{"id":"https://openalex.org/W188591515","doi":"https://doi.org/10.1007/978-1-4613-9647-5_19","title":"Exact Algorithms for the Matrix-Triangularization Subresultant PRS Method","display_name":"Exact Algorithms for the Matrix-Triangularization Subresultant PRS Method","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W188591515","doi":"https://doi.org/10.1007/978-1-4613-9647-5_19","mag":"188591515"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4613-9647-5_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_19","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"},"type":"book-chapter","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/A5017435174","display_name":"Alkiviadis G. Akritas","orcid":null},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alkiviadis G. Akritas","raw_affiliation_strings":["Department of Computer Science, University of Kansas, Lawrence, Kansas, 66045, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Kansas, Lawrence, Kansas, 66045, USA","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017435174"],"corresponding_institution_ids":["https://openalex.org/I146416000"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.11285714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"145","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9983000159263611,"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":0.9983000159263611,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9894000291824341,"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/gaussian-elimination","display_name":"Gaussian elimination","score":0.7643024921417236},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.7500948309898376},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.7186304330825806},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6833509802818298},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6157239079475403},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6088743209838867},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5891456007957458},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5103301405906677},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5042883157730103},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4812459647655487},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46819955110549927},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4546726644039154},{"id":"https://openalex.org/keywords/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.43336641788482666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3899800181388855},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3657170236110687},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32100439071655273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19807901978492737},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1596616804599762},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12537458539009094}],"concepts":[{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.7643024921417236},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7500948309898376},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.7186304330825806},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6833509802818298},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6157239079475403},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6088743209838867},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5891456007957458},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5103301405906677},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5042883157730103},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4812459647655487},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46819955110549927},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4546726644039154},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.43336641788482666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3899800181388855},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3657170236110687},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32100439071655273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19807901978492737},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1596616804599762},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12537458539009094},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4613-9647-5_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_19","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1526783510","https://openalex.org/W1527913126","https://openalex.org/W1547030694","https://openalex.org/W1966711586","https://openalex.org/W1977340462","https://openalex.org/W1982902239","https://openalex.org/W1984439761","https://openalex.org/W2027319428","https://openalex.org/W2029317328","https://openalex.org/W2032951732","https://openalex.org/W2100279776","https://openalex.org/W2317736117","https://openalex.org/W2321254302","https://openalex.org/W4237949527","https://openalex.org/W4252937307"],"related_works":["https://openalex.org/W1984910481","https://openalex.org/W2154733965","https://openalex.org/W1608773862","https://openalex.org/W2366394750","https://openalex.org/W2161621882","https://openalex.org/W2393337705","https://openalex.org/W4388257762","https://openalex.org/W2366738637","https://openalex.org/W2170618847","https://openalex.org/W1419838"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}