{"id":"https://openalex.org/W1963954905","doi":"https://doi.org/10.1145/1088309.1088319","title":"A note on abnormal polynomial remainder sequences","display_name":"A note on abnormal polynomial remainder sequences","publication_year":1975,"publication_date":"1975-08-01","ids":{"openalex":"https://openalex.org/W1963954905","doi":"https://doi.org/10.1145/1088309.1088319","mag":"1963954905"},"language":"en","primary_location":{"id":"doi:10.1145/1088309.1088319","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1088309.1088319","pdf_url":null,"source":{"id":"https://openalex.org/S4210226623","display_name":"ACM SIGSAM Bulletin","issn_l":"0163-5824","issn":["0163-5824","1557-9492"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGSAM Bulletin","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/A5109947282","display_name":"S. C. Johnson","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. C. Johnson","raw_affiliation_strings":["Bell Laboratories, Murray Hill, New Jersey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Murray Hill, New Jersey","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109947282"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08655404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"3","first_page":"28","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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":0.9993000030517578,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.992900013923645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.9837110042572021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7537533044815063},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.6488638520240784},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6403016448020935},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6292481422424316},{"id":"https://openalex.org/keywords/divisor","display_name":"Divisor (algebraic geometry)","score":0.6112625598907471},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.5411429405212402},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5383063554763794},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5125010013580322},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4861578643321991},{"id":"https://openalex.org/keywords/division-algorithm","display_name":"Division algorithm","score":0.44764822721481323},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44327303767204285},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.31285855174064636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1357152760028839},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0817776620388031}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.9837110042572021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7537533044815063},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.6488638520240784},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6403016448020935},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6292481422424316},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.6112625598907471},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.5411429405212402},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5383063554763794},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5125010013580322},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4861578643321991},{"id":"https://openalex.org/C190715199","wikidata":"https://www.wikidata.org/wiki/Q3526714","display_name":"Division algorithm","level":3,"score":0.44764822721481323},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44327303767204285},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.31285855174064636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1357152760028839},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0817776620388031},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1088309.1088319","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1088309.1088319","pdf_url":null,"source":{"id":"https://openalex.org/S4210226623","display_name":"ACM SIGSAM Bulletin","issn_l":"0163-5824","issn":["0163-5824","1557-9492"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGSAM Bulletin","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1655990431","https://openalex.org/W1966711586","https://openalex.org/W2008957088","https://openalex.org/W2048960085","https://openalex.org/W2100279776"],"related_works":["https://openalex.org/W2079394275","https://openalex.org/W4308351151","https://openalex.org/W2081416615","https://openalex.org/W1571629760","https://openalex.org/W2037752989","https://openalex.org/W1965811650","https://openalex.org/W2189175587","https://openalex.org/W2167814173","https://openalex.org/W2094525129","https://openalex.org/W2119235173"],"abstract_inverted_index":{"Polynomial":[0],"Remainder":[1],"Sequences":[2],"(PRS)":[3],"have":[4,91],"been":[5],"used":[6],"in":[7,57,76,80,100],"the":[8,26,29,35,38,66,69,77,81,86,96,101],"computation":[9],"of":[10,14,28,37,68,95],"greatest":[11,62],"common":[12,63],"divisors":[13],"polynomials":[15],"for":[16],"many":[17],"years.":[18],"We":[19],"call":[20],"a":[21,60],"polynomial":[22,55],"division":[23,56],"abnormal":[24,43,51,54],"if":[25],"degree":[27,36],"remainder":[30],"is":[31,45],"strictly":[32],"less":[33],"than":[34],"divisor":[39,64],"minus":[40],"one;":[41],"an":[42],"PRS":[44,88],"one":[46,50],"with":[47],"at":[48],"least":[49],"division.":[52],"An":[53],"general":[58],"implies":[59],"nontrivial":[61],"among":[65],"coefficients":[67],"remainder;":[70],"this":[71],"can":[72],"lead":[73],"to":[74],"inefficiencies":[75],"later":[78],"computations":[79],"PRS.These":[82],"results":[83],"suggest":[84],"that":[85],"\"classical\"":[87],"methods":[89],"may":[90],"not":[92],"exploited":[93],"all":[94],"algebraic":[97],"structure":[98],"available":[99],"problem.":[102]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
