{"id":"https://openalex.org/W1705547420","doi":"https://doi.org/10.1142/s0218196715500435","title":"Computing Hermitian determinantal representations of hyperbolic curves","display_name":"Computing Hermitian determinantal representations of hyperbolic curves","publication_year":2015,"publication_date":"2015-11-26","ids":{"openalex":"https://openalex.org/W1705547420","doi":"https://doi.org/10.1142/s0218196715500435","mag":"1705547420"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196715500435","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500435","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5089198431","display_name":"Daniel Plaumann","orcid":"https://orcid.org/0000-0002-3376-6841"},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Daniel Plaumann","raw_affiliation_strings":["Department of Mathematics and Statistics, Universit\u00e4t Konstanz, Zukunftskolleg, Box 216 78457 Konstanz, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Universit\u00e4t Konstanz, Zukunftskolleg, Box 216 78457 Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068824685","display_name":"Rainer Sinn","orcid":"https://orcid.org/0000-0001-9456-6889"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rainer Sinn","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, GA 30332, USA","School of Mathematics , Georgia Institute of Technology , 686 Cherry Street NW, Atlanta , GA , 30332 , USA"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Mathematics , Georgia Institute of Technology , 686 Cherry Street NW, Atlanta , GA , 30332 , USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021128761","display_name":"David E Speyer","orcid":"https://orcid.org/0000-0003-4540-2559"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David E. Speyer","raw_affiliation_strings":["Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008168066","display_name":"Cynthia Vinzant","orcid":"https://orcid.org/0000-0001-8140-598X"},"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":"Cynthia Vinzant","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089198431"],"corresponding_institution_ids":["https://openalex.org/I189712700"],"apc_list":null,"apc_paid":null,"fwci":1.7526,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84727165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"08","first_page":"1327","last_page":"1336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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":0.9994999766349792,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8865858316421509},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7798633575439453},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6059901118278503},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5978695154190063},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5361964702606201},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5061799883842468},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5045567750930786},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4468654990196228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15137284994125366},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06823614239692688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8865858316421509},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7798633575439453},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6059901118278503},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5978695154190063},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5361964702606201},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5061799883842468},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5045567750930786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4468654990196228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15137284994125366},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06823614239692688},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196715500435","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500435","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W101224644","https://openalex.org/W1480381100","https://openalex.org/W1678969163","https://openalex.org/W1877476807","https://openalex.org/W1997454240","https://openalex.org/W2008564600","https://openalex.org/W2025202934","https://openalex.org/W2088097425"],"related_works":["https://openalex.org/W3196977684","https://openalex.org/W4317464059","https://openalex.org/W4378757502","https://openalex.org/W4385248177","https://openalex.org/W2994793674","https://openalex.org/W4244117186","https://openalex.org/W1985551943","https://openalex.org/W3047404910","https://openalex.org/W1599337099","https://openalex.org/W2077036309"],"abstract_inverted_index":{"Every":[0],"real":[1],"hyperbolic":[2],"form":[3],"in":[4,43],"three":[5],"variables":[6],"can":[7],"be":[8],"realized":[9],"as":[10],"the":[11,32,35,48,71],"determinant":[12],"of":[13,17,34,70],"a":[14,21,67],"linear":[15,74],"net":[16],"Hermitian":[18],"matrices":[19],"containing":[20],"positive":[22],"definite":[23],"matrix.":[24],"Such":[25],"representations":[26,54],"are":[27,55],"an":[28,63],"algebraic":[29],"certificate":[30],"for":[31,51],"hyperbolicity":[33],"polynomial":[36],"and":[37,76],"their":[38],"existence":[39],"has":[40],"been":[41],"proved":[42],"several":[44],"different":[45],"ways.":[46],"However,":[47],"resulting":[49],"algorithms":[50],"computing":[52],"determinantal":[53],"computationally":[56],"intensive.":[57],"In":[58],"this":[59],"note,":[60],"we":[61],"present":[62],"algorithm":[64],"that":[65],"reduces":[66],"large":[68],"part":[69],"problem":[72],"to":[73],"algebra":[75],"discuss":[77],"its":[78],"numerical":[79],"implementation.":[80]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
