{"id":"https://openalex.org/W1981241857","doi":"https://doi.org/10.1137/0203010","title":"Polynomials with Rational Coefficients Which are Hard to Compute","display_name":"Polynomials with Rational Coefficients Which are Hard to Compute","publication_year":1974,"publication_date":"1974-06-01","ids":{"openalex":"https://openalex.org/W1981241857","doi":"https://doi.org/10.1137/0203010","mag":"1981241857"},"language":"en","primary_location":{"id":"doi:10.1137/0203010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0203010","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5007475314","display_name":"Volker Strassen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Volker Strassen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5007475314"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5417,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.92368544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"3","issue":"2","first_page":"128","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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":0.9977999925613403,"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":0.9961000084877014,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9932000041007996,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.746113657951355},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.7342840433120728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6495345234870911},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6116692423820496},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5564195513725281},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5174163579940796},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4728408455848694},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.4612518548965454},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4600323438644409},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.41974714398384094},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34201592206954956},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2512720227241516},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11706474423408508}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.746113657951355},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.7342840433120728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6495345234870911},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6116692423820496},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5564195513725281},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5174163579940796},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4728408455848694},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.4612518548965454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4600323438644409},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.41974714398384094},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34201592206954956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2512720227241516},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11706474423408508},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0203010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0203010","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W588540832","https://openalex.org/W2051422959","https://openalex.org/W2577261694","https://openalex.org/W4387330249"],"related_works":["https://openalex.org/W2074052495","https://openalex.org/W3191608549","https://openalex.org/W2990042598","https://openalex.org/W2376336218","https://openalex.org/W2340379058","https://openalex.org/W1569256320","https://openalex.org/W2046635137","https://openalex.org/W2126812508","https://openalex.org/W2004289501","https://openalex.org/W2614739812"],"abstract_inverted_index":{"We":[0,45],"present":[1],"specific":[2],"polynomials":[3,57],"in":[4,58,68],"$\\mathbb{C}[x]$":[5,59],"with":[6],"algebraic":[7],"or":[8],"rational":[9],"coefficients":[10],"which":[11],"are":[12,21],"hard":[13],"to":[14,55],"compute":[15,56],"(even":[16],"though":[17],"arbitrary":[18],"complex":[19],"numbers":[20],"allowed":[22],"as":[23],"inputs":[24],"for":[25],"the":[26,49],"computation).":[27],"Examples":[28],"are:":[29],"$\\sum_{\\delta":[30,38],"=":[31,39],"0}^d":[32,40],"e^{2\\pi":[33],"i/2^\\delta":[34],"}":[35,42],"x^\\delta":[36,43],"$,":[37],"2^{2^\\delta":[41],"$.":[44],"also":[46],"show":[47],"that":[48],"minimum":[50],"number":[51],"of":[52],"arithmetic":[53],"operations":[54],"is":[60],"itself":[61],"computable.":[62],"Finally,":[63],"we":[64],"study":[65],"computational":[66],"complexity":[67],"finite-dimensional":[69],"algebras":[70],"over":[71],"an":[72],"algebraically":[73],"closed":[74],"field.":[75]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}