{"id":"https://openalex.org/W1988025893","doi":"https://doi.org/10.1145/2442829.2442859","title":"Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions","display_name":"Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions","publication_year":2012,"publication_date":"2012-07-22","ids":{"openalex":"https://openalex.org/W1988025893","doi":"https://doi.org/10.1145/2442829.2442859","mag":"1988025893"},"language":"en","primary_location":{"id":"doi:10.1145/2442829.2442859","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000788715","display_name":"Feng Guo","orcid":"https://orcid.org/0000-0001-6320-3348"},"institutions":[{"id":"https://openalex.org/I4210158522","display_name":"PLA Academy of Military Science","ror":"https://ror.org/05ct4s596","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210158522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Guo","raw_affiliation_strings":["AMSS Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AMSS Beijing, China","institution_ids":["https://openalex.org/I4210158522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056874049","display_name":"Erich Kaltofen","orcid":"https://orcid.org/0000-0003-2739-3230"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erich L. Kaltofen","raw_affiliation_strings":["NCSU Raleigh, North Carolina","NCSU, Raleigh, North Carolina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NCSU Raleigh, North Carolina","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"NCSU, Raleigh, North Carolina","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026679766","display_name":"Lihong Zhi","orcid":"https://orcid.org/0000-0001-9973-2217"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization, AMSS Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization, AMSS Beijing, China","institution_ids":["https://openalex.org/I4210129227"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3455,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.78287921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"195","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9980000257492065,"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":0.9976999759674072,"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":0.7758079171180725},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7535656690597534},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7083243131637573},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5871623754501343},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5800821185112},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5403793454170227},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4972369968891144},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48510587215423584},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.44018369913101196},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41895759105682373},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.415319561958313},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36578428745269775},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3481028378009796},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2342987060546875},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13887476921081543},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10291999578475952}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7758079171180725},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7535656690597534},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7083243131637573},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5871623754501343},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5800821185112},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5403793454170227},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4972369968891144},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48510587215423584},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.44018369913101196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41895759105682373},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.415319561958313},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36578428745269775},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3481028378009796},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2342987060546875},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13887476921081543},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10291999578475952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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":3,"locations":[{"id":"doi:10.1145/2442829.2442859","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.259.9820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.259.9820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ncsu.edu/%7Ekaltofen/bibliography/12/GKZ12.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.756.6794","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.6794","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/1203.0253.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1487813288","display_name":null,"funder_award_id":"CCF-0830347, CCF-1115772 (Kaltofen)","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G2723946483","display_name":null,"funder_award_id":"91118001, 60821002/F02, 60911130369, 10871194","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W360528349","https://openalex.org/W1534704094","https://openalex.org/W1559197676","https://openalex.org/W1631846348","https://openalex.org/W1638969837","https://openalex.org/W1647006788","https://openalex.org/W1963753244","https://openalex.org/W1967073510","https://openalex.org/W1967344706","https://openalex.org/W1992003601","https://openalex.org/W1995320256","https://openalex.org/W2002341633","https://openalex.org/W2003232014","https://openalex.org/W2016389104","https://openalex.org/W2045252454","https://openalex.org/W2060507785","https://openalex.org/W2064131066","https://openalex.org/W2065053468","https://openalex.org/W2071040500","https://openalex.org/W2085729541","https://openalex.org/W2101676748","https://openalex.org/W2154406034","https://openalex.org/W2165281529","https://openalex.org/W2912522929","https://openalex.org/W2963650905","https://openalex.org/W3105811395","https://openalex.org/W4233252806","https://openalex.org/W4238665603","https://openalex.org/W4300272898","https://openalex.org/W6651166734"],"related_works":["https://openalex.org/W2029638535","https://openalex.org/W2493494838","https://openalex.org/W2963700124","https://openalex.org/W4297923520","https://openalex.org/W2624196447","https://openalex.org/W2077924482","https://openalex.org/W2771160919","https://openalex.org/W4301659259","https://openalex.org/W1571037741","https://openalex.org/W4298028631"],"abstract_inverted_index":{"We":[0],"deploy":[1],"numerical":[2],"semidefinite":[3,17,79],"programming":[4],"and":[5],"conversion":[6],"to":[7,11,54,78],"exact":[8],"rational":[9,21],"inequalities":[10],"certify":[12],"that":[13],"for":[14,62],"a":[15,26,46],"positive":[16],"input":[18,48],"polynomial":[19],"or":[20],"function,":[22],"any":[23],"representation":[24],"as":[25],"fraction":[27],"of":[28,30,41,68,75],"sums-of-squares":[29],"polynomials":[31,37],"with":[32],"real":[33],"coefficients":[34],"must":[35],"contain":[36],"in":[38],"the":[39,73],"denominator":[40,64],"degree":[42],"no":[43],"less":[44],"than":[45],"given":[47],"lower":[49],"bound.":[50],"By":[51],"Artin's":[52],"solution":[53],"Hilbert's":[55],"17th":[56],"problems,":[57],"such":[58],"representations":[59],"always":[60],"exist":[61],"some":[63],"degree.":[65],"Our":[66],"certificates":[67],"infeasibility":[69],"are":[70],"based":[71],"on":[72],"generalization":[74],"Farkas's":[76],"Lemma":[77],"programming.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
