_strings":["Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, Lille, France"],"raw_orcid":"https://orcid.org/0000-0002-2285-7801","affiliations":[{"raw_affiliation_string":"Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, Lille, France","institution_ids":["https://openalex.org/I7454413","https://openalex.org/I2279609970","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090583072"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I7454413"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3580609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"284","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9146000146865845,"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":0.9146000146865845,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.030899999663233757,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.02019999921321869,"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/subring","display_name":"Subring","score":0.8946999907493591},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.7663999795913696},{"id":"https://openalex.org/keywords/symmetric-polynomial","display_name":"Symmetric polynomial","score":0.5939000248908997},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.5856000185012817},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5674999952316284},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.5439000129699707},{"id":"https://openalex.org/keywords/minimal-polynomial","display_name":"Minimal polynomial (linear algebra)","score":0.5213000178337097},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.5148000121116638},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5116999745368958},{"id":"https://openalex.org/keywords/alternating-polynomial","display_name":"Alternating polynomial","score":0.5112000107765198}],"concepts":[{"id":"https://openalex.org/C21714298","wikidata":"https://www.wikidata.org/wiki/Q929536","display_name":"Subring","level":3,"score":0.8946999907493591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7965999841690063},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.7663999795913696},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.5939000248908997},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.5856000185012817},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5674999952316284},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.5439000129699707},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.5213000178337097},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.5148000121116638},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5116999745368958},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.5112000107765198},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.49790000915527344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4848000109195709},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.47999998927116394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4569000005722046},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.4068000018596649},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.40310001373291016},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3862999975681305},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.3758000135421753},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.36090001463890076},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.3264000117778778},{"id":"https://openalex.org/C144825994","wikidata":"https://www.wikidata.org/wiki/Q4378669","display_name":"Primitive element","level":3,"score":0.31150001287460327},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C123450019","wikidata":"https://www.wikidata.org/wiki/Q5532677","display_name":"Generic polynomial","level":5,"score":0.2759999930858612},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.27480000257492065},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.2718999981880188},{"id":"https://openalex.org/C41620472","wikidata":"https://www.wikidata.org/wiki/Q1458669","display_name":"Primitive polynomial","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.263700008392334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2612000107765198},{"id":"https://openalex.org/C173832452","wikidata":"https://www.wikidata.org/wiki/Q162608","display_name":"Algebraic element","level":5,"score":0.25850000977516174}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3747199.3747572","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747572","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2504.21708","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.21708","pdf_url":"https://arxiv.org/pdf/2504.21708","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05052659v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05052659","pdf_url":"https://hal.science/hal-05052659/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The International Symposium on Symbolic and Algebraic Computation (ISSAC) 2025, Jul 2025, Guanajuato, Mexico","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.2504.21708","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.21708","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1145/3747199.3747572","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747572","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1564055510","https://openalex.org/W1602083394","https://openalex.org/W1907666253","https://openalex.org/W1972071236","https://openalex.org/W1973342538","https://openalex.org/W1978946312","https://openalex.org/W2007215420","https://openalex.org/W2013548162","https://openalex.org/W2022078407","https://openalex.org/W2037381995","https://openalex.org/W2040860090","https://openalex.org/W2060624832","https://openalex.org/W2063911803","https://openalex.org/W2065337200","https://openalex.org/W2080132708","https://openalex.org/W2080589685","https://openalex.org/W2081257302","https://openalex.org/W2082002555","https://openalex.org/W2083368929","https://openalex.org/W2084801848","https://openalex.org/W2086134965","https://openalex.org/W2098867933","https://openalex.org/W2111028162","https://openalex.org/W2112271215","https://openalex.org/W2123578039","https://openalex.org/W2126534535","https://openalex.org/W2130918732","https://openalex.org/W2140702311","https://openalex.org/W2147588253","https://openalex.org/W2188410026","https://openalex.org/W2279788372","https://openalex.org/W2314507527","https://openalex.org/W2319466955","https://openalex.org/W2472524164","https://openalex.org/W2752491749","https://openalex.org/W2909832064","https://openalex.org/W2923569601","https://openalex.org/W2955705967","https://openalex.org/W3081736912","https://openalex.org/W3127148005","https://openalex.org/W3137691494","https://openalex.org/W4231832815","https://openalex.org/W4239141340","https://openalex.org/W4283813461","https://openalex.org/W4312972796","https://openalex.org/W4376504252","https://openalex.org/W4379933108","https://openalex.org/W4394896760"],"related_works":[],"abstract_inverted_index":{"Let":[0,32],"\\(\\mathcal":[1,30,33,39,53],"{R}=":[2],"\\mathbb":[3,63],"{K}[x_1,":[4],"\\dots":[5,65],",":[6,66],"x_n]\\)":[7],"be":[8,49],"a":[9,14,58,128],"multivariate":[10],"polynomial":[11,110,130],"ring":[12],"over":[13],"field":[15],"\\(\\mathbb":[16],"{K}\\)":[17],"of":[18,38,52,93,101,116],"characteristic":[19],"0.":[20],"Consider":[21],"n":[22,112],"algebraically":[23],"independent":[24],"elements":[25],"g1,":[26,43,88,106,132],"\u2026,":[27,44,73,89,107,133],"gn":[28,134],"in":[29,98,111],"{R}\\).":[31],"{S}\\)":[34],"denote":[35],"the":[36,99,102,114],"subring":[37],"{R}\\)":[40],"generated":[41],"by":[42],"gn,":[45,108],"and":[46,87,105,109,131],"let":[47],"h":[48,70,86,104],"an":[50,80],"element":[51,60],"{S}\\).":[54],"Then,":[55],"there":[56],"exists":[57],"unique":[59],"\\({f}":[61],"\\in":[62],"{K}[u_1,":[64],"u_n]\\)":[67],"such":[68],"that":[69],"=":[71],"f(g1,":[72],"gn).":[74],"In":[75],"this":[76],"paper,":[77],"we":[78],"provide":[79],"algorithm":[81,95],"for":[82],"computing":[83],"f,":[84],"given":[85],"gn.":[90],"The":[91],"complexity":[92],"our":[94],"is":[96,118,127],"linear":[97],"size":[100],"input,":[103],"when":[113,125],"degree":[115],"f":[117,126],"fixed.":[119],"Previous":[120],"works":[121],"are":[122,135],"mostly":[123],"known":[124],"symmetric":[129,142],"elementary":[136],"symmetric,":[137,139],"homogeneous":[138],"or":[140],"power":[141],"polynomials.":[143]},"counts_by_year":[],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}