{"id":"https://openalex.org/W2089113283","doi":"https://doi.org/10.1145/1145768.1145810","title":"Complexity of the resolution of parametric systems of polynomial equations and inequations","display_name":"Complexity of the resolution of parametric systems of polynomial equations and inequations","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W2089113283","doi":"https://doi.org/10.1145/1145768.1145810","mag":"2089113283"},"language":"en","primary_location":{"id":"doi:10.1145/1145768.1145810","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00078795","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111488193","display_name":"Guillaume Moroz","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Guillaume Moroz","raw_affiliation_strings":["Laboratoire d'Informatique de l'Universit\u00e9 Pierre et Marie Curie-Paris 6, Paris, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique de l'Universit\u00e9 Pierre et Marie Curie-Paris 6, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210159731"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111488193"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210159731"],"apc_list":null,"apc_paid":null,"fwci":1.6853,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.84266832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"246","last_page":"253"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.984499990940094,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.98089998960495,"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/discriminant","display_name":"Discriminant","score":0.7176750898361206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6882157325744629},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5919782519340515},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5766376256942749},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5515416264533997},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5282998085021973},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49572479724884033},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.47630178928375244},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.4432833790779114},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3519013524055481},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3379697799682617},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.31925445795059204},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25782310962677},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24180850386619568},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1581103503704071},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1375122368335724},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07992789149284363}],"concepts":[{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.7176750898361206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6882157325744629},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5919782519340515},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5766376256942749},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5515416264533997},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5282998085021973},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49572479724884033},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47630178928375244},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.4432833790779114},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3519013524055481},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3379697799682617},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.31925445795059204},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25782310962677},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24180850386619568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1581103503704071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1375122368335724},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07992789149284363},{"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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1145768.1145810","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.487.571","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-spiral.lip6.fr/~moroz/moroz_2006_issac.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01351450v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01351450","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":"International Symposium on Symbolic and Algebraic Computation, Jul 2006, Genova, Italy. pp.246-253, &#x27E8;10.1145/1145768.1145810&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:inria-00078795v2","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00078795","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":"[Research Report] RR-5929, INRIA. 2006","raw_type":"Reports"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00078795v2","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00078795","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":"[Research Report] RR-5929, INRIA. 2006","raw_type":"Reports"},"sustainable_development_goals":[{"score":0.7599999904632568,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W64656188","https://openalex.org/W1483607134","https://openalex.org/W1761033158","https://openalex.org/W1781640942","https://openalex.org/W1862515573","https://openalex.org/W1971022195","https://openalex.org/W1993600232","https://openalex.org/W2003425586","https://openalex.org/W2005220910","https://openalex.org/W2009219363","https://openalex.org/W2012079420","https://openalex.org/W2016390696","https://openalex.org/W2017027749","https://openalex.org/W2018615018","https://openalex.org/W2027800264","https://openalex.org/W2035153735","https://openalex.org/W2037381995","https://openalex.org/W2038345254","https://openalex.org/W2048019015","https://openalex.org/W2059724486","https://openalex.org/W2062918650","https://openalex.org/W2069711915","https://openalex.org/W2086656575","https://openalex.org/W2099172492","https://openalex.org/W2151549243","https://openalex.org/W2282767181","https://openalex.org/W3114063815","https://openalex.org/W3217399827","https://openalex.org/W4205227699","https://openalex.org/W4231216667","https://openalex.org/W4243098353","https://openalex.org/W4285719527","https://openalex.org/W4292096448","https://openalex.org/W4300976429","https://openalex.org/W6653289175"],"related_works":["https://openalex.org/W2606674369","https://openalex.org/W3161230432","https://openalex.org/W1771259603","https://openalex.org/W1487201914","https://openalex.org/W4241330371","https://openalex.org/W4367190712","https://openalex.org/W1993180032","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W2327776271"],"abstract_inverted_index":{"Consider":[0],"a":[1,40,61,112,125],"parametric":[2,37],"system":[3,38],"of":[4,43,49,60,69,78,94],"n":[5,13],"polynomial":[6,10],"equations":[7],"and":[8,15,51,73],"r":[9],"inequations":[11],"in":[12,30,109,121],"unknowns":[14],"s":[16],"parameters,":[17],"with":[18],"rational":[19],"coefficients.":[20,80],"A":[21],"recurrent":[22],"problem":[23],"is":[24,100],"to":[25],"determine":[26],"some":[27,83],"open":[28],"set":[29],"the":[31,35,47,58,67,70,76,87,92,95,117],"parameter":[32],"space":[33],"where":[34],"considered":[36],"admits":[39],"constant":[41],"number":[42],"real":[44],"solutions.":[45],"Following":[46],"works":[48],"Lazard":[50],"Rouillier,":[52],"this":[53,110],"can":[54],"be":[55],"done":[56],"by":[57,102],"computation":[59],"discriminant":[62,98,119],"variety.":[63],"Let":[64],"d":[65],"bound":[66,75],"degree":[68,93],"input's":[71],"polynomials,":[72],"\u03c3":[74],"bit-size":[77],"their":[79],"Based":[81],"on":[82,124],"usual":[84],"assumptions":[85],"for":[86],"applications":[88],"we":[89,107],"prove":[90],"that":[91],"computed":[96],"minimal":[97,118],"variety":[99,120],"bounded":[101],"D":[103],":=":[104],"(n+r)d(n+1).":[105],"Moreover":[106],"provide":[108],"case":[111],"deterministic":[113,126],"method":[114],"which":[115],"computes":[116],"\u03c3O(1)DO(n+s)":[122],"bit-operations":[123],"Turing":[127],"machine.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
