{"id":"https://openalex.org/W2033345656","doi":"https://doi.org/10.1145/2382585.2382588","title":"PyDEC","display_name":"PyDEC","publication_year":2012,"publication_date":"2012-11-01","ids":{"openalex":"https://openalex.org/W2033345656","doi":"https://doi.org/10.1145/2382585.2382588","mag":"2033345656"},"language":"en","primary_location":{"id":"doi:10.1145/2382585.2382588","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2382585.2382588","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/A5108095852","display_name":"Nathan Bell","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nathan Bell","raw_affiliation_strings":["Google Inc","GOOGLE INC "],"affiliations":[{"raw_affiliation_string":"Google Inc","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"GOOGLE INC ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016423606","display_name":"Anil N. Hirani","orcid":"https://orcid.org/0000-0003-3506-1703"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anil N. Hirani","raw_affiliation_strings":["University of Illinois at Urbana-Champaign","University of Illinois at Urbana Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108095852"],"corresponding_institution_ids":["https://openalex.org/I1291425158"],"apc_list":null,"apc_paid":null,"fwci":4.4926,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.94741189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"39","issue":"1","first_page":"1","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/python","display_name":"Python (programming language)","score":0.8180041313171387},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6930302381515503},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5961996912956238},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5874728560447693},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.4751065671443939},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.45215415954589844},{"id":"https://openalex.org/keywords/algebraic-topology","display_name":"Algebraic topology","score":0.42308133840560913},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42059633135795593},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38656193017959595},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.38649410009384155},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.37431997060775757},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3311571478843689},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3267296552658081},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.21502718329429626},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20410695672035217},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11532348394393921}],"concepts":[{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.8180041313171387},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6930302381515503},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5961996912956238},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5874728560447693},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.4751065671443939},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45215415954589844},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.42308133840560913},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42059633135795593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38656193017959595},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38649410009384155},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.37431997060775757},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3311571478843689},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3267296552658081},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.21502718329429626},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20410695672035217},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11532348394393921},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2382585.2382588","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2382585.2382588","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":[{"id":"https://openalex.org/G6270532715","display_name":null,"funder_award_id":"DMS-0645604","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W33620505","https://openalex.org/W73123583","https://openalex.org/W162238331","https://openalex.org/W625634629","https://openalex.org/W1482414980","https://openalex.org/W1496383623","https://openalex.org/W1522382323","https://openalex.org/W1525296983","https://openalex.org/W1544007752","https://openalex.org/W1644780190","https://openalex.org/W1794690746","https://openalex.org/W1881147112","https://openalex.org/W1959151597","https://openalex.org/W1969813054","https://openalex.org/W1975359839","https://openalex.org/W1976058996","https://openalex.org/W1983033166","https://openalex.org/W1989748191","https://openalex.org/W1994578392","https://openalex.org/W2002243081","https://openalex.org/W2015745797","https://openalex.org/W2025734987","https://openalex.org/W2034024171","https://openalex.org/W2049707725","https://openalex.org/W2055218847","https://openalex.org/W2063974361","https://openalex.org/W2076518146","https://openalex.org/W2077944288","https://openalex.org/W2083561088","https://openalex.org/W2092284067","https://openalex.org/W2102295719","https://openalex.org/W2106724205","https://openalex.org/W2110114082","https://openalex.org/W2117709682","https://openalex.org/W2118228880","https://openalex.org/W2120103450","https://openalex.org/W2128095813","https://openalex.org/W2130406232","https://openalex.org/W2131341034","https://openalex.org/W2135744173","https://openalex.org/W2138486270","https://openalex.org/W2139118972","https://openalex.org/W2143783905","https://openalex.org/W2144044408","https://openalex.org/W2146292423","https://openalex.org/W2169266183","https://openalex.org/W2500846120","https://openalex.org/W2792644458","https://openalex.org/W2950437322","https://openalex.org/W2951900371","https://openalex.org/W3013843370","https://openalex.org/W3103476862","https://openalex.org/W4205424143","https://openalex.org/W4234635957","https://openalex.org/W4242566991","https://openalex.org/W4245654886","https://openalex.org/W4292023735","https://openalex.org/W6631144761","https://openalex.org/W6632463257"],"related_works":["https://openalex.org/W3187193180","https://openalex.org/W106542691","https://openalex.org/W4287027380","https://openalex.org/W1699080303","https://openalex.org/W4297799326","https://openalex.org/W3116064965","https://openalex.org/W2364741597","https://openalex.org/W2897624483","https://openalex.org/W1492103595","https://openalex.org/W4214505573"],"abstract_inverted_index":{"This":[0],"article":[1],"describes":[2],"the":[3,17,46,89],"algorithms,":[4],"features,":[5],"and":[6,48,61,97,120],"implementation":[7],"of":[8,19,72,91,101],"PyDEC,":[9],"a":[10,82],"Python":[11,105],"library":[12],"for":[13,44,107],"computations":[14],"related":[15,63],"to":[16,78,88,117],"discretization":[18],"exterior":[20,54,59],"calculus.":[21],"PyDEC":[22,114],"facilitates":[23],"inquiry":[24],"into":[25],"both":[26],"physical":[27,119],"problems":[28,36,122],"on":[29,37],"manifolds":[30],"as":[31,33,95],"well":[32,87],"purely":[34],"topological":[35,64,121],"abstract":[38],"complexes.":[39],"We":[40,111],"describe":[41],"efficient":[42],"algorithms":[43,67],"constructing":[45],"operators":[47],"objects":[49],"that":[50],"arise":[51],"in":[52,62,70],"discrete":[53],"calculus,":[55,60],"lowest-order":[56],"finite":[57],"element":[58],"problems.":[65],"Our":[66],"are":[68],"formulated":[69],"terms":[71],"high-level":[73],"matrix":[74],"operations":[75],"which":[76],"extend":[77],"arbitrary":[79],"dimension.":[80],"As":[81],"result,":[83],"our":[84],"implementations":[85],"map":[86],"facilities":[90],"numerical":[92,109],"libraries":[93,103],"such":[94,102],"NumPy":[96],"SciPy.":[98],"The":[99],"availability":[100],"makes":[104],"suitable":[106],"prototyping":[108],"methods.":[110],"demonstrate":[112],"how":[113],"is":[115],"used":[116],"solve":[118],"through":[123],"several":[124],"concise":[125],"examples.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2016-06-24T00:00:00"}
