{"id":"https://openalex.org/W2944483747","doi":"https://doi.org/10.1137/20m1325484","title":"The Algebraic Boundary of the Sonc-Cone","display_name":"The Algebraic Boundary of the Sonc-Cone","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W2944483747","doi":"https://doi.org/10.1137/20m1325484","mag":"2944483747"},"language":"en","primary_location":{"id":"doi:10.1137/20m1325484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1325484","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-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/A5054230410","display_name":"Jens Forsg\u00e5rd","orcid":"https://orcid.org/0000-0003-3172-985X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jens Forsg\u00e5rd","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3172-985X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059450802","display_name":"Timo de Wolff","orcid":"https://orcid.org/0000-0003-0883-1389"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Timo de Wolff","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6742,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.85188562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":"3","first_page":"468","last_page":"502"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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/T11435","display_name":"Polynomial and algebraic computation","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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9871000051498413,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9854999780654907,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.8261535167694092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8077707886695862},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5706341862678528},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5434262752532959},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5379579067230225},{"id":"https://openalex.org/keywords/stratification","display_name":"Stratification (seeds)","score":0.5089988708496094},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.5075560808181763},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5002942085266113},{"id":"https://openalex.org/keywords/dual-cone-and-polar-cone","display_name":"Dual cone and polar cone","score":0.45123156905174255},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3653576374053955},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3527609705924988},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3393632769584656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3341587781906128},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09969604015350342},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.06591370701789856}],"concepts":[{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.8261535167694092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8077707886695862},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5706341862678528},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5434262752532959},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5379579067230225},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.5089988708496094},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.5075560808181763},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5002942085266113},{"id":"https://openalex.org/C24484764","wikidata":"https://www.wikidata.org/wiki/Q2687694","display_name":"Dual cone and polar cone","level":3,"score":0.45123156905174255},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3653576374053955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3527609705924988},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3393632769584656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3341587781906128},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09969604015350342},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.06591370701789856},{"id":"https://openalex.org/C88548481","wikidata":"https://www.wikidata.org/wiki/Q2397491","display_name":"Seed dormancy","level":4,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C3527866","wikidata":"https://www.wikidata.org/wiki/Q162267","display_name":"Dormancy","level":3,"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/C100701293","wikidata":"https://www.wikidata.org/wiki/Q193838","display_name":"Germination","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1325484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1325484","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.7799999713897705,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1659542519","display_name":"Topics in tropical and real geometry","funder_award_id":"159240","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5231257468","display_name":null,"funder_award_id":"2016-06596","funder_id":"https://openalex.org/F4320321033","funder_display_name":"Svenska Forskningsr\u00e5det Formas"},{"id":"https://openalex.org/G5540742269","display_name":null,"funder_award_id":"WO 2206/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7252648079","display_name":null,"funder_award_id":"TOP1EW.15.313","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321033","display_name":"Svenska Forskningsr\u00e5det Formas","ror":"https://ror.org/03pjs1y45"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1966518517","https://openalex.org/W1977415556","https://openalex.org/W1982292900","https://openalex.org/W2033911254","https://openalex.org/W2034201396","https://openalex.org/W2043653908","https://openalex.org/W2054267869","https://openalex.org/W2071040500","https://openalex.org/W2071727942","https://openalex.org/W2085729541","https://openalex.org/W2086720359","https://openalex.org/W2131440188","https://openalex.org/W2239251014","https://openalex.org/W2799036797","https://openalex.org/W2895618514","https://openalex.org/W2963758142","https://openalex.org/W2963864495","https://openalex.org/W2963917343","https://openalex.org/W3104064817","https://openalex.org/W4233252806"],"related_works":["https://openalex.org/W2371409811","https://openalex.org/W4223479902","https://openalex.org/W2043823063","https://openalex.org/W2550463706","https://openalex.org/W2070847262","https://openalex.org/W2579736672","https://openalex.org/W241962579","https://openalex.org/W2972593485","https://openalex.org/W2484043914","https://openalex.org/W2184361932"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,24,45,64],"explore":[4],"the":[5,9,26,29,52,55,70,73,76],"connections":[6],"between":[7,51],"nonnegativity,":[8],"theory":[10],"of":[11,28,39,69,72],"$A$-discriminants,":[12],"and":[13,54,63],"tropical":[14,40],"geometry.":[15],"For":[16],"an":[17,43],"integral":[18],"support":[19,61],"set":[20],"$A":[21],"\\subset":[22],"\\mathbb{Z}^n$,":[23],"cover":[25],"boundary":[27,71],"sonc-cone":[30,53,74],"by":[31,37],"semialgebraic":[32,67],"sets":[33],"that":[34],"are":[35],"parametrized":[36],"families":[38],"hypersurfaces.":[41],"As":[42],"application,":[44],"give":[46],"sufficient":[47],"conditions":[48],"for":[49,59],"equality":[50],"sparse":[56],"nonnegativity":[57],"cone":[58],"generic":[60],"sets,":[62],"describe":[65],"a":[66],"stratification":[68],"in":[75],"univariate":[77],"case.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}