{"id":"https://openalex.org/W2080010241","doi":"https://doi.org/10.1145/1086837.1086853","title":"Formal representations for algebraic numbers","display_name":"Formal representations for algebraic numbers","publication_year":1974,"publication_date":"1974-08-01","ids":{"openalex":"https://openalex.org/W2080010241","doi":"https://doi.org/10.1145/1086837.1086853","mag":"2080010241"},"language":"en","primary_location":{"id":"doi:10.1145/1086837.1086853","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1086837.1086853","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/A5069838321","display_name":"Dennis Weeks","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103999","display_name":"Integrated Systems Incorporation (United States)","ror":"https://ror.org/01et00j38","country_code":"US","type":"company","lineage":["https://openalex.org/I4210103999"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dennis Weeks","raw_affiliation_strings":["Xebec Systems, Inc., Sunnyvale, Calif"],"affiliations":[{"raw_affiliation_string":"Xebec Systems, Inc., Sunnyvale, Calif","institution_ids":["https://openalex.org/I4210103999"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069838321"],"corresponding_institution_ids":["https://openalex.org/I4210103999"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.24647619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"3","first_page":"91","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9919000267982483,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/algebraic-number","display_name":"Algebraic number","score":0.701757550239563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6857484579086304},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6295906901359558},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5080759525299072},{"id":"https://openalex.org/keywords/algebraic-extension","display_name":"Algebraic extension","score":0.4924961030483246},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.48546913266181946},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48302873969078064},{"id":"https://openalex.org/keywords/algebraic-element","display_name":"Algebraic element","score":0.42973411083221436},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42835694551467896},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34908318519592285},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2881123423576355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.03752261400222778}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.701757550239563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6857484579086304},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6295906901359558},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5080759525299072},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.4924961030483246},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.48546913266181946},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48302873969078064},{"id":"https://openalex.org/C173832452","wikidata":"https://www.wikidata.org/wiki/Q162608","display_name":"Algebraic element","level":5,"score":0.42973411083221436},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42835694551467896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34908318519592285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2881123423576355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.03752261400222778},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1086837.1086853","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1086837.1086853","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1490274092","https://openalex.org/W1555289940","https://openalex.org/W1560124954","https://openalex.org/W1602863873","https://openalex.org/W1969390424","https://openalex.org/W1990590352","https://openalex.org/W2014570670","https://openalex.org/W2040904008","https://openalex.org/W2082364592","https://openalex.org/W2135926107","https://openalex.org/W2796856612"],"related_works":["https://openalex.org/W3090789507","https://openalex.org/W2952673830","https://openalex.org/W3022554530","https://openalex.org/W4386874608","https://openalex.org/W2080206629","https://openalex.org/W2025761369","https://openalex.org/W4233995141","https://openalex.org/W2538026592","https://openalex.org/W2741895122","https://openalex.org/W2408624816"],"abstract_inverted_index":{"Recent":[0],"literature":[1],"(e.g.,":[2],"[12])":[3],"shows":[4],"a":[5,37],"growing":[6],"interest":[7,25],"in":[8,14],"the":[9,17,27,42],"representation":[10],"of":[11,16,23],"algebraic":[12,32],"numbers":[13],"terms":[15],"polynomials":[18],"they":[19],"satisfy.":[20],"The":[21],"basis":[22],"this":[24],"is":[26],"observation":[28],"that":[29],"for":[30],"every":[31],"number":[33],"\u03b1":[34],"there":[35],"exists":[36],"unique":[38],"polynomial":[39],"p(x)":[40],"having":[41],"following":[43],"properties:":[44]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
