{"id":"https://openalex.org/W2592432152","doi":"https://doi.org/10.1515/forma-2016-0020","title":"Homography in \u211d\u2119","display_name":"Homography in \u211d\u2119","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2592432152","doi":"https://doi.org/10.1515/forma-2016-0020","mag":"2592432152"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2016-0020","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0020","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2016-0020","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.1515/forma-2016-0020","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068514239","display_name":"Roland Coghetto","orcid":"https://orcid.org/0000-0002-4901-0766"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roland Coghetto","raw_affiliation_strings":["Rue de la Brasserie 5, 7100 La Louvi\u00e8re, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rue de la Brasserie 5, 7100 La Louvi\u00e8re, Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068514239"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5613,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82442159,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"4","first_page":"239","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9909999966621399,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9909999966621399,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homography","display_name":"Homography","score":0.7483124136924744},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6683944463729858},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.5655872225761414},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5615590810775757},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.5284554958343506},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.5253545641899109},{"id":"https://openalex.org/keywords/real-projective-plane","display_name":"Real projective plane","score":0.4753318130970001},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.4512764513492584},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.44525817036628723},{"id":"https://openalex.org/keywords/collineation","display_name":"Collineation","score":0.43947741389274597},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.4052492082118988},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3966847062110901},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39331790804862976},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21241769194602966},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10247939825057983}],"concepts":[{"id":"https://openalex.org/C28751775","wikidata":"https://www.wikidata.org/wiki/Q2112539","display_name":"Homography","level":4,"score":0.7483124136924744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6683944463729858},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.5655872225761414},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5615590810775757},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.5284554958343506},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.5253545641899109},{"id":"https://openalex.org/C37470923","wikidata":"https://www.wikidata.org/wiki/Q633815","display_name":"Real projective plane","level":5,"score":0.4753318130970001},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.4512764513492584},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.44525817036628723},{"id":"https://openalex.org/C163434512","wikidata":"https://www.wikidata.org/wiki/Q390741","display_name":"Collineation","level":4,"score":0.43947741389274597},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.4052492082118988},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3966847062110901},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39331790804862976},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21241769194602966},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10247939825057983},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/forma-2016-0020","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0020","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2016-0020","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/5558","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/5558","pdf_url":"http://hdl.handle.net/11320/5558","source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:cde178226b0f445e93fb28fff8fda566","is_oa":false,"landing_page_url":"https://doaj.org/article/cde178226b0f445e93fb28fff8fda566","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 24, Iss 4, Pp 239-251 (2016)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/forma-2016-0020","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0020","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2016-0020","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2592432152.pdf","grobid_xml":"https://content.openalex.org/works/W2592432152.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W365379550","https://openalex.org/W1523528291","https://openalex.org/W1572941424","https://openalex.org/W1577444404","https://openalex.org/W2047483812","https://openalex.org/W2104238184","https://openalex.org/W2128980051","https://openalex.org/W2150348213","https://openalex.org/W2158768890","https://openalex.org/W2161470005","https://openalex.org/W2295728669","https://openalex.org/W2403661435","https://openalex.org/W2502358513","https://openalex.org/W2555605597","https://openalex.org/W2749041799"],"related_works":["https://openalex.org/W199354996","https://openalex.org/W4313240746","https://openalex.org/W2030745060","https://openalex.org/W2001751485","https://openalex.org/W1978908735","https://openalex.org/W2187623611","https://openalex.org/W2047215877","https://openalex.org/W65502696","https://openalex.org/W2008064857","https://openalex.org/W3190357833"],"abstract_inverted_index":{"Summary":[0],"The":[1],"real":[2,30,110],"projective":[3,31,85,99,111],"plane":[4,100],"has":[5],"been":[6],"formalized":[7],"in":[8,15,36,72,92,105,108],"Isabelle/HOL":[9],"by":[10,17,41,49,94,118],"Timothy":[11],"Makarios":[12],"[13]":[13],"and":[14,22,48,68,123],"Coq":[16],"Nicolas":[18],"Magaud,":[19],"Julien":[20],"Narboux":[21],"Pascal":[23],"Schreck":[24],"[12].":[25],"Some":[26],"definitions":[27],"on":[28,65],"the":[29,37,59,66,69,84,89,102,109,115,127],"spaces":[32],"were":[33],"introduced":[34],"early":[35],"Mizar":[38,60],"Mathematical":[39],"Library":[40],"Wojciech":[42,50],"Leonczuk":[43],"[9],":[44],"Krzysztof":[45],"Prazmowski":[46],"[10]":[47],"Skaba":[51],"[18].":[52],"In":[53],"this":[54],"article,":[55],"we":[56,81,113,124],"check":[57],"with":[58],"system":[61],"[4],":[62],"some":[63],"properties":[64],"determinants":[67],"Grassmann-Pl\u00fccker":[70],"relation":[71],"rank":[73],"3":[74,96,130],"[2],":[75],"[1],":[76],"[7],":[77],"[16],":[78],"[17].":[79],"Then":[80],"show":[82,125],"that":[83,126],"space":[86],"induced":[87,117],"(in":[88,101],"sense":[90,103],"defined":[91,104],"[9])":[93],"\u211d":[95],"is":[97],"a":[98,119],"[10]).":[106],"Finally,":[107],"plane,":[112],"define":[114],"homography":[116],"3-by-3":[120],"invertible":[121],"matrix":[122],"images":[128],"of":[129],"collinear":[131],"points":[132],"are":[133],"themselves":[134],"collinear.":[135]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2017-03-16T00:00:00"}