{"id":"https://openalex.org/W2019644066","doi":"https://doi.org/10.1145/1089263.1089266","title":"Efficient polynomial substitutions of a sparse argument","display_name":"Efficient polynomial substitutions of a sparse argument","publication_year":1981,"publication_date":"1981-08-01","ids":{"openalex":"https://openalex.org/W2019644066","doi":"https://doi.org/10.1145/1089263.1089266","mag":"2019644066"},"language":"en","primary_location":{"id":"doi:10.1145/1089263.1089266","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1089263.1089266","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1089263.1089266","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":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/1089263.1089266","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048657171","display_name":"William H. Rowan","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William H. Rowan","raw_affiliation_strings":["U.C. Berkeley","U.C. BERKELEY"],"affiliations":[{"raw_affiliation_string":"U.C. Berkeley","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"U.C. BERKELEY","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048657171"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15636201,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"3","first_page":"17","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9991000294685364,"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":0.9991000294685364,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9979000091552734,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.7603294253349304},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.7003085017204285},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.6211763024330139},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6175662279129028},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.616140604019165},{"id":"https://openalex.org/keywords/sums-of-powers","display_name":"Sums of powers","score":0.5007891654968262},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43165579438209534},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.43047747015953064},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38868623971939087},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3371129631996155},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13432103395462036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12700843811035156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7603294253349304},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7003085017204285},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.6211763024330139},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6175662279129028},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.616140604019165},{"id":"https://openalex.org/C46221946","wikidata":"https://www.wikidata.org/wiki/Q15051202","display_name":"Sums of powers","level":2,"score":0.5007891654968262},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43165579438209534},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.43047747015953064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38868623971939087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3371129631996155},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13432103395462036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12700843811035156},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1089263.1089266","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1089263.1089266","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1089263.1089266","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":{"id":"doi:10.1145/1089263.1089266","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1089263.1089266","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1089263.1089266","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2019644066.pdf","grobid_xml":"https://content.openalex.org/works/W2019644066.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1964970431","https://openalex.org/W1982395629","https://openalex.org/W2034212384","https://openalex.org/W2056748176","https://openalex.org/W2528130235"],"related_works":["https://openalex.org/W2108371780","https://openalex.org/W2989875800","https://openalex.org/W2009896212","https://openalex.org/W3160845651","https://openalex.org/W3046867571","https://openalex.org/W4210984194","https://openalex.org/W1968615564","https://openalex.org/W1633071293","https://openalex.org/W4299896541","https://openalex.org/W2019644066"],"abstract_inverted_index":{"Methods":[0],"are":[1],"presented":[2],"for":[3],"taking":[4],"powers":[5],"of":[6,24,35,56,62,64,70,73],"symbolic":[7],"polynomials":[8,14],"and":[9],"substituting":[10],"them":[11],"into":[12],"univariate":[13],"with":[15],"scalar":[16],"coefficients.":[17],"It":[18],"is":[19,27],"shown":[20],"that":[21],"the":[22,25,33,52,57,68,74],"size":[23],"result":[26],"a":[28,41,46],"sharp":[29],"lower":[30],"bound":[31],"on":[32],"number":[34],"coefficient":[36,65],"multiplications":[37],"required":[38],"to":[39,45],"raise":[40],"completely":[42],"sparse":[43],"polynomial":[44],"power.":[47],"Other":[48],"theoretical":[49],"results":[50],"prove":[51],"optimality":[53],"or":[54],"near-optimality":[55],"methods":[58],"given,":[59],"in":[60],"terms":[61],"numbers":[63],"operations,":[66],"under":[67],"condition":[69],"complete":[71],"sparsity":[72],"argument.":[75]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
