{"id":"https://openalex.org/W3138716390","doi":"https://doi.org/10.1145/3457341.3457347","title":"Smooth points on semi-algebraic sets","display_name":"Smooth points on semi-algebraic sets","publication_year":2020,"publication_date":"2020-09-01","ids":{"openalex":"https://openalex.org/W3138716390","doi":"https://doi.org/10.1145/3457341.3457347","mag":"3138716390"},"language":"en","primary_location":{"id":"doi:10.1145/3457341.3457347","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3457341.3457347","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","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/A5082261268","display_name":"Katherine Harris","orcid":"https://orcid.org/0009-0002-3075-1430"},"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":true,"raw_author_name":"Katherine Harris","raw_affiliation_strings":["North Carolina State University"],"affiliations":[{"raw_affiliation_string":"North Carolina State University","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007214938","display_name":"Jonathan D. Hauenstein","orcid":"https://orcid.org/0000-0002-9252-8210"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan D. Hauenstein","raw_affiliation_strings":["University of Notre Dame"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086594308","display_name":"\u00c1gnes Sz\u00e1nt\u00f3","orcid":null},"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":"Agnes Szanto","raw_affiliation_strings":["North Carolina State University"],"affiliations":[{"raw_affiliation_string":"North Carolina State University","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082261268"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":0.6468,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.73868359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"54","issue":"3","first_page":"105","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9750999808311462,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.972000002861023,"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/algebraic-number","display_name":"Algebraic number","score":0.6564844846725464},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.6436915397644043},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5923467874526978},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.592247486114502},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5694229006767273},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.546107292175293},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5323168635368347},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5271603465080261},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.478903204202652},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4681779444217682},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4667017459869385},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.46302810311317444},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45618927478790283},{"id":"https://openalex.org/keywords/algebraic-surface","display_name":"Algebraic surface","score":0.4192368984222412},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39559537172317505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3556118607521057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3271850645542145},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1889897584915161},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06927406787872314}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6564844846725464},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.6436915397644043},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5923467874526978},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.592247486114502},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5694229006767273},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.546107292175293},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5323168635368347},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5271603465080261},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.478903204202652},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4681779444217682},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4667017459869385},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.46302810311317444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45618927478790283},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.4192368984222412},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39559537172317505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3556118607521057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3271850645542145},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1889897584915161},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06927406787872314},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3457341.3457347","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3457341.3457347","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1986180644","https://openalex.org/W2075032588","https://openalex.org/W2158516852","https://openalex.org/W2477102426","https://openalex.org/W2809451380","https://openalex.org/W2963709552","https://openalex.org/W4293258886"],"related_works":["https://openalex.org/W2076085433","https://openalex.org/W2170846659","https://openalex.org/W2064443887","https://openalex.org/W158059085","https://openalex.org/W3145075634","https://openalex.org/W1984537908","https://openalex.org/W2393967034","https://openalex.org/W1674516527","https://openalex.org/W2066092589","https://openalex.org/W2952227937"],"abstract_inverted_index":{"Many":[0],"algorithms":[1],"for":[2,94,121],"determining":[3],"properties":[4],"of":[5,28,36,44,76,88,90,115],"semi-algebraic":[6,48],"sets":[7],"rely":[8],"upon":[9],"the":[10,25,34,86,91,95,112,118],"ability":[11],"to":[12,65,105,110],"compute":[13,111],"smooth":[14,37],"points":[15,27,38],"[1].":[16],"We":[17,100],"present":[18],"a":[19,45,83],"simple":[20],"procedure":[21],"based":[22],"on":[23,58,85],"computing":[24],"critical":[26],"some":[29],"well-chosen":[30],"function":[31],"that":[32],"guarantees":[33],"computation":[35],"in":[39,54],"each":[40],"connected":[41],"bounded":[42],"component":[43],"real":[46,113],"atomic":[47],"set.":[49],"Our":[50],"technique":[51],"is":[52,63,79],"intuitive":[53],"principal,":[55],"performs":[56],"well":[57],"previously":[59],"difficult":[60],"examples,":[61],"and":[62],"straightforward":[64],"implement":[66],"using":[67],"existing":[68],"numerical":[69],"algebraic":[70,116],"geometry":[71],"software.":[72],"The":[73],"practical":[74],"efficiency":[75],"our":[77,103],"approach":[78],"demonstrated":[80],"by":[81],"solving":[82],"conjecture":[84],"number":[87],"equilibria":[89],"Kuramoto":[92],"model":[93],"n":[96],"=":[97],"4":[98],"case.":[99],"also":[101],"apply":[102],"method":[104],"design":[106],"an":[107],"efficient":[108],"algorithm":[109],"dimension":[114],"sets,":[117],"original":[119],"motivation":[120],"this":[122],"research.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
