{"id":"https://openalex.org/W2785480650","doi":"https://doi.org/10.1145/3208976.3208996","title":"Irredundant Triangular Decomposition","display_name":"Irredundant Triangular Decomposition","publication_year":2018,"publication_date":"2018-07-11","ids":{"openalex":"https://openalex.org/W2785480650","doi":"https://doi.org/10.1145/3208976.3208996","mag":"2785480650"},"language":"en","primary_location":{"id":"doi:10.1145/3208976.3208996","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3208976.3208996","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3208976.3208996","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3208976.3208996","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Gleb Pogudin","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gleb Pogudin","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York, NY, USA","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":null,"display_name":"Agnes Szanto","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Agnes Szanto","raw_affiliation_strings":["North Carolina State University, Raleigh, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04055676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"311","last_page":"318"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6783000230789185},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.6071000099182129},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5874999761581421},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5690000057220459},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5202000141143799},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.3605000078678131},{"id":"https://openalex.org/keywords/algebraic-variety","display_name":"Algebraic variety","score":0.3156999945640564}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7397000193595886},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6783000230789185},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.6071000099182129},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5874999761581421},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5690000057220459},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5202000141143799},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45080000162124634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4334999918937683},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.3605000078678131},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32910001277923584},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.2703000009059906},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C6077466","wikidata":"https://www.wikidata.org/wiki/Q5156597","display_name":"Complex quadratic polynomial","level":3,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3208976.3208996","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3208976.3208996","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3208976.3208996","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1802.01624","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.01624","pdf_url":"https://arxiv.org/pdf/1802.01624","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1145/3208976.3208996","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3208976.3208996","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3208976.3208996","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2213365449","display_name":null,"funder_award_id":"60098-00 48","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G3395555127","display_name":null,"funder_award_id":"Y464-N18","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4797646019","display_name":null,"funder_award_id":"CCF-1563942","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4805568812","display_name":"CAREER: CISE-CCF-AF-Algebra: DMS-Algebra: Computational Differential Algebra","funder_award_id":"0952591","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4817279656","display_name":null,"funder_award_id":"1563942","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G61283242","display_name":null,"funder_award_id":"CCF-1563942","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6298019863","display_name":null,"funder_award_id":"CCF-0952591, CCF-1563942, DMS-1413859","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7816252006","display_name":null,"funder_award_id":"CCF-0952591","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8364977450","display_name":"Computational Differential and Difference Algebra, a special session at the Applications of Computer Algebra 2014 Conference, July 9 - 12, 2014.","funder_award_id":"1413859","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309102","display_name":"City University of New York","ror":"https://ror.org/00453a208"},{"id":"https://openalex.org/F4320310013","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2785480650.pdf","grobid_xml":"https://content.openalex.org/works/W2785480650.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W399280277","https://openalex.org/W1965823846","https://openalex.org/W1967579587","https://openalex.org/W1975442862","https://openalex.org/W1976392590","https://openalex.org/W1978946312","https://openalex.org/W1990451653","https://openalex.org/W1996430549","https://openalex.org/W2039228526","https://openalex.org/W2053029682","https://openalex.org/W2077186096","https://openalex.org/W2077378514","https://openalex.org/W2080132708","https://openalex.org/W2084690469","https://openalex.org/W2127928734","https://openalex.org/W2149364930","https://openalex.org/W2150489476","https://openalex.org/W4237539763","https://openalex.org/W6645380117","https://openalex.org/W6713000677","https://openalex.org/W6829164290"],"related_works":[],"abstract_inverted_index":{"Triangular":[0],"decomposition":[1,123,168],"is":[2,88,170],"a":[3,26,132],"classic,":[4],"widely":[5],"used":[6],"and":[7,55,105,162,172],"well-developed":[8],"way":[9],"to":[10,78,97,118,149],"represent":[11],"algebraic":[12,127],"varieties":[13],"with":[14],"many":[15],"applications.":[16],"In":[17,111],"particular,":[18],"there":[19],"exist":[20],"-":[21,40],"sharp":[22],"degree":[23,83,152],"bounds":[24,153],"for":[25,44,56,91,154],"single":[27],"triangular":[28,46,69,122,144,160],"set":[29,128,133],"in":[30,51,60,86,136,158],"terms":[31],"of":[32,35,65,101,109,124,134,177],"intrinsic":[33,82,151],"data":[34],"the":[36,52,61,66,81,98,102,106,155,159,175],"variety":[37],"it":[38,76],"represents,":[39],"powerful":[41],"randomized":[42],"algorithms":[43,67],"computing":[45,68],"decompositions":[47,70],"using":[48],"Hensel":[49,94,164],"lifting":[50,95,165],"zero-dimensional":[53],"case":[54],"irreducible":[57],"varieties.":[58],"However,":[59],"general":[62],"case,":[63],"most":[64],"produce":[71],"embedded":[72],"components,":[73],"which":[74],"makes":[75],"impossible":[77],"directly":[79],"apply":[80,163],"bounds.":[84],"This,":[85],"turn,":[87],"an":[89,116,120,125],"obstacle":[90],"efficiently":[92],"applying":[93],"due":[96],"higher":[99],"degrees":[100],"output":[103],"polynomials":[104,135,156],"lower":[107],"probability":[108,176],"success.":[110,178],"this":[112,142],"paper,":[113],"we":[114,146,173],"give":[115,150],"algorithm":[117,169],"compute":[119],"irredundant":[121,143],"arbitrary":[126],"W":[129],"defined":[130],"by":[131],"C[x1,":[137],"x2,":[138],"...,":[139],"xn].":[140],"Using":[141],"decomposition,":[145],"are":[147],"able":[148],"appearing":[157],"sets":[161],"techniques.":[166],"Our":[167],"randomized,":[171],"analyze":[174]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2018-02-23T00:00:00"}
