{"id":"https://openalex.org/W2735656302","doi":"https://doi.org/10.1145/3056528","title":"Algorithm 976","display_name":"Algorithm 976","publication_year":2017,"publication_date":"2017-07-14","ids":{"openalex":"https://openalex.org/W2735656302","doi":"https://doi.org/10.1145/3056528","mag":"2735656302"},"language":"en","primary_location":{"id":"doi:10.1145/3056528","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3056528","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5110283172","display_name":"Daniel A. Brake","orcid":null},"institutions":[{"id":"https://openalex.org/I124727415","display_name":"University of Wisconsin\u2013Eau Claire","ror":"https://ror.org/03mnm0t94","country_code":"US","type":"education","lineage":["https://openalex.org/I124727415"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel A. Brake","raw_affiliation_strings":["University of Wisconsin Eau Claire, Garfield Avenue, Eau Claire, WI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin Eau Claire, Garfield Avenue, Eau Claire, WI","institution_ids":["https://openalex.org/I124727415"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089126031","display_name":"Daniel J. Bates","orcid":"https://orcid.org/0000-0003-2985-0554"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel J. Bates","raw_affiliation_strings":["Colorado State University, Fort Collins, CO"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Colorado State University, Fort Collins, CO","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032431412","display_name":"Wenrui Hao","orcid":"https://orcid.org/0000-0002-6925-7424"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenrui Hao","raw_affiliation_strings":["Pennsylvania State University, University Park, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pennsylvania State University, University Park, PA","institution_ids":["https://openalex.org/I130769515"]}]},{"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, Notre Dame, IN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Notre Dame, Notre Dame, IN","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103556278","display_name":"Andrew J. Sommese","orcid":null},"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":"Andrew J. Sommese","raw_affiliation_strings":["University of Notre Dame, Notre Dame, IN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Notre Dame, Notre Dame, IN","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050683196","display_name":"Charles W. Wampler","orcid":"https://orcid.org/0000-0002-9790-1600"},"institutions":[{"id":"https://openalex.org/I118136607","display_name":"General Motors (United States)","ror":"https://ror.org/05addee68","country_code":"US","type":"company","lineage":["https://openalex.org/I118136607"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles W. Wampler","raw_affiliation_strings":["General Motors, Mound Road, Warren, MI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"General Motors, Mound Road, Warren, MI","institution_ids":["https://openalex.org/I118136607"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.223,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86875064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"1","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/decomposition","display_name":"Decomposition","score":0.5997735857963562},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5615484714508057},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.5222921371459961},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4928901195526123},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4798026382923126},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.46869397163391113},{"id":"https://openalex.org/keywords/cad","display_name":"CAD","score":0.4551697373390198},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4527851939201355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45194578170776367},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4369610548019409},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.43590715527534485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41571933031082153},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.25776219367980957},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1676170527935028},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.13719195127487183},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10793349146842957}],"concepts":[{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5997735857963562},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5615484714508057},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.5222921371459961},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4928901195526123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4798026382923126},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.46869397163391113},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.4551697373390198},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4527851939201355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45194578170776367},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4369610548019409},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.43590715527534485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41571933031082153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25776219367980957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1676170527935028},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.13719195127487183},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10793349146842957},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3056528","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3056528","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W59564462","https://openalex.org/W216244286","https://openalex.org/W293694841","https://openalex.org/W647818151","https://openalex.org/W1487859867","https://openalex.org/W1570420806","https://openalex.org/W1595559231","https://openalex.org/W1969549682","https://openalex.org/W1972896450","https://openalex.org/W1986084578","https://openalex.org/W1986180644","https://openalex.org/W1986859143","https://openalex.org/W1989369020","https://openalex.org/W1993702408","https://openalex.org/W2000538555","https://openalex.org/W2007860444","https://openalex.org/W2013758375","https://openalex.org/W2027411255","https://openalex.org/W2035257781","https://openalex.org/W2035352599","https://openalex.org/W2038780582","https://openalex.org/W2059173068","https://openalex.org/W2061179469","https://openalex.org/W2062754393","https://openalex.org/W2066058234","https://openalex.org/W2067437385","https://openalex.org/W2067705970","https://openalex.org/W2083126079","https://openalex.org/W2114046979","https://openalex.org/W2131474035","https://openalex.org/W2135406786","https://openalex.org/W2148900625","https://openalex.org/W2167360454","https://openalex.org/W2170316960","https://openalex.org/W2326362648","https://openalex.org/W3217399827","https://openalex.org/W4229917934"],"related_works":["https://openalex.org/W637098845","https://openalex.org/W2410116073","https://openalex.org/W2068608913","https://openalex.org/W3044972437","https://openalex.org/W2275866607","https://openalex.org/W2315696258","https://openalex.org/W1908932129","https://openalex.org/W2332669313","https://openalex.org/W2587289131","https://openalex.org/W2365000768"],"abstract_inverted_index":{"Bertini_real":[0,75],"is":[1],"a":[2,14,29,36,41,65,100],"compiled":[3],"command":[4],"line":[5],"program":[6],"for":[7,96],"numerically":[8,90],"decomposing":[9],"the":[10,51,73,93,106,114],"real":[11,115],"portion":[12],"of":[13,18,31,67],"positive-dimensional":[15],"complex":[16],"component":[17],"an":[19],"algebraic":[20,54],"set.":[21],"The":[22,44],"software":[23],"uses":[24],"homotopy":[25],"continuation":[26],"to":[27,39,50,72,81],"solve":[28],"series":[30],"systems":[32],"via":[33],"regeneration":[34],"from":[35],"witness":[37],"set":[38,66],"compute":[40],"cell":[42],"decomposition.":[43],"implemented":[45,94],"decomposition":[46,55,95,104],"algorithms":[47],"are":[48],"similar":[49],"well-known":[52],"cylindrical":[53],"(CAD)":[56],"first":[57],"established":[58],"by":[59,84],"Collins":[60],"in":[61],"that":[62],"they":[63],"produce":[64],"connected":[68,80],"cells.":[69],"In":[70],"contrast":[71],"CAD,":[74],"produces":[76],"cells":[77],"with":[78],"midpoints":[79],"boundary":[82],"points":[83],"homotopies,":[85],"which":[86],"can":[87],"easily":[88],"be":[89],"tracked.":[91],"Furthermore,":[92],"surfaces":[97],"naturally":[98],"yields":[99],"triangulation.":[101],"This":[102],"CAD-like":[103],"captures":[105],"topological":[107],"information":[108],"and":[109,121],"permits":[110],"further":[111],"computation":[112],"on":[113],"sets,":[116],"such":[117],"as":[118],"sampling,":[119],"visualization,":[120],"three-dimensional":[122],"printing.":[123]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-07-21T00:00:00"}
