{"id":"https://openalex.org/W2026362159","doi":"https://doi.org/10.1145/1499799.1499931","title":"Very fast computation of polynomial remainder sequence coefficient signs","display_name":"Very fast computation of polynomial remainder sequence coefficient signs","publication_year":1976,"publication_date":"1976-01-01","ids":{"openalex":"https://openalex.org/W2026362159","doi":"https://doi.org/10.1145/1499799.1499931","mag":"2026362159"},"language":"en","primary_location":{"id":"doi:10.1145/1499799.1499931","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1499799.1499931","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the June 7-10, 1976, national computer conference and exposition on - AFIPS '76","raw_type":"proceedings-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/A5022773625","display_name":"James R. Pinkert","orcid":null},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James R. Pinkert","raw_affiliation_strings":["University of Tennessee, Knoxville, Tennessee","UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE"],"affiliations":[{"raw_affiliation_string":"University of Tennessee, Knoxville, Tennessee","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022773625"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16407215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"957","last_page":"957"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9970999956130981,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9970999956130981,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9793000221252441,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9621000289916992,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/remainder","display_name":"Remainder","score":0.9353114366531372},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6550147533416748},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.643417239189148},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.600074827671051},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5630795359611511},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5560958981513977},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5420871376991272},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4849822521209717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48037582635879517},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4766479432582855},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.46327516436576843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.443744957447052},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.417267769575119},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3471369445323944},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.34159642457962036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3277876675128937},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13848042488098145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09485256671905518}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.9353114366531372},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6550147533416748},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.643417239189148},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.600074827671051},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5630795359611511},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5560958981513977},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5420871376991272},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4849822521209717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48037582635879517},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4766479432582855},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.46327516436576843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.443744957447052},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.417267769575119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3471369445323944},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.34159642457962036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3277876675128937},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13848042488098145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09485256671905518},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1499799.1499931","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1499799.1499931","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the June 7-10, 1976, national computer conference and exposition on - AFIPS '76","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1510815417","https://openalex.org/W2752853835"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2990487117","https://openalex.org/W2012882356","https://openalex.org/W109635080","https://openalex.org/W2377262226","https://openalex.org/W4285295794","https://openalex.org/W2098412892","https://openalex.org/W2531534085","https://openalex.org/W2387705642","https://openalex.org/W2372016227"],"abstract_inverted_index":{"Polynomial":[0],"remainder":[1],"sequences":[2],"are":[3,27],"the":[4,21,25,31,34,37,43,56,72,75],"basis":[5],"of":[6,18,24,36,51,74,83,95,98],"many":[7],"important":[8],"algorithms":[9],"in":[10,64],"symbolic":[11],"and":[12,53],"algebraic":[13],"manipulation.":[14],"In":[15],"a":[16,47,61],"number":[17],"these":[19],"algorithms,":[20],"actual":[22],"coefficients":[23,45,76],"sequence":[26],"not":[28],"required;":[29],"rather,":[30],"method":[32,85],"uses":[33],"signs":[35,73],"coefficients.":[38],"Present":[39],"techniques,":[40],"however,":[41],"compute":[42],"exact":[44,80],"(or":[46],"mixed":[48],"radix":[49],"representation":[50],"them),":[52],"then":[54],"obtain":[55,71],"signs.":[57],"This":[58],"paper":[59],"discusses":[60],"new":[62],"approach":[63],"which":[65],"interval":[66],"arithmetic":[67],"is":[68],"used":[69],"to":[70],"without":[77],"computing":[78,92],"their":[79],"values.":[81],"Comparisons":[82],"this":[84],"with":[86],"analogous":[87],"standard":[88],"techniques":[89],"show":[90],"empirical":[91],"time":[93],"reductions":[94],"two":[96],"orders":[97],"magnitude":[99],"for":[100],"even":[101],"relatively":[102],"small":[103],"cases.":[104]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}