{"id":"https://openalex.org/W2052147861","doi":"https://doi.org/10.1090/s0025-5718-06-01878-3","title":"Fast computation of a rational point of a variety over a finite field","display_name":"Fast computation of a rational point of a variety over a finite field","publication_year":2006,"publication_date":"2006-07-20","ids":{"openalex":"https://openalex.org/W2052147861","doi":"https://doi.org/10.1090/s0025-5718-06-01878-3","mag":"2052147861"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01878-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01878-3","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01878-3/S0025-5718-06-01878-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01878-3/S0025-5718-06-01878-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049527337","display_name":"Antonio Cafure","orcid":null},"institutions":[{"id":"https://openalex.org/I53241121","display_name":"Fundaci\u00f3n Ciencias Exactas y Naturales","ror":"https://ror.org/05rxmkq09","country_code":"AR","type":"nonprofit","lineage":["https://openalex.org/I53241121"]},{"id":"https://openalex.org/I24354313","display_name":"University of Buenos Aires","ror":"https://ror.org/0081fs513","country_code":"AR","type":"education","lineage":["https://openalex.org/I24354313"]}],"countries":["AR"],"is_corresponding":true,"raw_author_name":"Antonio Cafure","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabell\u00c3\u00b3n I (1428) Buenos Aires, Argentina","Departamento de Matem\u00e1tica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabell\u00f3n I (1428) Buenos Aires, Argentina"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabell\u00c3\u00b3n I (1428) Buenos Aires, Argentina","institution_ids":["https://openalex.org/I53241121"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabell\u00f3n I (1428) Buenos Aires, Argentina","institution_ids":["https://openalex.org/I53241121","https://openalex.org/I24354313"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050319969","display_name":"Guillermo Matera","orcid":null},"institutions":[{"id":"https://openalex.org/I4210095825","display_name":"Centro Cient\u00edfico Tecnol\u00f3gico - San Juan","ror":"https://ror.org/00kwm3d29","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210095825","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I35953669","display_name":"National University of General Sarmiento","ror":"https://ror.org/01k6h2m87","country_code":"AR","type":"education","lineage":["https://openalex.org/I35953669"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Guillermo Matera","raw_affiliation_strings":["Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Guti\u00c3\u00a9rrez 1150 (1613) Los Polvorines, Buenos Aires, Argentina; and National Council of Science and Technology (CONICET), Argentina","Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Guti\u00e9rrez 1150 (1613) Los Polvorines, Buenos Aires, Argentina","National Council of Science and Technology (CONICET), Argentina"],"affiliations":[{"raw_affiliation_string":"Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Guti\u00c3\u00a9rrez 1150 (1613) Los Polvorines, Buenos Aires, Argentina; and National Council of Science and Technology (CONICET), Argentina","institution_ids":["https://openalex.org/I35953669"]},{"raw_affiliation_string":"Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Guti\u00e9rrez 1150 (1613) Los Polvorines, Buenos Aires, Argentina","institution_ids":["https://openalex.org/I35953669"]},{"raw_affiliation_string":"National Council of Science and Technology (CONICET), Argentina","institution_ids":["https://openalex.org/I4210095825"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049527337"],"corresponding_institution_ids":["https://openalex.org/I24354313","https://openalex.org/I53241121"],"apc_list":null,"apc_paid":null,"fwci":2.0222,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86252487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"75","issue":"256","first_page":"2049","last_page":"2085"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998999834060669,"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":0.9998999834060669,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.992900013923645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8839196562767029},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7118014097213745},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5995064377784729},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5096995830535889},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5050638318061829},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4834378659725189},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.477897047996521},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4552045166492462},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4489915072917938},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4361172914505005},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.43318116664886475},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43020883202552795},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3003889322280884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2081473171710968},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1847904920578003},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08638298511505127}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8839196562767029},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7118014097213745},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5995064377784729},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5096995830535889},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5050638318061829},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4834378659725189},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.477897047996521},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4552045166492462},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4489915072917938},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4361172914505005},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.43318116664886475},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43020883202552795},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3003889322280884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2081473171710968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1847904920578003},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08638298511505127},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-06-01878-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01878-3","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01878-3/S0025-5718-06-01878-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:RDI UBA:artiaex:paper_00255718_v75_n256_p2049_Cafure_oai","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12110/paper_00255718_v75_n256_p2049_Cafure","pdf_url":null,"source":{"id":"https://openalex.org/S4306402562","display_name":"Repositorio Digital Institucional de la Universidad de Buenos Aires (Universidad de Buenos Aires)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24354313","host_organization_name":"Universidad de Buenos Aires","host_organization_lineage":["https://openalex.org/I24354313"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Math. Comput. 2006;75(256):2049-2085","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.6616","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.6616","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0406085v1.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01878-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01878-3","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01878-3/S0025-5718-06-01878-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320335478","display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2052147861.pdf","grobid_xml":"https://content.openalex.org/works/W2052147861.grobid-xml"},"referenced_works_count":80,"referenced_works":["https://openalex.org/W32754932","https://openalex.org/W64656188","https://openalex.org/W138638854","https://openalex.org/W161165520","https://openalex.org/W208025404","https://openalex.org/W269145335","https://openalex.org/W656708819","https://openalex.org/W1454988622","https://openalex.org/W1483218536","https://openalex.org/W1487675067","https://openalex.org/W1489774662","https://openalex.org/W1495410784","https://openalex.org/W1498067247","https://openalex.org/W1504054803","https://openalex.org/W1512914916","https://openalex.org/W1518341038","https://openalex.org/W1521050514","https://openalex.org/W1540815697","https://openalex.org/W1561337879","https://openalex.org/W1562183207","https://openalex.org/W1564514837","https://openalex.org/W1569499052","https://openalex.org/W1581386393","https://openalex.org/W1583871653","https://openalex.org/W1589642341","https://openalex.org/W1590894046","https://openalex.org/W1599026900","https://openalex.org/W1642071661","https://openalex.org/W1788589662","https://openalex.org/W1828839365","https://openalex.org/W1931868030","https://openalex.org/W1964605445","https://openalex.org/W1972632202","https://openalex.org/W1973993014","https://openalex.org/W1978946312","https://openalex.org/W1979472156","https://openalex.org/W1992373021","https://openalex.org/W2006394656","https://openalex.org/W2011693299","https://openalex.org/W2022078407","https://openalex.org/W2022841156","https://openalex.org/W2024848692","https://openalex.org/W2035153735","https://openalex.org/W2037381995","https://openalex.org/W2038345254","https://openalex.org/W2051234010","https://openalex.org/W2059724486","https://openalex.org/W2076593831","https://openalex.org/W2078088136","https://openalex.org/W2080132708","https://openalex.org/W2080589685","https://openalex.org/W2088922099","https://openalex.org/W2091991289","https://openalex.org/W2095017199","https://openalex.org/W2126534535","https://openalex.org/W2130918732","https://openalex.org/W2134386365","https://openalex.org/W2139917777","https://openalex.org/W2148531294","https://openalex.org/W2170975953","https://openalex.org/W2319466955","https://openalex.org/W2330548796","https://openalex.org/W2396676183","https://openalex.org/W2609052583","https://openalex.org/W2621142884","https://openalex.org/W2995200218","https://openalex.org/W3133728983","https://openalex.org/W3151140615","https://openalex.org/W4210639400","https://openalex.org/W4234426551","https://openalex.org/W4247890365","https://openalex.org/W4249549360","https://openalex.org/W4250550876","https://openalex.org/W4292096448","https://openalex.org/W4298054792","https://openalex.org/W4299537077","https://openalex.org/W4300076833","https://openalex.org/W4302438091","https://openalex.org/W6629294917","https://openalex.org/W6635778417"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W2019471580","https://openalex.org/W2168299207","https://openalex.org/W2952352711","https://openalex.org/W2068656449","https://openalex.org/W1909918105","https://openalex.org/W2612896625","https://openalex.org/W2963158646","https://openalex.org/W3141524051"],"abstract_inverted_index":{"We":[0],"exhibit":[1],"a":[2,7,16,21,41,81],"probabilistic":[3],"algorithm":[4,63],"which":[5,83],"computes":[6],"rational":[8],"point":[9],"of":[10,34,37,44,59,67,74,89,92],"an":[11],"absolutely":[12],"irreducible":[13],"variety":[14],"over":[15],"finite":[17],"field":[18,39,76],"defined":[19],"by":[20,55],"reduced":[22],"regular":[23],"sequence.":[24],"Its":[25],"time-space":[26],"complexity":[27],"is":[28,53,84],"roughly":[29,85],"quadratic":[30],"in":[31],"the":[32,35,38,45,51,56,60,72,75,86,90,93],"logarithm":[33],"cardinality":[36,73],"and":[40],"geometric":[42],"invariant":[43],"input":[46,94],"system.":[47,61],"This":[48],"invariant,":[49],"called":[50],"degree,":[52],"bounded":[54],"B\u00e9zout":[57],"number":[58],"Our":[62],"works":[64],"for":[65],"fields":[66],"any":[68],"characteristic,":[69],"but":[70],"requires":[71],"to":[77],"be":[78],"greater":[79],"than":[80],"quantity":[82],"fourth":[87],"power":[88],"degree":[91],"variety.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}