{"id":"https://openalex.org/W4221166333","doi":"https://doi.org/10.48550/arxiv.2202.06115","title":"Trinomials and Deterministic Complexity Limits for Real Solving","display_name":"Trinomials and Deterministic Complexity Limits for Real Solving","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4221166333","doi":"https://doi.org/10.48550/arxiv.2202.06115"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2202.06115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/2202.06115","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026831254","display_name":"Erick Boniface","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boniface, Erick","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073898364","display_name":"Weixun Deng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deng, Weixun","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005847878","display_name":"J. Maurice Rojas","orcid":"https://orcid.org/0000-0002-1657-2674"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rojas, J. Maurice","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":61},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Symbolic Computing in Algebraic Geometry and Cryptography","score":0.9996,"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":"Symbolic Computing in Algebraic Geometry and Cryptography","score":0.9996,"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":"Floating-Point Arithmetic in Scientific Computation","score":0.9888,"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/T12069","display_name":"Monomial Ideals and Algebraic Properties","score":0.9849,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/trinomial","display_name":"Trinomial","score":0.92644626},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.669387},{"id":"https://openalex.org/keywords/polynomial-systems","display_name":"Polynomial Systems","score":0.519545},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.48888248}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.92644626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7795614},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.669387},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.62961406},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6115569},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6108101},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5897766},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5707459},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5519822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49107575},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.48888248},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.46192023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08981079},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2202.06115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2202.06115","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2202.06115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4389362338","https://openalex.org/W4377371889","https://openalex.org/W4288359693","https://openalex.org/W3008325063","https://openalex.org/W2942775028","https://openalex.org/W2113623403","https://openalex.org/W2062250216","https://openalex.org/W2055932080","https://openalex.org/W1968512104","https://openalex.org/W1862126075"],"abstract_inverted_index":{"Consider":[0],"a":[1,65,87,148,159,186,203,228,237],"univariate":[2],"polynomial":[3,88,94,209,232],"f":[4,19,38,201],"in":[5,16,24,71,92,95,137,207,210],"Z[x]":[6],"with":[7,125],"degree":[8],"d,":[9],"exactly":[10],"t":[11],"monomial":[12],"terms,":[13],"and":[14,39,112,176,212],"coefficients":[15],"{-H,...,H}.":[17],"Solving":[18,69],"over":[20,90],"the":[21,31,56,81,96,138,164,198,213],"reals,":[22],"R,":[23],"polynomial-time":[25,135,149],"can":[26,118,196],"be":[27],"defined":[28],"as":[29],"counting":[30],"exact":[32],"number":[33],"of":[34,37,50,59,67,85,119,161,163,182,200,216,231],"real":[35],"roots":[36],"then":[40],"finding":[41],"(for":[42],"each":[43],"such":[44,54],"root":[45],"z)":[46],"an":[47,170],"approximation":[48],"w":[49,60],"logarithmic":[51,214],"height":[52,215],"(log(dH))^{O(1)}":[53,75],"that":[55,134,154,190,234],"Newton":[57],"iterates":[58],"have":[61],"error":[62],"decaying":[63],"at":[64,179,202],"rate":[66],"O((1/2)^{2^i}).":[68],"efficiently":[70],"this":[72,102],"sense,":[73],"using":[74],"deterministic":[76,100],"bit":[77],"operations,":[78],"is":[79,142],"arguably":[80],"most":[82],"honest":[83],"formulation":[84],"solving":[86,175],"equation":[89],"R":[91],"time":[93,208],"input":[97,165],"size.":[98],"Unfortunately,":[99],"algorithms":[101],"fast":[103,173],"are":[104],"known":[105,220],"only":[106,221],"for":[107,110,115,129,144,156,191,222,240],"t=2,":[108],"unknown":[109],"t=3,":[111],"provably":[113],"impossible":[114],"t=4.":[116],"(One":[117],"course":[120],"resort":[121],"to":[122],"older":[123],"techniques":[124],"complexity":[126],"(d\\log":[127],"H)^{O(1)}":[128],"t>=4.)":[130],"We":[131,146,167,225],"give":[132,147],"evidence":[133],"real-solving":[136],"strong":[139],"sense":[140],"above":[141],"possible":[143],"t=3:":[145],"algorithm":[150],"employing":[151],"A-hypergeometric":[152],"series":[153],"works":[155],"all":[157],"but":[158],"fraction":[160],"1/Omega(log(dH))":[162],"f.":[166],"also":[168,226],"show":[169,189],"equivalence":[171],"between":[172],"trinomial":[174],"sign":[177,199],"evaluation":[178],"rational":[180,204],"points":[181],"small":[183],"height.":[184],"As":[185],"consequence,":[187],"we":[188,195],"\"most\"":[192],"trinomials":[193],"f,":[194],"compute":[197],"point":[205],"r":[206],"log(dH)":[211],"r.":[217],"(This":[218],"was":[219],"binomials":[223],"before.)":[224],"mention":[227],"related":[229],"family":[230],"systems":[233],"should":[235],"admit":[236],"similar":[238],"speed-up":[239],"solving.":[241]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4221166333","counts_by_year":[],"updated_date":"2024-10-26T08:23:24.925163","created_date":"2022-04-03"}
