{"id":"https://openalex.org/W3014174926","doi":"https://doi.org/10.1080/00029890.2019.1704165","title":"Polynomial Roots with Common Tails","display_name":"Polynomial Roots with Common Tails","publication_year":2020,"publication_date":"2020-03-30","ids":{"openalex":"https://openalex.org/W3014174926","doi":"https://doi.org/10.1080/00029890.2019.1704165","mag":"3014174926"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2019.1704165","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1704165","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-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/A5013584344","display_name":"Gregory P. Dresden","orcid":null},"institutions":[{"id":"https://openalex.org/I184889055","display_name":"Washington and Lee University","ror":"https://ror.org/05r9xgf14","country_code":"US","type":"education","lineage":["https://openalex.org/I184889055"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gregory Dresden","raw_affiliation_strings":["Mathematics Department, Washington and Lee University","Mathematics Department, Washington and Lee University, Lexington, VA 24450"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Washington and Lee University","institution_ids":["https://openalex.org/I184889055"]},{"raw_affiliation_string":"Mathematics Department, Washington and Lee University, Lexington, VA 24450","institution_ids":["https://openalex.org/I184889055"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074813410","display_name":"Saimon Islam","orcid":null},"institutions":[{"id":"https://openalex.org/I184889055","display_name":"Washington and Lee University","ror":"https://ror.org/05r9xgf14","country_code":"US","type":"education","lineage":["https://openalex.org/I184889055"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Saimon Islam","raw_affiliation_strings":["Mathematics Department, Washington and Lee University","Mathematics Department, Washington and Lee University, Lexington, VA 24450"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Washington and Lee University","institution_ids":["https://openalex.org/I184889055"]},{"raw_affiliation_string":"Mathematics Department, Washington and Lee University, Lexington, VA 24450","institution_ids":["https://openalex.org/I184889055"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057303630","display_name":"Prakriti Panthi","orcid":null},"institutions":[{"id":"https://openalex.org/I184889055","display_name":"Washington and Lee University","ror":"https://ror.org/05r9xgf14","country_code":"US","type":"education","lineage":["https://openalex.org/I184889055"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prakriti Panthi","raw_affiliation_strings":["Mathematics Department, Washington and Lee University","Mathematics Department, Washington and Lee University, Lexington, VA 24450"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Washington and Lee University","institution_ids":["https://openalex.org/I184889055"]},{"raw_affiliation_string":"Mathematics Department, Washington and Lee University, Lexington, VA 24450","institution_ids":["https://openalex.org/I184889055"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039931864","display_name":"Anukriti Shrestha","orcid":null},"institutions":[{"id":"https://openalex.org/I184889055","display_name":"Washington and Lee University","ror":"https://ror.org/05r9xgf14","country_code":"US","type":"education","lineage":["https://openalex.org/I184889055"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anukriti Shrestha","raw_affiliation_strings":["Mathematics Department, Washington and Lee University","Mathematics Department, Washington and Lee University, Lexington, VA 24450"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Washington and Lee University","institution_ids":["https://openalex.org/I184889055"]},{"raw_affiliation_string":"Mathematics Department, Washington and Lee University, Lexington, VA 24450","institution_ids":["https://openalex.org/I184889055"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115602751","display_name":"Jiahao Zhang","orcid":"https://orcid.org/0009-0000-5263-9541"},"institutions":[{"id":"https://openalex.org/I184889055","display_name":"Washington and Lee University","ror":"https://ror.org/05r9xgf14","country_code":"US","type":"education","lineage":["https://openalex.org/I184889055"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiahao Zhang","raw_affiliation_strings":["Mathematics Department, Washington and Lee University","Mathematics Department, Washington and Lee University, Lexington, VA 24450"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Washington and Lee University","institution_ids":["https://openalex.org/I184889055"]},{"raw_affiliation_string":"Mathematics Department, Washington and Lee University, Lexington, VA 24450","institution_ids":["https://openalex.org/I184889055"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5013584344"],"corresponding_institution_ids":["https://openalex.org/I184889055"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06137184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"4","first_page":"316","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9470999836921692,"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":0.9470999836921692,"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":0.9395999908447266,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9279999732971191,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/mathematics","display_name":"Mathematics","score":0.7814391255378723},{"id":"https://openalex.org/keywords/factoring","display_name":"Factoring","score":0.6901232004165649},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6065309643745422},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5428014993667603},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5087886452674866},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.47697529196739197},{"id":"https://openalex.org/keywords/properties-of-polynomial-roots","display_name":"Properties of polynomial roots","score":0.46179935336112976},{"id":"https://openalex.org/keywords/factorization-of-polynomials","display_name":"Factorization of polynomials","score":0.42672795057296753},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41368231177330017},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3818973898887634},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.13844916224479675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10377448797225952}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7814391255378723},{"id":"https://openalex.org/C177225278","wikidata":"https://www.wikidata.org/wiki/Q192674","display_name":"Factoring","level":2,"score":0.6901232004165649},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6065309643745422},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5428014993667603},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5087886452674866},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.47697529196739197},{"id":"https://openalex.org/C107775665","wikidata":"https://www.wikidata.org/wiki/Q12859399","display_name":"Properties of polynomial roots","level":4,"score":0.46179935336112976},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.42672795057296753},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41368231177330017},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3818973898887634},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.13844916224479675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10377448797225952},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2019.1704165","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1704165","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W290527292","https://openalex.org/W1510478584","https://openalex.org/W1542908046","https://openalex.org/W1566908256","https://openalex.org/W1648142191","https://openalex.org/W2008975666","https://openalex.org/W2066309176","https://openalex.org/W2077027667","https://openalex.org/W2134386818","https://openalex.org/W2187260333","https://openalex.org/W2202294341","https://openalex.org/W2487302930","https://openalex.org/W2787492615","https://openalex.org/W3175367423","https://openalex.org/W4232016380","https://openalex.org/W4285719527","https://openalex.org/W4300937596","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W35972422","https://openalex.org/W190860662","https://openalex.org/W1532092761","https://openalex.org/W1988566873","https://openalex.org/W2357242572","https://openalex.org/W2478375851","https://openalex.org/W2071852476","https://openalex.org/W2049820802","https://openalex.org/W2365657438","https://openalex.org/W1530287661"],"abstract_inverted_index":{"How":[0],"many":[1],"irreducible":[2],"polynomials":[3,25],"have":[4,15,27],"real":[5],"roots":[6],"which,":[7],"when":[8],"expressed":[9],"as":[10],"simple":[11],"continued":[12],"fractions,":[13],"all":[14,23],"common":[16],"tails?":[17],"We":[18],"show":[19],"how":[20],"to":[21,36],"identify":[22],"such":[24],"(they":[26],"degree":[28],"at":[29],"most":[30],"six),":[31],"and":[32,42],"we":[33],"establish":[34],"connections":[35],"linear":[37],"fractional":[38],"transforms,":[39],"Galois":[40],"groups,":[41],"some":[43],"factoring":[44],"techniques":[45],"that":[46],"date":[47],"back":[48],"hundreds":[49],"of":[50],"years.":[51]},"counts_by_year":[],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
