{"id":"https://openalex.org/W2122502082","doi":"https://doi.org/10.1145/2465506.2465515","title":"Certified symbolic manipulation","display_name":"Certified symbolic manipulation","publication_year":2013,"publication_date":"2013-06-25","ids":{"openalex":"https://openalex.org/W2122502082","doi":"https://doi.org/10.1145/2465506.2465515","mag":"2122502082"},"language":"en","primary_location":{"id":"doi:10.1145/2465506.2465515","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465506.2465515","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th 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/A5057485552","display_name":"Laureano Lamb\u00e1n","orcid":"https://orcid.org/0000-0003-2383-2689"},"institutions":[{"id":"https://openalex.org/I168974976","display_name":"Universidad de La Rioja","ror":"https://ror.org/0553yr311","country_code":"ES","type":"education","lineage":["https://openalex.org/I168974976"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Laureano Lamb\u00e1n","raw_affiliation_strings":["University of La Rioja, La Rioja, Spain","University of La Rioja, La Rioja, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"University of La Rioja, La Rioja, Spain","institution_ids":["https://openalex.org/I168974976"]},{"raw_affiliation_string":"University of La Rioja, La Rioja, Spain#TAB#","institution_ids":["https://openalex.org/I168974976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081352175","display_name":"Francisco J. Mart\u00edn-Mateos","orcid":"https://orcid.org/0000-0002-9795-1683"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco J. Mart\u00edn-Mateos","raw_affiliation_strings":["University of Seville, Seville, Spain"],"affiliations":[{"raw_affiliation_string":"University of Seville, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034271146","display_name":"Julio Rubio","orcid":"https://orcid.org/0000-0002-4282-3692"},"institutions":[{"id":"https://openalex.org/I168974976","display_name":"Universidad de La Rioja","ror":"https://ror.org/0553yr311","country_code":"ES","type":"education","lineage":["https://openalex.org/I168974976"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Julio Rubio","raw_affiliation_strings":["University of La Rioja, La Rioja, Spain","University of La Rioja, La Rioja, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"University of La Rioja, La Rioja, Spain","institution_ids":["https://openalex.org/I168974976"]},{"raw_affiliation_string":"University of La Rioja, La Rioja, Spain#TAB#","institution_ids":["https://openalex.org/I168974976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063746909","display_name":"Jos\u00e9\u2013Luis Ruiz\u2013Reina","orcid":"https://orcid.org/0000-0003-1021-3256"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9-Luis Ruiz-Reina","raw_affiliation_strings":["University of Seville, Seville, Spain"],"affiliations":[{"raw_affiliation_string":"University of Seville, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057485552"],"corresponding_institution_ids":["https://openalex.org/I168974976"],"apc_list":null,"apc_paid":null,"fwci":0.4809,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77023068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"243","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10142","display_name":"Formal Methods in Verification","score":0.9976000189781189,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/correctness","display_name":"Correctness","score":0.7297776937484741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.72362220287323},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6253294944763184},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.5631848573684692},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.45989304780960083},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.4590853750705719},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.45805323123931885},{"id":"https://openalex.org/keywords/coalgebra","display_name":"Coalgebra","score":0.42520707845687866},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40430116653442383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2237468957901001},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08701235055923462}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7297776937484741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.72362220287323},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6253294944763184},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.5631848573684692},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.45989304780960083},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.4590853750705719},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45805323123931885},{"id":"https://openalex.org/C2778249326","wikidata":"https://www.wikidata.org/wiki/Q1777803","display_name":"Coalgebra","level":3,"score":0.42520707845687866},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40430116653442383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2237468957901001},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08701235055923462},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2465506.2465515","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465506.2465515","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W125173713","https://openalex.org/W1597068544","https://openalex.org/W1605757265","https://openalex.org/W1964618504","https://openalex.org/W1976974717","https://openalex.org/W1983320296","https://openalex.org/W1995030868","https://openalex.org/W2027737519","https://openalex.org/W2034552599","https://openalex.org/W2034711041","https://openalex.org/W2036798279","https://openalex.org/W2122778257","https://openalex.org/W6635592456","https://openalex.org/W6678469545","https://openalex.org/W6982277959"],"related_works":["https://openalex.org/W55831818","https://openalex.org/W4295798319","https://openalex.org/W1819460135","https://openalex.org/W353523607","https://openalex.org/W2147643247","https://openalex.org/W3098927713","https://openalex.org/W2774311601","https://openalex.org/W3106543884","https://openalex.org/W4389158536","https://openalex.org/W4323929316"],"abstract_inverted_index":{"Certified":[0],"symbolic":[1,80],"manipulation":[2],"is":[3,51],"an":[4,106],"emerging":[5],"new":[6],"field":[7],"where":[8],"programs":[9],"are":[10,141],"accompanied":[11],"by":[12],"certificates":[13],"that,":[14],"suitably":[15],"interpreted,":[16],"ensure":[17],"the":[18,21,33,44,63,88,114,123,130,138,148],"correctness":[19,42],"of":[20,53,65,95,102,108,118,129],"algorithms.":[22],"In":[23],"this":[24,109],"paper,":[25],"we":[26,112],"focus":[27],"on":[28],"algebraic":[29],"algorithms":[30],"implemented":[31],"in":[32,43,67,76,90,116,122],"proof":[34,64],"assistant":[35],"ACL2,":[36],"which":[37],"allows":[38],"us":[39],"to":[40,61],"verify":[41],"same":[45,149],"programming":[46],"environment.":[47],"The":[48],"case":[49],"study":[50],"that":[52,145],"bivariate":[54],"simplicial":[55],"polynomials,":[56],"a":[57,126],"data":[58],"structure":[59],"used":[60],"help":[62,99],"properties":[66,101],"Simplicial":[68,70],"Topology.":[69],"polynomials":[71],"can":[72,83],"be":[73,84],"computationally":[74],"interpreted":[75],"two":[77],"ways.":[78],"As":[79,93,105],"expressions,":[81],"they":[82,98,146],"handled":[85],"algorithmically,":[86],"increasing":[87],"automation":[89],"ACL2":[91,117,139],"proofs.":[92],"representations":[94],"functional":[96],"operators,":[97],"proving":[100],"categorical":[103],"morphisms.":[104],"application":[107],"second":[110],"view,":[111],"present":[113],"definition":[115],"some":[119],"morphisms":[120],"involved":[121],"Eilenberg-Zilber":[124],"reduction,":[125],"central":[127],"part":[128],"Kenzo":[131,152],"computer":[132],"algebra":[133],"system.":[134],"We":[135],"have":[136],"proved":[137],"implementations":[140],"correct":[142],"and":[143],"tested":[144],"get":[147],"results":[150],"as":[151],"does.":[153]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
