{"id":"https://openalex.org/W3008736057","doi":"https://doi.org/10.1515/jmc-2020-0009","title":"On the condition number of the Vandermonde matrix of the <i>n</i> th cyclotomic polynomial","display_name":"On the condition number of the Vandermonde matrix of the <i>n</i> th cyclotomic polynomial","publication_year":2020,"publication_date":"2020-11-25","ids":{"openalex":"https://openalex.org/W3008736057","doi":"https://doi.org/10.1515/jmc-2020-0009","mag":"3008736057"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2020-0009","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0009","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0009/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0009/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Antonio J. Di Scala","orcid":null},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio J. Di Scala","raw_affiliation_strings":["Politecnico di Torino, Department of Mathematical Sciences , Corso Duca degli Abruzzi 24 , Torino , Italy"],"affiliations":[{"raw_affiliation_string":"Politecnico di Torino, Department of Mathematical Sciences , Corso Duca degli Abruzzi 24 , Torino , Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Carlo Sanna","orcid":null},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Carlo Sanna","raw_affiliation_strings":["Politecnico di Torino, Department of Mathematical Sciences , Corso Duca degli Abruzzi 24 , Torino , Italy"],"affiliations":[{"raw_affiliation_string":"Politecnico di Torino, Department of Mathematical Sciences , Corso Duca degli Abruzzi 24 , Torino , Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":null,"display_name":"Edoardo Signorini","orcid":null},"institutions":[{"id":"https://openalex.org/I1298633626","display_name":"Telecom Italia Lab","ror":"https://ror.org/01rt74q71","country_code":"IT","type":"facility","lineage":["https://openalex.org/I1298633626","https://openalex.org/I137543953"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Edoardo Signorini","raw_affiliation_strings":["Telsy Elettronica e Telecomunicazioni S.p.A. , Corso Svizzera 185 , Torino , Italy"],"affiliations":[{"raw_affiliation_string":"Telsy Elettronica e Telecomunicazioni S.p.A. , Corso Svizzera 185 , Torino , Italy","institution_ids":["https://openalex.org/I1298633626"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I177477856"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":0.4078,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.68319314,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"174","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.5573999881744385,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.5573999881744385,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.17870000004768372,"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":0.04170000180602074,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.9100000262260437},{"id":"https://openalex.org/keywords/cyclotomic-polynomial","display_name":"Cyclotomic polynomial","score":0.8578000068664551},{"id":"https://openalex.org/keywords/cyclotomic-field","display_name":"Cyclotomic field","score":0.6496999859809875},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5403000116348267},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4934000074863434},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47130000591278076},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4406999945640564},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.39959999918937683},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.3824000060558319}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.9100000262260437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8781999945640564},{"id":"https://openalex.org/C76253118","wikidata":"https://www.wikidata.org/wiki/Q1051983","display_name":"Cyclotomic polynomial","level":3,"score":0.8578000068664551},{"id":"https://openalex.org/C127843967","wikidata":"https://www.wikidata.org/wiki/Q1554628","display_name":"Cyclotomic field","level":2,"score":0.6496999859809875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5442000031471252},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5403000116348267},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47130000591278076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45179998874664307},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4406999945640564},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.39959999918937683},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.37700000405311584},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.35280001163482666},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.34850001335144043},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.3278999924659729},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C164810661","wikidata":"https://www.wikidata.org/wiki/Q1358313","display_name":"Ring of integers","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.2802000045776367},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.2784000039100647},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.27549999952316284},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.27489998936653137},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.25}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/jmc-2020-0009","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0009","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0009/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.08120","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.08120","pdf_url":"https://arxiv.org/pdf/2002.08120","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"},{"id":"pmh:oai:doaj.org/article:0e23c0c378044c1ea541075b106dc4a8","is_oa":true,"landing_page_url":"https://doaj.org/article/0e23c0c378044c1ea541075b106dc4a8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 15, Iss 1, Pp 174-178 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jmc-2020-0009","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0009","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0009/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G196523654","display_name":null,"funder_award_id":"Dipartimento di Eccellenza MIUR 2018-2022.","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G2573627744","display_name":null,"funder_award_id":"GNSAGA","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G3178914890","display_name":null,"funder_award_id":"2018-2022","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G3483349834","display_name":null,"funder_award_id":"MIUR 2018-2022","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3524703739","display_name":null,"funder_award_id":"18-2022","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3830323789","display_name":null,"funder_award_id":"INdAM","funder_id":"https://openalex.org/F4320334045","funder_display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni"},{"id":"https://openalex.org/G4956079712","display_name":null,"funder_award_id":"2018-2022","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G7698256304","display_name":null,"funder_award_id":"GNSAGA","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320313985","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3008736057.pdf","grobid_xml":"https://content.openalex.org/works/W3008736057.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1491861813","https://openalex.org/W2007466965","https://openalex.org/W2098290658","https://openalex.org/W2795036470","https://openalex.org/W4388288424"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Recently,":[1],"Blanco-Chac\u00f3n":[2],"proved":[3],"the":[4,7,31,39,46,56],"equivalence":[5],"between":[6],"Ring":[8],"Learning":[9,14],"With":[10,15],"Errors":[11,16],"and":[12,87],"Polynomial":[13],"problems":[17],"for":[18,30,71],"some":[19,27,53],"families":[20],"of":[21,38,59],"cyclotomic":[22,49],"number":[23,33],"fields":[24],"by":[25],"giving":[26],"upper":[28],"bounds":[29],"condition":[32],"Cond(":[34,67],"V":[35,42,60,68],"n":[36,43,47,61,69,72],")":[37,70],"Vandermonde":[40],"matrix":[41],"associated":[44],"to":[45],"th":[48],"polynomial.":[50],"We":[51],"prove":[52],"results":[54],"on":[55],"singular":[57],"values":[58],"and,":[62],"in":[63],"particular,":[64],"we":[65],"determine":[66],"=":[73],"2":[74],"k":[75,80],"p":[76,88],"\u2113":[77,82],",":[78,81],"where":[79],"\u2265":[83],"0":[84],"are":[85],"integers":[86],"is":[89],"an":[90],"odd":[91],"prime":[92],"number.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2020-03-06T00:00:00"}