{"id":"https://openalex.org/W2565924041","doi":"https://doi.org/10.1145/3018610.3018622","title":"A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations","display_name":"A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations","publication_year":2016,"publication_date":"2016-12-22","ids":{"openalex":"https://openalex.org/W2565924041","doi":"https://doi.org/10.1145/3018610.3018622","mag":"2565924041"},"language":"en","primary_location":{"id":"doi:10.1145/3018610.3018622","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3018610.3018622","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01510979","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109222954","display_name":"\u00c9rik Martin-Dorel","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"\u00c9rik Martin-Dorel","raw_affiliation_strings":["IRIT, France / Paul Sabatier University, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT, France / Paul Sabatier University, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210119061"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101715842","display_name":"Pierre Le Roux","orcid":"https://orcid.org/0000-0002-0512-0437"},"institutions":[{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Roux","raw_affiliation_strings":["ONERA, France","ONERA - The French Aerospace Lab [Toulouse] (F-31055 Toulouse - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ONERA, France","institution_ids":["https://openalex.org/I2801658355"]},{"raw_affiliation_string":"ONERA - The French Aerospace Lab [Toulouse] (F-31055 Toulouse - France)","institution_ids":["https://openalex.org/I2801658355"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"90","last_page":"99"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9950000047683716,"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/decidability","display_name":"Decidability","score":0.6247671842575073},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.617878794670105},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5628789067268372},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5498365163803101},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5319585800170898},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5167950391769409},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45676565170288086},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42407771944999695},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.42381057143211365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.399884432554245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3666490912437439},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3319603204727173},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12320694327354431}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.6247671842575073},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.617878794670105},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5628789067268372},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5498365163803101},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5319585800170898},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5167950391769409},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45676565170288086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42407771944999695},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.42381057143211365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.399884432554245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3666490912437439},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3319603204727173},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12320694327354431},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3018610.3018622","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3018610.3018622","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01510979v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01510979","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The 6th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP 2017), Jan 2017, Paris, France. pp.90 - 99, &#x27E8;10.1145/3018610.3018622&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01510979v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01510979","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The 6th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP 2017), Jan 2017, Paris, France. pp.90 - 99, &#x27E8;10.1145/3018610.3018622&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5333426614","display_name":"Combining Analyses for the Study of Numerical Invariants","funder_award_id":"ANR-12-INSE-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6942917955","display_name":null,"funder_award_id":"ANR-11-LABX-0040-CIMI","funder_id":"https://openalex.org/F4320335230","funder_display_name":"Centre International de Math\u00e9matiques et Informatique de Toulouse"},{"id":"https://openalex.org/G7786692064","display_name":"Centre International de Math\u00e9matiques et d'Informatique (de Toulouse)","funder_award_id":"ANR-11-LABX-0040","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320335230","display_name":"Centre International de Math\u00e9matiques et Informatique de Toulouse","ror":"https://ror.org/017tgbk05"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1534704094","https://openalex.org/W1786112247","https://openalex.org/W1967344706","https://openalex.org/W1999613943","https://openalex.org/W2048468434","https://openalex.org/W2113181166","https://openalex.org/W2138211565","https://openalex.org/W2157264766","https://openalex.org/W2290255244","https://openalex.org/W2912522929","https://openalex.org/W3100674527","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2331020993","https://openalex.org/W2972379433","https://openalex.org/W4383764068","https://openalex.org/W1481826604","https://openalex.org/W1797057780","https://openalex.org/W1501430220","https://openalex.org/W3187762542","https://openalex.org/W1587864502","https://openalex.org/W2583753471","https://openalex.org/W1505636692"],"abstract_inverted_index":{"Polynomial":[0],"positivity":[1,28],"over":[2],"the":[3,13,53,63,74],"real":[4],"field":[5],"is":[6],"known":[7],"to":[8,70,82,94],"be":[9,40,95],"decidable":[10],"but":[11,20],"even":[12],"best":[14],"algorithms":[15],"remain":[16],"costly.":[17],"An":[18],"incomplete":[19],"often":[21,91],"efficient":[22],"alternative":[23],"consists":[24],"in":[25,38,73,84],"looking":[26],"for":[27,55],"witnesses":[29],"as":[30,98],"sum":[31],"of":[32,58,62],"squares":[33],"decompositions.":[34],"Such":[35],"decompositions":[36],"can":[37],"practice":[39],"obtained":[41],"through":[42],"convex":[43],"optimization.":[44],"Unfortunately,":[45],"these":[46],"methods":[47,65],"only":[48],"yield":[49],"approximate":[50],"solutions.":[51],"Hence":[52],"need":[54],"formal":[56],"verification":[57,90],"such":[59],"witnesses.":[60],"State":[61],"art":[64],"rely":[66],"on":[67],"heuristic":[68],"roundings":[69],"exact":[71],"solutions":[72,78],"rational":[75,99],"field.":[76],"These":[77],"are":[79],"then":[80],"easy":[81],"verify":[83],"a":[85],"proof":[86],"assistant.":[87],"However,":[88],"this":[89],"turns":[92],"out":[93],"very":[96],"costly,":[97],"coefficients":[100],"may":[101],"blow":[102],"up":[103],"during":[104],"computations.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
