{"id":"https://openalex.org/W3212452327","doi":"https://doi.org/10.4230/lipics.calco.2021.9","title":"From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra ((Co)algebraic pearls)","display_name":"From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra ((Co)algebraic pearls)","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3212452327","doi":"https://doi.org/10.4230/lipics.calco.2021.9","mag":"3212452327"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://drops.dagstuhl.de/opus/volltexte/2021/15364/pdf/LIPIcs-CALCO-2021-9.pdf/","pdf_url":null,"source":{"id":"https://openalex.org/S4306418018","display_name":"Conference on Algebra and Coalgebra in Computer Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":[],"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/A5004609161","display_name":"Filippo Bonchi","orcid":"https://orcid.org/0000-0002-3433-723X"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Filippo Bonchi","raw_affiliation_strings":["University of Pisa, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"University of Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028800605","display_name":"Alessandro Di Giorgio","orcid":"https://orcid.org/0000-0002-6428-6461"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alessandro Di Giorgio","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016173850","display_name":"Fabio Zanasi","orcid":"https://orcid.org/0000-0001-6457-1345"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Fabio Zanasi","raw_affiliation_strings":["University College London, London, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University College London, London, United Kingdom","institution_ids":["https://openalex.org/I45129253"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.102,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.305691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":57,"max":67},"biblio":{"volume":null,"issue":null,"first_page":"19","last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9987,"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":0.9987,"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":0.998,"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":0.9894,"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/diagrammatic-reasoning","display_name":"Diagrammatic reasoning","score":0.9105153},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.8386544},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.69135815},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5590035},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.533869}],"concepts":[{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.9105153},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8386544},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.69135815},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6408628},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5934731},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5590035},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.533869},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48180646},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.47112486},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.41306692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28742802},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28622925},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28317702},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.137624},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08269602},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://drops.dagstuhl.de/opus/volltexte/2021/15364/pdf/LIPIcs-CALCO-2021-9.pdf/","pdf_url":null,"source":{"id":"https://openalex.org/S4306418018","display_name":"Conference on Algebra and Coalgebra in Computer Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W305179105","https://openalex.org/W3029929813","https://openalex.org/W281488709","https://openalex.org/W2606052059","https://openalex.org/W2566556943","https://openalex.org/W2523438967","https://openalex.org/W2476840684","https://openalex.org/W2388943681","https://openalex.org/W2387827566","https://openalex.org/W2359081528","https://openalex.org/W2332833600","https://openalex.org/W2247464275","https://openalex.org/W2213266491","https://openalex.org/W2146187364","https://openalex.org/W2106998325","https://openalex.org/W2093266057","https://openalex.org/W2061616249","https://openalex.org/W2057073102","https://openalex.org/W203702460","https://openalex.org/W2019363812"],"abstract_inverted_index":{"Farkas'":[0,33],"lemma":[1,34],"is":[2],"a":[3,39],"celebrated":[4],"result":[5],"on":[6],"the":[7,57],"solutions":[8],"of":[9,11],"systems":[10],"linear":[12,51],"inequalities,":[13],"which":[14],"finds":[15],"application":[16],"pervasively":[17],"in":[18,35],"mathematics":[19],"and":[20,31,41,59],"computer":[21],"science.":[22],"In":[23],"this":[24],"work":[25],"we":[26,48],"show":[27,49],"how":[28,50,60],"to":[29],"formulate":[30],"prove":[32],"diagrammatic":[36],"polyhedral":[37],"algebra,":[38],"sound":[40],"complete":[42],"graphical":[43],"calculus":[44,58],"for":[45],"polyhedra.":[46],"Furthermore,":[47],"programs":[52],"can":[53,65],"be":[54,66],"modeled":[55],"within":[56],"some":[61],"famous":[62],"duality":[63],"results":[64],"proved.":[67]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3212452327","counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2024-12-15T10:33:53.025453","created_date":"2021-11-22"}