{"id":"https://openalex.org/W2901954812","doi":"https://doi.org/10.1090/mcom/3517","title":"A fast randomized geometric algorithm for computing Riemann-Roch spaces","display_name":"A fast randomized geometric algorithm for computing Riemann-Roch spaces","publication_year":2020,"publication_date":"2020-01-08","ids":{"openalex":"https://openalex.org/W2901954812","doi":"https://doi.org/10.1090/mcom/3517","mag":"2901954812"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3517","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3517","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.08237","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041420106","display_name":"Aude Le Gluher","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Aude Le Gluher","raw_affiliation_strings":["CARAMBA project, Universit\u00c3\u00a9 de Lorraine; and Inria Nancy \u00e2\u0080\u0093 Grand Est; and CNRS, UMR 7503, LORIA, Nancy, France","CARAMBA project, Universit\u00e9 de Lorraine","CNRS, UMR 7503, LORIA, Nancy, France","Inria Nancy \u2013 Grand Est"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CARAMBA project, Universit\u00c3\u00a9 de Lorraine; and Inria Nancy \u00e2\u0080\u0093 Grand Est; and CNRS, UMR 7503, LORIA, Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I4210121838","https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CARAMBA project, Universit\u00e9 de Lorraine","institution_ids":["https://openalex.org/I90183372"]},{"raw_affiliation_string":"CNRS, UMR 7503, LORIA, Nancy, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Inria Nancy \u2013 Grand Est","institution_ids":["https://openalex.org/I4210127166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056341371","display_name":"Pierre-Jean Spaenlehauer","orcid":"https://orcid.org/0000-0001-7906-0505"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre-Jean Spaenlehauer","raw_affiliation_strings":["CARAMBA project, INRIA Nancy \u00e2\u0080\u0093 Grand Est; and Universit\u00c3\u00a9 de Lorraine; and CNRS, UMR 7503, LORIA, Nancy, France","Universit\u00e9 de Lorraine","CNRS, UMR 7503, LORIA, Nancy, France","CARAMBA project, INRIA Nancy \u2013 Grand Est"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CARAMBA project, INRIA Nancy \u00e2\u0080\u0093 Grand Est; and Universit\u00c3\u00a9 de Lorraine; and CNRS, UMR 7503, LORIA, Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I4210121838","https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine","institution_ids":["https://openalex.org/I90183372"]},{"raw_affiliation_string":"CNRS, UMR 7503, LORIA, Nancy, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CARAMBA project, INRIA Nancy \u2013 Grand Est","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041420106"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I4210127166","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":1.3118,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84360521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"89","issue":"325","first_page":"2399","last_page":"2433"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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/T11435","display_name":"Polynomial and algebraic computation","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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.8504905700683594},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.6246291995048523},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4079328179359436},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3224124312400818},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2929517328739166}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8504905700683594},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.6246291995048523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4079328179359436},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3224124312400818},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2929517328739166}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3517","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3517","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.08237","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.08237","pdf_url":"https://arxiv.org/pdf/1811.08237","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01930573v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01930573","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2020, 89, pp.2399-2433. &#x27E8;10.1090/mcom/3517&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.08237","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.08237","pdf_url":"https://arxiv.org/pdf/1811.08237","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6000000238418579,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310925","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97"},{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1511314663","https://openalex.org/W1527509877","https://openalex.org/W1562183207","https://openalex.org/W1572461035","https://openalex.org/W1594960997","https://openalex.org/W1695659029","https://openalex.org/W1976677460","https://openalex.org/W1980117595","https://openalex.org/W1989603733","https://openalex.org/W2001901358","https://openalex.org/W2049707341","https://openalex.org/W2067754486","https://openalex.org/W2068958514","https://openalex.org/W2080132708","https://openalex.org/W2082180697","https://openalex.org/W2082637948","https://openalex.org/W2084801848","https://openalex.org/W2098626016","https://openalex.org/W2108371780","https://openalex.org/W2108866759","https://openalex.org/W2120248756","https://openalex.org/W2130918732","https://openalex.org/W2141363069","https://openalex.org/W2475905526","https://openalex.org/W2583623140","https://openalex.org/W2610855961","https://openalex.org/W2809375912","https://openalex.org/W2969268864","https://openalex.org/W3103484676","https://openalex.org/W3144798926","https://openalex.org/W4205630623","https://openalex.org/W4253198034","https://openalex.org/W4296292757"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,10,42,58,83,243,329],"probabilistic":[3],"variant":[4],"of":[5,12,315],"Brill-Noether\u2019s":[6],"algorithm":[7,107,320],"for":[8,246],"computing":[9,316],"basis":[11],"the":[13,269,307,313,335],"Riemann-Roch":[14,317],"space":[15],"<inline-formula":[16,44,63,88,111,214,228,250,275,341],"content-type=\"math/mathml\">":[17,45,64,89,112,215,229,251,276,342],"<mml:math":[18,46,65,90,113,216,230,252,277,343],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,47,66,91,114,217,231,253,278,344],"alttext=\"upper":[20,48,115,254,279,345],"L":[21],"left-parenthesis":[22,117,119,121,132,347,349,351,361],"upper":[23,68,123,133,285,310,353,362,373],"D":[24,134,255,280,363],"right-parenthesis\">":[25,143,376],"<mml:semantics>":[26,50,70,93,144,219,233,258,287,377],"<mml:mrow>":[27,145,288,378],"<mml:mi>L</mml:mi>":[28],"<mml:mo":[29,32,147,149,152,158,166,181,188,194,196,380,382,385,391,399],"stretchy=\"false\">(</mml:mo>":[30,148,153,159,182,381,386,392],"<mml:mi>D</mml:mi>":[31,51,184,260,290,296],"stretchy=\"false\">)</mml:mo>":[33,167,189,195,197,400],"</mml:mrow>":[34,75,164,174,198,297,397],"<mml:annotation":[35,52,76,95,199,221,237,263,298],"encoding=\"application/x-tex\">L(D)</mml:annotation>":[36],"</mml:semantics>":[37,54,79,97,208,223,239,265,301],"</mml:math>":[38,55,80,98,209,224,240,266,302],"</inline-formula>":[39,56,81,99,210,225,241,267,303],"associated":[40],"to":[41],"divisor":[43,272],"D\">":[49,286],"encoding=\"application/x-tex\">D</mml:annotation>":[53],"on":[57,312],"projective":[59],"nodal":[60],"plane":[61],"curve":[62],"alttext=\"double-struck":[67],"C\">":[69],"<mml:mrow":[71,160,168,393],"class=\"MJX-TeXAtom-ORD\">":[72,161,169,394],"<mml:mi":[73,162,395],"mathvariant=\"double-struck\">C</mml:mi>":[74,163,396],"encoding=\"application/x-tex\">\\mathbb":[77],"{C}</mml:annotation>":[78],"over":[82],"sufficiently":[84],"large":[85],"perfect":[86],"field":[87],"alttext=\"k\">":[92,218],"<mml:mi>k</mml:mi>":[94,220],"encoding=\"application/x-tex\">k</mml:annotation>":[96,222],".":[100,304],"Our":[101,319],"main":[102],"result":[103],"shows":[104],"that":[105,274,326,328],"this":[106],"requires":[108],"at":[109],"most":[110],"O":[116,346],"max":[118,348],"degree":[120,131,350,360],"double-struck":[122,352],"C":[124,354],"right-parenthesis":[125,138,142,355,367,369],"Superscript":[126,139,356],"2":[127],"omega":[128,140],"Baseline":[129,137,141,283,358,366],"comma":[130,359],"Subscript":[135,256,281,364],"plus":[136,282,365],"<mml:mi>O</mml:mi>":[146,379],"movablelimits=\"true\"":[150,383],"form=\"prefix\">max</mml:mo>":[151,384],"<mml:mi>deg</mml:mi>":[154,177,387,404],"<mml:mo>":[155,178,293,388,405],"\u2061":[156,179,389],"</mml:mo>":[157,180,295,390],"<mml:msup>":[165,187,398],"<mml:mn>2</mml:mn>":[170],"<mml:mi>":[171,190,234],"\u03c9":[172,191,235],"</mml:mi>":[173,192,236],"</mml:msup>":[175,193,402],"<mml:mo>,</mml:mo>":[176,403],"<mml:msub>":[183,259,289],"<mml:mo>+</mml:mo>":[185,261,291],"</mml:msub>":[186,262,292],"encoding=\"application/x-tex\">O(\\max":[200],"(\\deg":[201],"(\\mathbb":[202],"{C})^{2\\omega":[203],"},":[204],"\\deg":[205],"(D_+)^\\omega":[206],"))</mml:annotation>":[207],"arithmetic":[211],"operations":[212],"in":[213],",":[226],"where":[227],"alttext=\"omega\">":[232],"encoding=\"application/x-tex\">\\omega</mml:annotation>":[238],"is":[242,268,338],"feasible":[244],"exponent":[245],"matrix":[247],"multiplication":[248],"and":[249],"plus\">":[257],"encoding=\"application/x-tex\">D_+</mml:annotation>":[264],"smallest":[270],"effective":[271],"such":[273],"greater-than-or-equal-to":[284],"\u2265":[294],"encoding=\"application/x-tex\">D_+\\geq":[299],"D</mml:annotation>":[300],"This":[305],"improves":[306],"best":[308],"known":[309],"bounds":[311],"complexity":[314],"spaces.":[318],"may":[321],"fail,":[322],"but":[323],"we":[324],"show":[325],"provided":[327],"few":[330],"mild":[331],"assumptions":[332],"are":[333],"satisfied,":[334],"failure":[336],"probability":[337],"bounded":[339],"by":[340],"4":[357],"squared":[368],"slash":[370],"StartAbsoluteValue":[371],"script":[372],"E":[374],"EndAbsoluteValue":[375],"<mml:mn>4</mml:mn>":[401]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2018-11-29T00:00:00"}